c26f9ae · Idris-dev · git.iko.soy

git.iko.soy/Idris-dev

Merge pull request #1540 from edwinb/master

Remove papers directory

commitc26f9aead8c4c6ddf6e3b33be56329340ad5c0ba authorEdwin Brady <edwin.brady@gmail.com> dateTue 23 Sep 2014, 22:50 (12 years ago) parent7572017 8751795

21 files changed−17894

compare with master

unifiedsplit

papers/impl-paper/Makefiledeleted−43

@@ -1,43 +0,0 @@

1−PAPER = impldtp

2−

3−all: ${PAPER}.pdf

4−

5−TEXFILES = ${PAPER}.tex intro.tex conclusions.tex hll.tex\

6− typechecking.tex elaboration.tex delab.tex \

7− syntax.tex

8−

9−DIAGS =

10−

11−SOURCES = ${TEXFILES} ${DIAGS} macros.ltx library.bib

12−

13−DITAA = java -jar ~/Downloads/ditaa.jar

14−

15−${PAPER}.pdf: ${SOURCES}

16−# dvipdf ${PAPER}.dvi

17− pdflatex ${PAPER}

18− -bibtex ${PAPER}

19− -pdflatex ${PAPER}

20− -pdflatex ${PAPER}

21−

22−${PAPER}.ps: ${PAPER}.dvi

23− dvips -o ${PAPER}.ps ${PAPER}

24−

25−${PAPER}.dvi: $(SOURCES)

26− -latex ${PAPER}

27− -bibtex ${PAPER}

28− -latex ${PAPER}

29− -latex ${PAPER}

30−

31−progress:

32− wc -w ${TEXFILES}

33−

34−%.png : %.diag

35− $(DITAA) -o -E $<

36−

37−todropbox:

38− cp ${SOURCES} ~/Dropbox/TeX/ImplDTP/

39−

40−fromdropbox:

41− cp ~/Dropbox/TeX/ImplDTP/* .

42−

43−.PHONY: all progress todropbox fromdropbox

papers/impl-paper/acmtrans.bstdeleted−1770

@@ -1,1770 +0,0 @@

1−% "ACM Transactions" BibTeX style, acmtrans.bst

2−% for BibTeX version 0.99c, LaTeX version 3.141

3−% Revised 28-MARCH-1996

4−% Revised 30-JUNE-1995

5−% Revised 15-JAN-1996

6−% $Header: acmtrans.bst,v 1.2 96/01/17 09:05:38 boyland Exp $

7−%

8−% Hacked by John T. Boyland at University of California, Berkeley

9−% (with assistance by John R. Hauser)

10−% Hacked by Andrew W. Appel and Rebecca L. Davies at Princeton University,

11−% based on a "chicago.bst" by Glenn Paulley at U. Waterloo,

12−% which was based on "newapa.bst" found at ymir.claremont.edu.

13−%

14−% Citation format: [author-last-name year]

15−% [author-last-name and author-last-name year]

16−% [author-last-name, author-last-name, and author-last-name year]

17−% [author-last-name et al. year]

18−% [author-last-name]

19−% author-last-name [year]

20−% [author-last-name and author-last-name]

21−% [author-last-name et al.]

22−% [year] or [year,year]

23−% year or year,year

24−%

25−% Reference list ordering: alphabetical by author or whatever passes

26−% for author in the absence of one.

27−%

28−% This BibTeX style has support for abbreviated author lists and for

29−% year-only citations. This is done by having the citations

30−% actually look like

31−%

32−% \citeauthoryear{full-author-info}{abbrev-author-info}{year}

33−%

34−% The LaTeX style has to have the following (or similar)

35−%

36−% \let\@internalcite\cite

37−% \def\fullcite{\def\citeauthoryear##1##2##3{##1, ##3}\@internalcite}

38−% \def\fullciteA{\def\citeauthoryear##1##2##3{##1}\@internalcite}

39−% \def\shortcite{\def\citeauthoryear##1##2##3{##2, ##3}\@internalcite}

40−% \def\shortciteA{\def\citeauthoryear##1##2##3{##2}\@internalcite}

41−% \def\citeyear{\def\citeauthoryear##1##2##3{##3}\@internalcite}

42−%

43−% These TeX macro definitions are found in acmtrans.sty. Additional

44−% commands to manipulate different components of a citation can be defined

45−% so that, for example, you can list author's names without parentheses

46−% if using a citation as a noun or object in a sentence.

47−%

48−% Features of acmtrans.bst:

49−% ========================

50−%

51−% - all authors appear last name first.

52−% - all pages are listed xx-xx, (no pp.) and are at the end of the reference

53−% - publishers are identified as publisher, address

54−% - conferences papers (inproceedings) may give city of conference,

55−% date of conference, and journal that the proceedings appear in.

56−% - months abbreviated to max four letters (eg. Mar.)

57−% - volume of a series indicated after the title of the series

58−% - editors appear after edited title and are identified by a trailing "Eds."

59−% not in parentheses. Editor names are not given in small caps.

60−% (unless there is no author line)

61−% - names terminated with a period even if there is no first name.

62−% - editions are indicated trailing after the work, not in parentheses.

63−% - "et al." citations have a protected period to avoid bad spacing (jrh)

64−% - "address" required when publisher given

65−% - series (roman) and volume are in a sentence separate from (book-)title

66−%

67−%

68−% Features of chicago.bst:

69−% =======================

70−%

71−% - full names used in citations, but abbreviated citations are available

72−% (see above)

73−% - if an entry has a "month", then the month and year are also printed

74−% as part of that bibitem.

75−% - all conjunctions use "and" instead of "\&"

76−% - major modification from Chicago Manual of Style (13th ed.) is that

77−% only the first author in a reference appears last name first-

78−% additional authors appear as J. Q. Public.

79−% - pages are listed as "pp. xx-xx" in all entry types except

80−% article entries.

81−% - book, inbook, and manual use "location: publisher" (or organization)

82−% for address and publisher. All other types list publishers separately.

83−% - "pp." are used to identify page numbers for all entry types except

84−% articles.

85−% - organization is used as a citation label if neither author nor editor

86−% is present (for manuals).

87−% - "et al." is used for long author and editor lists, or when "others"

88−% is used.

89−%

90−% Modifications and bug fixes from newapa.bst:

91−% ===========================================

92−%

93−% - added month, year to bib entries if month is present

94−% - fixed bug with In proceedings, added necessary comma after title

95−% - all conjunctions changed to "and" from "\&"

96−% - fixed bug with author labels in my.full.label: "et al." now is

97−% generated when "others" is an author name

98−% - major modification from Chicago Manual of Style (13th ed.) is that

99−% only the first author in a reference appears last name first-

100−% additional authors appear as J. Q. Public.

101−% - pages are listed as "pp. xx-xx" in all entry types except

102−% article entries. Unnecessary (IMHO) "()" around page numbers

103−% were removed, and page numbers now don't end with a period.

104−% - created chicago.sty for use with this bibstyle (required).

105−% - fixed bugs in FUNCTION {format.vol.num.pages} for missing volume,

106−% number, and /or pages. Renamed to format.jour.vol.

107−% - fixed bug in formatting booktitles: additional period an error if

108−% book has a volume.

109−% - fixed bug: editors usually given redundant period before next clause

110−% (format.editors.dot) removed.

111−% - added label support for organizations, if both author and editor

112−% are missing (from alpha.bst). If organization is too long, then

113−% the key field is used for abbreviated citations.

114−% - In proceedings or books of several volumes, no comma was written

115−% between the "Volume x" and the page numbers (this was intentional

116−% in newapa.bst). Fixed.

117−% - Some journals may not have volumes/numbers, only month/year (eg.

118−% IEEE Computer). Fixed bug in article style that assumed volume/number

119−% was always present.

120−%

121−% Original documentation for newapa.sty:

122−% =====================================

123−%

124−% This version was made by modifying the master file made by

125−% Oren Patashnik (PATASHNIK@SCORE.STANFORD.EDU), and the 'named' BibTeX

126−% style of Peter F. Patel-Schneider.

127−%

129−% Copying of this file is authorized only if either

130−% (1) you make absolutely no changes to your copy, including name, or

131−% (2) if you do make changes, you name it something other than 'newapa.bst'.

132−% There are undoubtably bugs in this style. If you make bug fixes,

133−% improvements, etc. please let me know. My e-mail address is:

134−% spencer@cgrg.ohio.state.edu or 71160.3141@compuserve.com

135−%

136−% This style was made from 'plain.bst', 'named.bst', and 'apalike.bst',

137−% with lots of tweaking to make it look like APA style, along with tips

138−% from Young Ryu and Brian Reiser's modifications of 'apalike.bst'.

139−

140−ENTRY

141− { address

142− author

143− booktitle

144− chapter

145− city % jtb: added

146− date % jtb: added

147− edition

148− editor

149− howpublished

150− institution

151− journal

152− key

153− month

154− note

155− number

156− organization

157− pages

158− publisher

159− school

160− series

161− title

162− type

163− volume

164− year

165− }

166− {}

167− { label.year extra.label sort.year sort.label }

168−

169−INTEGERS { output.state before.all mid.sentence after.sentence after.block }

170−

171−FUNCTION {init.state.consts}

172−{ #0 'before.all :=

173− #1 'mid.sentence :=

174− #2 'after.sentence :=

175− #3 'after.block :=

176−}

177−

178−STRINGS { s t u }

179−

180−FUNCTION {output.nonnull}

181−{ 's :=

182− output.state mid.sentence =

183− { ", " * write$ }

184− { output.state after.block =

185− { add.period$ write$

186− newline$

187− "\newblock " write$

188− }

189− { output.state before.all =

190− 'write$

191− { add.period$ " " * write$ }

192− if$

193− }

194− if$

195− mid.sentence 'output.state :=

196− }

197− if$

198− s

199−}

200−

201−% Use a colon to separate output. Used only for address/publisher

202−% combination in book/inbook types, address/institution for manuals,

203−% and organization:publisher for proceedings (inproceedings).

204−%

205−FUNCTION {output.nonnull.colon}

206−{ 's :=

207− output.state mid.sentence =

208− { ": " * write$ }

209− { output.state after.block =

210− { add.period$ write$

211− newline$

212− "\newblock " write$

213− }

214− { output.state before.all =

215− 'write$

216− { add.period$ " " * write$ }

217− if$

218− }

219− if$

220− mid.sentence 'output.state :=

221− }

222− if$

223− s

224−}

225−

226−FUNCTION {output}

227−{ duplicate$ empty$

228− 'pop$

229− 'output.nonnull

230− if$

231−}

232−

233−FUNCTION {output.colon}

234−{ duplicate$ empty$

235− 'pop$

236− 'output.nonnull.colon

237− if$

238−}

239−

240−FUNCTION {output.check}

241−{ 't :=

242− duplicate$ empty$

243− { pop$ "empty " t * " in " * cite$ * warning$ }

244− 'output.nonnull

245− if$

246−}

247−

248−FUNCTION {output.check.colon}

249−{ 't :=

250− duplicate$ empty$

251− { pop$ "empty " t * " in " * cite$ * warning$ }

252− 'output.nonnull.colon

253− if$

254−}

255−

256−FUNCTION {output.year.check}

257−{ year empty$

258− { "empty year in " cite$ * warning$ }

259− { write$

260− " " year * extra.label *

261− mid.sentence 'output.state :=

262− }

263− if$

264−}

265−

266−

267−FUNCTION {fin.entry}

268−{ add.period$

269− write$

270− newline$

271−}

272−

273−FUNCTION {new.block}

274−{ output.state before.all =

275− 'skip$

276− { after.block 'output.state := }

277− if$

278−}

279−

280−FUNCTION {new.sentence}

281−{ output.state after.block =

282− 'skip$

283− { output.state before.all =

284− 'skip$

285− { after.sentence 'output.state := }

286− if$

287− }

288− if$

289−}

290−

291−FUNCTION {not}

292−{ { #0 }

293− { #1 }

294− if$

295−}

296−

297−FUNCTION {and}

298−{ 'skip$

299− { pop$ #0 }

300− if$

301−}

302−

303−FUNCTION {or}

304−{ { pop$ #1 }

305− 'skip$

306− if$

307−}

308−

309−FUNCTION {new.block.checka}

310−{ empty$

311− 'skip$

312− 'new.block

313− if$

314−}

315−

316−FUNCTION {new.block.checkb}

317−{ empty$

318− swap$ empty$

319− and

320− 'skip$

321− 'new.block

322− if$

323−}

324−

325−FUNCTION {new.sentence.checka}

326−{ empty$

327− 'skip$

328− 'new.sentence

329− if$

330−}

331−

332−FUNCTION {new.sentence.checkb}

333−{ empty$

334− swap$ empty$

335− and

336− 'skip$

337− 'new.sentence

338− if$

339−}

340−

341−FUNCTION {field.or.null}

342−{ duplicate$ empty$

343− { pop$ "" }

344− 'skip$

345− if$

346−}

347−

348−%

349−% Emphasize the top string on the stack.

350−%

351−FUNCTION {emphasize}

352−{ duplicate$ empty$

353− { pop$ "" }

354− { "{\em " swap$ * "}" * }

355− if$

356−}

357−

358−%

359−% Emphasize the top string on the stack, but add a trailing space.

360−%

361−FUNCTION {emphasize.space}

362−{ duplicate$ empty$

363− { pop$ "" }

364− { "{\em " swap$ * "\/}" * }

365− if$

366−}

367−

368−%

369−% Emphasize the top string on stack, add a trailing comma and space.

370−%

371−FUNCTION {emphasize.comma}

372−{ duplicate$ empty$

373− { pop$ "" }

374− { "{\em " swap$ * ",\/}" * }

375− if$

376−}

377−

378−INTEGERS { nameptr namesleft numnames }

379−%

380−% Format bibliographical entries with the first author last name first,

381−% and subsequent authors with initials followed by last name.

382−% All names are formatted in this routine.

383−%

384−

385−FUNCTION {format.names}

386−{ 's :=

387− #1 'nameptr := % nameptr = 1;

388− s num.names$ 'numnames := % numnames = num.name$(s);

389− numnames 'namesleft :=

390− { namesleft #0 > }

391−

392− { nameptr #1 =

393− {"{\sc " s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ * "}" * 't := }

394− {"{\sc " s nameptr "{vv~}{ll}{, jj}{, f.}" format.name$ * "}" * 't := }

395− if$

396− nameptr #1 >

397− { namesleft #1 >

398− { ", " * t * }

399− { numnames #2 >

400− { "," * }

401− 'skip$

402− if$

403− t "{\sc others}" =

404− { " {\sc et~al\mbox{.}}" * } % jrh: avoid spacing problems

405− { " {\sc and} " * t * } % from Chicago Manual of Style

406− if$

407− }

408− if$

409− }

410− 't

411− if$

412− nameptr #1 + 'nameptr := % nameptr += 1;

413− namesleft #1 - 'namesleft := % namesleft =- 1;

414− }

415− while$

416−}

417−

418−FUNCTION {my.full.label}

419−{ 's :=

420− #1 'nameptr := % nameptr = 1;

421− s num.names$ 'numnames := % numnames = num.name$(s);

422− numnames 'namesleft :=

423− { namesleft #0 > }

424−

425− { s nameptr "{vv~}{ll}" format.name$ 't := % get the next name

426− nameptr #1 >

427− { namesleft #1 >

428− { ", " * t * }

429− { numnames #2 >

430− { "," * }

431− 'skip$

432− if$

433− t "others" =

434− { " et~al\mbox{.}" * } % jrh: avoid spacing problems

435− { " and " * t * } % from Chicago Manual of Style

436− if$

437− }

438− if$

439− }

440− 't

441− if$

442− nameptr #1 + 'nameptr := % nameptr += 1;

443− namesleft #1 - 'namesleft := % namesleft =- 1;

444− }

445− while$

446−

447−}

448−

449−FUNCTION {format.names.fml}

450−%

451−% Format names in "familiar" format, with first initial followed by

452−% last name. Like format.names, ALL names are formatted.

453−% jtb: The names are NOT put in small caps

454−%

455−{ 's :=

456− #1 'nameptr := % nameptr = 1;

457− s num.names$ 'numnames := % numnames = num.name$(s);

458− numnames 'namesleft :=

459− { namesleft #0 > }

460−

461− { "{" s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ * "}" * 't :=

462−

463− nameptr #1 >

464− { namesleft #1 >

465− { ", " * t * }

466− { numnames #2 >

467− { "," * }

468− 'skip$

469− if$

470− t "{others}" =

471− { " {et~al\mbox{.}}" * }

472− { " {and} " * t * }

473−% { " {\&} " * t * }

474− if$

475− }

476− if$

477− }

478− 't

479− if$

480− nameptr #1 + 'nameptr := % nameptr += 1;

481− namesleft #1 - 'namesleft := % namesleft =- 1;

482− }

483− while$

484−}

485−

486−FUNCTION {format.authors}

487−{ author empty$

488− { "" }

489− { author format.names add.period$} % jtb: add period if none before

490− if$

491−}

492−

493−FUNCTION {format.key}

494−{ empty$

495− { key field.or.null }

496− { "" }

497− if$

498−}

499−

500−%

501−% Format editor names for use in the "in" types: inbook, incollection,

502−% inproceedings: first initial, then last names. When editors are the

503−% LABEL for an entry, then format.editor is used which lists editors

504−% by last name first.

505−%

506−FUNCTION {format.editors.fml}

507−{ editor empty$

508− { "" }

509− { editor format.names.fml

510− editor num.names$ #1 >

511− { ", Eds." * } % jtb: removed parentheses

512− { ", Ed." * } % jtb: removed parentheses

513− if$

514− }

515− if$

516−}

517−

518−%

519−% Format editor names for use in labels, last names first.

520−%

521−FUNCTION {format.editors}

522−{ editor empty$

523− { "" }

524− { editor format.names

525− editor num.names$ #1 >

526− { ", Eds." * } % jtb: removed parentheses

527− { ", Ed." * } % jtb: removed parentheses

528− if$

529− }

530− if$

531−}

532−

533−FUNCTION {format.title}

534−{ title empty$

535− { "" }

536− { title "t" change.case$ }

537− if$

538−}

539−

540−% Note that the APA style requres case changes

541−% in article titles. The following does not

542−% change cases. If you perfer it, uncomment the

543−% following and comment out the above.

544−

545−%FUNCTION {format.title}

546−%{ title empty$

547−% { "" }

548−% { title }

549−% if$

550−%}

551−

552−FUNCTION {n.dashify}

553−{ 't :=

554− ""

555− { t empty$ not }

556− { t #1 #1 substring$ "-" =

557− { t #1 #2 substring$ "--" = not

558− { "--" *

559− t #2 global.max$ substring$ 't :=

560− }

561− { { t #1 #1 substring$ "-" = }

562− { "-" *

563− t #2 global.max$ substring$ 't :=

564− }

565− while$

566− }

567− if$

568− }

569− { t #1 #1 substring$ *

570− t #2 global.max$ substring$ 't :=

571− }

572− if$

573− }

574− while$

575−}

576−

577−FUNCTION {format.btitle}

578−{ edition empty$

579− { title emphasize }

580− { title empty$

581− { title emphasize } % jtb: what is this supposed to do ?!?

582− { "{\em " title * "\/}, " * edition * " ed." * } % jtb: no parens for ed.

583− if$

584− }

585− if$

586−}

587−

588−FUNCTION {format.emphasize.booktitle}

589−{ edition empty$

590− { booktitle emphasize }

591− { booktitle empty$

592− { booktitle emphasize } % jtb: what is this supposed to do ?!?

593− { "{\em " booktitle * "\/}, " * edition * " ed." * } % jtb: no ()s for ed.

594− if$

595− }

596− if$

597− }

598−

599−% jtb: if the preceding string (the title of the conference) is non-empty,

600−% jtb: append the location, otherwise leave empty (so as to trigger the

601−% jtb: error message in output.check

602−FUNCTION {format.city}

603−{ duplicate$ empty$

604− { }

605− { city empty$

606− { date empty$

607− { }

608− { " (" * date * ")" * }

609− if$

610− }

611− { date empty$

612− { " (" * city * ")" * }

613− { " (" * city * ", " * date * ")" * }

614− if$

615− }

616− if$

617− }

618− if$

619−}

620−

621−FUNCTION {tie.or.space.connect}

622−{ duplicate$ text.length$ #3 <

623− { "~" }

624− { " " }

625− if$

626− swap$ * *

627−}

628−

629−FUNCTION {either.or.check}

630−{ empty$

631− 'pop$

632− { "can't use both " swap$ * " fields in " * cite$ * warning$ }

633− if$

634−}

635−

636−% jtb: If there is a series, this is added and the volume trails after it.

637−% jtb: Otherwise, "Vol" is Capitalized.

638−FUNCTION {format.bvolume}

639−{ volume empty$

640− { "" }

641− { series empty$

642− { "Vol." volume tie.or.space.connect}

643− { series ", " * "vol." volume tie.or.space.connect *}

644− if$

645− "volume and number" number either.or.check

646− }

647− if$

648−}

649−

650−FUNCTION {format.number.series}

651−{ volume empty$

652− { number empty$

653− { series field.or.null }

654− { output.state mid.sentence =

655− { "Number" } % gnp - changed to mixed case always

656− { "Number" }

657− if$

658− number tie.or.space.connect

659− series empty$

660− { "there's a number but no series in " cite$ * warning$ }

661− { " in " * series * }

662− if$

663− }

664− if$

665− }

666− { "" }

667− if$

668−}

669−

670−INTEGERS { multiresult }

671−

672−FUNCTION {multi.page.check}

673−{ 't :=

674− #0 'multiresult :=

675− { multiresult not

676− t empty$ not

677− and

678− }

679− { t #1 #1 substring$

680− duplicate$ "-" =

681− swap$ duplicate$ "," =

682− swap$ "+" =

683− or or

684− { #1 'multiresult := }

685− { t #2 global.max$ substring$ 't := }

686− if$

687− }

688− while$

689− multiresult

690−}

691−

692−FUNCTION {format.pages}

693−{ pages empty$

694− { "" }

695− { pages multi.page.check

696− { pages n.dashify } % gnp - removed () % jtb: removed pp.

697− { pages }

698− if$

699− }

700− if$

701−}

702−

703−% By Young (and Spencer)

704−% GNP - fixed bugs with missing volume, number, and/or pages

705−%

706−% Format journal, volume, number, pages for article types.

707−%

708−FUNCTION {format.jour.vol}

709−{ journal empty$

710− { "no journal in " cite$ * warning$

711− "" }

712− { journal emphasize.space }

713− if$

714− number empty$

715− { volume empty$

716− { "no number and no volume in " cite$ * warning$

717− "" * }

718− { "~{\em " * Volume * "}" * }

719− if$

720− }

721− { volume empty$

722− {"no volume for " cite$ * warning$

723− "~" * number * }

724− { "~" *

725− volume emphasize.comma

726− "~" * number * * }

727− if$

728− month empty$

729− {}

730− {" (" * month * ")" *}

731− if$

732− }

733− if$

734− pages empty$

735− {"page numbers missing in " cite$ * warning$

736− "" * } % gnp - place a null string on the stack for output

737− { duplicate$ empty$

738− { pop$ format.pages }

739− { ", " * pages n.dashify * } % gnp - removed pp. for articles

740− if$

741− }

742− if$

743−}

744−

745−FUNCTION {format.chapter.pages}

746−{ chapter empty$

747− 'format.pages

748− { type empty$

749− { "Chapter" } % gnp - changed to mixed case

750− { type "t" change.case$ }

751− if$

752− chapter tie.or.space.connect

753− pages empty$

754− {"page numbers missing in " cite$ * warning$} % gnp - added check

755− { ", " * format.pages * }

756− if$

757− }

758− if$

759−}

760−

761−% jtb: format for collections or proceedings not appearing in a journal

762−FUNCTION {format.in.emphasize.booktitle}

763−{ booktitle empty$

764− { "" }

765− { "In " format.emphasize.booktitle * }

766− if$

767−}

768−

769−% jtb: format for proceedings appearing in a journal

770−FUNCTION {format.in.booktitle}

771−{ booktitle empty$

772− { "" }

773− { "In " booktitle * }

774− if$

775−}

776−

777−FUNCTION {format.in.ed.booktitle}

778−{ booktitle empty$

779− { "" }

780− { editor empty$

781− { "In " format.emphasize.booktitle * }

782− % jtb: swapped editor location

783− { "In " format.emphasize.booktitle * ", " * format.editors.fml * }

784− if$

785− }

786− if$

787−}

788−

789−FUNCTION {format.thesis.type}

790−{ type empty$

791− 'skip$

792−% {pop$

793− {{ "" }

794− type "t" change.case$}

795− if$

796−}

797−

798−FUNCTION {format.tr.number}

799−{ type empty$

800− { "Tech. Rep." }

801− 'type

802− if$

803− number empty$

804− { "t" change.case$ }

805− { number tie.or.space.connect }

806− if$

807−}

808−

809−FUNCTION {format.article.crossref}

810−{ "See"

811− "\citeN{" * crossref * "}" *

812−}

813−

814−FUNCTION {format.crossref.editor}

815−{ editor #1 "{vv~}{ll}" format.name$

816− editor num.names$ duplicate$

817− #2 >

818− { pop$ " et~al\mbox{.}" * } % jrh: avoid spacing problems

819− { #2 <

820− 'skip$

821− { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =

822− { " et~al\mbox{.}" * } % jrh: avoid spacing problems

823− { " and " * editor #2 "{vv~}{ll}" format.name$ * }

824− if$

825− }

826− if$

827− }

828− if$

829−}

830−

831−FUNCTION {format.book.crossref}

832−{ volume empty$

833− { "empty volume in " cite$ * "'s crossref of " * crossref * warning$

834− "In "

835− }

836− { "Volume" volume tie.or.space.connect % gnp - changed to mixed case

837− " of " *

838− }

839− if$

840− editor empty$

841− editor field.or.null author field.or.null =

842− or

843− { key empty$

844− { series empty$

845− { "need editor, key, or series for " cite$ * " to crossref " *

846− crossref * warning$

847− "" *

848− }

849− { "{\em " * series * "\/}" * }

850− if$

851− }

852− { key * }

853− if$

854− }

855− { format.crossref.editor * }

856− if$

857− " \citeN{" * crossref * "}" *

858−}

859−

860−FUNCTION {format.incoll.inproc.crossref}

861−{ "See"

862− " \citeN{" * crossref * "}" *

863−}

864−

865−% format.lab.names:

866−%

867−% determines "short" names for the abbreviated author information.

868−% "Long" labels are created in calc.label, using the routine my.full.label

869−% to format author and editor fields.

870−%

871−% There are 4 cases for labels. (n=3 in the example)

872−% a) one author Foo

873−% b) one to n Foo, Bar and Baz

874−% c) use of "and others" Foo, Bar et al.

875−% d) more than n Foo et al.

876−%

877−FUNCTION {format.lab.names}

878−{ 's :=

879− s num.names$ 'numnames :=

880− numnames #2 > % change number to number of others allowed before

881− % forcing "et al".

882− { s #1 "{vv~}{ll}" format.name$ " et~al\mbox{.}" * } % jrh: \mbox{} added

883− {

884− numnames #1 - 'namesleft :=

885− #2 'nameptr :=

886− s #1 "{vv~}{ll}" format.name$

887− { namesleft #0 > }

888− { nameptr numnames =

889− { s nameptr "{ff }{vv }{ll}{ jj}" format.name$ "others" =

890− { " et~al\mbox{.}" * } % jrh: avoid spacing problems

891− { " and " * s nameptr "{vv~}{ll}" format.name$ * }

892− if$

893− }

894− { ", " * s nameptr "{vv~}{ll}" format.name$ * }

895− if$

896− nameptr #1 + 'nameptr :=

897− namesleft #1 - 'namesleft :=

898− }

899− while$

900− }

901− if$

902−}

903−

904−FUNCTION {author.key.label}

905−{ author empty$

906− { key empty$

907− { "no key, author in " cite$ * warning$

908− cite$ #1 #3 substring$ }

909− 'key

910− if$

911− }

912− { author format.lab.names }

913− if$

914−}

915−

916−FUNCTION {editor.key.label}

917−{ editor empty$

918− { key empty$

919− { "no key, editor in " cite$ * warning$

920− cite$ #1 #3 substring$ }

921− 'key

922− if$

923− }

924− { editor format.lab.names }

925− if$

926−}

927−

928−FUNCTION {author.key.organization.label}

929−%

930−% added - gnp. Provide label formatting by organization if author is null.

931−%

932−{ author empty$

933− { organization empty$

934− { key empty$

935− { "no key, author or organization in " cite$ * warning$

936− cite$ #1 #3 substring$ }

937− 'key

938− if$

939− }

940− { organization }

941− if$

942− }

943− { author format.lab.names }

944− if$

945−}

946−

947−FUNCTION {editor.key.organization.label}

948−%

949−% added - gnp. Provide label formatting by organization if editor is null.

950−%

951−{ editor empty$

952− { organization empty$

953− { key empty$

954− { "no key, editor or organization in " cite$ * warning$

955− cite$ #1 #3 substring$ }

956− 'key

957− if$

958− }

959− { organization }

960− if$

961− }

962− { editor format.lab.names }

963− if$

964−}

965−

966−FUNCTION {author.editor.key.label}

967−{ author empty$

968− { editor empty$

969− { key empty$

970− { "no key, author, or editor in " cite$ * warning$

971− cite$ #1 #3 substring$ }

972− 'key

973− if$

974− }

975− { editor format.lab.names }

976− if$

977− }

978− { author format.lab.names }

979− if$

980−}

981−

982−FUNCTION {calc.label}

983−%

984−% Changed - GNP. See also author.organization.sort, editor.organization.sort

985−% Form label for BibTeX entry. The classification of which fields are used

986−% for which type of entry (book, inbook, etc.) are taken from alpha.bst.

987−% The change here from newapa is to also include organization as a

988−% citation label if author or editor is missing.

989−%

990−{ type$ "book" =

991− type$ "inbook" =

992− or

993− 'author.editor.key.label

994− { type$ "proceedings" =

995− 'editor.key.organization.label

996− { type$ "manual" =

997− 'author.key.organization.label

998− 'author.key.label

999− if$

1000− }

1001− if$

1002− }

1003− if$

1004−

1005− author empty$ % generate the full label citation information.

1006− { editor empty$

1007− { organization empty$

1008− { "no author, editor, or organization in " cite$ * warning$

1009− "??" }

1010− { organization }

1011− if$

1012− }

1013− { editor my.full.label }

1014− if$

1015− }

1016− { author my.full.label }

1017− if$

1018−

1019−% leave label on the stack, to be popped when required.

1020−

1021− "}{" * swap$ * "}{" *

1022−% year field.or.null purify$ #-1 #4 substring$ *

1023−%

1024−% save the year for sort processing afterwards (adding a, b, c, etc.)

1025−%

1026− year field.or.null purify$ #-1 #4 substring$

1027− 'label.year :=

1028−}

1029−

1030−FUNCTION {output.bibitem}

1031−{ newline$

1032−

1033− "\bibitem[\protect\citeauthoryear{" write$

1034− calc.label write$

1035− sort.year write$

1036− "}]{" write$

1037−

1038− cite$ write$

1039− "}" write$

1040− newline$

1041− ""

1042− before.all 'output.state :=

1043−}

1044−

1045−FUNCTION {article}

1046−{ output.bibitem

1047− format.authors

1048− "author" output.check

1049− author format.key output % added

1050− output.year.check % added

1051− new.block

1052− format.title

1053− "title" output.check

1054− new.block

1055− crossref missing$

1056− { format.jour.vol output

1057− }

1058− { format.article.crossref output.nonnull

1059− format.pages output

1060− }

1061− if$

1062− new.block

1063− note output

1064− fin.entry

1065−}

1066−

1067−FUNCTION {book}

1068−{ output.bibitem

1069− author empty$

1070− { format.editors

1071− "author and editor" output.check }

1072− { format.authors

1073− output.nonnull

1074− crossref missing$

1075− { "author and editor" editor either.or.check }

1076− 'skip$

1077− if$

1078− }

1079− if$

1080− output.year.check % added

1081− new.block

1082− format.btitle

1083− "title" output.check

1084− crossref missing$

1085− { new.sentence % jtb: start a new sentence for series/volume

1086− format.bvolume output

1087− new.block

1088− format.number.series output

1089− new.sentence

1090− publisher "publisher" output.check

1091− address "address" output.check % jtb: require address

1092− }

1093− { new.block

1094− format.book.crossref output.nonnull

1095− }

1096− if$

1097− new.block

1098− note output

1099− fin.entry

1100−}

1101−

1102−FUNCTION {booklet}

1103−{ output.bibitem

1104− format.authors output

1105− author format.key output % added

1106− output.year.check % added

1107− new.block

1108− format.title

1109− "title" output.check

1110− new.block

1111− howpublished output

1112− address output

1113− new.block

1114− note output

1115− fin.entry

1116−}

1117−

1118−FUNCTION {inbook}

1119−{ output.bibitem

1120− author empty$

1121− { format.editors

1122− "author and editor" output.check

1123− }

1124− { format.authors output.nonnull

1125− crossref missing$

1126− { "author and editor" editor either.or.check }

1127− 'skip$

1128− if$

1129− }

1130− if$

1131− output.year.check % added

1132− new.block

1133− format.btitle

1134− "title" output.check

1135− crossref missing$

1136− { new.sentence % jtb: start a new sentence for series/volume

1137− format.bvolume output

1138− new.block

1139− format.number.series output

1140− new.sentence

1141− publisher "publisher" output.check

1142− address "address" output.check % jtb: require address

1143− format.chapter.pages

1144− "chapter and pages" output.check % jtb: moved from before publisher

1145− }

1146− { format.chapter.pages "chapter and pages" output.check

1147− new.block

1148− format.book.crossref output.nonnull

1149− }

1150− if$

1151− new.block

1152− note output

1153− fin.entry

1154−}

1155−

1156−FUNCTION {incollection}

1157−{ output.bibitem

1158− format.authors

1159− "author" output.check

1160− author format.key output % added

1161− output.year.check % added

1162− new.block

1163− format.title

1164− "title" output.check

1165− new.block

1166− crossref missing$

1167− { format.in.ed.booktitle

1168− "booktitle" output.check

1169− new.sentence % jtb: start a new sentence for series/volume

1170− format.bvolume output

1171− format.number.series output

1172− new.sentence

1173− publisher "publisher" output.check

1174− address "address" output.check % jtb: require address

1175− format.chapter.pages output % gnp - was special.output.nonnull

1176−% left out comma before page numbers

1177− % jtb: moved from before publisher

1178− }

1179− { format.incoll.inproc.crossref

1180− output.nonnull

1181− format.chapter.pages output

1182− }

1183− if$

1184− new.block

1185− note output

1186− fin.entry

1187−}

1188−

1189−FUNCTION {inproceedings}

1190−{ output.bibitem

1191− format.authors

1192− "author" output.check

1193− author format.key output % added

1194− output.year.check % added

1195− new.block

1196− format.title

1197− "title" output.check

1198− new.block

1199− crossref missing$

1200− { journal missing$ % jtb: proceedings appearing in journals

1201− { format.in.emphasize.booktitle format.city "booktitle" output.check

1202− format.editors.fml output

1203− new.sentence % jtb: start a new sentence for series/volume

1204− format.bvolume output

1205− format.number.series output

1206− new.sentence

1207− organization output

1208− publisher "publisher" output.check % jtb: require publisher (?)

1209− address "address" output.check % jtb: require address

1210− format.pages output % jtb: moved from before publisher

1211− }

1212− % jtb: new:

1213− { format.in.booktitle format.city "booktitle" output.check

1214− format.editors.fml output

1215− new.sentence

1216− format.jour.vol output

1217− }

1218− if$

1219− }

1220− { format.incoll.inproc.crossref output.nonnull

1221− format.pages output

1222− }

1223− if$

1224− new.block

1225− note output

1226− fin.entry

1227−}

1228−

1229−FUNCTION {conference} { inproceedings }

1230−

1231−FUNCTION {manual}

1232−{ output.bibitem

1233− author empty$

1234− { editor empty$

1235− { organization "organization" output.check

1236− organization format.key output } % if all else fails, use key

1237− { format.editors "author and editor" output.check }

1238− if$

1239− }

1240− { format.authors output.nonnull }

1241− if$

1242− output.year.check % added

1243− new.block

1244− format.btitle

1245− "title" output.check

1246− organization address new.block.checkb

1247− % jtb: back to normal style: organization, address

1248− organization "organization" output.check

1249− address output

1250− new.block

1251− note output

1252− fin.entry

1253−}

1254−

1255−FUNCTION {mastersthesis}

1256−{ output.bibitem

1257− format.authors

1258− "author" output.check

1259− author format.key output % added

1260− output.year.check % added

1261− new.block

1262− format.title

1263− "title" output.check

1264− new.block

1265− "M.S.\ thesis" format.thesis.type output.nonnull

1266− school "school" output.check

1267− address output

1268− new.block

1269− note output

1270− fin.entry

1271−}

1272−

1273−FUNCTION {misc}

1274−{ output.bibitem

1275− format.authors output

1276− author format.key output % added

1277− output.year.check % added

1278− title howpublished new.block.checkb

1279− format.title output

1280− new.block

1281− howpublished output

1282− new.block

1283− note output

1284− fin.entry

1285−}

1286−

1287−FUNCTION {phdthesis}

1288−{ output.bibitem

1289− format.authors

1290− "author" output.check

1291− author format.key output % added

1292− output.year.check % added

1293− new.block

1294− format.title

1295− "title" output.check

1296− new.block

1297− format.thesis.type "Ph.D. thesis" output.nonnull

1298− school "school" output.check

1299− address output

1300− new.block

1301− note output

1302− fin.entry

1303−}

1304−

1305−FUNCTION {proceedings}

1306−{ output.bibitem

1307− editor empty$

1308− { organization output

1309− organization format.key output } % gnp - changed from author format.key

1310− { format.editors output.nonnull }

1311− if$

1312−% author format.key output % gnp - removed (should be either

1313−% editor or organization

1314− output.year.check % added (newapa)

1315− new.block

1316− format.btitle format.city "title" output.check % jtb: added city

1317− new.sentence

1318− format.bvolume output

1319− format.number.series output

1320− new.sentence

1321− organization output

1322− % jtb: normal order: publisher, address

1323− publisher output

1324− address output

1325− new.block

1326− note output

1327− fin.entry

1328−}

1329−

1330−FUNCTION {techreport}

1331−{ output.bibitem

1332− format.authors

1333− "author" output.check

1334− author format.key output % added

1335− output.year.check % added

1336− new.block

1337− format.title

1338− "title" output.check

1339− new.block

1340− format.tr.number output % jtb: moved month ...

1341− institution "institution" output.check

1342− address output

1343− new.sentence

1344− month output % jtb: ... to here (no parens)

1345− new.block

1346− note output

1347− fin.entry

1348−}

1349−

1350−FUNCTION {unpublished}

1351−{ output.bibitem

1352− format.authors

1353− "author" output.check

1354− author format.key output % added

1355− output.year.check % added

1356− new.block

1357− format.title

1358− "title" output.check

1359− new.block

1360− note "note" output.check

1361− fin.entry

1362−}

1363−

1364−FUNCTION {default.type} { misc }

1365−

1366−MACRO {jan} {"Jan."}

1367−

1368−MACRO {feb} {"Feb."}

1369−

1370−MACRO {mar} {"Mar."} % jtb: corrected: was "March"

1371−

1372−MACRO {apr} {"Apr."} % jtb: corrected: was "April"

1373−

1374−MACRO {may} {"May"}

1375−

1376−MACRO {jun} {"June"}

1377−

1378−MACRO {jul} {"July"}

1379−

1380−MACRO {aug} {"Aug."}

1381−

1382−MACRO {sep} {"Sept."}

1383−

1384−MACRO {oct} {"Oct."}

1385−

1386−MACRO {nov} {"Nov."}

1387−

1388−MACRO {dec} {"Dec."}

1389−

1390−MACRO {acmcs} {"ACM Comput. Surv."}

1391−

1392−MACRO {acmlett} {"ACM Lett. Program. Lang. Syst."}

1393−

1394−MACRO {acta} {"Acta Inf."}

1395−

1396−MACRO {ai} {"Artificial Intelligence"}

1397−

1398−MACRO {al} {"Ada Lett."}

1399−

1400−MACRO {acr} {"Adv. Comput. Res."}

1401−

1402−MACRO {bit} {"Bit"}

1403−

1404−MACRO {cacm} {"Commun. ACM"}

1405−

1406−MACRO {cj} {"Comput. J."}

1407−

1408−MACRO {cn} {"Comput. Netw."}

1409−

1410−MACRO {cl} {"Comput. Lang."}

1411−

1412−MACRO {ibmjrd} {"IBM J. Res. and Development"}

1413−

1414−MACRO {ibmsj} {"IBM Systems Journal"}

1415−

1416−MACRO {ict} {"Inf. Contr."}

1417−

1418−MACRO {ieebcs} {"IEE/BCS Softw. Eng. J."}

1419−

1420−MACRO {ieees} {"IEEE Softw."}

1421−

1422−MACRO {ieeese} {"IEEE Trans. Softw. Eng."}

1423−

1424−MACRO {ieeetc} {"IEEE Trans. Comput."}

1425−

1426−MACRO {ieeetcad}

1427− {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}

1428−

1429−MACRO {ieeetpds} {"IEEE Trans. Parall. Distrib. Syst."}

1430−

1431−MACRO {ieeetit} {"IEEE Trans. Inf. Theory"}

1432−

1433−MACRO {ipl} {"Inf. Process. Lett."}

1434−

1435−MACRO {icp} {"Inf. Comput."}

1436−

1437−MACRO {ist} {"Inf. Softw. Tech."}

1438−

1439−MACRO {ijsa} {"Int. J. Supercomput. Appl."}

1440−

1441−MACRO {ijpp} {"Int. J. Parallel Program."}

1442−

1443−MACRO {jlp} {"J. Logic Program."}

1444−

1445−MACRO {jfp} {"J. Funct. Program."}

1446−

1447−MACRO {jcss} {"J. Comput. Syst. Sci."}

1448−

1449−MACRO {jsmrp} {"J. Softw. Maint. Res. Pract."}

1450−

1451−MACRO {jss} {"J. Syst. Softw."}

1452−

1453−MACRO {jlc} {"J. Logic and Comput."}

1454−

1455−MACRO {jlsc} {"J. Lisp Symb. Comput."}

1456−

1457−MACRO {lpls} {"Lett. Program. Lang. Syst."}

1458−

1459−MACRO {mor} {"Math. Oper. Res."}

1460−

1461−MACRO {mscs} {"Math. Struct. Comput. Sci."}

1462−

1463−MACRO {mst} {"Math. Syst. Theor."} % jtb: was Math. Syst. Theory

1464− % jtb: (if you ask me, I prefer the old way)

1465−MACRO {ngc} {"New Gen. Comput."}

1466−

1467−MACRO {scp} {"Sci. Comput. Program."}

1468−

1469−MACRO {sicomp} {"SIAM J. Comput."}

1470−

1471−MACRO {spe} {"Softw. Pract. Exper."}

1472−

1473−MACRO {tocs} {"ACM Trans. Comput. Syst."}

1474−

1475−MACRO {tods} {"ACM Trans. Database Syst."}

1476−

1477−MACRO {tog} {"ACM Trans. Graphics"}

1478−

1479−MACRO {toms} {"ACM Trans. Math. Softw."}

1480−

1481−MACRO {toois} {"ACM Trans. Office Inf. Syst."}

1482−

1483−MACRO {toplas} {"ACM Trans. Program. Lang. Syst."}

1484−

1485−MACRO {tocl} {"ACM Trans. On Comp. Logic"}

1486−

1487−MACRO {tcs} {"Theor. Comput. Sci."} % jtb: was Theor. Comp. Sci.

1488−

1489−MACRO {tr} {"Tech. Rep."}

1490−

1491−READ

1492−

1493−FUNCTION {sortify}

1494−{ purify$

1495− "l" change.case$

1496−}

1497−

1498−INTEGERS { len }

1499−

1500−FUNCTION {chop.word}

1501−{ 's :=

1502− 'len :=

1503− s #1 len substring$ =

1504− { s len #1 + global.max$ substring$ }

1505− 's

1506− if$

1507−}

1508−

1509−

1510−

1511−FUNCTION {sort.format.names}

1512−{ 's :=

1513− #1 'nameptr :=

1514− ""

1515− s num.names$ 'numnames :=

1516− numnames 'namesleft :=

1517− { namesleft #0 > }

1518− { nameptr #1 >

1519− { " " * }

1520− 'skip$

1521− if$

1522− s nameptr "{vv{ } }{ll{ }}{ f{ }}{ jj{ }}" format.name$ 't :=

1523− nameptr numnames = t "others" = and

1524− { " et~al" * }

1525− { t sortify * }

1526− if$

1527− nameptr #1 + 'nameptr :=

1528− namesleft #1 - 'namesleft :=

1529− }

1530− while$

1531−}

1532−

1533−FUNCTION {sort.format.title}

1534−{ 't :=

1535− "A " #2

1536− "An " #3

1537− "The " #4 t chop.word

1538− chop.word

1539− chop.word

1540− sortify

1541− #1 global.max$ substring$

1542−}

1543−

1544−FUNCTION {author.sort}

1545−{ author empty$

1546− { key empty$

1547− { "to sort, need author or key in " cite$ * warning$

1548− "" }

1549− { key sortify }

1550− if$

1551− }

1552− { author sort.format.names }

1553− if$

1554−}

1555−

1556−FUNCTION {editor.sort}

1557−{ editor empty$

1558− { key empty$

1559− { "to sort, need editor or key in " cite$ * warning$

1560− ""

1561− }

1562− { key sortify }

1563− if$

1564− }

1565− { editor sort.format.names }

1566− if$

1567−}

1568−

1569−FUNCTION {author.editor.sort}

1570−{ author empty$

1571− { "missing author in " cite$ * warning$

1572− editor empty$

1573− { key empty$

1574− { "to sort, need author, editor, or key in " cite$ * warning$

1575− ""

1576− }

1577− { key sortify }

1578− if$

1579− }

1580− { editor sort.format.names }

1581− if$

1582− }

1583− { author sort.format.names }

1584− if$

1585−}

1586−

1587−FUNCTION {author.organization.sort}

1588−%

1589−% added - GNP. Stack author or organization for sorting (from alpha.bst).

1590−% Unlike alpha.bst, we need entire names, not abbreviations

1591−%

1592−{ author empty$

1593− { organization empty$

1594− { key empty$

1595− { "to sort, need author, organization, or key in " cite$ * warning$

1596− ""

1597− }

1598− { key sortify }

1599− if$

1600− }

1601− { organization sortify }

1602− if$

1603− }

1604− { author sort.format.names }

1605− if$

1606−}

1607−

1608−FUNCTION {editor.organization.sort}

1609−%

1610−% added - GNP. Stack editor or organization for sorting (from alpha.bst).

1611−% Unlike alpha.bst, we need entire names, not abbreviations

1612−%

1613−{ editor empty$

1614− { organization empty$

1615− { key empty$

1616− { "to sort, need editor, organization, or key in " cite$ * warning$

1617− ""

1618− }

1619− { key sortify }

1620− if$

1621− }

1622− { organization sortify }

1623− if$

1624− }

1625− { editor sort.format.names }

1626− if$

1627−}

1628−

1629−FUNCTION {presort}

1630−%

1631−% Presort creates the bibentry's label via a call to calc.label, and then

1632−% sorts the entries based on entry type. Chicago.bst adds support for

1633−% including organizations as the sort key; the following is stolen from

1634−% alpha.bst.

1635−%

1636−{ calc.label sortify % recalculate bibitem label

1637− year field.or.null purify$ #-1 #4 substring$ * % add year

1638− " "

1639− *

1640− type$ "book" =

1641− type$ "inbook" =

1642− or

1643− 'author.editor.sort

1644− { type$ "proceedings" =

1645− 'editor.organization.sort

1646− { type$ "manual" =

1647− 'author.organization.sort

1648− 'author.sort

1649− if$

1650− }

1651− if$

1652− }

1653− if$

1654− #1 entry.max$ substring$ % added for newapa

1655− 'sort.label := % added for newapa

1656− sort.label % added for newapa

1657− *

1658− " "

1659− *

1660− title field.or.null

1661− sort.format.title

1662− *

1663− #1 entry.max$ substring$

1664− 'sort.key$ :=

1665−}

1666−

1667−ITERATE {presort}

1668−

1669−SORT % by label, year, author/editor, title

1670−

1671−STRINGS { last.label next.extra }

1672−

1673−INTEGERS { last.extra.num }

1674−

1675−FUNCTION {initialize.extra.label.stuff}

1676−{ #0 int.to.chr$ 'last.label :=

1677− "" 'next.extra :=

1678− #0 'last.extra.num :=

1679−}

1680−

1681−FUNCTION {forward.pass}

1682−%

1683−% Pass through all entries, comparing current entry to last one.

1684−% Need to concatenate year to the stack (done by calc.label) to determine

1685−% if two entries are the same (see presort)

1686−%

1687−{ last.label

1688− calc.label year field.or.null purify$ #-1 #4 substring$ * % add year

1689− #1 entry.max$ substring$ = % are they equal?

1690− { last.extra.num #1 + 'last.extra.num :=

1691− last.extra.num int.to.chr$ 'extra.label :=

1692− }

1693− { "a" chr.to.int$ 'last.extra.num :=

1694− "" 'extra.label :=

1695− calc.label year field.or.null purify$ #-1 #4 substring$ * % add year

1696− #1 entry.max$ substring$ 'last.label := % assign to last.label

1697− }

1698− if$

1699−}

1700−

1701−FUNCTION {reverse.pass}

1702−{ next.extra "b" =

1703− { "a" 'extra.label := }

1704− 'skip$

1705− if$

1706− label.year extra.label * 'sort.year :=

1707− extra.label 'next.extra :=

1708−}

1709−

1710−EXECUTE {initialize.extra.label.stuff}

1711−

1712−ITERATE {forward.pass}

1713−

1714−REVERSE {reverse.pass}

1715−

1716−FUNCTION {bib.sort.order}

1717−{ sort.label

1718− " "

1719− *

1720− year field.or.null sortify

1721− *

1722− " "

1723− *

1724− title field.or.null

1725− sort.format.title

1726− *

1727− #1 entry.max$ substring$

1728− 'sort.key$ :=

1729−}

1730−

1731−ITERATE {bib.sort.order}

1732−

1733−SORT % by sort.label, year, title --- giving final bib. order.

1734−

1735−FUNCTION {begin.bib}

1736−

1737−{ preamble$ empty$

1738− 'skip$

1739− { preamble$ write$ newline$ }

1740− if$

1741− "\begin{thebibliography}{}" write$ newline$

1742−}

1743−

1744−

1745−EXECUTE {begin.bib}

1746−

1747−EXECUTE {init.state.consts}

1748−

1749−ITERATE {call.type$}

1750−

1751−FUNCTION {end.bib}

1752−{ newline$

1753− "\end{thebibliography}" write$ newline$

1754−}

1755−

1756−EXECUTE {end.bib}

1757−

1758−

1759−

1760−

1761−

1762−

1763−

1764−

1765−

1766−

1767−

1768−

1769−

1770−

papers/impl-paper/acmtrans2m.clsdeleted−1460

@@ -1,1460 +0,0 @@

1−% latex2e by nr 7/3/96

2−% acmtrans.cls revised 4/19/96

3−% revised again 31-JAN-1996 (see end of file)

4−% revised 5-14-1997 :

5−% Don't use sans-serif font in categories and descriptors

6−% include latexsym by default

7−% Define longpage and shortpage

8−% Adjusted from the acmtrans2e.cls file to the needs of ACM TOCL by

9−% Marco Aiello on June 14, 2000.

10−% Further changes made by Frederic Goualard on Sep. 27, 2000

11−% to take care of the indentation problem in the bibliography

12−% arising without the use of the hyperref package.

13−% Modularization to adapt to the needs of JACM, TOCL,

14−% TODAES, TODS, TOGS, TOMS, AND TOPLAS, by Marco Aiello on

15−% June 2001.

16−% Here is the basic framework that is needed to convert your paper

17−% into ACM Transactions format and bibliographic format. For a tutorial

18−% introduction, see ``instructions.tex'' (compile it with LaTeX) that

19−% accompanies the distribution of this style file.

20−%

21−% -> \documentclass{acmtrans2m}

22−% -> \markboth{}{}

23−% takes 2 arguments and it is for the left- and right-page headers:

24−% the first set of braces is assigned for author's name(s)

25−% and

26−% the second set of braces is assigned for the title

27−% (if the title is too long, contraction may be needed

28−% -> \title{}

29−% if the title is too long, it can be separated by \\

30−% -> \author{}

31−% author1 \\ author1 affiliation

32−% \and

33−% author2 \\ author2 affiliation

34−% -> \begin{abstract}

35−% -> \end{abstract}

36−%

37−% -> \category{}{}{}

38−% takes 3 arguments for the Computing Reviews Classification Scheme.

39−% ex: \category{D.3.3}{Programming Languages}{Language Constructs and

40−% Features}[data types and structures]

41−% the last argument, in square brackets, is optional.

42−% -> \terms{} (ex: \terms{Human Factors, Languages})

43−% -> \keywords{} (in alphabetical order \keywords{document processing, sequences,

44−% string searching, subsequences, substrings})

45−% -> \begin{document}

46−%

47−% -> \begin{bottomstuff}

48−% similar to \thanks

49−% for authors' addresses; research/grant statements

50−% -> \end{bottomstuff}

51−% -> \maketitle

52−%

53−% Now you can start the body of the paper; your figures, tables and

54−% use all the latex constructs.

55−%

56−% -> \begin{acks}

57−% acknowledgements

58−% -> \end{acks}

59−%

60−% -> \bibliographystyle{acmtrans}

61−% -> \bibliography{mybib_file}

62−%

63−% ****

64−% If your paper has been accepted with a separate (electronic only)

65−% appendix, you need to add the following control sequence:

66−%

67−%

68−% body of appendix

69−%!!!!!! \appendixhead has be cut into two: \appendixhead and \elecappendix

70−%!!!!!! See end of file. (jtb)

71−%

72−% -> \end{document}

73−%

74−% Do not worry about the other definitions in this style file

75−% Remember to compile: latex, bibtex, latex latex

76−%

77−% Bibliographic cite forms needed:

78−%

79−% \cite{key}

80−% which produces citations with author list and year.

81−% eg. [Brown 1978; Jarke, et al. 1985]

82−% \citeA{key}

83−% which produces citations with only the author list.

84−% eg. [Brown; Jarke, et al.]

85−% \citeN{key}

86−% which produces citations with the author list and year, but

87−% can be used as nouns in a sentence; no brackets appear around

88−% the author names, but only around the year.

89−% eg. Shneiderman [1978] states that......

90−% \citeN should only be used for a single citation.

91−% \citeNN{refkey1,refkey2} for author [ref1year; ref2year]

92−% \citeyear{key}

93−% which produces the year information only, within brackets.

94−%

95−% Abbreviated author lists use the ``et al.'' construct.

96−%

97−% The above are examples of required ACM bibliographic cite formats needed.

98−% *******************

99−% Here is the complete list of cite forms from the chicago bibliographic style

100−%

101−% \cite{key}

102−% which produces citations with abbreviated author list and year.

103−% \citeNP{key}

104−% which produces citations with abbreviated author list and year.

105−% \citeA{key}

106−% which produces only the abbreviated author list.

107−% \citeANP{key}

108−% which produces only the abbreviated author list.

109−% \citeN{key}

110−% which produces the abbreviated author list and year, with only the

111−% year in parentheses. Use with only one citation.

112−% \citeyear{key}

113−% which produces the year information only, within parentheses.

114−% \citeyearNP{key}

115−% which produces the year information only.

116−%

117−% Abbreviated author lists use the ``et al.'' construct.

118−%

119−% `NP' means `no parentheses'

120−%

121−

122−\NeedsTeXFormat{LaTeX2e}

123−\ProvidesClass{acmtrans2m} [1996/07/03 ACM Transactions class based on <23 April 96>]

124−\RequirePackage{latexsym}

125−%aiellom{

126−\RequirePackage{url}

127−

128−% Do not change the following! Use the appropriate acmtocl, acmtods, ... option

129−\def\@acmVolume{V} %the volume

130−\def\@acmNumber{N} %the number

131−\def\@acmYear{YY} %the last two digits of the year,

132−\def\@acmMonth{Month} %the month

133−\def\@journalName{ACM Journal Name} %the name of the ACM journal

134−\def\@journalNameShort{jn} %the acronym of the ACM journal

135−\def\@permissionCodeOne{0000-0000} %the permission code of the ACM journal

136−\def\@permissionCodeTwo{0000} %the permission code of the ACM journal part 2

137−\def\@pageCode{\acmPageCode} %the first page of the article in 4 digits

138−

139−

140−\newif\if@acmjacm

141−\newif\if@acmtocl

142−\newif\if@acmtodaes

143−\newif\if@acmtods

144−\newif\if@acmtogs

145−\newif\if@acmtoms

146−\newif\if@acmtoplas

147−

148−\DeclareOption{acmnow}{

149− \typeout{}

150− \typeout{Directly generating the Month and Year for footers from the clock.}

151− \def\@acmYear{\yearTwoDigits}

152− \def\@acmMonth{\monthWord}

153−}

154−

155−\DeclareOption{acmjacm}{

156− \typeout{}

157− \typeout{Using ACM, JACM's option: 2001/06/01 by Marco Aiello et al.}

158− \typeout{}

159− %\global\@acmjacmfalse

160− \global\@acmtoclfalse

161− \global\@acmtodaesfalse

162− \global\@acmtodsfalse

163− \global\@acmtogsfalse

164− \global\@acmtomsfalse

165− \global\@acmtoplasfalse

166− \global\@acmjacmtrue

167− \def\@journalName{Journal of the ACM}

168− \def\@journalNameShort{jacm}

169− \def\@permissionCodeOne{0004-5411}

170− \def\@permissionCodeTwo{0100}

171−}

172−

173−\DeclareOption{acmtocl}{

174− \typeout{}

175− \typeout{Using ACM, TOCL's option: 2001/06/01 by Marco Aiello et al.}

176− \typeout{}

177− \global\@acmjacmfalse

178− \global\@acmtoclfalse

179− \global\@acmtodaesfalse

180− \global\@acmtodsfalse

181− \global\@acmtogsfalse

182− \global\@acmtomsfalse

183− \global\@acmtoplasfalse

184− \global\@acmtocltrue

185− \def\@journalName{ACM Transactions on Computational Logic}

186− \def\@journalNameShort{tocl}

187− \def\@permissionCodeOne{1529-3785}

188− \def\@permissionCodeTwo{0700}

189−}

190−

191−\DeclareOption{acmtodaes}{

192− \typeout{}

193− \typeout{Using ACM, TODAES option: 2001/06/01 by Marco Aiello et al.}

194− \typeout{}

195− \global\@acmjacmfalse

196− \global\@acmtoclfalse

197− %\global\@acmtodaesfalse

198− \global\@acmtodsfalse

199− \global\@acmtogsfalse

200− \global\@acmtomsfalse

201− \global\@acmtoplasfalse

202− \global\@acmtodaestrue

203− \def\@journalName{ACM Transactions on Design Automation of Electronic Systems}

204− \def\@journalNameShort{todaes}

205− \def\@permissionCodeOne{1084-4309}

206− \def\@permissionCodeTwo{0400}

207−}

208−

209−\DeclareOption{acmtods}{

210− \typeout{}

211− \typeout{Using ACM, TODS's option: 2001/06/01 by Marco Aiello et al.}

212− \typeout{}

213− \global\@acmjacmfalse

214− \global\@acmtoclfalse

215− \global\@acmtodaesfalse

216− %\global\@acmtodsfalse

217− \global\@acmtogsfalse

218− \global\@acmtomsfalse

219− \global\@acmtoplasfalse

220− \global\@acmtodstrue

221− \def\@journalName{ACM Transactions on Database Systems}

222− \def\@journalNameShort{tods}

223− \def\@permissionCodeOne{0362-5915}

224− \def\@permissionCodeTwo{0300}

225−}

226−

227−\DeclareOption{acmtogs}{

228− \typeout{}

229− \typeout{Using ACM, TOGS's option: 2001/06/01 by Marco Aiello et al.}

230− \typeout{}

231− \global\@acmjacmfalse

232− \global\@acmtoclfalse

233− \global\@acmtodaesfalse

234− \global\@acmtodsfalse

235− %\global\@acmtogsfalse

236− \global\@acmtomsfalse

237− \global\@acmtoplasfalse

238− \global\@acmtogstrue

239− \def\@journalName{ACM Transactions on Graphics}

240− \def\@journalNameShort{togs}

241− \def\@permissionCodeOne{0730-0301}

242− \def\@permissionCodeTwo{0100}

243−}

244−

245−\DeclareOption{acmtoms}{

246− \typeout{}

247− \typeout{Using ACM, TOMS's option: 2001/06/01 by Marco Aiello et al.}

248− \typeout{}

249− \global\@acmjacmfalse

250− \global\@acmtoclfalse

251− \global\@acmtodaesfalse

252− \global\@acmtodsfalse

253− \global\@acmtogsfalse

254− %\global\@acmtomsfalse

255− \global\@acmtoplasfalse

256− \global\@acmtomstrue

257− \def\@journalName{ACM Transactions on Mathematical Software}

258− \def\@journalNameShort{toms}

259− \def\@permissionCodeOne{0098-3500}

260− \def\@permissionCodeTwo{1200}

261−}

262−

263−\DeclareOption{acmtoplas}{

264− \typeout{}

265− \typeout{Using ACM, TOPLAS option: 2001/06/01 by Marco Aiello et al.}

266− \typeout{}

267− \global\@acmjacmfalse

268− \global\@acmtoclfalse

269− \global\@acmtodaesfalse

270− \global\@acmtodsfalse

271− \global\@acmtogsfalse

272− \global\@acmtomsfalse

273− %\global\@acmtoplasfalse

274− \global\@acmtoplastrue

275− \def\@journalName{ACM Transactions on Programming Languages and Systems}

276− \def\@journalNameShort{toplas}

277− \def\@permissionCodeOne{0164-0925}

278− \def\@permissionCodeTwo{0500}

279−}

280−%}aiellom

281−

282−

283−

284−\if@compatibility\else

285−\DeclareOption{a4paper}

286− {\setlength\paperheight {297mm}%

287− \setlength\paperwidth {210mm}%

288− \def\special@paper{210mm,297mm}}

289−\DeclareOption{a5paper}

290− {\setlength\paperheight {210mm}%

291− \setlength\paperwidth {148mm}%

292− \def\special@paper{148mm,210mm}}

293−\DeclareOption{b5paper}

294− {\setlength\paperheight {250mm}%

295− \setlength\paperwidth {176mm}%

296− \setlength\voffset {-15mm}%

297− \setlength\hoffset {-20mm}%

298− \def\special@paper{176mm,250mm}}

299−\DeclareOption{letterpaper}

300− {\setlength\paperheight {11in}%

301− \setlength\paperwidth {8.5in}%

302− \def\special@paper{8.5in,11in}}

303−\DeclareOption{legalpaper}

304− {\setlength\paperheight {14in}%

305− \setlength\paperwidth {8.5in}%

306− \def\special@paper{8.5in,14in}}

307−\DeclareOption{executivepaper}

308− {\setlength\paperheight {10.5in}%

309− \setlength\paperwidth {7.25in}%

310− \def\special@paper{7.25in,10.5in}}

311−\DeclareOption{landscape}

312− {\setlength\@tempdima {\paperheight}%

313− \setlength\paperheight {\paperwidth}%

314− \setlength\paperwidth {\@tempdima}}

315−\fi

316−

317−\DeclareOption{checkMargin}{\setlength\overfullrule{5pt}}

318−\DeclareOption{final}{\setlength\overfullrule{0pt}}

319−

320−\DeclareOption{oneside}{\@twosidefalse \@mparswitchfalse}

321−\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}

322−

323−\DeclareOption{10pt}{\def\@ptsize{0}} %needed for amssymbols.sty

324−\DeclareOption{11pt}{\ClassError{acmtrans}{11pt style not supported}

325− {ACM transactions documents can be set in 10pt only}}

326−\DeclareOption{12pt}{\ClassError{acmtrans}{11pt style not supported}

327− {ACM transactions documents can be set in 10pt only}}

328−\newif\if@hyperref

329−\DeclareOption{hyperref}{%

330− \def\pages{\pageref{@firstpg}--\pageref{@lastpg}}%

331− \def\mypage{\thepage}%

332− \def\@getpagenum#1#2#3#4{#2}%

333− \def\pdfinfo#1#2{\pdfmark{pdfmark=/DOCINFO,Title=#1,Author=#2}}

334− \global\@hyperreftrue

335− }

336−\DeclareOption{nohyperref}{

337− \def\pages{\pageref{@firstpg}--\pageref{@lastpg}}%

338− \def\@getpagenum#1#2{#2}%

339− \def\mypage{\thepage}%

340− \def\pdfinfo#1#2{}%

341− \def\pdfbookmark#1#2{}%

342− \global\@hyperreffalse

343− }

344−\DeclareOption{notfinal}{

345− \def\pages{BD}%

346− \def\mypage{TBD}%

347− \def\@getpagenum#1#2{#2}%

348− \def\pdfinfo#1#2{}%

349− \def\pdfbookmark#1#2{}%

350− }

351−\DeclareOption{omitline}{\def\@abstractbottom{\relax}}

352−\DeclareOption{dontomitline}{\def\@abstractbottom{\if@acmjacm\else\hbox{\vrule height .2pt width 30pc}\fi}}

353−\ExecuteOptions{twoside,notfinal,10pt,dontomitline,nohyperref,letterpaper} % defaults

354−

355−

356−

357−\ProcessOptions

358−

359−%{aiellom to automatize the issue specific data

360−\def\acmVolume#1{\def\@acmVolume{#1}}

361−\def\acmNumber#1{\def\@acmNumber{#1}}

362−\def\acmYear#1{\def\@acmYear{#1}}

363−\def\acmMonth#1{\def\@acmMonth{#1}}

364−

365−

366−% Command to get the year from the system and display the last two digits

367−\newcommand{\ignoretwo}[2]{}

368−\newcommand{\yearTwoDigits}{\expandafter\ignoretwo\the\year}

369−%To transform the month number in its name in English

370−\newcommand{\monthWord}{\ifnum\the\month=1 January\fi\ifnum\the\month=2 February\fi\ifnum\the\month=3 March\fi\ifnum\the\month=4 April\fi\ifnum\the\month=5 May\fi\ifnum\the\month=6 June\fi\ifnum\the\month=7 July\fi\ifnum\the\month=8 August\fi\ifnum\the\month=9 September\fi\ifnum\the\month=10 October\fi\ifnum\the\month=11 November\fi\ifnum\the\month=12 December\fi}

371−% overright the \@setref definition, so that if a reference is undefined

372−% then it returns a number 0 and then the usual double boldface

373−% question marks ??

374−% this is necessary for the \acmPageCode command, otherwise it gives an error

375−% everytime the aux file is not there

376−\def\@setref#1#2#3{%

377− \ifx#1\relax

378− \number 0\relax

379− \protect\G@refundefinedtrue

380− \nfss@text{\reset@font\bfseries ??}%

381− \@latex@warning{Reference `#3' on page \thepage \space undefined}%

382− \else

383− \expandafter#2#1\null

384− \fi}

385−%make the code a four digits string based on the first page number

386−\newcommand{\acmPageCode}{\bgroup

387− \newcount\c@tempo

388− \setcounter{tempo}{\number\pageref{@firstpg}}\ifnum \c@tempo<1000 0\fi\ifnum \c@tempo<100 0\fi\ifnum \c@tempo<10 0\fi\ifnum \c@tempo<1 0\fi\pageref{@firstpg}

389− \egroup

390−}

391−%}aiellom

392−

393−

394−

395−\lineskip 1pt \normallineskip 1pt

396−\def\baselinestretch{1}

397−

398−\renewcommand\normalsize{%

399− \@setfontsize\normalsize\@xpt\@xiipt

400− \abovedisplayskip 6pt plus2pt minus1pt\belowdisplayskip \abovedisplayskip

401− \abovedisplayshortskip 6pt plus0pt minus 3pt

402− \belowdisplayshortskip 6pt plus0pt minus3pt\let\@listi\@listI}

403−

404−\newcommand\small{%

405− \@setfontsize\small\@ixpt{11pt}%

406− \abovedisplayskip 5pt plus 2pt minus 1pt\belowdisplayskip \abovedisplayskip

407− \abovedisplayshortskip 5pt plus0pt minus2pt\belowdisplayshortskip 5pt plus0pt

408− minus 2pt

409− \def\@listi{\leftmargin\leftmargini \topsep 5pt plus 2pt minus 1pt\parsep 0pt

410− plus .7pt

411− \itemsep 1.6pt plus .8pt}}

412−\newcommand\footnotesize{%

413−% \@setfontsize\footnotesize\@viiipt{10pt}

414− \@setsize\footnotesize{10pt}\viiipt\@viiipt

415− \abovedisplayskip 4pt plus 1pt minus 0pt\belowdisplayskip \abovedisplayskip

416− \abovedisplayshortskip 4pt plus 0pt minus 1pt\belowdisplayshortskip 4pt plus

417− 0pt minus 1pt

418− \def\@listi{\leftmargin\leftmargini \topsep 4pt plus 1pt minus

419− 0pt\parsep 0pt plus .5pt

420− \itemsep 1pt plus .7pt}}

421−

422−\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}

423−\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}

424−\newcommand\large{\@setfontsize\large\@xiipt{14}}

425−\newcommand\Large{\@setfontsize\Large\@xivpt{18}}

426−\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{20}}

427−\newcommand\huge{\@setfontsize\huge\@xxpt{25}}

428−\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}

429−

430−\normalsize

431−

432− \oddsidemargin .75in \evensidemargin .75in \marginparwidth .5in

433− \marginparsep .125in

434− \topmargin .25in \headheight 12pt\headsep 16pt

435− %% not in latex2e \footheight 10pt

436− \footskip 15pt

437−

438−\textheight 47pc \textwidth 30pc \columnsep 10pt \columnseprule 0pt

439−% next five lines added by K.R. Apt, March 20, 01

440−\advance\textheight-2.6pt

441−\newdimen\normaltextheight

442−\setlength\normaltextheight{\textheight}

443−%\renewcommand\rmdefault{pnc}

444−%\renewcommand\sfdefault{phv}

445−

446−

447−\footnotesep 7pt

448−\skip\footins 15pt plus 4pt minus 3pt

449−\floatsep 12pt plus 2pt minus 2pt

450−\textfloatsep \floatsep

451−\intextsep 1pc plus 1pc

452−%%% not in 2e %% \@maxsep 1pc

453−%%% not in 2e %% \@dblmaxsep 20pt

454−\dblfloatsep 12pt plus 2pt minus 2pt

455−\dbltextfloatsep 20pt plus 2pt minus 4pt

456−\@fptop 0pt plus 1fil \@fpsep 1pc plus 2fil \@fpbot 0pt plus 1fil

457−\@dblfptop 0pt plus 1fil \@dblfpsep 8pt plus 2fil \@dblfpbot 0pt plus 1fil

458−\marginparpush 6pt

459−

460−\parskip 0pt plus .1pt \parindent 10pt \partopsep 0pt

461−\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301

462−\@beginparpenalty -\@lowpenalty \@endparpenalty -\@lowpenalty \@itempenalty

463−-\@lowpenalty

464−

465−

466−\def\part{\@ucheadtrue

467− \@startsection{part}{9}{\z@}{-10pt plus -4pt minus

468− -2pt}{4pt}{\reset@font\normalsize\sffamily}}

469−\def\section{\@ucheadtrue

470− \@startsection{section}{1}{\z@}{-10pt plus -4pt minus

471− -2pt}{4pt}{\reset@font\normalsize\sffamily}}

472−\def\subsection{\@ucheadfalse

473− \@startsection{subsection}{2}{\z@}{-8pt plus -2pt minus

474− -1pt}{4pt}{\reset@font\normalsize\sffamily}}

475−\def\subsubsection{\@ucheadfalse

476− \@startsection{subsubsection}{3}{\parindent}{6pt plus

477−1pt}{-5pt}{\reset@font\normalsize\itshape}}

478−\def\paragraph{\@ucheadfalse

479− \@startsection{paragraph}{3}{\parindent}{6pt plus

480−1pt}{-5pt}{\reset@font\normalsize\itshape}}

481−

482−\renewcommand{\@seccntformat}[1]{\textup{\csname the#1\endcsname}}

483−

484−\gdef\@period{.}

485−\def\@trivlist{\@topsepadd\topsep

486−\if@noskipsec \gdef\@period{}\leavevmode\gdef\@period{.}\fi

487− \ifvmode \advance\@topsepadd\partopsep \else \unskip\par\fi

488− \if@inlabel \@noparitemtrue \@noparlisttrue

489− \else \@noparlistfalse \@topsep\@topsepadd \fi

490− \advance\@topsep \parskip

491− \leftskip\z@\rightskip\@rightskip \parfillskip\@flushglue

492− \@setpar{\if@newlist\else{\@@par}\fi} \global\@newlisttrue

493−\@outerparskip\parskip}

494−

495−

496−\def\@startsection#1#2#3#4#5#6{%

497− \if@noskipsec \leavevmode \fi

498− \par

499− \@tempskipa #4\relax

500− \@afterindenttrue

501− \ifdim \@tempskipa <\z@

502− \@tempskipa -\@tempskipa \@afterindentfalse

503− \fi

504− \if@nobreak

505− \everypar{}%

506− \else

507− \addpenalty\@secpenalty\addvspace\@tempskipa

508− \fi

509− \@ifstar

510− {\@ssect{#3}{#4}{#5}{#6}}%

511− {\@dblarg{\@sect{#1}{#2}{#3}{#4}{#5}{#6}}}}

512−\def\@sect#1#2#3#4#5#6[#7]#8{%

513− \ifnum #2>\c@secnumdepth

514− \let\@svsec\@empty

515− \else

516− \refstepcounter{#1}%

517− \if@uchead%

518− \protected@edef\@svsec{\@seccntformat{#1}.\quad\relax}%

519− \else%

520− \protected@edef\@svsec{\@seccntformat{#1}\quad\relax}%

521− \fi%

522− \fi

523− \@tempskipa #5\relax

524− \ifdim \@tempskipa>\z@

525− \begingroup

526− #6{%

527− \@hangfrom{\hskip #3\relax\@svsec}%

528− \interlinepenalty \@M \if@uchead\MakeUppercase{#8}\else#8\fi \@@par}%

529− \endgroup

530− \csname #1mark\endcsname{#7}%

531− \addcontentsline{toc}{#1}{%

532− \ifnum #2>\c@secnumdepth \else

533− \protect\numberline{\csname the#1\endcsname}%

534− \fi

535− #7}%

536− \else

537− \def\@svsechd{%

538− #6{\hskip #3\relax

539− \@svsec \if@uchead\Makeuppercase{#8}\else#8\fi}%

540− \csname #1mark\endcsname{#7}%

541− \addcontentsline{toc}{#1}{%

542− \ifnum #2>\c@secnumdepth \else

543− \protect\numberline{\csname the#1\endcsname}%

544− \fi

545− #7}}%

546− \fi

547− \@xsect{#5}}

548−

549−\def\@xsect#1{\@tempskipa #1\relax

550− \ifdim \@tempskipa>\z@

551− \par \nobreak

552− \vskip \@tempskipa

553− \@afterheading

554− \else \global\@nobreakfalse \global\@noskipsectrue

555− \everypar{\if@noskipsec \global\@noskipsecfalse

556− \clubpenalty\@M \hskip -\parindent

557− \begingroup \@svsechd\@period \endgroup \unskip

558− \hskip -#1

559− \else \clubpenalty \@clubpenalty

560− \everypar{}\fi}\fi\ignorespaces}

561−\newif\if@uchead\@ucheadfalse

562−

563−

564−\setcounter{secnumdepth}{3}

565−\newcounter{secnumbookdepth}

566−\setcounter{secnumbookdepth}{3}

567−

568−\newfont{\apbf}{cmbx9}

569−

570−\def\@withappendix#1{App--\number #1}

571−

572−\newcommand{\elecappendix}{

573−}

574−

575−\def\appenheader{\global\@topnum\z@ \global\@botroom \textheight \begin{figure}

576−\newfont{\sc}{cmcsc10}

577−\parindent\z@

578−\hbox{}

579−\vskip -\textfloatsep

580−\vskip 11pt

581−\hrule height .2pt width 30pc

582−\vskip 2pt\rule{0pt}{10pt}\ignorespaces}

583−\def\endappenheader{\end{figure}\gdef\appendixhead{}}

584−

585−\def\@appsec{}

586−

587−\def\appendix{\par

588− \setcounter{section}{0}

589− \setcounter{subsection}{0}

590− \def\@appsec{APPENDIX }

591− \def\thesection{\Alph{section}}

592− \def\theHsection{\Alph{section}}}

593−

594−

595−

596−\labelsep 5pt

597−\settowidth{\leftmargini}{(9)} \addtolength\leftmargini\labelsep

598−\settowidth{\leftmarginii}{(b)} \addtolength\leftmarginii\labelsep

599−\leftmarginiii \leftmarginii

600−\leftmarginiv \leftmarginii

601−\leftmarginv \leftmarginii

602−\leftmarginvi \leftmarginii

603−\leftmargin\leftmargini

604−\labelwidth\leftmargini\advance\labelwidth-\labelsep

605−\def\@listI{\leftmargin\leftmargini \parsep 0pt plus 1pt\topsep 6pt plus 2pt

606−minus 2pt\itemsep 2pt plus 1pt minus .5pt}

607−\let\@listi\@listI

608−\@listi

609−\def\@listii{\leftmargin\leftmarginii

610− \labelwidth\leftmarginii\advance\labelwidth-\labelsep

611− \topsep 0pt plus 1pt

612− \parsep 0pt plus .5pt

613− \itemsep \parsep}

614−\def\@listiii{\leftmargin\leftmarginiii

615− \labelwidth\leftmarginiii\advance\labelwidth-\labelsep

616− \topsep 0pt plus 1pt

617− \parsep 0pt plus .5pt

618− \itemsep \parsep}

619−\def\@listiv{\leftmargin\leftmarginiv

620− \labelwidth\leftmarginiv\advance\labelwidth-\labelsep}

621−\def\@listv{\leftmargin\leftmarginv

622− \labelwidth\leftmarginv\advance\labelwidth-\labelsep}

623−\def\@listvi{\leftmargin\leftmarginvi

624− \labelwidth\leftmarginvi\advance\labelwidth-\labelsep}

625−

626−

627−

628−

629−\def\enumerate{\ifnum \@enumdepth >3 \@toodeep\else

630− \advance\@enumdepth \@ne

631− \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list

632− {\csname label\@enumctr\endcsname}{\usecounter

633− {\@enumctr}\def\makelabel##1{##1\hss}}\fi}

634−\def\longenum{\ifnum \@enumdepth >3 \@toodeep\else

635− \advance\@enumdepth \@ne

636− \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list

637− {\csname label\@enumctr\endcsname}{\usecounter

638− {\@enumctr}\labelwidth\z@}\fi}

639−%\leftmargin\z@ \itemindent\parindent}\fi} - this indents each item in enumerate

640−\let\endlongenum\endlist

641−%%--------------------CHANGED: always roman parentheses. dave ---------------%%

642−\def\labelenumi{{\rm (}\arabic{enumi}\/{\rm )}}

643−\def\theenumi{\arabic{enumi}}

644−\def\labelenumii{{\rm (}\alph{enumii}\rm{)}}

645−\def\theenumii{\alph{enumii}}

646−\def\p@enumii{\theenumi}

647−\def\labelenumiii{\roman{enumiii}.}

648−\def\theenumiii{\roman{enumiii}}

649−\def\p@enumiii{\theenumi{\rm (}\theenumii{\rm )}}

650−\def\labelenumiv{\Alph{enumiv}.}

651−\def\theenumiv{\Alph{enumiv}}

652−\def\p@enumiv{\p@enumiii\theenumiii}

653−

654−\def\p@enumiv{\p@enumiii\theenumiii}

655−

656−\def\itemize{\list{---\hskip -\labelsep}{\settowidth

657− {\leftmargin}{---}\labelwidth\leftmargin

658− \addtolength{\labelwidth}{-\labelsep}}}

659−\let\enditemize\endlist

660−\def\longitem{\list{---}{\labelwidth\z@

661− \leftmargin\z@ \itemindent\parindent \advance\itemindent\labelsep}}

662−\let\endlongitem\endlist

663−\def\verse{\let\\=\@centercr

664− \list{}{\leftmargin 2pc

665− \itemindent -1.5em\listparindent \itemindent

666− \rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}

667−\let\endverse\endlist

668−\def\quotation{\list{}{\leftmargin 2pc \listparindent .5em

669− \itemindent\listparindent

670− \rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}

671−\let\endquotation=\endlist

672−\def\quote{\list{}{\leftmargin 2pc \rightmargin\leftmargin}\item[]}

673−\let\endquote=\endlist

674−

675−\def\description{\list{}{\listparindent\parindent\labelwidth\z@

676− \leftmargin\z@ \itemindent\parindent\advance\itemindent\labelsep

677− \def\makelabel##1{\it ##1.}}}

678−\let\enddescription\endlist

679−

680−\def\describe#1{\list{}{\listparindent\parindent\settowidth{\labelwidth}{#1}\leftmargin

681− \labelwidth\addtolength\leftmargin\labelsep\def\makelabel##1{##1\hfil}}}

682−\let\enddescribe\endlist

683−

684− \def\program{\ifx\@currsize\normalsize\small \else \rm \fi\tabbing}

685− \let\endprogram\endtabbing

686− \def\@begintheorem#1#2{\trivlist \item[\hskip 10pt\hskip

687− \labelsep{\sc{#1}\hskip 5pt\relax #2.}] \itshape}

688− % aiellom{: this is what makes the theorem environment with names

689− % ABOVE #1 is the word example, corollary, etc.

690− % #2 is the number

691− % \def\@opargbegintheorem#1#2#3{\trivlist

692− % \item[\hskip 10pt \hskip \labelsep{\sc #1\savebox\@tempboxa{#3}\ifdim

693− % \wd\@tempboxa>\z@ \hskip 5pt\relax \box\@tempboxa\fi.}] \itshape}

694− % is been changed to

695− % #1 is the word theorem, lemma, etc.

696− % #2 is the number

697− % #3 is the name of the theorem, lemma, etc.

698− \def\@opargbegintheorem#1#2#3{\trivlist

699− \item[\hskip 10pt \hskip

700−\labelsep{\sc{#1}\savebox\@tempboxa{\sc{#3}}\ifdim

701− \wd\@tempboxa>\z@ \hskip 5pt\relax \sc{#2} \box\@tempboxa\fi.}]

702−\itshape}

703− % aiellom}

704−

705−

706−

707−\newif\if@qeded\global\@qededfalse

708−\def\proof{\global\@qededfalse\@ifnextchar[{\@xproof}{\@proof}}

709−\def\endproof{\if@qeded\else\qed\fi\endtrivlist}

710−\def\qed{\unskip\kern 10pt{\unitlength1pt\linethickness{.4pt}\framebox(6,6){}}

711−\global\@qededtrue}

712−\def\@proof{\trivlist \item[\hskip 10pt\hskip

713− \labelsep{\sc Proof.}]\ignorespaces}

714−\def\@xproof[#1]{\trivlist \item[\hskip 10pt\hskip

715− \labelsep{\sc Proof #1.}]\ignorespaces}

716−

717−\def\newdef#1#2{\expandafter\@ifdefinable\csname #1\endcsname

718−{\@definecounter{#1}\expandafter\xdef\csname

719−the#1\endcsname{\@thmcounter{#1}}\global

720− \@namedef{#1}{\@defthm{#1}{#2}}\global

721− \@namedef{end#1}{\@endtheorem}}}

722−\def\@defthm#1#2{\refstepcounter

723− {#1}\@ifnextchar[{\@ydefthm{#1}{#2}}{\@xdefthm{#1}{#2}}}

724−\def\@xdefthm#1#2{\@begindef{#2}{\csname the#1\endcsname}\ignorespaces}

725−\def\@ydefthm#1#2[#3]{\trivlist \item[\hskip 10pt\hskip

726− \labelsep{\it #2\savebox\@tempboxa{#3}\ifdim

727− \wd\@tempboxa>\z@ \ \box\@tempboxa\fi.}]\ignorespaces}

728−\def\@begindef#1#2{\trivlist \item[\hskip 10pt\hskip

729− \labelsep{\it #1\ \rm #2.}]}

730−

731−\def\theequation{\arabic{equation}}

732−

733−\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn

734− \else \newpage \fi \thispagestyle{empty}\c@page\z@}

735−\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

736−

737−\arraycolsep 2.5pt \tabcolsep 6pt \arrayrulewidth .4pt \doublerulesep 2pt

738−\tabbingsep \labelsep

739−

740−\skip\@mpfootins = \skip\footins

741−\fboxsep = 3pt \fboxrule = .4pt

742−

743−\newcounter{part}

744−\newcounter{section}

745−\newcounter{subsection}[section]

746−\newcounter{subsubsection}[subsection]

747−\newcounter{paragraph}[subsubsection]

748−

749−\def\thepart{\Roman{part}}

750−\def\thesection {\arabic{section}}

751−\def\thesubsection {\thesection.\arabic{subsection}}

752−\def\thesubsubsection {\thesubsection.\arabic{subsubsection}}

753−\def\theparagraph {\thesubsubsection.\arabic{paragraph}}

754−

755−\def\@pnumwidth{1.55em}

756−\def\@tocrmarg {2.55em}

757−\def\@dotsep{4.5}

758−\setcounter{tocdepth}{3}

759−

760−\def\tableofcontents{\section*{Contents\@mkboth{CONTENTS}{CONTENTS}}

761− \@starttoc{toc}}

762−\def\l@part#1#2{\addpenalty{\@secpenalty}

763− \addvspace{2.25em plus 1pt} \begingroup

764− \@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip

765−-\@pnumwidth

766− {\large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par

767− \nobreak \endgroup}

768−\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}

769−\@tempdima 1.5em \begingroup

770− \parindent \z@ \rightskip \@pnumwidth

771− \parfillskip -\@pnumwidth

772− \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}\par

773− \endgroup}

774−\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}

775−\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}

776−\def\listoffigures{\section*{List of Figures\@mkboth

777− {LIST OF FIGURES}{LIST OF FIGURES}}\@starttoc{lof}}

778−\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}

779−\def\listoftables{\section*{List of Tables\@mkboth

780− {LIST OF TABLES}{LIST OF TABLES}}\@starttoc{lot}}

781−\let\l@table\l@figure

782−

783−

784−\def\thebibliography#1{\par\footnotesize

785−\@ucheadfalse

786−\@startsection{subsection}{2}{\z@}{16pt plus 2pt minus

787− 1pt}{2pt}{\sf}*{REFERENCES}%

788−\list{\arabic{enumi}.}{%

789− \settowidth{\labelwidth}{99.}%

790− \leftmargin\labelwidth

791− \advance\leftmargin\labelsep \topsep \z@ \parsep 0pt plus .1pt

792− \itemsep \parsep

793− \usecounter{enumi}}%

794− \def\newblock{\hskip .11em plus .33em minus .07em}

795− \sloppy

796− \widowpenalty=4500

797− \clubpenalty=4500

798− \sfcode`\.=1000\relax}

799−\let\endthebibliography=\endlist

800−

801−

802−\newif\if@restonecol

803−\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi

804−\columnseprule \z@

805−\columnsep 35pt\twocolumn[\section*{Index}]

806− \@mkboth{INDEX}{INDEX}\thispagestyle{plain}\parindent\z@

807− \parskip\z@ plus .3pt\relax\let\item\@idxitem}

808−\def\@idxitem{\par\hangindent 40pt}

809−\def\subitem{\par\hangindent 40pt \hspace*{20pt}}

810−\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}

811−\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}

812−\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}

813−

814−\def\footnoterule{\kern-3\p@

815− \hrule \@height 0.2\p@ \@width 47\p@

816− \kern 2.6\p@

817−}

818−

819−\long\def\@makefntext#1{\parindent 1em\noindent

820− $^{\@thefnmark}$#1}

821−

822−

823−\setcounter{topnumber}{3}

824−\def\topfraction{.99}

825−\setcounter{bottomnumber}{1}

826−\def\bottomfraction{.5}

827−\setcounter{totalnumber}{3}

828−\def\textfraction{.01}

829−\def\floatpagefraction{.85}

830−\setcounter{dbltopnumber}{2}

831−\def\dbltopfraction{.7}

832−\def\dblfloatpagefraction{.5}

833−

834−\long\def\@makecaption#1#2{\vskip 1pc \setbox\@tempboxa\hbox{#1.\hskip

835−1em\relax #2}

836− \ifdim \wd\@tempboxa >\hsize #1. #2\par \else \hbox

837−to\hsize{\hfil\box\@tempboxa\hfil}

838− \fi}

839−

840−\def\nocaption{\refstepcounter\@captype \par

841− \vskip 1pc \hbox to\hsize{\hfil \footnotesize Figure \thefigure

842− \hfil}}

843−

844−

845−\newcounter{figure}

846−\def\thefigure{\@arabic\c@figure}

847−\def\fps@figure{tbp}

848−\def\ftype@figure{1}

849−\def\ext@figure{lof}

850−\def\fnum@figure{Fig.\ \thefigure}

851−\def\figure{\let\normalsize\footnotesize \normalsize \@float{figure}}

852−\let\endfigure\end@float

853−\@namedef{figure*}{\@dblfloat{figure}}

854−\@namedef{endfigure*}{\end@dblfloat}

855−

856−\newcounter{table}

857−\def\thetable{\@Roman\c@table}

858−\def\fps@table{tbp}

859−\def\ftype@table{2}

860−\def\ext@table{lot}

861−\def\fnum@table{Table \thetable}

862−\def\table{\let\normalsize\footnotesize \normalsize\@float{table}}

863−\let\endtable\end@float

864−\@namedef{table*}{\@dblfloat{table}}

865−\@namedef{endtable*}{\end@dblfloat}

866−\def\acmtable#1{\@narrowfig #1\relax

867− \let\caption\@atcap \let\nocaption\@atnocap

868− \def\@tmpnf{}\@ifnextchar[{\@xntab}{\@ntab}}

869−\def\endacmtable{\hbox to \textwidth{\hfil

870−\vbox{\hsize \@narrowfig

871−\box\@nfcapbox

872−{\baselineskip 4pt \hbox{\vrule height .4pt width \hsize}}

873−\vskip -1pt

874−\box\@nfigbox\vskip -1pt

875−{\baselineskip 4pt \hbox{\vrule height .4pt width \hsize}}}\hfil}

876−\end@float}

877−\def\@xntab[#1]{\def\@tmpnf{[#1]}\@ntab}

878−\def\@ntab{\expandafter\table\@tmpnf

879− \setbox\@nfigbox\vbox\bgroup

880− \hsize \@narrowfig \@parboxrestore}

881−\def\@atmakecap #1#2{\setbox\@tempboxa\hbox{#1.\hskip 1em\relax #2}

882− \ifdim \wd\@tempboxa >\hsize \sloppy #1.\hskip 1em\relax #2 \par \else \hbox

883−to\hsize{\hfil\box\@tempboxa\hfil}

884− \fi}

885−\def\@atcap{\par\egroup\refstepcounter\@captype

886− \@dblarg{\@atcapx\@captype}}

887−\long\def\@atcapx#1[#2]#3{\setbox\@nfcapbox\vbox {\hsize \wd\@nfigbox

888− \@parboxrestore

889− \@atmakecap{\csname fnum@#1\endcsname}{\ignorespaces #3}\par}}

890−\def\@atnocap{\egroup \refstepcounter\@captype

891− \setbox\@nfcapbox\vbox {\hsize \wd\@nfigbox

892− \hbox to\hsize{\hfil \footnotesize Table \thetable\hfil}}}

893−

894−%

895−%% Narrow figures

896−%

897−\def\narrowfig#1{\@narrowfig #1\relax

898− \let\caption\@nfcap \let\nocaption\@nfnocap

899− \def\@tmpnf{}\@ifnextchar[{\@xnfig}{\@nfig}}

900−\def\endnarrowfig{\hbox to \textwidth{\if@nfeven

901− \box\@nfcapbox\hfil\box\@nfigbox

902− \else \box\@nfigbox\hfil\box\@nfcapbox\fi}\end@float}

903−\def\@xnfig[#1]{\def\@tmpnf{[#1]}\@nfig}

904−\def\@nfig{\expandafter\figure\@tmpnf

905− \setbox\@nfigbox\vbox\bgroup

906− \hsize \@narrowfig \@parboxrestore}

907−\def\@nfmakecap #1#2{\setbox\@tempboxa\hbox{#1.\hskip 1em\relax #2}

908− \ifdim \wd\@tempboxa >\hsize \sloppy #1.\hskip 1em\relax #2 \par \else \hbox

909−to\hsize{\if@nfeven\else\hfil\fi\box\@tempboxa\if@nfeven\hfil\fi}

910− \fi}

911−\def\@nfcap{\par\egroup\refstepcounter\@captype

912− \@dblarg{\@nfcapx\@captype}}

913−\long\def\@nfcapx#1[#2]#3{\@seteven

914− \setbox\@nfcapbox\vbox to \ht\@nfigbox

915− {\hsize \textwidth \advance\hsize -2pc \advance\hsize -\wd\@nfigbox

916− \@parboxrestore

917− \vfil

918− \@nfmakecap{\csname fnum@#1\endcsname}{\ignorespaces #3}\par

919− \vfil}}

920−\def\@nfnocap{\egroup \refstepcounter\@captype \@seteven

921− \setbox\@nfcapbox\vbox to \ht\@nfigbox

922− {\hsize \textwidth \advance\hsize -2pc \advance\hsize -\wd\@nfigbox

923− \@parboxrestore

924− \vfil

925− \hbox to\hsize{\if@nfeven\else\hfil\fi

926− \footnotesize Figure \thefigure

927− \if@nfeven\hfil\fi}

928− \vfil}}

929−\def\@seteven{\@nfeventrue

930− \@ifundefined{r@@nf\thefigure}{}{%

931− \edef\@tmpnf{\csname r@@nf\thefigure\endcsname}%

932− \edef\@tmpnf{\expandafter\@getpagenum\@tmpnf}%

933− \ifodd\@tmpnf\relax\@nfevenfalse\fi}%

934−\label{@nf\thefigure}\edef\@tmpnfx{\if@nfeven e\else o\fi}

935−\edef\@tmpnf{\write\@unused {\noexpand\ifodd \noexpand\c@page

936− \noexpand\if \@tmpnfx e\noexpand\@nfmsg{\thefigure} \noexpand\fi

937− \noexpand\else

938− \noexpand\if \@tmpnfx o\noexpand\@nfmsg{\thefigure}\noexpand\fi

939− \noexpand\fi }}\@tmpnf}

940−\def\@nfmsg#1{Bad narrowfig: Figure #1 on page \thepage}

941−

942−\newdimen\@narrowfig

943−\newbox\@nfigbox

944−\newbox\@nfcapbox

945−\newif\if@nfeven

946−

947−\def\and{\\ and\\}

948−\def\maketitle{\newpage \thispagestyle{titlepage}\par

949− \begingroup \lineskip = \z@\null \vskip -30pt\relax

950− \parindent\z@ \LARGE {\raggedright \hyphenpenalty\@M

951− %\sf \@title \par

952− \@title \par

953− \global\firstfoot %aiellom

954− \global\runningfoot %aiellom

955−}

956−\label{@firstpg}

957−{ \vskip 13.5pt\relax \normalsize \sf %vskip 13.5pt between title and author

958− \begingroup \addtolength{\baselineskip}{2pt}

959− \@author\par \vskip -2pt

960− \endgroup }

961− {\ifx \@categories\@empty

962− \else

963− \baselineskip 17pt\relax

964− \if@acmjacm\else\hbox{\vrule height .2pt width 30pc}\fi%to eliminate the lines for jacm

965− }

966− \vskip 8.5pt \footnotesize \box\@abstract \vskip 4pt\relax %vskip8.5 space above abstract

967− {\def\and{\unskip\/{\rm ; }}

968− Categories and Subject Descriptors: \@categories \fi}\par\vskip 4pt\relax

969− \box\@terms \vskip 4pt\relax

970− \box\@keywords \par

971− {\baselineskip 14pt\relax

972− \@abstractbottom

973− }

974− \vskip 23pt\relax

975− \endgroup

976−\let\maketitle\relax

977− % \gdef\@author{}\gdef\@title{}

978− \gdef\@categories{}}

979−

980−

981−\newbox\@abstract

982−\newbox\@terms

983−\newbox\@keywords

984−\def\abstract{\global\setbox\@abstract=\vbox\bgroup \everypar{}

985− \footnotesize \hsize 30pc \parindent 10pt \noindent

986− \rule{0pt}{10pt}\ignorespaces}

987−\def\endabstract{\egroup}

988−

989−\def\terms#1{\setbox\@terms=\vbox{\everypar{}

990− \footnotesize \hsize 30pc \parindent 0pt \noindent

991− General Terms: \ignorespaces #1}}

992−\def\keywords#1{\setbox\@keywords=\vbox{\everypar{}

993− \footnotesize \hsize 30pc \parindent 0pt \noindent

994− Additional Key Words and Phrases: \ignorespaces #1}

995−}

996−

997−\def\category#1#2#3{\@ifnextchar

998− [{\@category{#1}{#2}{#3}}{\@xcategory{#1}{#2}{#3}}}

999−\def\@category#1#2#3[#4]{\edef\@tempa{\ifx \@categories\@empty

1000− \else ; \fi}{\def\protect{\noexpand\protect

1001− \noexpand}\def\and{\noexpand\and}\xdef\@categories{\@categories\@tempa #1

1002−[{\bf #2}]:

1003− #3\kern\z@---\hskip\z@{\it #4}}}}

1004−\def\@xcategory#1#2#3{\edef\@tempa{\ifx \@categories\@empty \else ;

1005−\fi}{\def\protect{\noexpand\protect\noexpand}\def\and{\noexpand

1006− \and}\xdef\@categories{\@categories\@tempa #1 [{\bf #2}]: #3}}}

1007−\def\@categories{}

1008−\def\bottomstuff{\global\@topnum\z@ \global\@botroom \textheight \begin{figure}

1009−\parindent\z@

1010−\hbox{}

1011−\vskip -\textfloatsep

1012−\vskip 10pt

1013−\hrule height .2pt width 30pc

1014−\vskip 2pt\rule{0pt}{10pt}\ignorespaces}

1015−\def\endbottomstuff{\permission\end{figure}\gdef\permission{}}

1016−

1017−\newenvironment{ackslike}[1]

1018− {\par \footnotesize

1019− \@ucheadfalse

1020− \@startsection{subsection}{2}{\z@}{-16pt plus -2pt minus -1pt}{2pt}{\sf}*

1021− {\uppercase{#1}}\par\normalsize

1022− \pdfbookmark{Acknowledgments}{Ack}

1023− }

1024− {\par}

1025−\newenvironment{acks}{\begin{ackslike}{ACKNOWLEDGMENTS}}{\end{ackslike}}

1026−

1027−\def\received{\par\footnotesize\addvspace{18pt plus 0pt minus

1028−4pt}\parindent\z@}

1029−%the line below replaced by the line that follows (K.R. Apt, July 11, 2000

1030−%\def\endreceived{\label{@lastpg}\hskip-2pt\par}

1031−\def\endreceived{\label{@lastpg}\hskip-2pt\par\normalsize}

1032−

1033−\mark{{}{}}

1034−

1035−\def\ps@myheadings{\let\@mkboth\@gobbletwo

1036−\def\@oddhead{\hbox{}\hfill \small\sf \rightmark\hskip

1037−19pt{\Large$\cdot$}\hskip 17pt\mypage}

1038−\def\@oddfoot{\hbox{}\hfill\tiny\@runningfoot}

1039−\def\@evenhead{\small\sf\mypage \hskip 17pt{\Large$\cdot$}\hskip 19pt\leftmark\hfill \hbox{}}

1040−\def\@evenfoot{\tiny\@runningfoot\hfill\hbox{}}

1041−\def\sectionmark##1{}\def\subsectionmark##1{}}

1042−\def\@runningfoot{}

1043−\def\runningfoot{\def\@runningfoot{\@journalName, Vol.\ \@acmVolume, No.\ \@acmNumber, \@acmMonth\ 20\@acmYear.}}

1044−\def\@firstfoot{}

1045−\def\firstfoot{\def\@firstfoot{\@journalName, Vol.\ \@acmVolume, No.\ \@acmNumber, \@acmMonth\ 20\@acmYear, Pages \pages.}}

1046−\def\ps@titlepage{\let\@mkboth\@gobbletwo

1047−\def\@oddhead{}\def\@oddfoot{\hbox{}\hfill

1048−\tiny\@firstfoot}\def\@evenhead{}\def\@evenfoot{\tiny\@firstfoot\hfill\hbox{}}}

1049−

1050−\def\today{\ifcase\month\or

1051− January\or February\or March\or April\or May\or June\or

1052− July\or August\or September\or October\or November\or December\fi

1053− \space\number\day, \number\year}

1054−\def\@marrayclassiv{\@addtopreamble{$\displaystyle \@nextchar$}}

1055−\def\@marrayclassz{\ifcase \@lastchclass \@acolampacol \or \@ampacol \or

1056− \or \or \@addamp \or

1057− \@acolampacol \or \@firstampfalse \@acol \fi

1058−\edef\@preamble{\@preamble

1059− \ifcase \@chnum

1060− \hfil$\relax\displaystyle\@sharp$\hfil \or $\relax\displaystyle\@sharp$\hfil

1061− \or \hfil$\relax\displaystyle\@sharp$\fi}}

1062−\def\marray{\arraycolsep 2.5pt\let\@acol\@arrayacol \let\@classz\@marrayclassz

1063− \let\@classiv\@marrayclassiv \let\\\@arraycr\def\@halignto{}\@tabarray}

1064−\def\endmarray{\crcr\egroup\egroup}

1065−

1066−

1067−\ps@myheadings \pagenumbering{arabic} \onecolumn

1068−

1069−%-----------------------BIBLIOGRAPHY STUFF-------------------------

1070−% this is adapted (November 1993) by Andrew Appel and Rebecca Davies from

1071−%

1072−%%% filename = "chicago.sty",

1073−%%% version = "4", % MODIFIED!

1074−%%% date = "31 August 1992",

1075−%%% time = "09:42:44 199",

1076−%%% author = "Glenn Paulley",

1077−%%% address = "Data Structuring Group

1078−%%% Department of Computer Science

1079−%%% University of Waterloo

1080−%%% Waterloo, Ontario, Canada

1081−%%% N2L 3G1",

1082−%%% telephone = "(519) 885-1211",

1083−%%% FAX = "(519) 885-1208",

1084−%%% email = "gnpaulle@bluebox.uwaterloo.ca",

1085−

1086−%%% ====================================================================

1087−%

1088−% this file: Modification of chicago.sty for new ACM bibliography

1089−% style, which is similar (but not identical) to the ``Chicago'' style.

1090−%

1091−% chicago.sty: Style file for use with bibtex style chicago.bst, for

1092−% bibliographies formatted according to the 13th Edition of the Chicago

1093−% Manual of Style.

1094−%

1095−% 'newapa.bst' was made from 'plain.bst', 'named.bst', and 'apalike.bst',

1096−% with lots of tweaking to make it look like APA style, along with tips

1097−% from Young Ryu and Brian Reiser's modifications of 'apalike.bst'.

1098−% newapa.sty formed the basis of this style, chicago.sty. Author-date

1099−% references in newapa.bst formed the basis for chicago.bst. Chicagoa.bst

1100−% supports annotations.

1101−%

1102−% Version 4 (August, 1992):

1103−% - fixed chicago.bst and chicagoa.bst to handle long author lists in

1104−% sorting

1105−% - fixed chicago.bst and chicagoa.bst so that missing page numbers in

1106−% ``article'' entries are handled correctly

1107−% - modified chicago.sty to format entries with 2nd and subsequent lines

1108−% indented.

1109−%

1110−% Citation format: (author-last-name year)

1111−% (author-last-name and author-last-name year)

1112−% (author-last-name et al. year)

1113−% (author-last-name)

1114−% author-last-name

1115−% author-last-name (year)

1116−% (author-last-name and author-last-name)

1117−% (author-last-name et al.)

1118−% (year) or (year,year)

1119−% year or year,year

1120−%

1121−% Reference list ordering: alphabetical by author or whatever passes

1122−% for author in the absence of one.

1123−%

1124−% This BibTeX style has support for abbreviated author lists and for

1125−% year-only citations. This is done by having the citations

1126−% actually look like

1127−%

1128−% \citeauthoryear{full-author-info}{abbrev-author-info}{year}

1129−%

1130−% The LaTeX style has to have the following (or similar)

1131−%

1132−% \let\@internalcite\cite

1133−% \def\fullcite{\def\citeauthoryear##1##2##3{##1, ##3}\@internalcite}

1134−% \def\fullciteA{\def\citeauthoryear##1##2##3{##1}\@internalcite}

1135−% \def\shortcite{\def\citeauthoryear##1##2##3{##2, ##3}\@internalcite}

1136−% \def\shortciteA{\def\citeauthoryear##1##2##3{##2}\@internalcite}

1137−% \def\citeyear{\def\citeauthoryear##1##2##3{##3}\@internalcite}

1138−%

1139−%

1140−% -------------------------------------------------------------------------

1141−%

1142−% Citation macros.

1143−%

1144−\let\@internalcite\cite

1145−

1146−\def\cite{\def\@citeseppen{-1000}%

1147− \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}%

1148− \def\citeauthoryear##1##2##3{##2 ##3}\@internalcite}

1149−\def\citeXNP#1#2{%

1150− \def\@cite@label{#2}%

1151− \def\@cite##1##2{##1\if@tempswa , ##2\fi}%

1152− \def\citeauthoryear##1##2##3{\@cite@label}\@internalcite{#1}}

1153−% \def\@citeseppen{-1000}%

1154−% \def\@cite@label{#1}

1155−% \def\@cite##1##2{\if@tempswa ##2\fi}%

1156−% \def\citeauthoryear##1##2##3{##2 ##3}\@internalcite}

1157−\def\citeNP{\def\@citeseppen{-1000}%

1158− \def\@cite##1##2{##1\if@tempswa , ##2\fi}%

1159− \def\citeauthoryear##1##2##3{##2 ##3}\@internalcite}

1160−\def\citeN{\def\@citeseppen{-1000}%

1161− \def\@cite##1##2{##1\if@tempswa , ##2]\else{]}\fi}%

1162− \def\citeauthoryear##1##2##3{##2 [##3}\@citedata}

1163−\def\shortcite#1{\citeyear{#1}}

1164−\def\citeS#1{[\citeANP{#1} \citeyearNP{#1}]}

1165−\def\citeNS#1{\citeANP{#1} \citeyear{#1}}

1166−\def\citeNPS#1{\citeANP{#1} \citeyearNP{#1}}

1167−%testing year,year

1168−\def\citeNN{\def\@citeseppen{-1000}%

1169− \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}%

1170− \def\citeauthoryear##1##2##3{##3}\@citedata}

1171−

1172−\def\citeA{\def\@citeseppen{-1000}%

1173− \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}%

1174− \def\citeauthoryear##1##2##3{##2}\@internalcite}

1175−\def\citeANP{\def\@citeseppen{-1000}%

1176− \def\@cite##1##2{##1\if@tempswa , ##2\fi}%

1177− \def\citeauthoryear##1##2##3{##2}\@internalcite}

1178−

1179−\def\citeyear{\def\@citeseppen{-1000}%

1180− \def\@cite##1##2{[##1\if@tempswa , ##2\fi]}%

1181− \def\citeauthoryear##1##2##3{##3}\@citedata}

1182−\def\citeyearNP{\def\@citeseppen{-1000}%

1183− \def\@cite##1##2{##1\if@tempswa , ##2\fi}%

1184− \def\citeauthoryear##1##2##3{##3}\@citedata}

1185−

1186−%

1187−% \@citedata and \@citedatax:

1188−%

1189−% Place commas in-between citations in the same \citeyear, \citeyearNP,

1190−% or \citeN command.

1191−% Use something like \citeN{ref1,ref2,ref3} and \citeN{ref4} for a list.

1192−%

1193−\def\@citedata{%

1194− \@ifnextchar [{\@tempswatrue\@citedatax}%

1195− {\@tempswafalse\@citedatax[]}%

1196−}

1197−

1198−\def\@citedatax[#1]#2{%

1199−\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi%

1200− \def\@citea{}\@cite{\@for\@citeb:=#2\do%

1201− {\@citea\def\@citea{; }\@ifundefined% by Young

1202− {b@\@citeb}{{\bf ?}%

1203− \@warning{Citation `\@citeb' on page \thepage \space undefined}}%

1204−{\csname b@\@citeb\endcsname}}}{#1}}%

1205−

1206−% don't box citations, separate with ; and a space

1207−% also, make the penalty between citations negative: a good place to break.

1208−%

1209−\def\@citex[#1]#2{%

1210−\if@filesw\immediate\write\@auxout{\string\citation{#2}}\fi%

1211− \def\@citea{}\@cite{\@for\@citeb:=#2\do%

1212− {\@citea\def\@citea{; }\@ifundefined% by Young

1213− {b@\@citeb}{{\bf ?}%

1214− \@warning{Citation `\@citeb' on page \thepage \space undefined}}%

1215−{\csname b@\@citeb\endcsname}}}{#1}}%

1216−

1217−% (from apalike.sty)

1218−% No labels in the bibliography.

1219−%

1220−\def\@biblabel#1{}

1221−

1222−% (from apalike.sty)

1223−% Set length of hanging indentation for bibliography entries.

1224−%

1225−\newlength{\bibhang}

1226−\setlength{\bibhang}{2em}

1227−

1228−% Indent second and subsequent lines of bibliographic entries. Stolen

1229−% from openbib.sty: \newblock is set to {}.

1230−

1231−\newdimen\bibindent

1232−\bibindent=1em

1233−\@ifundefined{refname}%

1234− {\@ifundefined{chapter}%

1235− {\newcommand{\refname}{\footnotesize REFERENCES}}%

1236− {\newcommand{\refname}{\footnotesize BIBLIOGRAPHY}}%

1237− }%

1238− {}%

1239−\@ifundefined{chapter}%

1240− {\def\thebibliography#1{\footnotesize \section*{\refname\@mkboth

1241− {\uppercase{\refname}}{\uppercase{\refname}}}\list

1242− {[\arabic{enumi}]}{

1243− \settowidth\labelwidth{[#1]}

1244− \leftmargin\labelwidth

1245− \advance\leftmargin\labelsep

1246− \advance\leftmargin\bibindent

1247− \itemindent -\bibindent

1248− \listparindent \itemindent

1249− \parsep \z@

1250− \usecounter{enumi}}

1251− \def\newblock{}

1252− \sloppy

1253− \sfcode`\.=1000\relax}}

1254− {\def\thebibliography#1{\footnotesize \chapter*{\refname\@mkboth

1255− {\uppercase{\refname}}{\uppercase{\refname}}}\list

1256− {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}

1257− \leftmargin\labelwidth

1258− \advance\leftmargin\labelsep

1259− \advance\leftmargin\bibindent

1260− \itemindent -\bibindent

1261− \listparindent \itemindent

1262− \parsep \z@

1263− \usecounter{enumi}}

1264− \def\newblock{}

1265− \sloppy

1266− \sfcode`\.=1000\relax}}

1267−

1268−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

1269−

1270−% fixes to acm trans macro package

1271−% 31-JAN-1996

1272−% John Tang Boyland

1273−

1274−% newdef need to take the optional parameters of newtheorem

1275−\def\newdef#1{\@ifnextchar[{\@xnewdef{#1}}{\@ynewdef{#1}}}

1276−\def\@xnewdef#1[#2]#3{\newtheorem{italic@#1}[#2]{{\em #3}}\@newdef{#1}}

1277−\def\@ynewdef#1#2{\@ifnextchar[{\@xynewdef{#1}{#2}}{\@yynewdef{#1}{#2}}}

1278−\def\@xynewdef#1#2[#3]{\newtheorem{italic@#1}{{\em #2}}[#3]\@newdef{#1}}

1279−\def\@yynewdef#1#2{\newtheorem{italic@#1}{{\em #2}}\@newdef{#1}}

1280−% and now fix up definition, to change body to use roman font:

1281−\def\@newdef#1{\newenvironment{#1}{\@ifnextchar[{\@xstartdef{#1}}{\@ystartdef{#1}}}{\end{italic@#1}}}

1282−%changed by K.R. Apt on Sep. 27, 2000. It was: \def\@xstartdef#1[#2]{\begin{italic@#1}[#2]\rm}

1283−\def\@xstartdef#1[#2]{\begin{italic@#1}[{\em #2}]\rm}

1284−\def\@ystartdef#1{\begin{italic@#1}\rm}

1285−

1286−% footers produced too small (vpt), when ACM typsets them at 7.5pt (!).

1287−% A better compromise is viipt.

1288−\def\@oddfoot{\hbox{}\hfill\scriptsize\@runningfoot}

1289−\def\@evenfoot{\scriptsize\@runningfoot\hfill\hbox{}}

1290−

1291−% first footer was set to (vpt), when ACM typesets them at 6.5pt (!).

1292−% A better compromise is vipt.

1293−\def\firstfootsize{\@setsize\firstfootsize{7pt}\vipt\@vipt}

1294−\def\ps@titlepage{\let\@mkboth\@gobbletwo

1295−\def\@oddhead{}\def\@oddfoot{\hbox{}\hfill\firstfootsize\@firstfoot}%

1296−\def\@evenhead{}\def\@evenfoot{\firstfootsize\@firstfoot\hfill\hbox{}}}

1297−

1298−% new permission statement

1299−\long\def\permission{\par

1300−% linebreaks added to conform to the current style

1301−Permission to make digital/hard copy of all or part of this material without

1302−fee

1303−for personal or classroom use

1304−provided that the copies are not made or distributed for profit

1305−or commercial advantage, the ACM copyright/server notice, the title of the

1306−publication, and its date appear, and notice is given that copying is by

1307−permission of the ACM, Inc. To copy

1308−otherwise, to republish, to post on servers, or to redistribute to lists

1309−requires prior specific

1310−permission and/or a fee.\par

1311−\copyright\ 20\@acmYear\

1312−ACM \@permissionCodeOne/20\@acmYear/\@permissionCodeTwo-\@pageCode\$5.00 % aiellom

1313−}

1314−

1315−% make sure \permission doesn't get trashed

1316−\def\endbottomstuff{\permission\end{figure}}

1317−

1318−% alternate way of using citeyear

1319−% \def\shortcite#1{\citeyear{#1}

1320−% enumerations and longenums are wrong

1321−% 1. the second line in a paragraph of an enumerations in theorems

1322−% (or other trivlists) doesn't line up under the first

1323−% 1. the second line of a longenum doesn't properly wrap around

1324−% back to the left margin.

1325−

1326−% the original definition of \@listI doesn't set labelwidth

1327−\def\@listI{\leftmargin\leftmargini

1328− \labelwidth\leftmargini\advance\labelwidth-\labelsep

1329− \parsep 0pt plus 1pt

1330− \topsep 6pt plus 2pt minus 2pt

1331− \itemsep 2pt plus 1pt minus .5pt}

1332−\let\@listi\@listI

1333−\@listi

1334−

1335−% add set of \labelwidth and \itemindent

1336−\def\longenum{\ifnum \@enumdepth >3 \@toodeep\else

1337− \advance\@enumdepth \@ne

1338− \edef\@enumctr{enum\romannumeral\the\@enumdepth}\list

1339− {\csname label\@enumctr\endcsname}{\usecounter

1340− {\@enumctr}\labelwidth\z@\leftmargin\z@

1341− \itemindent\parindent \advance\itemindent\labelsep}\fi}

1342−

1343−% split electronic appendix into two parts:

1344−

1345−

1346−%aiellom{

1347−\def\appendixhead#1{\appendix

1348−\section*{ELECTRONIC APPENDIX}

1349−The electronic appendix for this article can be accessed in

1350− the ACM Digital Library by visiting the following URL:$\;$

1351− \url{http://www.acm.org/pubs/citations/journals/}{\tt \@journalNameShort /20\@acmYear-\@acmVolume-\@acmNumber/p\pageref{@firstpg}-#1}.

1352−% \quad \href{http://www.acm.org/tocl}{{\small http://www.acm.org/tocl} }

1353−}

1354−%aiellom}

1355−

1356−\long\def\elecappendix{

1357−\clearpage

1358−\makeatletter

1359−\pagenumbering{withappendix}

1360−\makeatother

1361−\appendix

1362−\par\noindent{\sc This document is the online-only appendix to:}\hfill \vskip 1em

1363−{\vbox{\Large\sf \parindent0pt\@title{}}}\vskip .5em

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papers/impl-paper/compiling.texdeleted−2

@@ -1,2 +0,0 @@

1−\section{Compiling}

2−

papers/impl-paper/conclusions.texdeleted−167

@@ -1,167 +0,0 @@

1−\section{Related Work}

2−

3−\label{sect:related}

4−

5−Dependently-typed programming languages have become more prominent in recent

6−years as tools for verifying software correctness, and several experimental

7−languages are being developed, in particular Agda \cite{norell2007thesis},

8−Epigram \cite{McBride2004a,Levitation2010} and Trellys \cite{Kimmell2012}.

9−Furthermore, recent extensions to Haskell~\cite{Vytiniotis2011}, implemented in the

10−Glasgow Haskell Compiler, are bringing more of the power of dependent types to

11−Haskell. The problem of refining high-level syntax to a core type theory also

12−applies to theorem provers based on dependent types such as

13−Coq~\cite{Bertot2004} and Matita~\cite{Asperti2011}.

14−

15−Checking advanced type system features in Haskell involves a type system

16−parameterised over an underlying constraint system $X$ which captures

17−constraints such as type classes, constrained data types and type families.

18−Types are checked using an inference algorithm

19−\textsc{OutsideIn(X)}~\cite{Vytiniotis2011}, which is stratified into an

20−inference engine independent of the constraint

21−system, and a constraint solver for $X$. An additional difficulty faced by

22−Haskell, and hence any extensions, is the desire to support type \emph{inference}, in

23−which principal types may be inferred for top-level functions. We have avoided

24−such difficulties since, in general, type

25−inference is undecidable for full dependent types. Indeed, it is not clear

26−that type inference is even desirable in many cases, as programmers

27−can use dependent types to state their intentions (hence a program

28−specification) more precisely. However in future work we

29−may consider adapting the \textsc{OutsideIn} approach to provide limited type

30−inference.

31−

32−An earlier implementation of \Idris{} was built on the \Ivor{} proof engine

33−\cite{Brady2006b}. This implementation differed in one important way --- unlike

34−the present implementation, there was limited separation between the type

35−theory and the high-level language. The type theory itself supported implicit

36−syntax and unification, with high-level constructs such as the \texttt{with}

37−rule implemented directly. Two important disadvantages were found with this

38−approach, however: firstly, the type checker is much more complicated when

39−combined with unification, making it harder to maintain; secondly, adding new

40−high-level features requires the type checker to support those features

41−directly. In contrast, elaboration by tactics gives a clean separation between

42−the low-level and high-level languages, and results in programs in a core

43−type theory which are separately checkable, perhaps even by an independently

44−written checker which implements the \TT{} rules directly.

45−

46−Matita uses a bi-directional refinement algorithm~\cite{Asperti}. This is a

47−type directed approach, maintaining a set of yet to be solved unification

48−problems and relying on a small kernel, similar to the approach we now take

49−with \Idris{}, but using refinement rules rather than

50−tactics. This leads to good error messages though it is not clear how

51−easy it would be to extend to additional high-level language features, unlike

52−the tactic-based approach.

53−

54−The Agda implementation is based on a type theory with

55−implicit syntax and pattern matching --- Norell gives an algorithm for type checking

56−a dependently-typed language with pattern matching and metavariables

57−\cite{norell2007thesis}. Unlike the present \Idris{} implementation, metavariables

58−and implicit arguments are part of the type theory. This has the advantage that

59−implicit arguments can be used more freely (for example, in higher order

60−function arguments) at the expense of complicating the type system.

61−

62−Epigram \cite{McBride2004a} and Oleg \cite{McBride1999}

63−have provided much of the inspiration for the \Idris{} elaborator. Indeed,

64−the hole and guess bindings of \TTdev{} are taken directly from Oleg.

65−\Epigram{} does not implement pattern matching directly, but rather translates

66−pattern matching into elimination rules \cite{McBride2002}. This has the

67−advantage that

68−elimination rules provide termination and coverage proofs \emph{by construction}.

69−Furthermore they simplify implementation of the evaluator and provide easy

70−optimisation opportunities \cite{Brady2003}. However, it requires the

71−implementation of extra machinery for constructor manipulation

72−\cite{McBride2006} and so we have avoided it in the present implementation.

73−

74−

75−

76−%[Observation: separate elaboration and type checking, sort of like in GHC which

77−%type checks the high level language and produces a type correct core language.

78−%Elaboration is effectively a type checker for the high level language, so we have

79−%a hope of providing reasonable error messages related to the original code.]

80−

81−\section{Conclusion}

82−

83−\label{sect:conclusion}

84−

85−In this paper, I have given an overview of the programming language \Idris{},

86−and its core type theory \TT{}, giving a detailed algorithm for translating

87−high-level programs into \TT{}.

88−\TT{} itself is deliberately small and simple, and the design has deliberately

89−resisted innovation so that we can rely on existing metatheoretic properties

90−being preserved. The kernel of the \Idris{} implementation consists of a type checker

91−and evaluator for \TT{} along with a pattern match compiler, which are implemented

92−in under 1000 lines of Haskell code. It is important that this kernel remains small

93−--- the correctness of the language implementation relies to a large extent on

94−the correctness of the underlying type system, and keeping the implementation small

95−reduces the possibility of errors.

96−

97−The approach we have taken to implementing the high-level language,

98−implementing an elaboration monad with tactics for program construction, allows

99−us to build programs on top of a small and unchanging kernel, rather than

100−extending the core language to deal with implicit syntax, unification and type

101−classes. High-level \Idris{} features are implemented by describing the

102−corresponding sequence of tactics to build an equivalent program in \TT{}, via

103−a development calculus of incomplete terms, \TTdev{}. A significant advantage

104−we have found with this approach is that higher level features can easily be

105−implemented in terms of existing elaborator components. For example, once we

106−have implemented elaboration for data types and functions, it is easy to add

107−several features:

108−

109−\begin{itemize}

110−\item \textbf{Type classes}: A dictionary is merely a record containing the

111−functions which implement a type class instance. Since we have a tactic-based

112−refinement engine, we can implement type class resolution as a tactic.

113−\item \textbf{\texttt{where} clauses}: We have access to local variables and

114−their types, so we can

115−elaborate \texttt{where} clauses at the point of definition simply by lifting

116−them to the top level.

117−\item \textbf{\texttt{case} expressions}: Similar to \texttt{where} clauses,

118−these are implemented by lifting the branches out to a top-level function.

119−\end{itemize}

120−

121−We do not need to make any changes to the core language type system in order to

122−implement these high-level features.

123−Other high-level features such as dependent records, tuples and monad comprehensions

124−can be added equally easily --- and indeed have been added in the full implementation.

125−Furthermore,

126−since we have taken a tactic-based approach to elaborating \Idris{} to \TT{},

127−it is possible to expose tactics to the programmer. This opens up

128−the possibility of implementing domain specific decision procedures, or

129−implementing user defined tactics in a style similar to Coq's \texttt{Ltac}

130−language \cite{Delahaye2000}. Although \TT{} is primarily intended as a core

131−language for \Idris{}, its rich type system also means that it could be used

132−as a core language for other high-level languages, especially when augmented

133−with primitive operators, and used to express additional properties of those

134−languages.

135−

136−We have not discussed the performance of the elaboration

137−algorithm, or described how \Idris{} compiles to executable code. In practice,

138−we have found performance to be acceptable --- for example, the \Idris{}

139−library (31 files, 3718 lines of code in total at the time of writing)

140−elaborates in around 12 seconds\footnote{On a MacBook Pro, 2.8GHz Intel Core 2

141−Duo, 4Gb RAM}. Profiling suggests that the main bottleneck is locating holes

142−in a proof term, which can be improved by choosing a better representation

143−for proof terms, perhaps based on a zipper \cite{Huet1997}. Compilation is made

144−straightforward by the Epic library \cite{brady2011epic}, with I/O and foreign

145−functions handled using command-response interaction trees \cite{Hancock2000}.

146−Although I have not yet run detailed benchmarks of the performance of compiled

147−code, I believe that rich type information and guaranteed termination will

148−allow aggressive optimisations~\cite{Brady2003,Brady2005}. I will investigate

149−this in future work.

150−

151−The objective of this implementation of \Idris{} is to provide a platform

152−for experimenting with realistic, general purpose programming with dependent

153−types, by implementing a Haskell-like language augmented with \emph{full}

154−dependent types.

155−In this paper, we have seen how such a high-level language can be implemented

156−by building on top of a small, well-understood, easy to reason about type

157−theory.

158−However, a programming language implementation is not an end in itself.

159−Programming languages exist to support research and practice in many different

160−domains. In future work, therefore, I plan to apply domain specific

161−language-based techniques to realistic problems in important safety critical

162−domains such as security and network protocol design and implementation. In

163−order to be successful, this will require a language which is expressive enough

164−to describe protocol specifications at a high-level, and robust enough to

165−guarantee correct implementation of those protocols. \Idris{}, I believe, is

166−the right tool for this work.

167−

papers/impl-paper/delab.texdeleted−159

@@ -1,159 +0,0 @@

1−\section{Reversing Elaboration}

2−

3−\label{sect:delab}

4−

5−As well as translating from \Idris{} to \TT{}, so that programs can be type

6−checked and evaluated, it is valuable to define the reverse transformation. This

7−serves two principal purposes:

8−

9−\begin{itemize}

10−\item To assist the user, it is preferable that the results of evaluation, and any

11−error messages produced by the elaborator, are presented in \Idris{} syntax

12−rather than \TT{}.

13−\item For correctness, we would like to ensure as far as possible that the

14−result of elaboration is equivalent to the original program. Informally, we can

15−achieve this by checking that reversing the elaboration process yields the original

16−program (with implicit arguments expanded).

17−\end{itemize}

18−

19−\noindent

20−In this section, we describe the process for reversing elaboration and the required

21−properties of the elaboration process as a whole. Fortunately, translating from

22−\TT{} to \Idris{} is significantly easier than \Idris{} to \TT{}, because it is

23−primarily \emph{erasing} information.

24−

25−\subsection{From \TT{} to \Idris{}}

26−

27−We define a meta-operation $\uninterp{\vt}$, which converts a \TT{} expression

28−$\vt$ to an \Idris{} expression which would elaborate to $\vt$:

29−

30−\DM{

31−\AR{

32−\begin{array}{rl}

33−\uninterp{\vx} &\mq\:\vx\\

34−\uninterp{\vc} &\mq\:\vc\\

35−\uninterp{\vx\;\ta} &\mq\:\vx\;(\vec{\MO{Impl}}\:\vx\:\ta) \\

36−\uninterp{\vf\:\va} &\mq\:\uninterp{\vf}\:\uninterp{\va}\\

37−\uninterp{\lam{\vx}{\vT}\SC\ve} &\mq \:\ilam{\vx}\uninterp{\ve} \\

38−\uninterp{\all{\vx}{\vT}\SC\ve} &\mq \:\piexp{\vx}{\uninterp{\vT}}\uninterp{\ve} \\

39−\uninterp{\LET\:\vx\defq\vt\Hab\vT\SC\ve} &\mq

40−\ilet{\vx}{\uninterp{\vt}}\uninterp{\ve}\\

41−\end{array}

42−\medskip\\

43−\begin{array}{rll}

44−\MO{Impl}\:\vx\:\va_i\:\mq

45−&

46−\iarg{\vn}{\ttinterp{\va_i}}&

47−\mbox{(if the $i$th argument to $\vx$ is implicit argument $\vn$)}\\

48−& \carg{\ttinterp{\va_i}} &

49−\mbox{(if the $i$th argument to $\vx$ is a constraint argument)}\\

50−& \ttinterp{\va_i} & \mbox{(otherwise)}

51−\end{array}

52−}

53−}

54−

55−\noindent

56−This is mostly a straightforward

57−traversal of the \TT{} expression, translating directly to an \Idris{} equivalent.

58−The interesting case is for applications of named functions,

59−$\uninterp{\vx\:\ta}$, where the arguments are translated to either implicit,

60−constraint or explicit arguments according to the definition of $\vx$.

61−Since only type declarations are allowed to have implicit or constraint arguments,

62−and $\uninterp{\cdot}$ translates \emph{expressions},

63−all function types are assumed to take explicit arguments.

64−

65−We also define an operation $\MO{Unelab}$, which translates \TT{} declarations

66−to corresponding \Idris{} declarations. This generates data declarations and

67−pattern matching definitions only --- it makes no attempt to reconstruct

68−\texttt{class}

69−or \texttt{instance} declarations, or rebuild \texttt{case} expressions.

70−First, we define the reverse elaboration of type declarations, which must reconstruct

71−which arguments are implicit or constraint arguments:

72−

73−\DM{

74−\AR{

75−\begin{array}{l}

76−\MO{UnelabType}\:(\vx\Hab\vt)\:\mq\:\vx\Hab\MO{UnelabTyDecl}\:0\:\vt

77−\end{array}

78−\medskip\\

79−\begin{array}{ll}

80−\MO{UnelabTyDecl}\:\vi\:(\all{\vy}{\vT}\SC\ve)

81−\mq & \piimp{\vy}{\uninterp{\vT}}(\MO{UnelabTyDecl}\:(\vi+1)\:\ve) \\

82− & \hg\mbox{(if the $i$th argument to $\vx$ is an implicit argument)} \\

83− & \piconst{\uninterp{\vT}}(\MO{UnelabTyDecl}\:(\vi+1)\:\ve) \\

84− & \hg\mbox{(if the $i$th argument to $\vx$ is a constraint argument)} \\

85− & \piexp{\vy}{\uninterp{\vT}}(\MO{UnelabTyDecl}\:(\vi+1)\:\ve) \\

86− & \hg\mbox{(otherwise)} \\

87−\end{array}

88−}

89−}

90−

91−\noindent

92−Using this, we define $\MO{Unelab}$ for top-level declarations. For pattern

93−matching clauses reversing elaboration proceeds as follows, discarding the explicit

94−pattern variable bindings and applying $\MO{UnelabType}$ to reconstruct

95−the type declaration:

96−

97−\DM{

98−\AR{

99−\MO{Unelab}\:(\vx\Hab\vt)\:\mq\:\MO{UnelabType}\:(\vx\Hab\vt)\\

100−\MO{Unelab}\:(\pat{\tx}{\tU}\SC\FN{f}\:\tts\:=\:\ve)

101−\:\mq\:\uninterp{\FN{f}\:\tts}\:=\:\uninterp{\ve}

102−}

103−}

104−

105−\noindent

106−For data type declarations, reverse elaboration proceeds as follows, applying $\MO{UnelabType}$

107−for each of the top-level type declarations:

108−

109−\DM{

110−\AR{

111−\MO{Unelab}\:(\Data\;\TC{T}\:(\tx\Hab\ttt)\Hab\vT\;\Where\;\vec{\VV{cons}})

112−\:\\

113−\hg\hg\mq\:\idata\:\MO{UnelabType}\:(\TC{T}\Hab\all{\tx}{\ttt}\SC\vT)\:\iwhere\:

114−(\vec{\MO{UnelabType}}\:\vec{\VV{cons}})

115−}

116−}

117−

118−

119−\subsection{Elaboration Properties}

120−

121−Elaboration satisfies two important properties. We limit our discussion of

122−these properties to \IdrisM{} without type classes, i.e. elaboration of type

123−declarations, functions, and data types. This is primarily because there is not

124−enough information in a \TT{} program alone to reverse elaboration fully. However, since

125−elaboration of the higher level \Idris{} constructs is implemented in terms of

126−the lower level \IdrisM{} constructs, we should not consider this a serious

127−limitation.

128−

129−Informally stated, the properties that elaboration satisfies are

130−i) that if elaboration is successful, the

131−resulting program is a well-typed \TT{} program; ii) elaboration preserves the

132−meaning of the original \Idris{} program. The first property is true by the

133−definition of elaboration --- elaboration fails if it attempts to construct an ill-typed

134−term at any point. Furthermore, the development calculus \TTdev{} ensures that

135−partial constructions are well-typed.

136−The second property can be stated as the following conjecture:

137−\\

138−

139−\noindent

140−\textbf{Conjecture: Preservation of meaning}\\

141−Given an \IdrisM{} declaration $\vd$, which is either a type declaration, a

142−pattern match clause, or a data type declaration,

143−if $\MO{Elab}\:\vd\:\mq\:\vt$, and $\MO{Unelab}\:\vt\:\mq\:\vd'$,

144−then $\MO{Match}\:\vd\:\vd'$ produces a valid match.

145−\\

146−

147−The output of $\MO{Unelab}$ is not necessarily equal to the input of $\MO{Elab}$

148−because elaboration fills in placeholder subexpressions. Therefore it suffices for

149−the input to match the output.

150−

151−We have not yet proved this conjecture. Its truth depends on the implementation

152−of $\MO{Elab}$ faithfully translating each construct, and we observe that the

153−present description of $\MO{Elab}$ elaborates each non-placeholder subexpression

154−according to the structure of the expression. However, since the truth of this

155−conjecture is crucial to the correctness of the implementation, the elaborator

156−checks \emph{dynamically} that meaning is preserved by evaluating

157−$\MO{Unelab}\:\vt$ and matching the input against the result. In practice, this

158−does not have a significant impact on performance.

159−

papers/impl-paper/elaboration.texdeleted−1956

@@ -1,1956 +0,0 @@

1−\newcommand{\ttinterp}[1]{\mathcal{E}\interp{#1}}

2−\newcommand{\ttpinterp}[1]{\mathcal{P}\interp{#1}}

3−\newcommand{\uninterp}[1]{\mathcal{T}\interp{#1}}

4−

5−\section{Elaborating \Idris{}}

6−

7−\label{sect:elaboration}

8−

9−An \Idris{} program consists of a series of declarations --- data types,

10−functions, classes and instances. In this section, we describe how these

11−high-level declarations are translated into a \TT{} program consisting of

12−inductive families and pattern matching function definitions. We will need to

13−work at the \remph{declaration} level, and at the \remph{expression} level,

14−defining the following meta-operations.

15−

16−\begin{itemize}

17−\item $\ttinterp{\cdot}$, which builds a \TT{} expression from an \Idris{} expression.

18−\item $\MO{Elab}$, which processes a top-level \Idris{} declaration by generating

19−one or more \TT{} declarations.

20−\item $\MO{TTDecl}$, which adds a top-level \TT{} declaration.

21−\end{itemize}

22−

23−

24−\subsection{The Development Calculus \TTdev}

25−

26−\TT{} expressions are built by using high-level \Idris{} expressions to

27−direct a tactic-based theorem prover, which builds the \TT{} expressions

28−step by step, by refinement. In order to build expressions in this way,

29−the type theory needs to support

30−\remph{incomplete} terms, and a method for term construction.

31−To achieve this, we extend \TT{} with \remph{holes},

32−calling the extended calculus \TTdev{}.

33−Holes stand for the parts of programs which have not yet been

34−instantiated; this largely follows the Oleg development

35−calculus~\cite{McBride1999}.

36−

37−The idea is to extend the syntax for binders with a \remph{hole}

38−binding and a \remph{guess} binding.

39−These extensions are given in Figure \ref{ttdev}.

40−The \remph{guess} binding is

41−similar to a $\LET$ binding, but without any computational force,

42−i.e. there are no reduction rules for guess bindings.

43−Using binders to represent holes is useful in a dependently-typed setting since

44−one value may determine another. Attaching a guess to a binder ensures that

45−instantiating one such variable also instantiates all of its dependencies.

46−%The

47−%typing rules for binders ensure that no $?$ bindings leak into types.

48−

49−\FFIG{

50−\begin{array}{c}

51−\vb ::= \ldots

52− \;\mid\; \hole{\vx}{\vt} \;\;(\mbox{hole binding}) \;\;

53− \;\mid\; \guess{\vx}{\vt}{\vt} \;\;(\mbox{guess})

54−\medskip\\

55−\mathsf{HoleVar}\;

56−\Rule{(\hole{\vx}{\vS})\in\Gamma}

57−{\Gamma\vdash\vx\Hab\vS}

58−\hg

59−\mathsf{GuessVar}\;

60−\Rule{(\guess{\vx}{\vS}{\vs})\in\Gamma}

61−{\Gamma\vdash\vx\Hab\vS}

62−\\

63−\mathsf{Hole}\;

64−\Rule{

65−\Gamma;\hole{\vx}{\vS}\proves\ve\Hab\vT

66−}

67−{

68−\Gamma\proves\hole{\vx}{\vS}\SC\ve\Hab\vT

69−}

70−%\hspace*{0.1cm}\vx\not\in\vT

71−\hg

72−\mathsf{Guess}\;

73−\Rule{

74−\Gamma;\guess{\vx}{\vS}{\ve_1}\proves\ve_2\Hab\vT

75−}

76−{

77−\Gamma\proves\guess{\vx}{\vS}{\ve_1}\SC\ve_2\Hab\vT

78−}

79−%\hspace*{0.1cm}\vx\not\in\vT

80−\end{array}

81−}

82−{\TTdev{} extensions}

83−{ttdev}

84−

85−

86−\subsection{Proof State}

87−

88−\label{sect:prfstate}

89−

90−We will build expressions in \TT{} from high-level \Idris{} expressions by

91−creating a top-level hole binding with the appropriate type, and refining it

92−according to the structure of the \Idris{} expression. Noting the Curry-Howard

93−correspondence between programs and proofs, and the relationship between our

94−method for elaboration and tactic-based theorem proving, we refer to a development as a \emph{proof}.

95−A proof state is a tuple, $(\vC, \Delta, \ve, \vP, \vQ)$, containing:

96−

97−\begin{itemize}

98−\item A global context, $\vC$, containing pattern matching definitions and their types

99−\item A local context, $\Delta$, containing pattern bindings

100−\item A proof term, $\ve$, in \TTdev{}

101−\item Unsolved unification problems, $\vP$

102−\begin{itemize}

103−\item These take the form $(\Gamma,\ve_1,\ve_2)$, i.e. the context in which

104−the problem is to be solved, and the expressions to be unified.

105−\end{itemize}

106−\item A hole queue, $\vQ$

107−%\item \remph{Deferred} definitions, $\vD$, for introducing global metavariables

108−\end{itemize}

109−

110−The \remph{hole queue} is a priority queue of names of hole and guess binders

111−$\langle\vx_1,\vx_2,\ldots,\vx_n\rangle$

112−in the proof term ---

113−ensuring that each bound name is unique. Holes refer to \remph{sub-goals}

114−in the proof. As a proof develops, unification problems arising from unsolved

115−holes may be introduced, and may be solved when those holes are instantiated.

116−When the hole queue is empty, and there are no remaining unification

117−problems, the proof term is complete.

118−

119−Creating a \TT{} expression from an \Idris{} expression involves creating

120−a new proof state, with an empty proof term, and using the high-level definition

121−to direct the building of a final proof state, with a complete proof term.

122−

123−In the implementation, the proof state is captured in an elaboration monad,

124−\texttt{Elab}, which is simply a state monad with exceptions.

125−Exceptions are captured by the option type $\MO{Result}$ which

126−either indicates success, or reports an error $\MO{Err}$:

127−

128−\DM{

129−\RW{data}\;\MO{Result}\;\vt\;=\;\MO{Success}\;\vt\;\mid\;\MO{Failure}\;\MO{Err}

130−}

131−

132−\noindent

133−If any operation fails during a proof (e.g. a sub-term fails to type check)

134−then the entire proof fails (i.e. returns $\MO{Failure}\;\ve$ with some error

135−message $\ve$) unless otherwise handled.

136−

137−The \texttt{Elab} monad supports various operations for querying and updating

138−the proof state, manipulating terms, generating fresh names, etc. However, we

139−will describe \Idris{} elaboration in terms of meta-operations on the proof

140−state, in order to capture the essence of the elaboration process without being

141−distracted by implementation details. These meta-operations include:

142−

143−\begin{itemize}

144−\item \demph{Queries} which retrieve values from the proof state, without modifying

145−the state. For example, we can:

146−\begin{itemize}

147−\item Get the type of the current sub-goal ($\MO{Type}$)

148−\item Get the current proof term ($\MO{Term}$)

149−\item Retrieve the local context $\Gamma$ at the current sub-goal

150−($\MO{Context}$)

151−\item Type check ($\MO{Check}$) or normalise ($\MO{Normalise}$) a term relative

152−to $\Gamma$

153−\end{itemize}

154−\item \demph{Unification}, which unifies two terms (potentially solving sub-goals) relative to $\Gamma$. This may introduce new unification problems

155−to the proof state

156−\item \demph{Tactics} which update the proof term. Tactics operate on the sub-term

157−at the binder specified by the head of the hole queue $\vQ$

158−\item \demph{Focussing} on a specific sub-goal, which brings a different sub-goal to the

159−head of the hole queue

160−%\item \demph{Deferring} a sub-goal, which adds a new definition to the global context

161−%$\vC$ which solves the sub-goal.

162−\end{itemize}

163−

164−Elaboration of an \Idris{} expression involves creating a new proof state,

165−running a series of tactics to build a complete proof term, then retrieving and

166−\remph{rechecking} the final proof term, which must be a \TT{} program (i.e.

167−does not contain any of the \TTdev{} extensions). We call a sub-term which

168−contains no hole or guess bindings \demph{pure}. Although a pure term does not

169−contain hole or guess bindings, it may nevertheless \remph{refer} to hole- or

170−guess-bound variables.

171−

172−The proof state is initialised with the $\MO{NewProof}$ operation. Given a

173−global context $\vC$, $\MO{NewProof}\;\vt$ sets up the proof state as:

174−

175−\DM{

176−(\vC, \cdot, \hole{\vx}{\vt}\SC\vx, \langle\rangle, \langle\vx\rangle)

177−}

178−

179−The local context is initially empty, and the initial hole queue is the $\vx$ standing for

180−the entire expression. The proof term is reset with the $\MO{NewTerm}$ operation.

181−In an existing proof state $(\vC, \Delta, \ve, \vP, \vQ)$,

182−$\MO{NewTerm}\;\vt$ discards the proof term and hole queue, and

183−updates the proof state to:

184−

185−\DM{

186−(\vC, \Delta, \hole{\vx}{\vt}\SC\vx, \langle\rangle, \langle\vx\rangle)

187−}

188−

189−Resetting the term and queue but retaining pattern bindings

190−allows the elaborator to use pattern bindings from the left

191−hand side of a pattern matching definition in the term on the right hand side.

192−

193−

194−\renewcommand{\Check}{\MO{Check}_\Gamma}

195−\newcommand{\Eval}{\MO{Normalise}_\Gamma}

196−\newcommand{\Unify}{\MO{Unify}_\Gamma}

197−\newcommand{\PrimUnify}{\MO{PrimUnify}_\Gamma}

198−\newcommand{\Subst}{\MO{Subst}}

199−

200−\subsection{Tactics}

201−

202−% Meta-operations Check, Normalise, Unify

203−In order to build \TT{} expressions from \Idris{} programs, we define a collection

204−of meta-operations for querying and modifying the proof state. Meta-operations

205−may have side-effects including failure, or updating the proof state, and

206−may fail. We have the following primitive meta-operations:

207−

208−\begin{itemize}

209−\item $\MO{Get}$ and $\MO{Put}$ which allow direct access to the proof state.

210−% Focus and Unfocus don't need to be primitive, we could show in terms of

211−% Get and Put

212−%\item $\MO{Focus}\;\vn$, which moves $\vn$ to the head of the hole queue.

213−%\item $\MO{Unfocus}$, which moves the current hole to the back of the hole queue.

214−\item $\Check\;\ve$, which type checks an expression $\ve$ relative to a context

215−$\Gamma$, returning its type.

216−$\MO{Check}$ will fail

217−if the expression is not well-typed.

218−\item $\MO{Convert}_\Gamma\;\ve_1\;\ve_2$, which checks that the well-typed

219−expressions $\ve_1$ and $\ve_2$ respect the cumulativity relation

220−(i.e. $\Gamma\proves\ve_1\cumul\ve_2$), and fails otherwise.

221−\item $\Eval\;\ve$, which evaluates a well-typed expression $\ve$ relative to a context

222−$\Gamma$, returning its normal form. $\MO{Normalise}$ reduces under binders,

223−but does not reduce definitions which are not total.

224−\item

225−$\PrimUnify\;\ve_1\;\ve_2$,

226−which attempts to unify $\ve_1$ and $\ve_2$ by finding the values with which

227−holes must be instantiated for $\ve_1$ and $\ve_2$ to be convertible relative

228−to $\Gamma$ (i.e. for $\Gamma\proves\ve_1\converts\ve_2$ to hold).

229−\item $\Subst\;\vx\;\ve$, which instantiates a hole $\vx$ directly with a term

230−$\ve$, typically arising from unification and removes $\vx$ from the hole

231−queue.

232−\end{itemize}

233−

234−\noindent

235−Additionally, we have $\MO{Focus}$, $\MO{Unfocus}$, $\MO{NewHole}$,

236−$\MO{NextHole}$ and $\MO{RemoveHole}$

237−operations which manipulate and inspect

238−the hole queue. $\MO{Focus}\;\vn$ moves a hole to the head of the hole queue:

239−

240−\DM{

241−\MO{Focus}\;\vn\;=\;\RW{do}\;\AR{

242−(\vC,\Delta,\ve,\vP,\vQ;\vn;\vQ')\gets\MO{Get}\\

243−\MO{Put}\;(\vC,\Delta,\ve,\vP,\vn;\vQ;\vQ')\\

244−}

245−}

246−

247−\noindent

248−$\MO{Focus}$ refers to a hole $\vn$ by name. Hole names are either given

249−explicitly in proofs, or chosen (as fresh names) by tactics.

250−Correspondingly, $\MO{Unfocus}$ moves the currently in focus hole to the

251−end of the hole queue:

252−

253−\DM{

254−\MO{Unfocus}\;=\;\RW{do}\;\AR{

255−(\vC,\Delta,\ve,\vP,\vn;\vQ)\gets\MO{Get}\\

256−\MO{Put}\;(\vC,\Delta,\ve,\vP,\vQ;\vn)\\

257−}

258−}

259−

260−\noindent

261−$\MO{NewHole}$ declares that a new hole has been created and is to be solved

262−next; $\MO{NextHole}$ returns the next hole to be solved, and $\MO{RemoveHole}$

263−removes a hole from the head of the queue:

264−

265−\DM{

266−\AR{

267−\MO{NewHole}\;\vn\;=\;\RW{do}\;\AR{

268−(\vC,\Delta,\ve,\vP,\vQ)\gets\MO{Get}\\

269−\MO{Put}\;(\vC,\Delta,\ve,\vP,\vn;\vQ)\\

270−}

271−\\

272−\MO{NextHole}\;=\;\RW{do}\;\AR{

273−(\vC,\Delta,\ve,\vP,\vn;\vQ)\gets\MO{Get}\\

274−\RW{return}\;\vn

275−}

276−\\

277−\MO{RemoveHole}\;=\;\RW{do}\;\AR{

278−(\vC,\Delta,\ve,\vP,\vn;\vQ)\gets\MO{Get}\\

279−\MO{Put}\;(\vC,\Delta,\ve,\vP,\vQ)

280−}

281−}

282−}

283−

284−\noindent

285−\demph{Tactics} are meta-operations which operate on the sub-term given by the

286−hole at the head of the hole queue in the proof state. They take the following

287−form:

288−

289−\DM{

290−\PA{\A\A}{

291−\MO{Tac}_\Gamma & \;\vec{\VV{args}} & \;\vt & \MoRet{\RW{do}\;\AR{

292−\ldots\\

293−\RW{return}\:\vt'}

294−}

295−}

296−}

297−

298−A tactic $\MO{Tac}$ takes a sequence of zero or more arguments

299−$\vec{\VV{args}}$ followed by the sub-term $\vt$ on which it is operating. It

300−runs relative to a context $\Gamma$ which contains all the bindings and pattern

301−bindings in scope at that point in the term. The sub-term $\vt$ will either be

302−a hole binding $\hole{\vx}{\vT}\SC\ve$ or a guess binding

303−$\guess{\vx}{\vT}{\vv}\SC\ve$. The tactic returns a new term $\vt'$ which can

304−take any form, provided it is well-typed, with a type convertible to the type

305−of $\vt$. Tactics may also have the side effect of updating the proof state,

306−therefore we will describe tactics in a pseudo-code with $\RW{do}$ notation.

307−

308−Tactics are executed by a higher level meta-operation $\MO{Tactic}$,

309−given in Figure \ref{runtac}, which

310−locates the appropriate sub-term, applies the tactic with the context

311−local to this sub-term, and

312−replaces the sub-term with the term returned by the

313−tactic. Note that monadic lifting is left implicit in this Figure, so that

314−the details of the algorithm are not obscured.

315−% It then updates the hole queue in the proof state, and updates holes which have

316−% been solved by unification. If the tactic creates new holes, these are automatically

317−% added to the \remph{head} of the hole queue.

318−

319−\FFIG{

320−\AR{

321−\MO{Tactic}\;\VV{tac}\;=\;\RW{do}\;\AR{

322−\ve\Gets\MO{Term}\\

323−\vh\Gets\MO{NextHole}\\

324−\ve'\Gets\MO{Tactic'}\;\langle\rangle\;\ve\\

325−\MO{SetTerm}\;\ve'

326−}

327−\medskip

328−\\

329−\PA{\A\A\A}{

330−\RW{where} \\

331−& \MO{Tactic'} & \Gamma & (\hole{\vx}{\vT}\SC\ve)

332−& \MoRet{\VV{tac}_\Gamma\;(\hole{\vx}{\vT}\SC\ve)\hg\mbox{if}\;\vx=\vh} \\

333−& \MO{Tactic'} & \Gamma & (\hole{\vx}{\vT}\SC\ve)

334−& \MoRet{

335−\RW{do}\; \AR{\vT'\Gets\;\MO{Tactic'}\;\Gamma\;\vT\\

336−\RW{return}\;(\hole{\vx}{\vT'}\SC \MO{Tactic'}\;(\Gamma;\hole{\vx}{\vT'})\;\ve)

337−\hg\RW{otherwise}}

338−}

339−\\

340−& \MO{Tactic'} & \Gamma & (\guess{\vx}{\vT}{\vv}\SC\ve)

341−& \MoRet{\VV{tac}_\Gamma\;(\guess{\vx}{\vT}{\vv}\SC\ve)\hg\mbox{if}\;\vx=\vh} \\

342−

343−& \MO{Tactic'} & \Gamma & (\guess{\vx}{\vT}{\vv}\SC\ve)

344−& \MoRet{\RW{do}\;\AR{\vv'\Gets\;\MO{Tactic'}\;\Gamma\;\vv\\

345−\vT'\Gets\;\MO{Tactic'}\;\Gamma\;\vT\\

346−\RW{return}\;(\guess{\vx}{\vT'}{\vv'}\SC

347−\MO{Tactic'}\;(\Gamma;\guess{\vx}{\vT'}{\vv'}\;\ve)

348−\hg\RW{otherwise}}} \\

349−

350−& \MO{Tactic'} & \Gamma & (\lam{\vx}{\vT}\SC\ve)

351−& \MoRet{

352−\RW{do}\; \AR{\vT'\Gets\;\MO{Tactic'}\;\Gamma\;\vT\\

353−\RW{return}\;(\lam{\vx}{\vT'}\SC \MO{Tactic'}\;(\Gamma;\lam{\vx}{\vT'})\;\ve)}

354−}

355−\\

356−& \MO{Tactic'} & \Gamma & (\all{\vx}{\vT}\SC\ve)

357−& \MoRet{

358−\RW{do}\; \AR{\vT'\Gets\;\MO{Tactic'}\;\Gamma\;\vT\\

359−\RW{return}\;(\all{\vx}{\vT'}\SC \MO{Tactic'}\;(\Gamma;\all{\vx}{\vT'})\;\ve)}

360−}

361−\\

362−& \MO{Tactic'} & \Gamma & (\LET\;\vx\defq\vv\Hab\vT\SC\ve)

363−& \MoRet{\RW{do}\;\AR{\vv'\Gets\;\MO{Tactic'}\;\Gamma\;\vv\\

364−\vT'\Gets\;\MO{Tactic'}\;\Gamma\;\vT\\

365−\RW{return}\;(\LET\;\vx\defq\vv'\Hab\vT'\SC

366−\MO{Tactic'}\;(\Gamma;\LET\;\vx\defq\vv'\Hab\vT')\;\ve)}} \\

367−& \MO{Tactic'} & \Gamma & (\vf\;\va) &

368−\MoRet{\RW{return}\;(\MO{Tactic'}\;\Gamma\;\vf)\; (\MO{Tactic'}\;\Gamma\;\va)}\\

369−& \MO{Tactic'} & \Gamma & \vt & \MoRet{\RW{return}\;\vt}

370−}

371−}

372−}

373−{Applying tactics to the proof state}

374−{runtac}

375−

376−In the remainder of this section, we will define a set of primitive tactics:

377−$\MO{Claim}$, $\MO{Fill}$ and $\MO{Solve}$ which are used to create and destroy

378−holes; and $\MO{Lambda}$, $\MO{Pi}$, $\MO{Let}$ and $\MO{Attack}$ which are

379−used to create binders. First, however, we must explain how unification is

380−applied during elaboration.

381−

382−\subsubsection{Unification}

383−

384−Unification is crucial to the success of elaboration --- it is unification

385−which finds values of implicit arguments, in particular. We do not require

386−unification to succeed immediately, in general, as instantiating a hole may

387−affect the solution to other unification problems. Instead,

388−$\PrimUnify\:\ve_1\:\ve_2$ may give one of the following results:

389−

390−\begin{itemize}

391−\item $\MO{Success}\;(\tx=\te, \tp)$, containing the solved holes mapping

392−$\vx$ to $\ve$, and a possibly empty set of blocked unification problems $\tp$.

393−If $\tp$ is empty, there is a solution unifying $\ve_1$ and $\ve_2$ in

394−the context $\Gamma$.

395−\item $\MO{Failure}\;\ve$, if no solution is found due to a failure to unify

396−sub-terms in normal form.

397−\end{itemize}

398−

399−$\MO{Unify}$ attempts to solve the given unification problem using

400−$\MO{PrimUnify}$,

401−then attempts to further refine existing problems in the proof

402−state. This operation is given in Figure \ref{unifyps}. After attempting to

403−solve the problem with $\MO{PrimUnify}$ and updating the proof term with

404−any solutions found, it updates the existing problems (with $\MO{SubstProblems}$

405−which applies $\MO{Subst}$ across the terms in the problems), then attempts to

406−resolve the existing problems with $\MO{ReUnify}$.

407−

408−\FFIG{

409−%\mbox{\textbf{[UNIFY ALGORITHM GOES HERE] }}

410−%Show how it uses a PrimUnify

411−%operation to update

412−%the proof state with new problems, and solve the old ones

413−\AR{

414−\Unify\;\ve_1\;\ve_2\;=\;\RW{do}\;

415−\AR{

416−(\tx=\te,\tp)\gets\PrimUnify\;\ve_1\;\ve_2\\

417−\vec{\MO{Subst}}\;\tx\;\te\\

418−\MO{SubstProblems}\;\tx\;\te\\

419−(\vC,\Delta,\VV{term},\tP,\vQ)\gets\MO{Get}\\

420−\vec{\MO{ReUnify}}\;\tP

421−}

422−\medskip

423−\\

424−\AR{

425−\MO{ReUnify}\;(\Gamma,\ve_1,\ve_2)\;=\;\RW{do}\;\AR{

426−(\tx=\te,\tp)\Gets\PrimUnify\;\ve_1\;\ve_2\\

427−\vec{\MO{Subst}}\;\tx\;\te\\

428−\RW{return}\;\tp

429−}

430−}

431−}

432−}

433−{The $\MO{Unify}$ meta-operation}

434−{unifyps}

435−

436−

437−\subsubsection{Creating and destroying holes}

438−

439−The $\MO{Claim}$ tactic, given a name and a type, adds a new hole binding in

440−the scope of the current goal $\vx$, adding the new binding to the hole queue, but

441−keeping $\vx$ at the head:

442−

443−\DM{

444−\PA{\A\A}{

445−\MO{Claim}_\Gamma & (\vy \Hab\vS) & (\hole{\vx}{\vT}\SC\ve) &

446− \MoRet{\RW{do}\;\AR{\MO{NewHole}\;\vy\\

447− \MO{Focus}\:\vx\\

448− \RW{return}\;\hole{\vy}{\vS}\SC\hole{\vx}{\vT}\SC\ve}} \\

449−}

450−}

451−

452−An obvious difficulty is in ensuring that names are unique throughout a proof

453−term. The implementation ensures that any hole created by the $\MO{NewHole}$

454−operation has a unique name by checking against existing names in scope and

455−modifying the name if necessary. In this paper, we will assume that all created

456−names are fresh.

457−

458−The $\MO{Fill}$ tactic, given a value $\vv$, attempts to solve the current goal

459−with $\vv$, creating a guess binding in its place. $\MO{Fill}$ attempts to

460−solve other holes by unifying the expected type of $\vx$ with the type of $\vv$:

461−

462−\DM{

463−\PA{\A\A}{

464−\MO{Fill}_\Gamma & \vv & (\hole{\vx}{\vT}\SC\ve) &

465− \MoRet{\RW{do}\;\AR{

466− \vT' \leftarrow \Check\;\vv\\

467− \Unify\;\vT\;\vT'\\

468− \RW{return}\;\guess{\vx}{\vT}{\vv}\SC\ve}

469− } \\

470−}

471−}

472−

473−\noindent

474−For example, consider the following proof term:

475−

476−\DM{

477−\AR{

478−\hole{\va}{\Type}\SC\hole{\vk}{\Nat}\SC

479−\hole{\vx}{\va}\SC\hole{\vxs}{\Vect\;\vk\;\va}\SC

480−\\

481−\hole{\vys}{\Vect\;(\suc\;\vk)\;\va}\SC\vys

482−}

483−}

484−

485−\noindent

486−If $\vx$ is in focus (i.e., at the head of the hole queue) and the elaborator

487−attempts to

488−$\MO{Fill}$ it with an $\TC{Int}$ value $42$, we have:

489−

490−\begin{itemize}

491−\item $\Check\;42\;\mq\;\TC{Int}$

492−\item Unifying $\TC{Int}$ with $\vA$ (the type of $\vx$) is only possible if

493−$\vA\;=\;\TC{Int}$, so solve $\vA$.

494−\end{itemize}

495−

496−\noindent

497−Therefore the resulting proof term is:

498−

499−\DM{

500−\AR{

501−\hole{\vk}{\Nat}\SC

502−\guess{\vx}{\TC{Int}}{42}\SC\hole{\vxs}{\Vect\;\vk\;\TC{Int}}\SC

503−\\

504−\hole{\vys}{\Vect\;(\suc\;\vk)\;\TC{Int}}\SC\vys

505−}

506−}

507−

508−The $\MO{Solve}$ tactic operates on a guess binding. If the guess is \remph{pure}, i.e., it

509−is a \TT{} term containing no hole or guess bindings, then the value attached to

510−the guess is substituted into its scope, and the corresponding hole removed

511−from the hole queue:

512−

513−\DM{

514−\PA{\A}{

515−\MO{Solve}_\Gamma & (\guess{\vx}{\vT}{\vv}\SC\ve) &

516− \MoRet{\RW{do}\;\AR{\MO{RemoveHole}\\

517− \RW{return}\;\ve[\vv/\vx]\hg\mbox{(if $\MO{Pure}\;\vv$)}}}

518−}

519−}

520−

521−The two step process, with $\MO{Fill}$ followed by $\MO{Solve}$, allows the elaborator

522−to work safely with incomplete terms, since an incomplete guess binding has no

523−computational force. Once a term is complete in a guess binding, it may be substituted into the

524−scope of the binding safely.

525−In each of these tactics, if any step fails, or the term in focus does not take

526−the correct form (e.g. is not a guess in the case of $\MO{Solve}$ or not a hole

527−in the case of $\MO{Claim}$ and $\MO{Fill}$) the entire tactic fails. We can

528−handle failure using the $\MO{Try}$ tactic combinator:

529−

530−\DM{

531−\PA{\A\A\A}{

532−\MO{Try}_\Gamma & \VV{t1} & \VV{t2} & \vt &

533− \MoRet{\RW{case}\;\AR{\VV{t1}_\Gamma\;\vt\;\RW{of}\\

534− \MO{Success}\;\vt'\cq\MO{Success}\;\vt'\\

535− \MO{Failure}\;\_\cq\VV{t2}_\Gamma\;\vt\\

536− }}

537−}

538−}

539−

540−We have a primitive tactic $\MO{Fail}$, which may be invoked by

541−any tactic which encounters a failure condition (for example, an unsolvable unification

542−problem) and is handled by $\MO{Try}$.

543−

544−\subsubsection{Creating binders}

545−

546−We also define primitive tactics for constructing binders. Creating a

547−$\lambda$-binding requires that the goal normalises to a function type:

548−

549−\DM{

550−\PA{\A\A}{

551−\MO{Lambda}_\Gamma & \vn & (\hole{\vx}{\vT}\SC\vx) &

552− \MoRet{\RW{do}\;\AR{

553− \all{\vy}{\vS}\SC\vT'\;\leftarrow\;\Eval\;\vT \\

554− \RW{return}\;\lam{\vn}{\vS}\SC\hole{\vx}{\vT'[\vn/\vy]}\SC\vx

555− }

556− }

557−}

558−}

559−

560−\noindent

561−Creating a $\forall$ binding requires that the goal type converts

562−with $\TC{Type}$:

563−

564−\DM{

565−\PA{\A\A}{

566−\MO{Pi}_\Gamma & (\vn\Hab\vS) & (\hole{\vx}{\Type}\SC\vx) &

567− \MoRet{\RW{do}\;\AR{

568− \vV\;\leftarrow\;\Check\;\vS\\

569− \MO{Convert}_\Gamma\;\vV\;\Type\\

570− \RW{return}\;\all{\vn}{\vS}\SC\hole{\vx}{\Type}\SC\vx

571− }

572− }

573−}

574−}

575−

576−\noindent

577−Creating a $\LET$ binding requires a type and a value.

578−

579−\DM{

580−\PA{\A\A}{

581−\MO{Let}_\Gamma & (\vn\Hab\vS\defq\vv) & (\hole{\vx}{\vT}\SC\vx) &

582− \MoRet{\RW{do}\;\AR{

583− \vV\;\leftarrow\;\Check\;\vS\\

584− \MO{Convert}_\Gamma\;\vV\;\Type\\

585− \vS'\;\leftarrow\;\Check\;\vv\\

586− \Unify\;\vS\;\vS'\\

587− \RW{return}\;\LET\;\vn\Hab\vS\defq\vv\SC\hole{\vx}{\vT}\SC\vx

588− }

589− }

590−}

591−}

592−

593−Each of these tactics require the term in focus to be of the form $\hole{\vx}{\vT}\SC\vx$.

594−This is important, because if the scope of the binding were an arbitrary expression $\ve$,

595−the binder would be scoped across this \emph{whole} expression rather than the subexpression

596−$\vx$ as intended.

597−The $\MO{Attack}$ tactic ensures that a hole

598−is in the appropriate form, creating a new hole $\vx'$ which is placed at the

599−head of the queue:

600−

601−\DM{

602−\PA{\A}{

603−\MO{Attack}_\Gamma & (\hole{\vx}{\vT}\SC\ve) &

604− \MoRet{\RW{do}\;\AR{

605− \MO{NewHole}\;\vx'\\

606− \RW{return}\;\guess{\vx}{\vT}{(\hole{\vx'}{\vT}\SC\vx')}\SC\ve}}

607−}

608−}

609−

610−\noindent

611−For example, consider the following proof term:

612−

613−\DM{

614−\hole{\vx}{\va\to\vb}\SC\vx\;\ve

615−}

616−

617−\noindent

618−If we try to instantiate $\vx$ with a $\lambda$-binding $\vn$ immediately,

619−without applying $\MO{Attack}$ first, the $\lambda$ will scope over the

620−entirety of $\vx\;\ve$, and the resulting term is not well-typed:

621−

622−\DM{

623−\AR{

624−\lam{\vn}{\va}\SC\hole{\vx}{\vb}\SC\vx\;\ve

625−}

626−}

627−

628−\noindent

629−If, on the other hand, we $\MO{Attack}$ the hole then instantiate it with

630−a $\lambda$-binding $\vn$, we get:

631−

632−\DM{

633−\begin{array}{ll}

634−\guess{\vx}{\va\to\vb}{\hole{\vx'}{\va\to\vb}\SC\vx'}\SC\vx\;\ve

635−& \hg\mbox{(after $\MO{Attack}$)}\\

636−\guess{\vx}{\va\to\vb}{\lam{\vn}{\va}\SC\hole{\vx'}{\vb}\SC\vx'}\SC\vx\;\ve

637−& \hg\mbox{(after $\MO{Lambda}\;\vn$)}

638−\end{array}

639−}

640−

641−\noindent

642−Now, once $\vx'$ has been instantiated, the guess for $\vx$ can safely be

643−closed with $\MO{Solve}$.

644−

645−\subsubsection{Pattern Binders}

646−

647−Finally, we can convert a hole binding to a pattern binding by giving the

648−pattern variable a name. This solves a hole

649−by adding the pattern binding to the proof state, and updating the proof term

650−with the pattern variable directly:

651−

652−\DM{

653−\PA{\A\A}{

654−\MO{Pat}_\Gamma & \vn & (\hole{\vx}{\vT}\SC\ve) &

655− \MoRet{\RW{do}\;\AR{

656− \MO{PatBind}\;(\vn\Hab\vT)\\

657− \RW{return}\;\ve[\vn/\vx]

658− }}

659−}

660−}

661−

662−The $\MO{PatBind}$ operation simply updates the proof state with the given pattern

663−binding. Once we have created bindings from the left hand side of a pattern

664−matching definition, for example, we can retain these bindings for use when

665−building the right hand side.

666−

667−\subsubsection{Example}

668−

669−To illustrate how tactics are applied, using $\MO{Tactic}$, to build a

670−complete term by refining a proof state, let us consider the following

671−\TT{} definition for the identity function:

672−

673−\DM{

674−\AR{

675−\FN{id}\Hab\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA \\

676−\FN{id}\;=\;\lam{\vA}{\Type}\SC\lam{\va}{\vA}\SC\va

677−}

678−}

679−

680−We can build $\FN{id}$ either as a complete term, or by applying a sequence of

681−tactics. To achieve this, we create a proof state initialised with the type of

682−$\FN{id}$ and apply a series of $\MO{Lambda}$ and $\MO{Fill}$ operations using

683−$\MO{Tactic}$. Note that the types on each $\MO{Lambda}$ are taken from

684−the goal type.

685−

686−\DM{

687−\AR{

688−\MO{MkId}\;\mq\;\RW{do}\;

689− \AR{

690− \MO{NewProof}\;\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA \\

691− \MO{Tactic}\;\MO{Attack} \\

692− \MO{Tactic}\;(\MO{Lambda}\;\vA) \\

693− \MO{Tactic}\;\MO{Attack} \\

694− \MO{Tactic}\;(\MO{Lambda}\;\va) \\

695− \MO{Tactic}\;(\MO{Fill}\;\va)\\

696− \MO{Tactic}\;\MO{Solve}\\

697− \MO{Tactic}\;\MO{Solve}\\

698− \MO{Tactic}\;\MO{Solve}\\

699− \MO{Term}

700− }

701−}

702−}

703−

704−\FFIG{

705−\begin{array}{lll}

706−\mbox{\textbf{Tactic}} & \mbox{\textbf{Resulting Proof Term}} &

707−\mbox{\textbf{Queue}}

708−\medskip

709−\\

710−\mbox{Initial state}

711−& \underline{\hole{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}\SC\vx}

712−& \langle\vx\rangle \\

713−%

714−\MO{Attack} &

715−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

716−\underline{\hole{\vh_0}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}\SC\vh_0}

717−}

718−\SC\vx

719−&

720−\langle\vh_0,\vx\rangle\\

721−%

722−\MO{Lambda}\;\vA &

723−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

724−\lam{\vA}{\Type}\SC\underline{

725−\hole{\vh_0}{\all{\va}{\vA}\SC\vA}\SC\vh_0

726−}

727−}

728−\SC\vx

729−&

730−\langle\vh_0,\vx\rangle\\

731−%

732−\MO{Attack} &

733−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

734−\lam{\vA}{\Type}\SC

735−\guess{\vh_0}{\all{\va}{\vA}\SC\vA}

736−{

737−\underline{

738−\hole{\vh_1}{\all{\va}{\vA}\SC\vA}\SC\vh_1}}

739−\SC\vh_0

740−}

741−\SC\vx

742−&

743−\langle\vh_1,\vh_0,\vx\rangle\\

744−%

745−\MO{Lambda}\;\va &

746−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

747−\lam{\vA}{\Type}\SC

748−\guess{\vh_0}{\all{\va}{\vA}\SC\vA}

749−{

750−\lam{\va}{\vA}\SC\underline{

751−\hole{\vh_1}{\vA}\SC\vh_1

752−}

753−}

754−\SC\vh_0

755−}

756−\SC\vx

757−&

758−\langle\vh_1,\vh_0,\vx\rangle\\

759−%

760−\MO{Fill}\;\va &

761−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

762−\lam{\vA}{\Type}\SC

763−%\\

764−%&

765−%\hg\hg\hg\hg\hg\hg\hg

766−\guess{\vh_0}{\all{\va}{\vA}\SC\vA}

767−{

768−\lam{\va}{\vA}\SC

769−\underline{

770−\guess{\vh_1}{\vA}{\va}\SC\vh_1

771−}

772−}

773−\SC\vh_0

774−}

775−\SC\vx

776−&

777−\langle\vh_1,\vh_0,\vx\rangle\\

778−%

779−\MO{Solve} &

780−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

781−\lam{\vA}{\Type}\SC

782−\underline{

783−\guess{\vh_0}{\all{\va}{\vA}\SC\vA}

784−{

785−\lam{\va}{\vA}\SC

786−\va

787−}

788−\SC\vh_0

789−}

790−}

791−\SC\vx

792−&

793−\langle\vh_0,\vx\rangle\\

794−%

795−\MO{Solve} &

796−\underline{

797−\guess{\vx}{\all{\vA}{\Type}\SC\all{\va}{\vA}\SC\vA}{

798−\lam{\vA}{\Type}\SC

799−\lam{\va}{\vA}\SC

800−\va

801−}

802−\SC\vx

803−}

804−&

805−\langle\vx\rangle\\

806−%

807−\MO{Solve} &

808−\lam{\vA}{\Type}\SC

809−\lam{\va}{\vA}\SC

810−\va

811−&

812−\langle\rangle\\

813−

814−\end{array}

815−}

816−{Proof state development for $\MO{MkId}$}

817−{mkidrefine}

818−

819−Figure \ref{mkidrefine} shows how each step of this sequence of tactics affects

820−the proof state and hole queue. In each step, the underlined fragment of the

821−term is the fragment in focus. One might observe that the

822−$\MO{Attack}$/$\MO{Solve}$ pairs are unnecessary in this case, as the term

823−is already in a form suitable for introduction. However, we retain these for

824−uniform treatment of introductions.

825−

826−To aid readability, we will elide $\MO{Tactic}$, and use a semi-colon to indicate

827−sequencing --- in the implementation we use wrapper functions for each tactic to

828−apply $\MO{Tactic}$.

829−Using this convention, we can build $\FN{id}$'s type and definition as shown

830−in Figure \ref{idelab}. Note that $\MO{Term}$ retrieves the proof term from the current proof

831−state. Both $\MO{MkIdType}$ and $\MO{MkId}$ finish by returning a completed \TT{} term.

832−Note in particular that each tactic which introduces a guess ($\MO{Fill}$

833−and $\MO{Attack}$) is closed with a $\MO{Solve}$.

834−

835−Setting up elaboration in this way, with a proof state captured in a monad,

836−and a primitive collection of tactics, makes it easy to derive more complex

837−tactics for elaborating higher level language constructs, in much the same way

838−as the \texttt{Ltac} language in Coq~\cite{Delahaye2000}. As a result, the

839−description of elaboration of a language construct (or a program such as

840−$\FN{id}$) bears a strong resemblance to

841−a Coq proof script.

842−

843−\FFIG{

844−\AR{

845−\MO{MkIdType}\;\mq\;\RW{do}\;

846− \AR{

847− \MO{NewProof}\;\Type\\

848− \MO{Attack} ; \MO{Pi}\;(\vA\Hab\Type) ;

849− \MO{Attack} ; \MO{Pi}\;(\va\Hab\vA) \\

850− \MO{Fill}\;\vA \\

851− \MO{Solve} ; \MO{Solve} ; \MO{Solve} \\

852− \MO{Term}

853− }

854− \medskip\\

855−\MO{MkId}\;\mq\;\RW{do}\;

856− \AR{

857− \vt\;\leftarrow\;\MO{MkIdType}; \MO{NewProof}\;\vt\\

858− \MO{Attack} ; \MO{Lambda}\;\vA ;

859− \MO{Attack} ; \MO{Lambda}\;\va \\

860− \MO{Fill}\;\va \\

861− \MO{Solve} ; \MO{Solve} ; \MO{Solve}\\

862− \MO{Term}

863− }

864−}

865−}

866−{Building $\FN{id}$ with tactics}

867−{idelab}

868−

869−%--- give unify in full, esp. as it solves sub-goals? Maybe...

870−

871−% Unify' G x t = Success (x, t) if ?x : t in G

872−% Unify' G t x = Success (x, t) if ?x : t in G

873−% Unify' G (b x. e) (b' x'. e') = Unify' G b b'; Unify' G;b e e'[x/x']

874−% Unify' G ((\x.e) x) e' = Unify' G e e'

875−% Unify' G e ((\x.e') x) = Unify' G e e'

876−% Unify' G (f es) (f' es') = vs <- Unify' G f f'; Injective f

877−

878−% Unify' G x y = Success () if G |- x == y

879−% Unify' G . . = Failure

880−

881−% Unify' G (\x : t . e) (\x : t' . e') = Unify' G t t'; Unify' G e e'

882−% ...

883−

884−

885−%\DM{

886−%}

887−

888−\subsection{System State}

889−

890−\label{sect:sysstate}

891−

892−To elaborate \Idris{} programs we will build expressions from high-level

893−declarations of functions, data types and classes, and add the resulting

894−definitions to a global system state.

895−The system state is a tuple, $(\vC,\vA,\vI)$, containing:

896−

897−\begin{itemize}

898−\item A global context, $\vC$, containing pattern matching definitions and their types

899−\item Implicit arguments, $\vA$, recording which arguments are implicit for each global name

900−\item Class information, $\vI$, containing method signatures and dictionaries for classes

901−\end{itemize}

902−

903−In the implementation, the system state is captured in a monad, \texttt{Idris},

904−which includes additional information such as syntax overloadings, command line

905−options, and optimisations, which do not concern us here.

906−

907−For each global name, $\vA$ records whether its arguments are explicit, implicit,

908−or class constraints. For example, recall the declaration

909−of \texttt{vAdd}:

910−

911−\begin{SaveVerbatim}{vAddImpT}

912−

913−vAdd : Num a => Vect n a -> Vect n a -> Vect n a

914−

915−\end{SaveVerbatim}

916−\useverb{vAddImpT}

917−

918−\noindent

919−Written in full, and giving each argument an explicit name, we get the

920−type declaration:

921−

922−\begin{SaveVerbatim}{vAddImpT}

923−

924−vAdd : (a : _) -> (n : _) -> (c : Num a) ->

925− (xs : Vect n a) -> (ys : Vect n a) -> Vect n a

926−

927−\end{SaveVerbatim}

928−\useverb{vAddImpT}

929−

930−\noindent

931−For \tFN{vAdd}, the state records that \texttt{a} and \texttt{n} are implicit,

932−\texttt{c} is a constraint, and \texttt{xs} and \texttt{ys} are explicit. When

933−the elaborator encounters an application of \tFN{vAdd}, it knows that unless these arguments

934−are given explicitly, the application must be expanded.

935−

936−\subsection{Elaborating Expressions}

937−

938−\newcommand{\piimp}[2]{\mbox{\texttt{\{$#1$ : $#2$\} -> }}}

939−%\mathtt{\{}#1\mathtt{:}#2\mbox{\texttt{\} -> }}}

940−\newcommand{\piexp}[2]{\mbox{\texttt{($#1$ : $#2$) -> }}}

941−%\newcommand{\piexp}[2]{\mathtt{(}#1\mathtt{:}#2\mbox{\texttt{) -> }}}

942−\newcommand{\piconst}[1]{\mbox{\texttt{$#1$ => }}}

943−\newcommand{\icase}{\mathtt{case}}

944−\newcommand{\iwith}{\mathtt{with}}

945−\newcommand{\idata}{\mathtt{data}}

946−\newcommand{\iclass}{\mathtt{class}}

947−\newcommand{\iinstance}{\mathtt{instance}}

948−\newcommand{\iwhere}{\mathtt{where}}

949−\newcommand{\iof}{\mathtt{of}}

950−\newcommand{\ilet}[2]{\mathtt{let}\;#1\;\mathtt{=}\;#2\;\mathtt{in}}

951−\newcommand{\ilam}[1]{\mathtt{\backslash}\;#1\;\mathtt{=>}}

952−\newcommand{\iarg}[2]{\mbox{\texttt{\{$#1$ = $#2$\}}}}

953−\newcommand{\ihab}[2]{\mbox{\texttt{$#1$ : $#2$}}}

954−\newcommand{\carg}[1]{\mbox{\texttt{\{\{$#1$\}\}}}}

955−\newcommand{\fatarrow}{\mbox{\texttt{=>}}}

956−\newcommand{\ibar}{\mbox{\texttt{|}}}

957−\newcommand{\mvar}[1]{\mbox{\texttt{?}}#1}

958−

959−\FFIG{

960−\AR{

961−\begin{array}{rll@{\hg}rll}

962−\ve, \vt ::= & \vc & (\mbox{constant}) &

963−\mid & \vx & (\mbox{variable}) \\

964−\mid & \ilam{\vx}\;\ve & (\mbox{lambda abstraction}) &

965−\mid & \ve\;\ta & (\mbox{function application}) \\

966−\mid & \ilet{\vx}{\ve}\;\ve & (\mbox{let binding}) &

967−\mid & \piexp{\vx}{\vt}\vt & (\mbox{explicit function space}) \\

968−%\mid & \icase\;\ve\;\iof\;\vec{\VV{alt}} & (\mbox{case expression}) &

969−%\mid & \mvar{\vx} & (\mbox{metavariable}) \\

970−\mid & \_ & (\mbox{placeholder})

971−\end{array}

972−\medskip\\

973−\begin{array}{rll}

974−\va :: = & \ve & (\mbox{normal argument}) \\

975−\mid & \iarg{\vx}{\ve} & (\mbox{implicit argument with value}) \\

976−\mid & \carg{\ve} & (\mbox{explicit class instance})

977−\end{array}

978−\medskip\\

979−\begin{array}{rll}

980−\VV{declty} ::= & \ve & (\mbox{expression}) \\

981−\mid & \piexp{\vx}{\vt}\VV{declty} & (\mbox{explicit function space}) \\

982−\mid & \piimp{\vx}{\vt}\VV{declty} & (\mbox{implicit function space}) \\

983−\mid & \VV{constr}\;\VV{declty} & (\mbox{constrained type}) \\

984−\end{array}

985−\medskip\\

986−\begin{array}{rll}

987−\VV{constr} ::= & \piconst{\ttt} & (\mbox{class constraint}) \\

988−\end{array}

989−}

990−}

991−{\IdrisM{} expressions}

992−{idrism}

993−

994−\FFIG{

995−\AR{

996−\begin{array}{rll}

997−\vd ::= & \ihab{\vx}{\VV{declty}} & (\mbox{type declaration}) \\

998−\mid & \VV{pclause} & (\mbox{pattern clause}) \\

999−\mid & \VV{ddecl} & (\mbox{data type declaration}) \\

1000−\mid & \VV{cdecl} & (\mbox{class declaration}) \\

1001−\mid & \VV{idecl} & (\mbox{instance declaration}) \\

1002−\end{array}

1003−\medskip\\

1004−\begin{array}{ll}

1005−\begin{array}{rll}

1006−\VV{pclause} ::= &

1007−\vx\;\ttt\;[\ibar\;\te]\mbox{\texttt{ = }}\ve \hg[\iwhere\;\td]\\

1008−\mid & \AR{

1009−\vx\;\ttt\;[\ibar\;\te]\;\iwith\;\ve\\

1010−\hg\vec{\VV{pclause}}

1011−}

1012−\end{array}

1013−&

1014−\begin{array}{rll}

1015−\VV{ddecl} ::= & \idata\;\ihab{\vx}{\VV{declty}}\;\iwhere\;\vec{\VV{con}}\\

1016−\VV{con} ::= & \ihab{\vx}{\VV{declty}}\\

1017−\medskip\\

1018−\VV{cdecl} ::= & \iclass\;[\VV{constr}]\;\vx\;(\ihab{\tx}{\ttt})\;\iwhere\;\td

1019−\\

1020−\VV{idecl} ::= & \iinstance\;[\VV{constr}]\;\vx\;\ttt\;\iwhere\;\td

1021−\end{array}

1022−\end{array}

1023−}

1024−}

1025−{\IdrisM{} declarations}

1026−{idrismd}

1027−

1028−We will use a subset of full \Idris{}, which we call \IdrisM{}, to explain

1029−elaboration of expressions. \IdrisM{} expression syntax is given in Figure

1030−\ref{idrism} and declaration syntax given in Figure \ref{idrismd}.

1031−\IdrisM{} is a subset of \Idris{} without syntactic sugar --- that is, without

1032−\texttt{do}-notation or infix operators --- and with implicit

1033−arguments in types bound explicitly

1034−(e.g. $\piimp{\va}{\_}\piimp{\vn}{\_}\TC{Vect}\;\vn\;\va$

1035−instead of simply $\Vect\;\vn\;\va$).

1036−Note that we separate implicit and type constraint bindings, to ensure that they

1037−only appear in top-level declarations.

1038−It is in general straightforward to

1039−convert full \Idris{} to \IdrisM{} --- syntactic sugar is implemented by a

1040−direct source transformation, and implicit arguments can be identified as the names

1041−which are free in a type in a non-function position.

1042−%

1043−\IdrisM{} differs from \TT{} in several important respects. It has implicit

1044−syntax and classes, and functions are applied to multiple arguments rather

1045−than one at a time.

1046−

1047−%Extensions over \TT{}: implicit syntax, case expressions. Functions are applied to

1048−%multiple arguments, rather than one at a time (this helps with implicit syntax).

1049−%\IdrisM{} also supports explicit \demph{metavariables}. A metavariable \texttt{?mvar}

1050−%creates a new global function \tFN{mvar}, with its type such that it would

1051−%be type correct to apply \tFN{mvar} to all of the variables in scope.

1052−

1053−%Implicit and type class arguments? Expanded at the application site (we need to know

1054−%it's the global name after all and we do that by type).

1055−

1056−To elaborate expressions, we define meta-operations $\ttinterp{\cdot}$ and

1057−$\ttpinterp{\cdot}$, which run relative to a proof state (see Section

1058−\ref{sect:prfstate}). $\ttpinterp{\cdot}$ elaborates \remph{patterns}, i.e.

1059−expressions on the left hand side of a pattern matching definition, whereas

1060−$\ttinterp{\cdot}$ elaborates expressions on the right hand side.

1061−Their effect is

1062−to update the proof state so that the hole in focus contains a representation

1063−of the given expression, by applying tactics. We assume that the proof state

1064−has already been set up, which means that elaboration can always be

1065−\remph{type-directed} since the proof state contains the type of the expression we

1066−are building.

1067−

1068−In all cases except the elaboration of variables and constants,

1069−$\ttpinterp{\vx}\;=\;\ttinterp{\vx}$.

1070−

1071−\subsubsection{Elaborating variables and constants}

1072−

1073−In the simplest cases, there is a direct translation from an \IdrisM{} expression to

1074−a \TT{} expression --- we build \TT{} representations of variables and constants using

1075−the \MO{Fill} tactic:

1076−

1077−\DM{

1078−\AR{

1079−\ttinterp{\vx}\;\mq\;\RW{do}\;\MO{Fill}\;\vx;\;\MO{Solve}\\

1080−\ttinterp{\vc}\;\mq\;\RW{do}\;\MO{Fill}\;\vc;\;\MO{Solve}\\

1081−}

1082−}

1083−

1084−Since $\MO{Fill}$ creates a guess binding, we use $\MO{Solve}$ to instantiate

1085−the guess. We need not concern ourselves with type checking variables or

1086−constants here --- $\MO{Fill}$ will handle this, type checking $\vx$ or $\vc$

1087−and unifying the result with the hole type. If there are any errors,

1088−elaboration will fail.

1089−

1090−If we are building the left hand side of a pattern clause, however, there is a

1091−problem, as it is the left hand side which \remph{defines} variables. In this

1092−context, we assume that attempting to elaborate a variable which does not type

1093−check means that the variable is a pattern variable:

1094−

1095−\DM{

1096−\ttpinterp{\vx}\;\mq\;

1097−\MO{Try}\;\AR{(\RW{do}\;\MO{Fill}\;\vx;\;\MO{Solve})\\

1098−(\MO{Pat}\;\vx)

1099−}

1100−}

1101−

1102−In Haskell, for comparison,

1103−pattern variables are all lower case, so type checking can assume that a

1104−lower case name in a pattern refers to a variable. In \Idris{} however, a

1105−name in a pattern may refer to a function, if forced by some dependency.

1106−

1107−We also need to elaborate \remph{placeholders}, which are subexpressions we expect to

1108−solve by unification. In this case, we simply move on to the next hole in the queue, moving

1109−the current hole to the end of the queue with $\MO{Unfocus}$:

1110−

1111−\DM{

1112−\ttinterp{\_}\;\mq\;\MO{Unfocus}

1113−}

1114−

1115−On encountering a placeholder, our assumption is that unification will

1116−eventually solve the hole. At the end of elaboration, any holes remaining

1117−unsolved on the left hand side become pattern variables. If there are any

1118−unsolved on the right hand side, elaboration is incomplete and an error will

1119−be reported when the resulting term is type checked.

1120−

1121−\subsubsection{Elaborating bindings}

1122−

1123−To elaborate a $\lambda$-binding, we $\MO{Attack}$ the hole, then apply the

1124−$\MO{Lambda}$ tactic, which will fail if the goal is not a function type. We

1125−then elaborate the scope and $\MO{Solve}$, which discharges the $\MO{Attack}$:

1126−

1127−\DM{

1128−\ttinterp{\ilam{\vx}\ve}\;\mq\;

1129−\RW{do}\;

1130−\AR{

1131−\MO{Attack};\;\MO{Lambda}\;\vx\\

1132−\ttinterp{\ve}\\

1133−\MO{Solve}

1134−}

1135−}

1136−

1137−Note that there is no type on the $\lambda$-binding in \IdrisM{}. There is no need --- since

1138−elaboration is type directed, the $\MO{Lambda}$ tactic finds the type of the binding by

1139−looking at the type of the hole. In full \Idris{}, types are allowed on bindings, and the

1140−elaborator merely checks that the given type is equivalent to the inferred type.

1141−

1142−Elaborating a function type is more tricky, since we have to elaborate the argument

1143−type (itself an \IdrisM{} expression) then elaborate the scope. To achieve this, we

1144−create a new goal $\vX$ for the argument type $\vt$, where $\vX$ is a fresh name,

1145−and introduce a function binding with argument type $\vX$. We can then focus on

1146−$\vX$, and elaborate it with the expression $\vt$. Finally, we elaborate the

1147−scope of the binding.

1148−

1149−\DM{

1150−\AR{

1151−\ttinterp{\piexp{\vx}{\vt}\ve}\;\mq\;

1152−\RW{do}\;

1153−\AR{

1154−\MO{Attack};\;\MO{Claim}\;(\vX\Hab\Type)\\

1155−\MO{Pi}\;(\vx\Hab\vX)\\

1156−\MO{Focus}\;\vX\\

1157−\ttinterp{\vt};\;

1158−\ttinterp{\ve}\\

1159−\MO{Solve}

1160−}

1161−}

1162−}

1163−

1164−Elaborating $\vt$ will involve solving unification problems, which will, if the

1165−program is type correct, solve $\vX$. After focussing on $\vX$ and elaborating

1166−$\vt$, there is no need to refocus on the hole representing the scope, as it was

1167−previously at the head of the hole queue before focussing on $\vX$.

1168−Elaboration of implicit and constraint

1169−argument types is exactly the same --- \TT{} makes no distinction between then.

1170−

1171−To elaborate a \texttt{let} binding, we take a similar approach, creating new subgoals

1172−for the \texttt{let}-bound value and its type, then elaborating the scope. Again,

1173−if elaborating the scope is successful, unification will solve the claimed variables

1174−$\vV$ and $\vX$.

1175−

1176−\DM{

1177−\ttinterp{\ilet{\vx}{\vv}\;{\ve}}\;\mq\;\RW{do}\;

1178−\AR{

1179−\MO{Attack};\;

1180−\MO{Claim}\;(\vX\Hab\Type);\;

1181−\MO{Claim}\;(\vV\Hab\vX)\\

1182−\MO{Let}\;(\vx\Hab\vX\defq\vV)\\

1183−\MO{Focus}\;\vV\\

1184−\ttinterp{\vv};\;

1185−\ttinterp{\ve}\\

1186−\MO{Solve}

1187−}

1188−}

1189−\subsubsection{Elaborating Applications}

1190−

1191−\label{sect:elabapps}

1192−

1193−There are two cases to consider when elaborating applications:

1194−

1195−\begin{itemize}

1196−\item Applying a global function name to arguments, some of which may be implicit.

1197−\item Applying an expression, which does not have implicit arguments, to an argument.

1198−\end{itemize}

1199−

1200−In the first case, the elaborator must expand the application to include implicit arguments.

1201−For example \texttt{vAdd xs ys} is expanded to

1202−\texttt{vAdd \{a=\_\} \{n=\_\} \{\{\_\}\} xs ys}, adding the implicit arguments

1203−\texttt{a} and \texttt{n} and a class instance argument. The meta-operation

1204−$\MO{Expand}\;\vx\;\ta$, given a global function name $\vx$ and the

1205−arguments supplied by the programmer $\ta$, returns a new argument list

1206−$\ta'$ with implicit and class arguments added. Each value in

1207−$\ta'$ is paired with an explicit name for the argument.

1208−

1209−Implicit arguments are solved by unification

1210−--- the type or value of another argument determines the value of an implicit argument,

1211−with the appeal to $\MO{Unify}$ in the $\MO{Fill}$ tactic solving as many extra holes

1212−as it can. However, unification problems can take several forms. For example, assuming

1213−$\vf$, $\vg$, $\vx$ are holes, we might have unification problems of the following

1214−forms:

1215−

1216−\DM{

1217−\AR{

1218−\MO{Unify}_\Gamma\;\vf\;\TC{Int}\\

1219−\MO{Unify}_\Gamma\;(\vf\;\vx)\;\TC{Int}\\

1220−\MO{Unify}_\Gamma\;(\vf\;\vx)\;(\vg\;\vx)\\

1221−}

1222−}

1223−

1224−The first problem has a solution: $\vf=\TC{Int}$. The second and third problems

1225−have no solution without further information. In the second case, we cannot

1226−conclude anything about $\vf$ or $\vx$ just from knowing that

1227−$\vf\;\vx\;=\;\TC{Int}$. In the third case, although we have $\vx\;=\;\vx$ in

1228−argument position, we cannot conclude that $\vf\;=\;\vg$ in general as a

1229−result.

1230−

1231−Once $\vf$ or $\vg$ is solved in some other way, perhaps by being given

1232−explicitly in another argument, these unification problems can make progress.

1233−Otherwise, unification blocks. In such a case, the elaborator stores the

1234−problem (i.e. the expressions to be unified with their local context) and

1235−refines it with further information when it becomes available.

1236−Elaborating a global function application makes a $\MO{Claim}$ for each

1237−argument in turn. Then the function is elaborated, applied to each of the

1238−claimed arguments. Each argument which has been given explicitly is

1239−elaborated.

1240−Finally, any class instance arguments are resolved with the

1241−built-in $\MO{Instance}$ tactic.

1242−

1243−\DM{

1244−\AR{

1245−\ttinterp{\vx\;\ta}\;\mq\;

1246−\RW{do}\;

1247−\AR{

1248−(\tn,\tv)\;\gets\;\MO{Expand}\;\vx\;\ta\\

1249−\vec{\MO{Claim}}\;(\tn\Hab\tT)\\

1250−\MO{Fill}\;\vx\;\tn\\

1251−\vec{\MO{ElabArg}}\;\tn\;\tv\hg\mbox{(for non-placeholder $\vv$)}\\

1252−\MO{Solve} \\

1253−\vec{\MO{Instance}}\;\tn\hg\mbox{(for class constraint argument $\vn$)}

1254−}

1255−\medskip

1256−\\

1257−\MO{ElabArg}\;\vn\;\vv\;\mq\;

1258−\MO{Focus}\;\vn;\;\ttinterp{\vv}

1259−}

1260−}

1261−

1262−The $\MO{Instance}$ tactic focuses on the given hole and searches the context for

1263−a class instance which would solve the goal directly. First, it examines the local

1264−context, then recursively searches the global context. $\MO{Instance}$ is covered

1265−in detail in Section \ref{sect:instance}.

1266−

1267−To elaborate a simple function application, of an arbitrary expression to an

1268−arbitrary argument (possibly with a dependent type), we need not worry about

1269−implicit arguments or class constraints. Instead, the function and argument are

1270−elaborated, and the results applied. Since elaboration is type directed,

1271−however, there must be an appropriate type for the function.

1272−

1273−\DM{

1274−\ttinterp{\ve\;\va}\;\mq\;\RW{do}\;

1275−\AR{

1276−\MO{Claim}\;(\vA\Hab\Type);\;\MO{Claim}\;(\vB\Hab\Type)\\

1277−\MO{Claim}\;(\vf\Hab\vA\to\vB);\;\MO{Claim}\;(\vs\Hab\vA)\\

1278−\MO{Focus}\;\vf;\;\ttinterp{\ve}\\

1279−\MO{Focus}\;\vs;\;\ttinterp{\va}\\

1280−}

1281−}

1282−

1283−%\subsubsection{Elaborating metavariables}

1284−

1285−%\subsubsection{Elaborating \texttt{case} expressions}

1286−

1287−\subsection{Elaborating Declarations}

1288−

1289−To elaborate declarations, we define a meta-operation $\MO{Elab}$, which runs

1290−relative to the system state (see Section \ref{sect:sysstate}) and has access to the

1291−current proof state. $\MO{Elab}$ uses $\ttinterp{\cdot}$ to help translate

1292−\IdrisM{} type, function and class declarations into \TT{} declarations.

1293−

1294−\newcommand{\edo}[1]{\RW{do}\;\AR{#1}}

1295−

1296−\subsubsection{Elaborating Type Declarations}

1297−

1298−Elaborating a type declaration involves creating a new proof state,

1299−translating the \IdrisM{} type to a \TT{} type, then adding the resulting type

1300−as a \TT{} declaration:

1301−

1302−\DM{

1303−\MO{Elab}\;(\vx\Hab\vt)\;\mq

1304−\;\edo{\MO{NewProof}\;\Type\\

1305− \ttinterp{\vt}\\

1306− \vt'\gets\MO{Term}\\

1307− \MO{TTDecl}\;(\vx\Hab\vt')

1308−}}

1309−

1310−The final $\MO{TTDecl}$ takes the result of elaboration, type checks it,

1311−and adds it to the global context if type checking succeeds. This final type check

1312−ensures that the elaboration process does not allow any ill-typed terms to creep

1313−into the context.

1314−

1315−\subsubsection{Elaborating Data Types}

1316−

1317−Elaborating a data declaration involves elaborating the type declaration itself,

1318−as a normal type declaration. This ensures that the type is in scope when

1319−elaborating the constructor types. Then using the results, the elaborator

1320−adds a \TT{} data declaration.

1321−

1322−\DM{

1323−\AR{

1324−\MO{Elab}\;(\idata\;\ihab{\vx}{\vt}\;\iwhere\;\tc)\\

1325−\hg\hg\mq\;\edo{\MO{NewProof}\;\Type\\

1326− \ttinterp{\vt}\\

1327− \vt'\gets\MO{Term}\\

1328− \MO{TTDecl}\;(\vx\Hab\vt')\\

1329− \tc'\gets\vec{\MO{ElabCon}}\;\tc\\

1330− \MO{TTDecl}\;(\Data\;\vx\Hab\vt'\;\Where\;\tc')

1331−}

1332−\AR{

1333−\MO{ElabCon}\;(\vx\Hab\vt)\\

1334−\hg\hg\mq\; \edo{\MO{NewProof}\;\Type\\

1335− \ttinterp{\vt}\\

1336− \vt'\gets\MO{Term}\\

1337− \RW{return}\;(\vx\Hab\vt')

1338−}

1339−}}}

1340−

1341−\subsubsection{Elaborating Pattern Matching}

1342−

1343−Elaborating a pattern matching definition works clause by clause, elaborating

1344−the left and right hand sides in turn. $\MO{ElabClause}$ returns the elaborated

1345−left and right hand sides, and may have the side effect of adding entries

1346−to the global context, such as definitions in $\iwhere$ clauses.

1347−First, let us consider the simplest case, with no $\iwhere$ clause:

1348−

1349−\DM{

1350−\MO{ElabClause}\;(\vx\;\ttt\;=\;\ve)\;\mq\;\ldots

1351−}

1352−

1353−How does the left hand side get elaborated, given that elaboration is type directed, and

1354−its type is not known until after elaboration?

1355−This can be achieved without any change to the elaborator by defining

1356−a type $\TC{Infer}$:

1357−

1358−\DM{

1359−\Data\hg\TC{Infer}\Hab\Type\hg\Where\hg\DC{MkInfer}\Hab\all{\va}{\Type}\SC\va\to\TC{Infer}

1360−}

1361−

1362−Now elaboration of the left hand side proceeds by elaborating $\DC{MkInfer}\;\_\;(\vx\;\ttt)$ and

1363−extracting the value and unified type when complete.

1364−

1365−\DM{

1366−\AR{

1367−\MO{ElabClause}\;(\vx\;\ttt\;=\;\ve)\;\mq\;\\

1368−\hg\hg\edo{

1369−\MO{NewProof}\;\TC{Infer};\;

1370−\ttpinterp{\DC{MkInfer}\;\_\;(\vx\;\ttt)}\\

1371−\DC{MkInfer}\;\vT\;\VV{lhs}\gets\MO{Term}\\

1372−\tp\gets\MO{Patterns}\\

1373−\MO{NewTerm}\;\vT;\;

1374−\ttinterp{\ve}\\

1375−\VV{rhs}\gets\MO{Term}\\

1376−\RW{return}\;(\RW{var}\;\tp\SC\VV{lhs}\;=\;\VV{rhs})

1377−}

1378−}

1379−}

1380−

1381−This infers a type for the left hand side, creating pattern variable bindings. Then,

1382−it elaborates the right hand side using the inferred type of the left hand side

1383−and the inferred pattern bindings, which are retrieved from the state with the

1384−$\MO{Patterns}$ operation. Finally, it returns a pattern clause in \TT{} form.

1385−Elaborating a collection of pattern clauses then proceeds by mapping $\MO{ElabClause}$ over

1386−the clauses and adding the resulting collection to \TT{}.

1387−

1388−\DM{

1389−\AR{

1390−\MO{Elab}\;\vec{\VV{pclause}}\;\mq\;

1391−\edo{

1392−\tc\gets\vec{\MO{ElabClause}}\;\vec{\VV{pclause}}\\

1393−\vec{\MO{TTDecl}}\;\tc

1394−}

1395−}

1396−}

1397−

1398−Elaborating a clause is made only slightly more complex by the presence of

1399−$\iwhere$ clauses. In this case, after elaborating the left hand side, the

1400−pattern-bound variables are added as extra arguments to the declarations in the

1401−$\iwhere$ block, which are then recursively elaborated before the right hand

1402−side.

1403−

1404−\DM{

1405−\AR{

1406−\MO{ElabClause}\;(\vx\;\ttt\;=\;\ve\;\iwhere\;\td)\;\mq\;\\

1407−\hg\hg\edo{

1408−\MO{NewProof}\;\TC{Infer};\;

1409−\ttpinterp{\DC{MkInfer}\;\_\;(\vx\;\ttt)}\\

1410−\DC{MkInfer}\;\vT\;\VV{lhs}\gets\MO{Term}\\

1411−\tp\gets\MO{Patterns}\\

1412−(\td', \ve') \gets\MO{Lift}\;\tp\;\td\;\ve\\

1413−\vec{\MO{Elab}}\;\td'\\

1414−\MO{NewTerm}\;\vT;\;

1415−\ttinterp{\ve'}\\

1416−\VV{rhs}\gets\MO{Term}\\

1417−\RW{return}\;(\RW{var}\;\tp\SC\VV{lhs}\;=\;\VV{rhs})

1418−}

1419−}

1420−}

1421−

1422−In \TT{}, all definitions must be at the top level. Therefore, the declarations

1423−in the $\iwhere$ block are lifted out, adding the pattern-bound names as additional arguments

1424−to ensure they are in scope, using the $\MO{Lift}$ operation. This also modifies

1425−the right hand side $\ve$ to use the lifted definitions, rather than the original.

1426−

1427−\subsubsection{Elaborating the \texttt{with} rule}

1428−

1429−The \texttt{with} rule allows \remph{dependent} pattern matching on intermediate values.

1430−Translating this into \TT{} involves constructing an auxiliary top-level

1431−definition for

1432−the intermediate pattern match. For example, recall \tFN{natToBin}:

1433−

1434−\useverb{natToBin}

1435−

1436−\noindent

1437−This is equivalent to the following, using top-level definitions only:

1438−

1439−\begin{SaveVerbatim}{natToBinw}

1440−

1441−natToBin : Nat -> List Bool

1442−natToBin Z = Nil

1443−natToBin k = natToBin' k (parity k)

1444−

1445−\end{SaveVerbatim}

1446−\begin{SaveVerbatim}{natToBinwp}

1447−

1448−natToBin' : (n : Nat) -> Parity n -> List Bool

1449−natToBin' (j + j) even = False :: natToBin j

1450−natToBin' (S (j + j)) odd = True :: natToBin j

1451−

1452−\end{SaveVerbatim}

1453−\useverb{natToBinw}

1454−

1455−\useverb{natToBinwp}

1456−

1457−\noindent

1458−Additionally, the elaborator abstracts over the term being analysed in the type

1459−of the generated auxiliary definition

1460−%\footnote{This is sometimes referred to

1461−%as ``magic \texttt{with}''.}

1462−and reorders the arguments as required.

1463−For example:

1464−

1465−\begin{SaveVerbatim}{magicwith}

1466−

1467−f : Nat -> Bool

1468−

1469−ftest : (n : Nat) -> so (f n) -> Nat

1470−ftest n x with (f n)

1471− | True = ...

1472− | False = ...

1473−

1474−\end{SaveVerbatim}

1475−\useverb{magicwith}

1476−

1477−\noindent

1478−Here, we may require the knowledge that \texttt{f n} is \texttt{True} or

1479−\texttt{False} in the appropriate case. The elaborator abstracts over

1480−\texttt{f n} in the auxiliary definition, specialising the type of

1481−\texttt{x} in each case:

1482−

1483−\begin{SaveVerbatim}{magicwithaux}

1484−

1485−ftest : (n : Nat) -> so (f n) -> Nat

1486−ftest n x = ftest' n (f n) x

1487−

1488−ftest' : (n : Nat) -> (p : Bool) -> so p -> Nat

1489−ftest' n True x = ...

1490−ftest' n False x = ...

1491−

1492−\end{SaveVerbatim}

1493−\useverb{magicwithaux}

1494−

1495−\noindent

1496−Elaboration of \texttt{with} builds the type declaration and auxiliary function

1497−automatically. The elaborator checks the left hand side, resulting in a set of

1498−patterns $\tp$, then infers a type $\vW$ for the expression $\vw$. The patterns

1499−$\tp$ are then split into those necessary to type $\vW$, and the rest ($\tp_w$

1500−and $\tp_n$ respectively) using

1501−$\MO{SplitContext}$. Then, it builds a new declaration, abstracting over

1502−the matched expression $\vw$ in the types of $\tp_n$.

1503−$\MO{Abstract}\;\ve\;\vw\;\vp$ simply replaces any occurrence of $\vw$ in

1504−$\vp$ with the name $\ve$.

1505−

1506−\DM{

1507−\AR{

1508−\MO{ElabClause}\;(\vx\;\ttt\;\iwith\;\vw\;\vec{\VV{pclause}})\;\mq\\

1509−\hg\hg\edo{

1510−\MO{NewProof}\;\TC{Infer};\;

1511−\ttpinterp{\DC{MkInfer}\;\_\;(\vx\;\ttt)}\\

1512−\DC{MkInfer}\;\vT\;\VV{lhs}\gets\MO{Term}\\

1513−\tp\gets\MO{Patterns}\\

1514−\MO{NewTerm}\;\TC{Infer};\;

1515−\ttinterp{\DC{MkInfer}\;\_\;\vw}\\

1516−\DC{MkInfer}\;\vW\;\vw'\gets\MO{Term}\\

1517−(\tp_w,\tp_n)\;\gets\;\MO{SplitContext}\;\vW\;\tp\\

1518−\MO{TTDecl}\;(\vx'\Hab\tp_{w}\to(\ve\Hab\vW)\to\vec{\MO{Abstract}}\;\ve\;\vw'\;\tp_{n}\to\vT)\\

1519−\tc'\gets\vec{\MO{MatchWith}}\;\tp\;\ttt\;\vec{\VV{pclause}}\\

1520−\vec{\MO{Elab}}\;\tc'\\

1521−\RW{return}\;(\RW{var}\;\tp\SC\VV{lhs}\;=\;\vx'\;\tp_{w}\;\vw'\;\tp_{n})

1522−}

1523−}

1524−}

1525−\DM{

1526−\AR{

1527−\MO{MatchWith}\;\tp_w\;\tp_n\;\ttt\;(\vx\;\tw\;\mid\;\ve\;\VV{rhs})\;\mq\\

1528−\hg\hg\edo{

1529−\tp'\gets\vec{\MO{Match}}\;\tw\;\ttt\\

1530−(\tp'_w,\tp'_n)\;\gets\;\MO{SplitPats}\;\tp_w\;\tp_n\;\tp'\\

1531−\RW{return}\;(\vx'\;\tp'_w\;\ve\;\tp'_{n}\;\VV{rhs})

1532−}

1533−}

1534−}

1535−

1536−A $\iwith$ block in a clause for $\vx$

1537−results in an auxiliary definition $\vx'$, where $\vx'$ is a fresh name,

1538−which takes an extra argument corresponding to the intermediate result which

1539−is to be matched.

1540−$\MO{MatchWith}$ matches the left hand side of the top-level definition against

1541−each $\VV{pclause}$, using the result of the match to build each pattern clause

1542−for $\vx'$.

1543−The clauses in the with block must be of a specific form: they must have an initial

1544−set of arguments $\tw$ which matches the outer clause arguments

1545−$\ttt$, and an extra argument

1546−$\ve$ which is the same type as the scrutinee of the \texttt{with}, $\vW$.

1547−The right hand side, $\VV{rhs}$, may either return a value directly, containing

1548−\texttt{where} clauses, or be a nested \texttt{with} block. In any case, it

1549−remains unchanged.

1550−$\MO{Match}\;\vw\;\vt$ returns a list of pattern bindings containing

1551−the variables in $\vt$ and their matches in $\vw$.

1552−The resulting matches are split, using $\MO{SplitPats}$, into matches for those

1553−variables necessary to type $\vW$ and the rest, as before.

1554−

1555−\subsubsection{Elaborating Class and Instance Declarations}

1556−

1557−Classes are implemented as dictionaries of functions for each instance,

1558−following the implementation of first class type classes in Coq~\cite{Sozeau2008}.

1559−Therefore, a class declaration elaborates to a record type containing all

1560−of the functions in the class, and an instance is simply an instance of the

1561−record. The methods are translated to top-level functions which extract the

1562−relevant function from the dictionary. For example, for the \texttt{Show}

1563−class, the \texttt{class} declaration is translated (in the elaborated code,

1564−using the surface \Idris{} syntax for readability)

1565−to:

1566−

1567−\begin{SaveVerbatim}{showdata}

1568−

1569−data Show : Type -> Type where

1570− InstanceShow : (show : a -> String) -> Show a

1571−

1572−show : Show a -> a -> String

1573−show (InstanceShow show') = show'

1574−

1575−\end{SaveVerbatim}

1576−\useverb{showdata}

1577−

1578−\noindent

1579−An instance for a type \texttt{a} is then a value of type \texttt{Show a}; for example for Nat:

1580−

1581−\begin{SaveVerbatim}{shownatf}

1582−

1583−showNat : Show Nat

1584−showNat = InstanceShow show' where

1585− show' : Nat -> String

1586− show' Z = "Z"

1587− show' (S k) = "s" ++ show k

1588−

1589−\end{SaveVerbatim}

1590−\useverb{shownatf}

1591−

1592−The call to \tFN{show} in the body of the instance uses the top-level \tFN{show}

1593−function, with the instance resolved by the elaborator.

1594−Where instances have constraints, these constraints are passed on to

1595−the function declaration for the instance. For example, for \texttt{Show (List a)}:

1596−

1597−\begin{SaveVerbatim}{showlista}

1598−

1599−showList : Show a => Show (List a)

1600−showList = InstanceShow show' where

1601− show' : List a -> String

1602− show' [] = "[]"

1603− show' (x :: xs) = show x ++ " :: " ++ show xs

1604−

1605−\end{SaveVerbatim}

1606−\useverb{showlista}

1607−

1608−\noindent

1609−Where classes have constraints, the

1610−constraints are again passed on to the data type declaration, and resolved by the

1611−elaborator. For example, for \texttt{Ord}:

1612−

1613−\begin{SaveVerbatim}{eqorda}

1614−

1615−class Eq a => Ord a where

1616− compare : a -> a -> Ordering

1617− max : a -> a -> a

1618− -- remaining methods elided

1619−

1620−\end{SaveVerbatim}

1621−\useverb{eqorda}

1622−

1623−\noindent

1624−This translates to:

1625−

1626−\begin{SaveVerbatim}{orddata}

1627−

1628−data Ord : Type -> Type where

1629− InstanceOrd : Eq a => (compare : a -> a -> Ordering) ->

1630− (max : a -> a -> a) -> Ord a

1631−

1632−\end{SaveVerbatim}

1633−

1634−\begin{SaveVerbatim}{orddatab}

1635−compare : Ord a -> a -> a -> Ordering

1636−compare (InstanceOrd compare' max') = compare'

1637−

1638−max : Ord a -> a -> a -> a

1639−max (InstanceOrd compare' max') = max'

1640−

1641−\end{SaveVerbatim}

1642−\useverb{orddata}

1643−

1644−\useverb{orddatab}

1645−

1646−\noindent

1647−The elaborator also adds functions to retrieve parent classes from a

1648−dictionary, to assist with class resolution. In this case:

1649−

1650−\begin{SaveVerbatim}{ordparent}

1651−

1652−OrdEq : Ord a -> Eq a

1653−OrdEq (InstanceOrd {{eq}} compare' max') = eq

1654−

1655−\end{SaveVerbatim}

1656−\useverb{ordparent}

1657−

1658−\noindent

1659−In general, \texttt{class} declarations are elaborated as follows:

1660−

1661−\DM{

1662−\AR{

1663−\MO{Elab}\;(\iclass\;\piconst{\tc}\TC{C}\;(\ta\Hab\ttt)\;\iwhere\;\td)

1664−\\

1665−\hg\hg

1666−\mq\;\RW{do}\;\AR{

1667−%(\vec{\VV{meth}}\Hab\ttt)\gets\td\\

1668−\MO{Elab}\;

1669−\AR{(\RW{data}\;\TC{C}\Hab(\ta\Hab\ttt)\to\Type\;\iwhere\\

1670−\hg\DC{InstanceC}\Hab\piconst{\tc}\td\to\TC{C}\;\ta)}\\

1671−\vec{\MO{ElabMeth}}\;\td\\ % (\vec{\VV{meth}}\Hab\ttt)\\

1672−\vec{\MO{ElabParent}}\;\tc

1673−}

1674−\medskip\\

1675−\MO{ElabMeth}\;(\vf\Hab\vt)\\

1676−\hg\hg\mq\;\RW{do}\;\AR{

1677−\MO{Elab}\;(\vf\Hab\TC{C}\;\ta\to\vt)\\

1678−\MO{Elab}\;(\vf\;(\DC{InstanceC}\;\vec{\VV{meth}})\;=\;\vec{\VV{meth}[\vf]})

1679−}

1680−\medskip\\

1681−\MO{ElabParent}\;\vc\\

1682−\hg\hg\mq\;\RW{do}\;\AR{

1683−\MO{Elab}\;(\VV{cC}\Hab\TC{C}\;\ta\to\vc)\\

1684−\MO{Elab}\;(\VV{cC}\;(\DC{InstanceC}\;\carg{\vc'}\;\vec{\VV{meth}})\;=\;\vc')

1685−}

1686−}

1687−}

1688−

1689−\noindent

1690−Then \texttt{instance} declarations are elaborated as follows. One complication

1691−is that the function definitions in an \texttt{instance} declaration do not

1692−have explicit types, so we must retrieve the method types from the system state

1693−and substitute $\TC{C}\;\ttt$, using $\MO{ExpandTypes}$.

1694−The name $\FN{instanceC}$ is a fresh name generated for the newly

1695−defined instance:

1696−

1697−\DM{

1698−\AR{

1699−\MO{Elab}\;(\iinstance\;\piconst{\tc}\TC{C}\;\ttt\;\iwhere\;\td)\\

1700−\hg\hg\mq\;\RW{do}\;\AR{

1701−(\vec{\VV{meth}}, \vec{\VV{ty}})\gets\MO{ExpandTypes}\;\td\\

1702−\vec{\VV{ty'}}\;=\;\vec{\VV{ty}}[\ttt/\ta]\\

1703−\MO{Elab}\;(\FN{instanceC}\Hab\piconst{\tc}\TC{C}\;\ttt)\\

1704−\MO{Elab}\;\AR{

1705−(\FN{instanceC}\;=\;\DC{InstanceC}\;\vec{\VV{meth'}}\;\iwhere

1706−\\

1707−\hg\vec{\VV{meth'}}\Hab\vec{\VV{ty'}}\\

1708−\hg\td

1709−)}

1710−}

1711−}

1712−}

1713−

1714−Adding default definitions is straightforward: simply insert the default definition where

1715−there is a method missing in an \texttt{instance} declaration.

1716−

1717−Here, we have added a higher level language construct

1718−(classes) simply by elaborating in terms of lower level language constructs

1719−(data types and functions). We achieve type class resolution by implementing a

1720−tactic, $\MO{Instance}$. We can build several extensions this way because we

1721−have effectively built, bottom up, an Embedded Domain Specific Language for

1722−constructing programs in \TT{}.

1723−

1724−\subsubsection{The $\MO{Instance}$ tactic}

1725−

1726−\label{sect:instance}

1727−

1728−When elaborating applications, recall that implicit arguments are filled in by

1729−unification as described in Section \ref{sect:elabapps}, and class

1730−constraints by an $\MO{Instance}$ tactic which searches the context for an

1731−instance of the required class.

1732−

1733−The $\MO{Instance}$ tactic begins by trying to find a solution in the local context,

1734−using the $\MO{Trivial}$ tactic, which attempts

1735−to solve the current goal with each local variable in turn. It is used as a very

1736−basic primitive for proof search, and is defined as follows:

1737−

1738−\DM{

1739−\AR{

1740−\MO{Trivial}\;\mq\;

1741−\RW{do}\;\AR{

1742− (\tv\Hab\ttt)\gets\MO{Context}\\

1743− \MO{TryAll}\;\tv

1744− }

1745−\medskip\\

1746−\MO{TryAll}\;(\vv_1,\vv_2\ldots)\;\mq\;\MO{Try}\;(\MO{Fill}\;\vv_1)\;(\MO{TryAll}\;\vv_2\ldots)

1747−\\

1748−\MO{TryAll}\;\langle\rangle\;\mq\;\MO{Fail}

1749−}

1750−}

1751−

1752−For example, in the following function, the class constraint required for

1753−the $\texttt{>}$ operator is resolved by finding an instance for \texttt{Ord a}

1754−in the local context:

1755−

1756−\begin{SaveVerbatim}{ordlocal}

1757−

1758−max : Ord a => a -> a -> a

1759−max x y = if (x > y) then x else y

1760−

1761−\end{SaveVerbatim}

1762−\useverb{ordlocal}

1763−

1764−If $\MO{Trivial}$ does not find a solution, $\MO{Instance}$ begins a global search,

1765−applying every class instance, and attempting to resolve the instance's parameters

1766−recursively. Given an instance function $\FN{instanceC}$ with parameters

1767−of type $\ttt$:

1768−

1769−\DM{

1770−\MO{TryInstance}\;\FN{instanceC}\;\mq\;\RW{do}\;

1771−\AR{

1772−\vec{\MO{Claim}}\;(\tx\Hab\ttt)\\

1773−\ttinterp{\FN{instanceC};\tx}\\

1774−\vec{\MO{Focus}}\;\tx;\;\vec{\MO{Instance}}

1775−}

1776−}

1777−

1778−We define $\MO{Instance}$ as follows, using $\MO{AllInstances}$ to retrieve

1779−all functions which define instances:

1780−

1781−\DM{

1782−\MO{Instance}\;\mq\;

1783−\MO{Try}\;

1784−\AR{

1785−\MO{Trivial}\\

1786−(\RW{do}\;\AR{

1787−\ti\gets\MO{AllInstances}\\

1788−\vec{\MO{TryInstance}}\;\ti

1789−)

1790−}

1791−}

1792−}

1793−

1794−In practice, for efficiency and to ensure that resolution terminates,

1795−we constrain the search by recording which instances are defined for each

1796−class, and by ensuring that a recursive call of $\MO{Instance}$ is either

1797−searching for a different class, or a structurally smaller instance of the

1798−current class.

1799−

1800−For example, in the following function, the constraints required by the

1801−\tFN{show} function are resolved by a global search which locates a \tTC{Show}

1802−instance for \tTC{List a}, which in turn requires a \tTC{Show} instance for

1803−\texttt{a}. In this case \texttt{a} is instantiated by \tTC{Int}, so resolution finishes

1804−by locating a \tTC{Show} instance for \tTC{Int}:

1805−

1806−\begin{SaveVerbatim}{showinst}

1807−

1808−main : IO ()

1809−main = putStrLn (show [1,2,3,4])

1810−

1811−\end{SaveVerbatim}

1812−\useverb{showinst}

1813−

1814−\subsection{Syntax Extensions}

1815−

1816−We now have a complete elaborator for \IdrisM{}, covering

1817−dependent pattern matching definitions and expansion of implicit arguments

1818−and classes. In order to make the language truly general purpose, however, we

1819−will need to add higher level extensions. Full \Idris{} is \IdrisM{} extended

1820−with \texttt{do}-notation, idiom brackets~\cite{McBride2007}, \texttt{case} expressions,

1821−pattern matching \texttt{let}, metavariables and tactic-based theorem proving.

1822−The majority of these extensions are straightforward transformations of high-level

1823−\Idris{} programs --- for example, \texttt{do}-notation can be reduced directly to

1824−\IdrisM{} function applications. Some, however, require further support. In this section,

1825−we complete the presentation of \IdrisM{} by extending it with metavariables

1826−and $\icase$ expressions:

1827−

1828−\DM{

1829−\AR{

1830−\begin{array}{rll@{\hg}rll}

1831−\ve ::= & \ldots \\

1832−\mid & \mvar{\vx} & (\mbox{metavariable}) &

1833−\mid & \icase\;\ve\;\iof\;\vec{\VV{alt}} & (\mbox{case expression}) \\

1834−\medskip\\

1835−\VV{alt} ::= & \ve\;\fatarrow\;\ve & (\mbox{case alternative})\\

1836−\end{array}

1837−}

1838−}

1839−

1840−\subsubsection{Metavariables}

1841−

1842−\demph{Metavariables} are terms which stand for incomplete programs. A

1843−metavariable serves a similar

1844−purpose to a hole binding in \TT{}, but gives rise to a global rather than a

1845−local variable. For example, the following is an incomplete definition of

1846−the vector append function, containing a metavariable \texttt{append\_rec}:

1847−

1848−\begin{SaveVerbatim}{vappmv}

1849−

1850−(++) : Vect n a -> Vect m a -> Vect (n + m) a

1851−Nil ++ ys = ys

1852−(x :: xs) ++ ys = x :: ?append_rec

1853−

1854−\end{SaveVerbatim}

1855−\useverb{vappmv}

1856−

1857−This generates a new (as yet undefined)

1858−function \texttt{append\_rec}, which takes all of the variables

1859−in scope at the point it is used, and returns a value of the required type.

1860−We can inspect the type of \texttt{append\_rec} at the \Idris{} prompt:

1861−

1862−\begin{SaveVerbatim}{appendrec}

1863−

1864−*vec> :t append_rec

1865−append_rec : (a : Type) -> (m : Nat) -> (n : Nat) -> a ->

1866− Vect n a -> Vect m a -> Vect (n + m) a

1867−

1868−\end{SaveVerbatim}

1869−\useverb{appendrec}

1870−

1871−Metavariables serve two purposes: Firstly, they aid type directed program development

1872−by allowing a programmer direct access to the inferred types of local variables, and

1873−the types of subexpressions. Secondly, they allow a separation of program structure

1874−from proof details. Metavariables can be solved either by directly editing program

1875−source, or by providing a definition elsewhere in the file. For example, we can later say:

1876−

1877−\begin{SaveVerbatim}{appendrec_def}

1878−

1879−append_rec a m n x xs ys = app xs ys

1880−

1881−\end{SaveVerbatim}

1882−\useverb{appendrec_def}

1883−

1884−Elaborating a metavariable involves adding a new top-level definition which is applied

1885−to all of the variables in local scope.

1886−

1887−\DM{

1888−\ttinterp{\mvar{\vx}}\;\mq\;

1889−\edo{

1890−(\tv\Hab\ttt)\gets\MO{Context}\\

1891−\vT\gets\MO{Type}\\

1892−\MO{TTDecl}\;(\vx\Hab(\tv\Hab\ttt)\to\vT)\\

1893−\ttinterp{\vx\;\tv}

1894−}

1895−}

1896−

1897−\subsubsection{\texttt{case} expressions}

1898−

1899−A \texttt{case} expression allows pattern matching on intermediate values. The difficulty

1900−in elaborating \texttt{case} expressions is that \TT{} allows matching only on

1901−\emph{top-level} values. Elaborating a \texttt{case} expression, therefore,

1902−involves creating a new top-level function standing for the expression, and applying it.

1903−The natural

1904−way to implement this is to use a metavariable. For example, we have already seen

1905−\texttt{lookup\_default}:

1906−

1907−\useverb{listlookup}

1908−

1909−\noindent

1910−This elaborates as follows:

1911−

1912−\begin{SaveVerbatim}{listlookupmv}

1913−

1914−lookup_default : Nat -> List a -> a -> a

1915−lookup_default i xs def =

1916− let scrutinee = list_lookup i xs in ?lookup_default_case

1917−

1918−lookup_default_case i xs def Nothing = def

1919−lookup_default_case i xs def (Just x) = x

1920−

1921−\end{SaveVerbatim}

1922−\useverb{listlookupmv}

1923−

1924−To elaborate a $\icase$ expression involves \texttt{let} binding the scrutinee

1925−of the $\icase$ expression, introducing a new name $\VV{scrutinee}$, and

1926−creating a metavariable $\VV{xcase}$ to implement the pattern matching. Then

1927−the elaborator builds a new pattern matching definition for $\VV{xcase}$ and

1928−elaborates it:

1929−

1930−\DM{

1931−\AR{

1932−\ttinterp{\icase\;\ve\;\iof\;\vec{\VV{alt}}}\;\mq\;

1933−\edo{

1934−\ttinterp{\ilet{\VV{scrutinee}}{\ve}\;\mvar{\VV{xcase}}}\\

1935−(\tv\Hab\ttt)\gets\MO{Context}\\

1936−\vec{\MO{MkCase}}\;\tv\;\VV{alt}\\

1937−}

1938−\medskip\\

1939−\MO{MkCase}\;\tv\;(\vl\;\fatarrow\;\vr)\;\mq\;\MO{Elab}\;(\VV{xcase}\;\tv\;\vl\;=\;\vr)

1940−}

1941−}

1942−

1943−Any nested $\icase$ expressions will be handled by the recursive call to

1944−$\MO{Elab}$. Again, because of the way we have set up an Embedded Domain Specific

1945−Language for describing elaboration, we have been able to implement a new higher

1946−level language feature in terms of elaboration of lower level language features.

1947−

1948−

1949−%\subsubsection{Tactic-implicit arguments}

1950−

1951−

1952−%\subsubsection{Pairs and Dependent Pairs}

1953−

1954−% Other extensions: do notation, idiom brackets, pairs, etc, are easily expressed

1955−% by transformations of the high level syntax

1956−

papers/impl-paper/hll.texdeleted−441

@@ -1,441 +0,0 @@

1−\section{\Idris{} --- the High Level Language}

2−

3−\label{sect:hll}

4−

5−\Idris{} is

6−a pure functional programming language with dependent types. It is

7−eagerly evaluated by default, and compiled via the Epic supercombinator

8−library~\cite{brady2011epic}, with irrelevant values and proof terms

9−automatically erased~\cite{Brady2003,Brady2005}.

10−In this section, I present some small examples to illustrate

11−the features of \Idris{}.

12−A full tutorial is available elsewhere \cite{idristutorial}.

13−

14−\subsection{Preliminaries}

15−

16−\Idris{} defines several primitive types: fixed width integers

17−\tTC{Int}, arbitrary width integers \tTC{Integer},

18−\tTC{Float} for numeric operations, \tTC{Char} and \tTC{String} for

19−text manipulation, and \tTC{Ptr} which represents foreign pointers.

20−There are also several data types declared in the library, including

21−\tTC{Bool}, with values \tDC{True} and \tDC{False}. All of the usual

22−arithmetic and comparison operators are defined for the primitive types.

23−

24−An \Idris{} program consists of a module declaration, followed by an optional

25−list of imports and a collection of definitions and declarations, for example:

26−

27−\begin{SaveVerbatim}{constprims}

28−

29−module Main

30−

31−x : Int

32−x = 42

33−

34−main : IO ()

35−main = putStrLn ("The answer is " ++ show x)

36−

37−\end{SaveVerbatim}

38−\useverb{constprims}

39−

40−\noindent

41−Like Haskell, the main function is called \texttt{main}, and input and output

42−is managed with an \texttt{IO} monad. Unlike Haskell, however, \remph{all}

43−top-level functions must have a type signature. This is due to type inference

44−being, in general, undecidable for languages with dependent types.

45−

46−A module declaration also opens a \remph{namespace}. The fully qualified names

47−declared in this module are \texttt{Main.x} and \texttt{Main.main}.

48−

49−\subsection{Data Types}

50−

51−Data types may be declared in a similar way to Haskell data types, with a

52−similar syntax. For example, Peano natural numbers and lists

53−are respectively declared in the library as follows:

54−

55−\begin{SaveVerbatim}{natdecl}

56−

57−data Nat = Z | S Nat

58−data List a = Nil | (::) a (List a)

59−

60−\end{SaveVerbatim}

61−\useverb{natdecl}

62−

63−\noindent

64−A standard example of a \remph{dependent} type is the type of ``lists with

65−length'', conventionally called ``vectors'' in the dependently-typed

66−programming literature. In \Idris{}, vectors are declared as follows:

67−

68−\begin{SaveVerbatim}{vectdecl}

69−

70−data Vect : Nat -> Type -> Type where

71− Nil : Vect Z a

72− (::) : a -> Vect k a -> Vect (S k) a

73−

74−\end{SaveVerbatim}

75−\useverb{vectdecl}

76−

77−\noindent

78−The above declaration creates a family of types. The syntax resembles a Haskell

79−GADT declaration: it explicitly states the type

80−of the type constructor \tTC{Vect} --- it takes a \tTC{Nat} and a type as

81−arguments, where \tTC{Type} stands for the type of types. We say that \tTC{Vect}

82−is \emph{indexed} over \tTC{Nat} and \emph{parameterised} by a type.

83−The distinction between parameters and indices is that a parameter is fixed

84−across an entire data structure, whereas an index may vary.

85−Note that constructor names may be overloaded (such as \texttt{Nil} and

86−\texttt{(::)} here) provided that they are declared in separate

87−namespaces.

88−

89−Note that in the library, \texttt{List} is declared in a module

90−\texttt{Prelude.List}, and \texttt{Vect} in a module \texttt{Prelude.Vect}, so

91−the fully qualified names of \texttt{Nil} are \texttt{Prelude.List.Nil} and

92−\texttt{Prelude.Vect.Nil}. They may be used qualified or unqualified; if

93−used unqualified the elaborator will disambiguate by type.

94−

95−\subsection{Functions}

96−

97−Functions are implemented by pattern matching. For example, the following

98−function defines concatenation of vectors, expressing in the type that

99−the resulting vector's length is the sum of the input lengths:

100−

101−\begin{SaveVerbatim}{vapp}

102−

103−(++) : Vect n a -> Vect m a -> Vect (n + m) a

104−Nil ++ ys = ys

105−(x :: xs) ++ ys = x :: xs ++ ys

106−

107−\end{SaveVerbatim}

108−\useverb{vapp}

109−

110−\noindent

111−Functions can also be defined \emph{locally} using \texttt{where} clauses. For

112−example, to define a function which reverses a list, we can use an auxiliary

113−function which accumulates the new, reversed list, and which does not need to

114−be visible globally:

115−

116−\begin{SaveVerbatim}{revwhere}

117−

118−reverse : List a -> List a

119−reverse xs = revAcc Nil xs where

120− revAcc : List a -> List a -> List a

121− revAcc acc Nil = acc

122− revAcc acc (x :: xs) = revAcc (x :: acc) xs

123−

124−\end{SaveVerbatim}

125−\useverb{revwhere}

126−

127−\subsubsection*{Totality checking}

128−

129−Internally, \Idris{} programs are checked for \emph{totality} --- that they

130−produce an answer in finite time for all possible inputs --- but they are not

131−\emph{required} to be total by default. Totality checking serves two

132−purposes: firstly, if a program terminates for all inputs

133−then its type gives a strong guarantee about the properties specified by its

134−type; secondly, we can optimise total programs more

135−aggressively~\cite{Brady2003}.

136−

137−Totality checking can be enforced by using the \texttt{total} keyword.

138−For example, the following definition is accepted:

139−

140−\begin{SaveVerbatim}{vaddt}

141−

142−total vAdd : Num a => Vect n a -> Vect n a -> Vect n a

143−vAdd Nil Nil = Nil

144−vAdd (x :: xs) (y :: ys) = x + y :: vAdd xs ys

145−

146−\end{SaveVerbatim}

147−\useverb{vaddt}

148−

149−\noindent

150−The elaborator can verify that this is total by checking that it covers all

151−possible patterns --- in this case, both arguments must be of the same form

152−as the type requires that the input vectors are the same length --- and that

153−recursive calls are on structurally smaller values.

154−

155−\Idris{} also supports coinductive definitions, though this and further

156−details of totality checking are beyond the scope of this paper; the totality

157−checker is implemented independently of elaboration and type checking.

158−

159−\subsection{Implicit Arguments}

160−

161−In order to understand how \Idris{} elaborates to an underlying type theory,

162−it is important to understand the notion of \remph{implicit} arguments.

163−To illustrate this, consider the finite sets:

164−

165−\begin{SaveVerbatim}{findecl}

166−

167−data Fin : Nat -> Type where

168− fZ : Fin (S k)

169− fS : Fin k -> Fin (S k)

170−

171−\end{SaveVerbatim}

172−\useverb{findecl}

173−

174−\noindent

175−As the name suggests, these are sets with a finite number of elements.

176−The declaration gives

177−\tDC{fZ} as the zeroth element of a finite set with \texttt{S k} elements,

178−and \texttt{fS n} as the

179−\texttt{n+1}th element of a finite set with \texttt{S k} elements.

180−

181−\tTC{Fin} is indexed by \tTC{Nat}, which represents the number of elements in

182−the set. Neither constructor targets \texttt{Fin Z}, because the empty

183−set has no elements. The following function uses an element

184−of a finite set as a bounds-safe index into a vector:

185−

186−\begin{SaveVerbatim}{vindex}

187−

188−index : Fin n -> Vect n a -> a

189−index fZ (x :: xs) = x

190−index (fS k) (x :: xs) = index k xs

191−

192−\end{SaveVerbatim}

193−\useverb{vindex}

194−

195−\noindent

196−Let us take a closer look at its type.

197−It takes two arguments, an element of the finite set of \texttt{n} elements, and a vector

198−with \texttt{n} elements of type \texttt{a}. But there are also two names,

199−\texttt{n} and \texttt{a}, which are not declared explicitly. These are \emph{implicit}

200−arguments to \texttt{index}. The type of \texttt{index} could also be written as:

201−

202−\begin{SaveVerbatim}{vindeximppl}

203−

204−index : {a:_} -> {n:_} -> Fin n -> Vect n a -> a

205−

206−\end{SaveVerbatim}

207−\useverb{vindeximppl}

208−

209−\noindent

210−This gives bindings for \texttt{a} and \texttt{n} with placeholders for

211−their types, to be inferred by the machine. These types could also be given explicitly:

212−

213−\begin{SaveVerbatim}{vindeximpty}

214−

215−index : {a:Type} -> {n:Nat} -> Fin n -> Vect n a -> a

216−

217−\end{SaveVerbatim}

218−\useverb{vindeximpty}

219−

220−\noindent

221−Implicit arguments, given in braces \texttt{\{\}} in the type signature, are

222−not given in applications of \texttt{index}; their values can be inferred from

223−the types of the \texttt{Fin n} and \texttt{Vect n a} arguments. Any name which

224−appears in a non-function position in a type signature, but which is otherwise

225−free, will be automatically bound as an implicit argument. Implicit arguments

226−can still be given explicitly in applications, using the syntax

227−\texttt{\{a=value\}} and \texttt{\{n=value\}}, for example:

228−

229−\begin{SaveVerbatim}{vindexexp}

230−

231−index {a=Int} {n=2} fZ (2 :: 3 :: Nil)

232−

233−\end{SaveVerbatim}

234−\useverb{vindexexp}

235−

236−\subsection{Classes}

237−

238−\Idris{} supports overloading in two ways. Firstly, as we have already seen

239−with the constructors of \texttt{List} and \texttt{Vect}, names can be

240−overloaded in an ad-hoc manner and resolved according to the context in which

241−they are used. This is mostly for convenience, to eliminate the need to

242−decorate constructor names in similarly structured data types, and eliminate

243−explicit qualification of ambiguous names where only one is well-typed --- this

244−is especially useful for disambiguating record field names, although records

245−are beyond the scope of this paper.

246−

247−Secondly, \Idris{} implements \remph{classes}, following Haskell's type

248−classes. This allows a more principled approach to overloading --- a class

249−gives a collection of overloaded operations which describe the interface for

250−\remph{instances} of that class. \Idris{} classes follow Haskell~98 type

251−classes, except that multiple parameters are supported, and that classes can be

252−parameterised by \remph{any} value, not just types.

253−Hence we refer to

254−them as \remph{classes} generally, rather than \remph{type classes}

255−specifically.

256−

257−A simple example is the \texttt{Show} class, which is defined in the

258−library and provides an interface for converting values to \texttt{String}s:

259−

260−\begin{SaveVerbatim}{showclass}

261−

262−class Show a where

263− show : a -> String

264−

265−\end{SaveVerbatim}

266−\useverb{showclass}

267−

268−\noindent

269−An instance of a class is defined with an \texttt{instance} declaration, which

270−provides implementations of the function for a specific type. For example:

271−

272−\begin{SaveVerbatim}{shownat}

273−

274−instance Show Nat where

275− show Z = "Z"

276− show (S k) = "s" ++ show k

277−

278−\end{SaveVerbatim}

279−\useverb{shownat}

280−

281−\noindent

282−Instance declarations can themselves have constraints. For example, to define a

283−\texttt{Show} instance for vectors, we need to know that there is a

284−\texttt{Show} instance for the element type, because we are going to use it to

285−convert each element to a \texttt{String}:

286−

287−\begin{SaveVerbatim}{showvec}

288−

289−instance Show a => Show (Vect n a) where

290− show xs = "[" ++ show' xs ++ "]" where

291− show' : Vect n a -> String

292− show' Nil = ""

293− show' (x :: Nil) = show x

294− show' (x :: xs) = show x ++ ", " ++ show' xs

295−

296−\end{SaveVerbatim}

297−\useverb{showvec}

298−

299−\noindent

300−Classes can also be extended. A logical next step from an equality relation

301−\texttt{Eq} for example is to define an ordering relation \texttt{Ord}. We can

302−define an \texttt{Ord} class which inherits methods from \texttt{Eq} as well as

303−defining some of its own:

304−

305−\begin{SaveVerbatim}{ord}

306−

307−data Ordering = LT | EQ | GT

308−

309−\end{SaveVerbatim}

310−\useverb{ord}

311−

312−\begin{SaveVerbatim}{eqord}

313−

314−class Eq a => Ord a where

315− compare : a -> a -> Ordering

316− (<) : a -> a -> Bool

317− -- etc

318−

319−\end{SaveVerbatim}

320−\useverb{eqord}

321−

322−\subsection{Matching on intermediate values}

323−

324−%\subsubsection{\texttt{let} bindings}

325−%

326−%Intermediate values can be calculated using \texttt{let} bindings:

327−%

328−%\begin{SaveVerbatim}{letb}

329−%

330−%mirror : List a -> List a

331−%mirror xs = let xs' = rev xs in

332−% app xs xs'

333−%

334−%\end{SaveVerbatim}

335−%\useverb{letb}

336−%

337−%\noindent

338−%Pattern matching is also supported in \texttt{let} bindings. For example, extracting

339−%fields from a record can be achieved as follows, as well as by pattern matching at the top level:

340−%

341−%\begin{SaveVerbatim}{letp}

342−%

343−%data Person = MkPerson String Int

344−%

345−%showPerson : Person -> String

346−%showPerson p = let MkPerson name age = p in

347−% name ++ " is " ++ show age ++ " years old"

348−%

349−%\end{SaveVerbatim}

350−%\useverb{letp}

351−

352−\subsubsection{\texttt{case} expressions}

353−

354−Intermediate values of \emph{non-dependent} types can be inspected using a

355−\texttt{case} expression. For example, \texttt{list\_lookup} looks up an index

356−in a list, returning \texttt{Nothing} if the index is out of bounds. This can

357−be used to write \texttt{lookup\_default}, which looks up an index and

358−returns a default value if the index is out of bounds:

359−

360−\begin{SaveVerbatim}{listlookup}

361−

362−lookup_default : Nat -> List a -> a -> a

363−lookup_default i xs def = case list_lookup i xs of

364− Nothing => def

365− Just x => x

366−

367−\end{SaveVerbatim}

368−\useverb{listlookup}

369−

370−The \texttt{case} construct is intended for simple analysis of intermediate

371−expressions to avoid the need to write auxiliary functions. It will

372−only work if each branch \emph{matches} a value of the same type, and

373−\emph{returns} a value of the same type.

374−

375−\subsubsection{The \texttt{with} rule}

376−

377−Often, matching is required on the result of an intermediate computation

378−with a dependent type.

379−\Idris{} provides a construct for this, the \texttt{with} rule,

380−inspired by views in \Epigram~\cite{McBride2004a},

381−which takes account of the

382−fact that matching on a value in a dependently-typed language can affect what

383−is known about the forms of other values.

384−%

385−For example, a \texttt{Nat} is either even or odd.

386−If it is even it will

387−be the sum of two equal \texttt{Nat}s. Otherwise, it is the sum of two equal \texttt{Nat}s

388−plus one:

389−

390−\begin{SaveVerbatim}{parity}

391−

392−data Parity : Nat -> Type where

393− even : Parity (n + n)

394− odd : Parity (S (n + n))

395−

396−\end{SaveVerbatim}

397−\useverb{parity}

398−

399−\noindent

400−We say \texttt{Parity} is a \emph{view} of \texttt{Nat}.

401−It has a \emph{covering function} which tests whether

402−it is even or odd and constructs the predicate accordingly:

403−

404−\begin{SaveVerbatim}{parityty}

405−

406−parity : (n:Nat) -> Parity n

407−

408−\end{SaveVerbatim}

409−\useverb{parityty}

410−

411−\noindent

412−Using this, a function which converts a natural number to a list

413−of binary digits (least significant first) is written as follows, using the \texttt{with}

414−rule:

415−

416−\begin{SaveVerbatim}{natToBin}

417−

418−natToBin : Nat -> List Bool

419−natToBin Z = Nil

420−natToBin k with (parity k)

421− natToBin (j + j) | even = False :: natToBin j

422− natToBin (S (j + j)) | odd = True :: natToBin j

423−

424−\end{SaveVerbatim}

425−\useverb{natToBin}

426−

427−\noindent

428−The value of the result of \texttt{parity k} affects the form of \texttt{k},

429−because the result

430−of \texttt{parity k} depends on \texttt{k}.

431−So, as well as the patterns for the result of the

432−intermediate computation (\texttt{even} and \texttt{odd}) right of the

433−\texttt{$\mid$}, the definition also expresses how

434−the results affect the other patterns left of the $\mid$. Note that there is a

435−function in the patterns (\texttt{+}) and repeated occurrences of \texttt{j} ---

436−this is allowed

437−because another argument has determined the form of these patterns. In general,

438−non-linear patterns are allowed \emph{only} when their value is forced by

439−some other argument.

440−

441−

papers/impl-paper/impldtp.texdeleted−159

@@ -1,159 +0,0 @@

1−\RequirePackage{amsmath}

2−\documentclass{jfp1}

3−%\documentclass[acmtoplas]{acmtrans2m}

4−

5−\usepackage[draft]{comments}

6−%\usepackage[final]{comments}

7−% \newcommand{\comment}[2]{[#1: #2]}

8−\newcommand{\khcomment}[1]{\comment{KH}{#1}}

9−\newcommand{\ebcomment}[1]{\comment{EB}{#1}}

10−

11−\usepackage{epsfig}

12−%\usepackage{path}

13−\usepackage{url}

14−\usepackage{fancyvrb}

15−

16−\newenvironment{template}{\sffamily}

17−

18−%\usepackage{graphics,epsfig}

19−\usepackage{stmaryrd}

20−\usepackage{amsmath}

21−

22−\input{./macros.ltx}

23−\input{./library.ltx}

24−

25−\NatPackage

26−\FinPackage

27−

28−\newcounter{per}

29−\setcounter{per}{1}

30−

31−\newcommand{\Ivor}{\textsc{Ivor}}

32−\newcommand{\Idris}{\textsc{Idris}}

33−\newcommand{\IdrisM}{\textsc{Idris}$^-$}

34−\newcommand{\TT}{\textsf{TT}}

35−\newcommand{\TTdev}{\textsf{TT$_{dev}$}}

36−\newcommand{\Funl}{\textsc{Funl}}

37−\newcommand{\Agda}{\textsc{Agda}}

38−\newcommand{\LamPi}{$\lambda_\Pi$}

39−

40−\newcommand{\perule}[1]{\vspace*{0.1cm}\noindent

41−\begin{center}

42−\fbox{

43−\begin{minipage}{7.5cm}\textbf{Rule \theper:} #1\addtocounter{per}{1}

44−\end{minipage}}

45−\end{center}

46−\vspace*{0.1cm}

47−}

48−

49−\newcommand{\mysubsubsection}[1]{

50−\noindent

51−\textbf{#1}

52−}

53−\newcommand{\hdecl}[1]{\texttt{#1}}

54−

55−

56−\title

57−[Idris, a General Purpose Dependently Typed Programming Language]

58−{Idris, a General Purpose Dependently Typed Programming Language:

59−Design and Implementation}

60−%Implementing General Purpose Dependently Typed Programming Languages}

61−%\subtitle{Implementing Domain Specific Languages by Overloading}

62−

63−\author[Edwin Brady]

64−{EDWIN BRADY\\

65−School of Computer Science, University of St Andrews, St Andrews,

66−KY16 9SX, UK}

67−

68−\begin{document}

69−

70−\maketitle

71−

72−\begin{abstract}

73−Many components of a dependently-typed programming language are by now well

74−understood, for example the underlying type theory, type checking, unification and

75−evaluation. How to combine these components into a realistic and usable

76−high-level language is, however, folklore, discovered anew by successive

77−language implementators. In this paper, I describe the implementation of

78−\Idris{}, a new dependently-typed functional programming language.

79−\Idris{} is intended to be a \emph{general purpose} programming language

80−and as such provides high-level concepts such as implicit syntax,

81−type classes and \texttt{do} notation.

82−I describe the high-level language and the underlying type theory, and present

83−a tactic-based method for \emph{elaborating} concrete high-level syntax with

84−implicit arguments and type classes into a fully explicit type theory.

85−Furthermore, I show how this method facilitates the implementation of new

86−high-level language constructs.

87−

88−%I describe the implementation of a dependently typed functional

89−%programming language, \Idris{}. Much has been written about various

90−%aspects of dependently typed language implementation (e.g. checking

91−%dependent types, unification, optimisation) but nothing yet about how

92−%to bring it all together into a complete, practical, usable tool. This paper

93−%attempts to do so. In particular, I explain what is needed to turn

94−%concrete syntax with implicit arguments into fully elaborated type

95−%theory, using unification and a tactic engine.

96−\end{abstract}

97−

98−

99−%\category{D.3.2}{Programming Languages}{Language

100−% Classifications}[Applicative (functional) Languages]

101−%\category{D.3.4}{Programming Languages}{Processors}[Compilers]

102−%\terms{Languages, Verification, Performance}

103−%\keywords{Dependent Types, Typechecking}

104−

105−

106−%\begin{bottomstuff}

107−%Author's address: Edwin Brady, School of Computer Science, North Haugh, St Andrews,

108−%KY16 9SX

109−%\end{bottomstuff}

110−

111−\input{intro.tex}

112−

113−%\input{overview.tex}

114−

115−\input{hll.tex}

116−

117−\input{typechecking.tex}

118−

119−%\input{proofstate.tex}

120−

121−\input{elaboration.tex}

122−

123−\input{delab.tex}

124−

125−%\input{compiling.tex}

126−

127−%\input{syntax.tex}

128−

129−\input{conclusions.tex}

130−

131−\section*{Acknowledgements}

132−

133−This work was funded by the Scottish Informatics and Computer Science Alliance

134−(SICSA) and by EU Framework 7 Project No. 248828 (ADVANCE). My thanks to

135−Philip H\"{o}lzenspies, Kevin Hammond, Vilhelm Sj\"{o}berg, Falko Spiller

136−and Nathan Collins

137−for their comments on an earlier draft of this paper, and to the anonymous

138−referees for their many insightful and constructive comments.

139−

140−\bibliographystyle{jfp}

141−\bibliography{library.bib}

142−

143−\appendix

144−

145−%\section{TODOs}

146−%\listoftodos{}

147−

148−%\section{Elaboration meta-operations}

149−

150−%It's possible that it would be useful to have a quick reference of meta-operations

151−%used by the elaborator here.

152−

153−%They are: $\ttinterp{\cdot}$, $\MO{Elab}$, $\MO{TTDecl}$,

154−%$\MO{NewProof}$, $\MO{NewTerm}$,

155−%$\MO{Term}$, $\MO{Type}$, $\MO{Context}$, $\MO{Patterns}$, $\MO{Lift}$, $\MO{Expand}$.

156−

157−%\input{code}

158−

159−\end{document}

papers/impl-paper/intro.texdeleted−196

@@ -1,196 +0,0 @@

1−\section{Introduction}

2−

3−Dependently-typed programming languages, such as Agda \cite{norell2007thesis}

4−and Coq \cite{Bertot2004}, have emerged in recent years as a promising approach

5−to ensuring the correctness of software. Type checking ensures a program has

6−the intended meaning; \emph{dependent} types, where types may be predicated

7−on values, allow a programmer to give a program a more precise type and

8−hence have increased confidence of its correctness.

9−The \Idris{} language

10−\cite{Brady2011a} aims to take this idea further, by providing support for

11−verification of \emph{general purpose} systems software. In contrast to Agda and Coq,

12−which have arisen from the theorem proving community, \Idris{} takes Haskell as

13−its main influence. Recent Haskell extensions such as GADTs and type families have

14−given some of the power of dependent types to Haskell programmers. In the short

15−term this approach has a clear advantage, since it builds on a mature language

16−infrastructure with extensive library support.

17−Taking a longer term view, however,

18−these extensions are inherently limited in that they are required to maintain

19−backwards compatibility with existing Haskell implementations. \Idris{}, being a new

20−language, has no such limitation, essentially asking the question:

21−

22−\begin{center}

23−\emph{``What if Haskell had \emph{full} dependent types?''}

24−\end{center}

25−

26−By \emph{full} dependent types, we mean that there is no restriction on which

27−values may appear in types. It is important for the sake of usability of a

28−programming language to provide a notation which allows programmers to express

29−high-level concepts in a natural way. Taking Haskell as a starting point means

30−that \Idris{} offers a variety of high-level structures such as type

31−classes, \texttt{do}-notation, primitive types and monadic I/O, for example.

32−Furthermore, a goal of \Idris{} is to support high-level domain-specific

33−language implementation, providing appropriate notation for \emph{domain

34−experts} and \emph{systems programmers}, who should not be required to be type

35−theorists in order to solve programming problems. Nevertheless, it is

36−important for the sake of correctness of the language implementation to have a

37−well-defined core language with well-understood meta-theory \cite{Altenkirch2010}.

38−How can we achieve both of these goals?

39−

40−This paper describes a method for elaborating a high-level dependently-typed

41−functional programming language to a low-level core based on dependent

42−type theory. The method involves building an elaboration monad which captures

43−the state of incomplete programs and a collection of \emph{tactics} used by the

44−machine to refine programs, directed by high-level syntax. As we shall see,

45−this method allows higher level language constructs to be elaborated in a

46−straightforward manner, without compromising the simplicity of the underlying

47−type theory.

48−

49−\subsection{Contributions}

50−

51−A dependently-typed programming language relies on several components, many of

52−which are now well understood. For example, we rely on a type checker for

53−the core type theory \cite{Chapman2005epigram,loh2010tutorial}, a

54−unification algorithm \cite{Miller1992} and an evaluator. However, it is less

55−well understood how to combine these components effectively into a practical

56−programming language.

57−

58−The primary contribution of this paper is a tactic-based method for translating

59−programs in a high-level dependently-typed programming language to a small core

60−type theory, \TT{}, based on UTT \cite{luo1994}. The paper describes the

61−structure of an elaboration monad capturing proof and system state, and

62−introduces a collection of \remph{tactics} which the machine uses to

63−manipulate incomplete programs. Secondly, the paper gives a detailed

64−description of the core type theory used by \Idris{}, including a full

65−description of the typing rules. Finally, through describing the specific

66−tactics, the paper shows how to extend \Idris{} with higher level features.

67−While we apply these ideas to \Idris{} specifically, the method for term

68−construction is equally applicable to other typed programming languages, and

69−indeed the tactics themselves are applicable to any high-level language which

70−can be explained in terms of \TT{}.

71−

72−\subsection{Outline}

73−

74−Translating an \Idris{} source program to an executable proceeds through several

75−phases, illustrated below:

76−

77−\begin{center}

78−\DM{

79−\mbox{\Idris{}}

80−\;

81−\xrightarrow{\mathrm{ (desugaring) }}

82−\;

83−\mbox{\IdrisM{}}

84−\;

85−\xrightarrow{\mathrm{ (elaboration) }}

86−\;

87−\mbox{\TT{}}

88−\;

89−\xrightarrow{\mathrm{ (compilation) }}

90−\;

91−\mbox{Executable}

92−}

93−\end{center}

94−

95−\noindent

96−The main focus of this paper is the elaboration phase, which translates

97−a desugared language \IdrisM{} into a core language \TT{}. In order to put

98−this into its proper context, I give an overview of the high-level language

99−\Idris{} in Section \ref{sect:hll} and explain the core language \TT{} and

100−its typing rules in Section \ref{sect:typechecking};

101−Section \ref{sect:elaboration} describes the elaboration process itself,

102−beginning with a tactic-based system for constructing

103−\TT{} programs, then introducing the desugared language \IdrisM{} and

104−showing how this is translated into \TT{} using tactics;

105−Section

106−\ref{sect:delab} describes the process for translating \TT{} back to \Idris{}

107−and properties of the translation; finally,

108−Section \ref{sect:related} discusses related work and Section \ref{sect:conclusion}

109−concludes.

110−

111−\subsection{Typographical conventions}

112−

113−This paper presents programs in two different but related languages: a high-level

114−language \Idris{} intended for programmers, and a low-level language \TT{} to

115−which \Idris{} is elaborated. We distinguish these languages typographically as

116−follows:

117−

118−\begin{itemize}

119−\item \Idris{} programs are written in \texttt{typewriter} font, as they are written

120−in a conventional text editor. We use \texttt{e$_i$} to stand for non-terminal

121−expressions.

122−\item \TT{} programs are written in mathematical notation, with names arising

123−from \Idris{} expressions written in \texttt{typewriter} font. We use vector notation

124−$\te$ to stand for sequences of expressions.

125−\end{itemize}

126−

127−Additionally, we describe the translation from \Idris{} to \TT{} in the form

128−of \emph{meta-operations}, which in practice are Haskell programs. Meta-operations

129−are operations on \Idris{} and \TT{} syntax, and are identified by their names being

130−in $\MO{SmallCaps}$.

131−

132−\subsection{Elaboration Example}

133−

134−A simple example of an \Idris{}

135−program is the following, which adds corresponding

136−elements of vectors of the same length:

137−

138−\begin{SaveVerbatim}{vadd}

139−

140−vAdd : Num a => Vect n a -> Vect n a -> Vect n a

141−vAdd Nil Nil = Nil

142−vAdd (x :: xs) (y :: ys) = x + y :: vAdd xs ys

143−

144−\end{SaveVerbatim}

145−\useverb{vadd}

146−

147−\noindent

148−This illustrates some basic features of \Idris{}:

149−

150−\begin{itemize}

151−\item Functions are defined by pattern matching, with a top-level type signature.

152−Names which are free in the type signature (\texttt{a} and \texttt{n}) here

153−are implicitly bound.

154−\item The type system ensures that both input vectors are the same length (\texttt{n})

155−and have the same element type (\texttt{a}), and that the element type and length

156−are preserved in the output vector.

157−\item Functions can be overloaded using \remph{classes}. Here, the element type

158−of the vector \texttt{a} must be numeric and therefore supports the \texttt{+} operator.

159−\item Unlike Haskell, a single colon is used for type signatures, and a double

160−colon for the cons operator, emphasising the importance of types.

161−\end{itemize}

162−

163−\noindent

164−\Idris{} programs elaborate into a small core language, \TT{}, which is a $\lambda$-calculus

165−with dependent types, augmented with algebraic data types and pattern matching.

166−\TT{} programs are fully explicitly typed, including the names \texttt{a} and \texttt{n}

167−in the type signature, and the names bound in each pattern match clause.

168−Classes are also made explicit.

169−The \TT{} translation of \texttt{vAdd} is:

170−

171−\DM{

172−\AR{

173−\FN{vAdd} \Hab(\va\Hab\Type)\to(\vn\Hab\Nat)\to\TC{Num}\;\va\to

174− \Vect\;\vn\;\va\to\Vect\;\vn\;\va\to\Vect\;\vn\;\va\\

175−\RW{var}\;\va\Hab\Type,\;\vc\Hab\TC{Num}\;\va\SC\\

176−\hg\FN{vAdd} \; \va \; \Z \; \vc \; (\DC{Nil}\;\va) \; (\DC{Nil}\;\va) \;

177−\cq\;\DC{Nil}\;\va \\

178−\RW{var}\;\AR{

179−\va\Hab\Type,\;\vk\Hab\Nat,\;\vc\Hab\TC{Num}\;\va,\\

180−\vx\Hab\va,\;\vxs\Hab\Vect\;\vk\;\va,\;

181−\vy\Hab\va,\;\vys\Hab\Vect\;\vk\;\va

182−\SC

183−\\

184−\FN{vAdd} \; \va \; (\suc\;\vk) \; \vc

185− \; ((\DC{::})\;\va\;\vk\;\vx\;\vxs)

186− \; ((\DC{::})\;\va\;\vk\;\vy\;\vys)

187− \\

188− \hg\hg\cq\:((\DC{::})\;\va\;\vk\;((+)\;\vc\;\vx\;\vy)\; (\FN{vAdd}\;\va\;\vk\;\vc\;\vxs\;\vys))

189−}

190−}

191−}

192−

193−\noindent

194−The rest of this paper describes \Idris{} and \TT{}, and systematically explains

195−how to translate from one to the other.

196−

papers/impl-paper/jfp.bstdeleted−1316

@@ -1,1316 +0,0 @@

1−% CUP Journal of Functional Programming bibliography style

2−% v1.0, released 22nd May 1995

4−

5−% This BibTeX 0.99 style file is intended for documents that use the

6−% author-date citation system. It should be used in conjunction with the

7−% authordate1-4.sty (or equivalent) LaTeX style-option.

8−%

9−% In deciding on the bibliography layout to be implemented, the following

10−% works have been consulted:

11−% 1. British Standard 5605: "Citing publications by bibliographic

12−% references", 1978.

13−% 2. British Standard 1629: "Bibliographic references", 1976.

14−% (Note: There is now a 1989 edition.)

15−% 3. "Copy-editing" by Judith Butcher, Cambridge University Press, 1981.

16−% 4. "The Oxford Dictionary for Writers and Editors", Oxford University

17−% Press, 1981 (for abbreviations).

18−% 5. "The Chicago Manual of Style", Chicago University Press, 1982.

19−%

20−% Discretion has been used in certain matters. In particular:

21−% - Titles are italic except when there is a "contribution title" and

22−% a "main publication title", in which case the "contribution title"

23−% is roman while the "main publication title" is italic.

24−% - When there is a PUBLISHER, it is assumed that ADDRESS contains "place of

25−% publication"; output is of the form "place-of-publication: publisher".

26−% When there is an ORGANIZATION as well as a PUBLISHER, output is of the

27−% form "place-of-publication: publisher, for organization". Otherwise,

28−% it is assumed that ADDRESS is a postal address, and output is of the

29−% form "institution, address", "organization, address", "school, address"

30−% or "howpublished, address".

31−% - If there is a MONTH but no VOLUME or NUMBER for a journal-article, the

32−% MONTH is used on the assumption that it contains information that is

33−% equivalent to VOLUME or NUMBER. MONTH is ignored for other documents

34−% that have a PUBLISHER, but output after YEAR for anything else.

35−% - When CHAPTER and/or PAGES are specified with INBOOK, it is assumed that

36−% these fields are being used to pick out particular pages of interest

37−% (as an alternative to using the optional [...] argument of \cite);

38−% the information is put at the very end of the entry, in line with BS 1629.

39−% When CHAPTER and/or PAGES are specified for INCOLLECTION or INPROCEEDINGS,

40−% it is assumed that the fields are being used to specify the location of

41−% the part/article of interest; the information is put before the

42−% BOOKTITLE, in line with Chicago's treatment of "parts" and "chapters".

43−% - Since "volume" can be used in various ways (see page 219 of Butcher),

44−% this file assumes that, when there is a SERIES, any VOLUME and NUMBER

45−% refer to position in the SERIES (i.e. Butcher's meaning 4).

46−% If there is a VOLUME but no SERIES, it is assumed that VOLUME refers

47−% to a volume within a particular work (i.e. Butcher's meaning 1, 2 or 3).

48−% For INPROCEEDINGS and INCOLLECTION, this information goes after the

49−% BOOKTITLE. (If you prefer to have volume information before EDITOR,

50−% as on page 449 of Chicago, you can set TYPE = "Vol." with INCOLLECTION.)

51−%

52−% This file differs from authordate1.bst, authordate3.bst and

53−% authordate4.bst in that:

54−% - Titles of journals, articles and boooks are "downstyle". Apart from the

55−% first character, and the first character following : and white space,

56−% uppercase letters are converted to lowercase unless protected by {}.

57−% - Author's and editor's names are in roman.

58−%

59−% The combination of authordate2.bst and authordate1-4.sty allows citations

60−% of the form \shortcite{bloggs-60} as well as the usual \cite{bloggs-60}.

61−% When

62−% ... \cite{bloggs-60} ... \shortcite{bloggs-60} ...

63−% appears in the input file,

64−% ... (Bloggs, 1960) ... (1960) ...

65−% appears in the final document.

66−%

67−% This file was developed from apalike.bst. It also uses code taken from

68−% acm.bst, aaai-named.bst, btxbst.doc, ieeetr.bst and siam.bst.

69−%

70−% David Rhead

71−% Cripps Computing Centre

72−% Nottingham University

73−% March 1990

74−%

75−

76−ENTRY

77− { address

78− author

79− booktitle

80− chapter

81− edition

82− editor

83− howpublished

84− institution

85− journal

86− key

87− month

88− note

89− number

90− organization

91− pages

92− publisher

93− school

94− series

95− title

96− type

97− volume

98− year

99− }

100− {}

101− { label extra.label sort.label }

102−

103−INTEGERS { output.state before.all mid.sentence after.sentence after.block }

104−

105−FUNCTION {init.state.consts}

106−{ #0 'before.all :=

107− #1 'mid.sentence :=

108− #2 'after.sentence :=

109− #3 'after.block :=

110−}

111−

112−STRINGS { s t }

113−

114−FUNCTION {output.nonnull}

115−{ 's :=

116− output.state mid.sentence =

117− { ", " * write$ }

118− { output.state after.block =

119− { add.period$ write$

120− newline$

121− "\newblock " write$

122− }

123− { output.state before.all =

124− 'write$

125− { add.period$ " " * write$ }

126− if$

127− }

128− if$

129− mid.sentence 'output.state :=

130− }

131− if$

132− s

133−}

134−

135−FUNCTION {output}

136−{ duplicate$ empty$

137− 'pop$

138− 'output.nonnull

139− if$

140−}

141−

142−FUNCTION {output.check}

143−{ 't :=

144− duplicate$ empty$

145− { pop$ "empty " t * " in " * cite$ * warning$ }

146− 'output.nonnull

147− if$

148−}

149−

150−FUNCTION {output.year.month.check}

151−{ year empty$

152− { "empty year in " cite$ * warning$ }

153− { add.period$ write$

154− month empty$

155− { " (" year * extra.label * ")" * % ajw

156− after.sentence 'output.state :=

157− }

158− { " " year * extra.label * " (" * month * ")." *

159− after.sentence 'output.state :=

160− }

161− if$

162− }

163− if$

164−}

165−

166−FUNCTION {output.year.check}

167−{ year empty$

168− { "empty year in " cite$ * warning$ }

169− { add.period$ write$

170− " (" year * extra.label * ")" * % ajw

171− after.sentence 'output.state :=

172− }

173− if$

174−}

175−

176−FUNCTION {output.bibitem}

177−{ newline$

178− "\bibitem[" write$

179− label write$

180− "]{" write$

181− cite$ write$

182− "}" write$

183− newline$

184− ""

185− before.all 'output.state :=

186−}

187−

188−FUNCTION {fin.entry}

189−{ add.period$

190− write$

191− newline$

192−}

193−

194−FUNCTION {new.block}

195−{ output.state before.all =

196− 'skip$

197− { after.block 'output.state := }

198− if$

199−}

200−

201−FUNCTION {new.sentence}

202−{ output.state after.block =

203− 'skip$

204− { output.state before.all =

205− 'skip$

206− { after.sentence 'output.state := }

207− if$

208− }

209− if$

210−}

211−

212−FUNCTION {not}

213−{ { #0 }

214− { #1 }

215− if$

216−}

217−

218−FUNCTION {and}

219−{ 'skip$

220− { pop$ #0 }

221− if$

222−}

223−

224−FUNCTION {or}

225−{ { pop$ #1 }

226− 'skip$

227− if$

228−}

229−

230−FUNCTION {new.block.checkb}

231−{ empty$

232− swap$ empty$

233− and

234− 'skip$

235− 'new.block

236− if$

237−}

238−

239−FUNCTION {field.or.null}

240−{ duplicate$ empty$

241− { pop$ "" }

242− 'skip$

243− if$

244−}

245−

246−FUNCTION {boldface}

247−{ duplicate$ empty$

248− { pop$ "" }

249− { "{\bf " swap$ * "}" * }

250− if$

251−}

252−

253−FUNCTION {emphasize}

254−{ duplicate$ empty$

255− { pop$ "" }

256− { "{\em " swap$ * "}" * }

257− if$

258−}

259−

260−INTEGERS { nameptr namesleft numnames }

261−

262−

263−FUNCTION {format.names}

264−{ 's :=

265− #1 'nameptr :=

266− s num.names$ 'numnames :=

267− numnames 'namesleft :=

268− { namesleft #0 > }

269− { s nameptr "{vv~}{ll}{, jj}{, ff}" format.name$ 't :=

270− nameptr #1 >

271− { namesleft #1 >

272− { ", " * t * }

273− { t "others" =

274− { ", {\em et~al.\ }\relax" * }

275− { ", \& " * t * } % Butcher, pages

276− if$ % 186-189.

277− }

278− if$

279− }

280− 't

281− if$

282− nameptr #1 + 'nameptr :=

283− namesleft #1 - 'namesleft :=

284− }

285− while$

286−}

287−

288−FUNCTION {format.authors}

289−{ author empty$

290− { "" }

291− { author format.names }

292− if$

293−}

294−

295−FUNCTION {format.key}

296−{ empty$

297− { key field.or.null }

298− { "" }

299− if$

300−}

301−

302−FUNCTION {format.editors}

303−{ editor empty$

304− { "" }

305− { editor format.names

306− editor num.names$ #1 > % Use ODWE abbrevs.

307− { " (eds)" * } % to avoid

308− { " (ed)" * } % ambiguity between

309− if$ % "editor" and

310− } % "edition".

311− if$

312−}

313−

314−FUNCTION {format.title} % Howells example

315−{ title empty$ % in BS 5605 comes

316− { "" } % out wrong because

317− { title "t" change.case$ } % Patashnik

318− if$ % capitalizes

319−} % after a colon.

320−

321−FUNCTION {n.dashify}

322−{ 't :=

323− ""

324− { t empty$ not }

325− { t #1 #1 substring$ "-" =

326− { t #1 #2 substring$ "--" = not

327− { "--" *

328− t #2 global.max$ substring$ 't :=

329− }

330− { { t #1 #1 substring$ "-" = }

331− { "-" *

332− t #2 global.max$ substring$ 't :=

333− }

334− while$

335− }

336− if$

337− }

338− { t #1 #1 substring$ *

339− t #2 global.max$ substring$ 't :=

340− }

341− if$

342− }

343− while$

344−}

345−

346−FUNCTION {format.btitle}

347−{ title empty$

348− { "" }

349− { title "t" change.case$ emphasize }

350− if$

351−}

352−

353−FUNCTION {tie.or.space.connect}

354−{ duplicate$ text.length$ #3 <

355− { "~" }

356− { " " }

357− if$

358− swap$ * *

359−}

360−

361−FUNCTION {either.or.check}

362−{ empty$

363− 'pop$

364− { "can't use both " swap$ * " fields in " * cite$ * warning$ }

365− if$

366−}

367−

368−INTEGERS { multiresult }

369−

370−FUNCTION {multi.page.check}

371−{ 't :=

372− #0 'multiresult :=

373− { multiresult not

374− t empty$ not

375− and

376− }

377− { t #1 #1 substring$

378− duplicate$ "-" =

379− swap$ duplicate$ "," =

380− swap$ "+" =

381− or or

382− { #1 'multiresult := }

383− { t #2 global.max$ substring$ 't := }

384− if$

385− }

386− while$

387− multiresult

388−}

389−

390−FUNCTION {format.numberinseries}

391−{ number empty$

392− { "" }

393− { number multi.page.check

394− { ", nos. " number n.dashify tie.or.space.connect }

395− { ", no. " number tie.or.space.connect }

396− if$

397− }

398− if$

399−}

400−

401−FUNCTION {booklike.series.volume.number} % Chicago, pages

402−{ series empty$ % 450-451.

403− { volume empty$

404− { " " }

405− { " Vol. " volume * }

406− if$

407− }

408− {

409− volume empty$

410− { number empty$

411− { series }

412− { series format.numberinseries * }

413− if$

414− }

415− { number empty$

416− { series ", vol. " volume * * }

417− { series ", vol. " * volume * format.numberinseries * }

418− if$

419− }

420− if$

421− }

422− if$

423−}

424−

425−FUNCTION {incollectionlike.series.volume.number}

426−{ series empty$

427− { volume empty$

428− { " " }

429− { " vol. " volume * }

430− if$

431− }

432− { new.block

433− volume empty$

434− { number empty$

435− { series }

436− { series format.numberinseries * }

437− if$

438− }

439− { number empty$

440− { series ", vol. " volume * * }

441− { series ", vol. " * volume * format.numberinseries * }

442− if$

443− }

444− if$

445− }

446− if$

447−}

448−

449−FUNCTION {format.edition}

450−{ edition empty$

451− { "" }

452− { output.state mid.sentence =

453− { edition "l" change.case$ " edn." * }

454− { edition "t" change.case$ " edn." * }

455− if$

456− }

457− if$

458−}

459−

460−FUNCTION {format.pages}

461−{ pages empty$

462− { "" }

463− { pages multi.page.check

464− { "" pages n.dashify tie.or.space.connect }

465− { "" pages tie.or.space.connect }

466− if$

467− }

468− if$

469−}

470−

471−FUNCTION {format.pagesinbook} % By the time the

472−{ pages empty$ % reader has read

473− { "" } % address, pub'r,

474− { pages multi.page.check % note (where the

475− { "Pages " pages n.dashify tie.or.space.connect } % note may end with

476− { "Page " pages tie.or.space.connect } % numbers), s/he

477− if$ % may not recognise

478− } % a number-range as

479− if$ % meaning pages.

480−} % Avoid ambiguity

481− % (Butcher, p.181).

482−

483−FUNCTION {format.vol.num.date.pages}

484−{ volume empty$

485− { month empty$

486− { "" }

487− { month }

488− if$

489− }

490− { volume boldface field.or.null

491− number empty$

492− { month empty$

493− 'skip$

494− { "(" month * ")" * * }

495− if$

496− }

497− { "(" number * ")" * *

498− volume empty$

499− { "there's a number but no volume in " cite$ * warning$ }

500− 'skip$

501− if$

502− }

503− if$

504− }

505− if$

506− pages empty$

507− 'skip$

508− { duplicate$ empty$

509− { pop$ format.pages }

510− { ", " * pages n.dashify * }

511− if$

512− }

513− if$

514−}

515−

516−FUNCTION {format.chapter.pages.inbook}

517−{ chapter empty$

518− 'format.pagesinbook

519− { type empty$

520− { "Chap." }

521− { type }

522− if$

523− chapter tie.or.space.connect

524− pages empty$

525− 'skip$

526− { ", " * format.pagesinbook "l" change.case$ * }

527− if$

528− }

529− if$

530−}

531−

532−FUNCTION {format.chapter.pages.incoll}

533−{ chapter empty$

534− { pages empty$

535− { " " } % ajw

536− { "{\em " format.pagesinbook " of:} " * * }

537− if$

538− }

539− { type empty$

540− { "{\em Chap. " chapter * }

541− { "{\em " type * " " * chapter * }

542− if$

543− pages empty$

544− { " of:} " * }

545− { ", " * format.pagesinbook "l" change.case$ " of:} " * * }

546− if$

547− }

548− if$

549−}

550−

551−FUNCTION {format.in.ed.booktitle} % Achieves effect

552−{ booktitle empty$ % shown in 16.51

553− { "" } % of Chicago, at

554− { editor empty$ % expense of not

555− { format.chapter.pages.incoll % achieving effects

556− booktitle "t" change.case$ emphasize * } % shown in 16.50

557− { format.chapter.pages.incoll % of Chicago, on

558− format.editors * ", " * % page 189 of

559− booktitle "t" change.case$ emphasize * } % Butcher and in

560− if$ % 4.4 of BS 1629.

561− }

562− if$

563−}

564−

565−FUNCTION {format.thesis.type}

566−{ type empty$

567− 'skip$

568− { pop$

569− type "t" change.case$

570− }

571− if$

572−}

573−

574−FUNCTION {format.tr.number}

575−{ type empty$

576− { "Tech. rept." } % ODWE abbrevs.

577− 'type

578− if$

579− number empty$

580− { "t" change.case$ }

581− { number tie.or.space.connect }

582− if$

583−}

584−

585−FUNCTION {format.addr.pub}

586−{ publisher empty$

587− { "" }

588− { address empty$

589− { "" }

590− { address ": " * }

591− if$

592− publisher *

593− }

594− if$

595−}

596−

597−FUNCTION {format.addr.pub.org} % If there's an

598−{ address empty$ % an organization

599− { publisher * ", for " * organization * } % and a publisher

600− { address ": " * publisher * ", for " * organization * } % too.

601− if$

602−}

603−

604−FUNCTION {format.addr.inst}

605−{ address empty$

606− { institution empty$

607− { "" }

608− { institution }

609− if$

610− }

611− { institution empty$

612− { "" }

613− { institution ", " * }

614− if$

615− address *

616− }

617− if$

618−}

619−

620−FUNCTION {format.addr.org}

621−{ address empty$

622− { organization empty$

623− { "" }

624− { organization }

625− if$

626− }

627− { organization empty$

628− { "" }

629− { organization ", " * }

630− if$

631− address *

632− }

633− if$

634−}

635−

636−FUNCTION {format.article.crossref}

637−{ "{\em In:}"

638− " \cite{" * crossref * "}" *

639−}

640−

641−FUNCTION {format.book.crossref}

642−{ volume empty$

643− { "empty volume in " cite$ * "'s crossref of " * crossref * warning$

644− "{\em In:}"

645− }

646− { " Vol." volume tie.or.space.connect

647− " of " *

648− }

649− if$

650− "\cite{" * crossref * "}" *

651−}

652−

653−FUNCTION {format.incoll.inproc.crossref}

654−{ "{\em In:}"

655− " \cite{" * crossref * "}" *

656−}

657−

658−FUNCTION {article}

659−{ output.bibitem

660− format.authors "author" output.check

661− author format.key output

662− output.year.check

663− new.block

664− format.title "title" output.check

665− new.block

666− crossref missing$

667− { journal "t" change.case$ emphasize

668− "journal" output.check

669− format.vol.num.date.pages output

670− }

671− { format.article.crossref output.nonnull

672− format.pages output

673− }

674− if$

675− new.block

676− note output

677− fin.entry

678−}

679−

680−FUNCTION {book}

681−{ output.bibitem

682− author empty$

683− { format.editors "author and editor" output.check

684− editor format.key output

685− }

686− { format.authors output.nonnull

687− crossref missing$

688− { "author and editor" editor either.or.check }

689− 'skip$

690− if$

691− }

692− if$

693− output.year.check

694− new.block

695− format.btitle "title" output.check

696− crossref missing$

697− { new.sentence

698− format.edition output

699− new.block

700− booklike.series.volume.number output

701− new.block

702− format.addr.pub "publisher" output.check

703− }

704− { new.block

705− format.book.crossref output.nonnull

706− }

707− if$

708− new.block

709− note output

710− fin.entry

711−}

712−

713−FUNCTION {booklet}

714−{ output.bibitem

715− format.authors output

716− author format.key output

717− output.year.month.check

718− new.block

719− format.btitle "title" output.check

720− new.block

721− howpublished output

722− address output

723− new.block

724− note output

725− fin.entry

726−}

727−

728−FUNCTION {inbook}

729−{ output.bibitem

730− author empty$

731− { format.editors "author and editor" output.check

732− editor format.key output

733− }

734− { format.authors output.nonnull

735− crossref missing$

736− { "author and editor" editor either.or.check }

737− 'skip$

738− if$

739− }

740− if$

741− output.year.check

742− new.block

743− format.btitle "title" output.check

744− crossref missing$

745− { new.sentence

746− format.edition output

747− new.block

748− booklike.series.volume.number output

749− new.block

750− format.addr.pub "publisher" output.check

751− }

752− { new.block

753− format.book.crossref output.nonnull

754− }

755− if$

756− new.block

757− note output

758− new.block % BS 1629 (rather

759− format.chapter.pages.inbook "chapter and pages" output.check

760− fin.entry % than Chicago,

761−} % p. 451)

762−

763−FUNCTION {incollection}

764−{ output.bibitem

765− author empty$

766− { format.editors "editor" output.check

767− editor format.key output }

768− { format.authors "author" output.check

769− author format.key output }

770− if$

771− output.year.check

772− new.block

773− format.title "title" output.check

774− new.block

775− crossref missing$ % Chapter and/or

776− { format.in.ed.booktitle output % page numbers can

777− format.edition output % come out via this

778− incollectionlike.series.volume.number output % route, too.

779− new.block

780− format.addr.pub "publisher" output.check

781− }

782− { format.incoll.inproc.crossref output.nonnull

783− new.block

784− }

785− if$

786− new.block

787− note output

788− fin.entry

789−}

790−

791−FUNCTION {inproceedings}

792−{ output.bibitem

793− format.authors "author" output.check

794− author format.key output

795− publisher empty$

796− { output.year.month.check }

797− { output.year.check }

798− if$

799− new.block

800− format.title "title" output.check

801− new.block

802− crossref missing$

803− { format.in.ed.booktitle "booktitle" output.check

804− incollectionlike.series.volume.number output

805− new.block

806− publisher empty$

807− {

808− organization empty$

809− 'skip$

810− { format.addr.org output }

811− if$

812− }

813− {

814− organization empty$

815− { format.addr.pub output }

816− { format.addr.pub.org output }

817− if$

818− }

819− if$

820− }

821− { format.incoll.inproc.crossref output.nonnull

822− }

823− if$

824− new.block

825− note output

826− fin.entry

827−}

828−

829−FUNCTION {conference} { inproceedings }

830−

831−FUNCTION {manual}

832−{ output.bibitem

833− format.authors output

834− author format.key output

835− output.year.month.check

836− new.block

837− format.btitle "title" output.check

838− new.sentence

839− format.edition output

840− new.block

841− organization address new.block.checkb

842− format.addr.org output

843− new.block

844− note output

845− fin.entry

846−}

847−

848−FUNCTION {mastersthesis}

849−{ output.bibitem

850− format.authors "author" output.check

851− author format.key output

852− output.year.month.check

853− new.block

854− format.btitle "title" output.check

855− new.block

856− "M.Phil. thesis" format.thesis.type output.nonnull % ODWE abbrev.

857− school "school" output.check

858− address output

859− new.block

860− note output

861− fin.entry

862−}

863−

864−FUNCTION {misc}

865−{ output.bibitem

866− format.authors output

867− author format.key output

868− output.year.month.check

869− new.block

870− format.btitle output

871− new.block

872− howpublished output

873− new.block

874− note output

875− fin.entry

876−}

877−

878−FUNCTION {phdthesis}

879−{ output.bibitem

880− format.authors "author" output.check

881− author format.key output

882− output.year.month.check

883− new.block

884− format.btitle "title" output.check

885− new.block

886− "Ph.D. thesis" format.thesis.type output.nonnull % Butcher,

887− school "school" output.check % page 174.

888− address output

889− new.block

890− note output

891− fin.entry

892−}

893−

894−FUNCTION {proceedings}

895−{ output.bibitem

896− format.editors "author and editor" output.check

897− editor format.key output

898− publisher empty$

899− { output.year.month.check }

900− { output.year.check }

901− if$

902− new.block

903− format.btitle "title" output.check

904− new.block

905− booklike.series.volume.number output

906− new.block

907− publisher empty$

908− {

909− organization empty$

910− 'skip$

911− { format.addr.org output }

912− if$

913− }

914− {

915− organization empty$

916− { format.addr.pub output }

917− { format.addr.pub.org output }

918− if$

919− }

920− if$

921− new.block

922− note output

923− fin.entry

924−}

925−

926−FUNCTION {techreport}

927−{ output.bibitem

928− format.authors "author" output.check

929− author format.key output

930− output.year.month.check

931− new.block

932− format.btitle "title" output.check

933− new.block

934− format.tr.number output.nonnull

935− new.sentence

936− format.addr.inst "institution" output.check

937− new.block

938− note output

939− fin.entry

940−}

941−

942−FUNCTION {unpublished}

943−{ output.bibitem

944− format.authors "author" output.check

945− author format.key output

946− output.year.month.check

947− new.block

948− format.btitle "title" output.check

949− new.block

950− note "note" output.check

951− fin.entry

952−}

953−

954−FUNCTION {default.type} { misc }

955−

956−MACRO {jan} {"Jan."} % ODWE, "months", &

957− % Chicago, p. 383.

958−MACRO {feb} {"Feb."}

959−

960−MACRO {mar} {"Mar."}

961−

962−MACRO {apr} {"Apr."}

963−

964−MACRO {may} {"May"}

965−

966−MACRO {jun} {"June"}

967−

968−MACRO {jul} {"July"}

969−

970−MACRO {aug} {"Aug."}

971−

972−MACRO {sep} {"Sept."}

973−

974−MACRO {oct} {"Oct."}

975−

976−MACRO {nov} {"Nov."}

977−

978−MACRO {dec} {"Dec."}

979−

980−MACRO {acmcs} {"ACM Computing Surveys"}

981−

982−MACRO {acta} {"Acta Informatica"}

983−

984−MACRO {cacm} {"Communications of the ACM"}

985−

986−MACRO {ibmjrd} {"IBM Journal of Research and Development"}

987−

988−MACRO {ibmsj} {"IBM Systems Journal"}

989−

990−MACRO {ieeese} {"IEEE Transactions on Software Engineering"}

991−

992−MACRO {ieeetc} {"IEEE Transactions on Computers"}

993−

994−MACRO {ieeetcad}

995− {"IEEE Transactions on Computer-Aided Design of Integrated Circuits"}

996−

997−MACRO {ipl} {"Information Processing Letters"}

998−

999−MACRO {jacm} {"Journal of the ACM"}

1000−

1001−MACRO {jcss} {"Journal of Computer and System Sciences"}

1002−

1003−MACRO {scp} {"Science of Computer Programming"}

1004−

1005−MACRO {sicomp} {"SIAM Journal on Computing"}

1006−

1007−MACRO {tocs} {"ACM Transactions on Computer Systems"}

1008−

1009−MACRO {tods} {"ACM Transactions on Database Systems"}

1010−

1011−MACRO {tog} {"ACM Transactions on Graphics"}

1012−

1013−MACRO {toms} {"ACM Transactions on Mathematical Software"}

1014−

1015−MACRO {toois} {"ACM Transactions on Office Information Systems"}

1016−

1017−MACRO {toplas} {"ACM Transactions on Programming Languages and Systems"}

1018−

1019−MACRO {tcs} {"Theoretical Computer Science"}

1020−

1021−READ

1022−

1023−FUNCTION {sortify}

1024−{ purify$

1025− "l" change.case$

1026−}

1027−

1028−INTEGERS { len }

1029−

1030−FUNCTION {chop.word}

1031−{ 's :=

1032− 'len :=

1033− s #1 len substring$ =

1034− { s len #1 + global.max$ substring$ }

1035− 's

1036− if$

1037−}

1038−

1039−FUNCTION {format.lab.names}

1040−{ 's :=

1041− s #1 "{vv~}{ll}" format.name$

1042− s num.names$ duplicate$

1043− #2 >

1044−%%%%% { pop$ " {\em et~al.\ }\relax" * }

1045− { pop$ " {\em et~al.}\relax" * }

1046− { #2 <

1047− 'skip$

1048− { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =

1049− { " {\em et~al.\ }\relax" * }

1050− { " \& " * s #2 "{vv~}{ll}" format.name$ * }

1051− if$

1052− }

1053− if$

1054− }

1055− if$

1056−}

1057−

1058−FUNCTION {author.key.label}

1059−{ author empty$

1060− { key empty$

1061− { cite$ #1 #3 substring$ }

1062− 'key

1063− if$

1064− }

1065− { author format.lab.names }

1066− if$

1067−}

1068−

1069−FUNCTION {author.editor.key.label}

1070−{ author empty$

1071− { editor empty$

1072− { key empty$

1073− { cite$ #1 #3 substring$ }

1074− 'key

1075− if$

1076− }

1077− { editor format.lab.names }

1078− if$

1079− }

1080− { author format.lab.names }

1081− if$

1082−}

1083−

1084−FUNCTION {editor.key.label}

1085−{ editor empty$

1086− { key empty$

1087− { cite$ #1 #3 substring$ }

1088− 'key

1089− if$

1090− }

1091− { editor format.lab.names }

1092− if$

1093−}

1094−

1095−FUNCTION {calc.label}

1096− { type$ "book" =

1097− type$ "inbook" =

1098− type$ "incollection" = % For sensible

1099− or or % treatment of

1100− 'author.editor.key.label % Singer in

1101− { type$ "proceedings" = % BS 1629.

1102− 'editor.key.label

1103− 'author.key.label

1104− if$

1105− }

1106− if$

1107− duplicate$

1108− year empty$

1109− {

1110− "\protect\citename{" swap$ * ", }" *

1111− "n.d." * 'label := % Chicago,

1112− } % page 457.

1113− {

1114− "\protect\citename{" swap$ * ", }" *

1115− year

1116− *

1117− 'label :=

1118− }

1119− if$

1120− year field.or.null purify$ *

1121− sortify 'sort.label :=

1122−}

1123−

1124−

1125−FUNCTION {sort.format.names} % To produce the

1126−{ 's := % order of entries

1127− #1 'nameptr := % specified in item

1128− "" % (3) on page 187

1129− s num.names$ 'numnames := % of Butcher.

1130− numnames 'namesleft :=

1131− { namesleft #0 > nameptr #3 < and } % Only 1st 2 names

1132− { nameptr #1 > % matter for

1133− { " " * } % sorting.

1134− 'skip$

1135− if$ % Anything that's

1136− nameptr #2 = numnames #2 > and % "et al" goes

1137− { "zzzzz" * } % after works by 2

1138− { % authors.

1139− s nameptr "{vv{ } }{ll{ }}{ ff{ }}{ jj{ }}" format.name$ 't :=

1140− nameptr numnames = t "others" = and

1141− { "zzzzz" * }

1142− { t sortify * }

1143− if$

1144− }

1145− if$

1146− nameptr #1 + 'nameptr :=

1147− namesleft #1 - 'namesleft :=

1148− }

1149− while$

1150−}

1151−

1152−FUNCTION {sort.format.title}

1153−{ 't :=

1154− "A " #2

1155− "An " #3

1156− "The " #4 t chop.word

1157− chop.word

1158− chop.word

1159− sortify

1160− #1 global.max$ substring$

1161−}

1162−

1163−FUNCTION {author.sort}

1164−{ author empty$

1165− { key empty$

1166− { "to sort, need author or key in " cite$ * warning$

1167− ""

1168− }

1169− { key sortify }

1170− if$

1171− }

1172− { author sort.format.names }

1173− if$

1174−}

1175−

1176−FUNCTION {author.editor.sort}

1177−{ author empty$

1178− { editor empty$

1179− { key empty$

1180− { "to sort, need author, editor, or key in " cite$ * warning$

1181− ""

1182− }

1183− { key sortify }

1184− if$

1185− }

1186− { editor sort.format.names }

1187− if$

1188− }

1189− { author sort.format.names }

1190− if$

1191−}

1192−

1193−FUNCTION {editor.sort}

1194−{ editor empty$

1195− { key empty$

1196− { "to sort, need editor or key in " cite$ * warning$

1197− ""

1198− }

1199− { key sortify }

1200− if$

1201− }

1202− { editor sort.format.names }

1203− if$

1204−}

1205−

1206−FUNCTION {presort} % Two sorting

1207−{ calc.label % passes, from

1208− label sortify % apalike.bst.

1209− " "

1210− *

1211− type$ "book" =

1212− type$ "inbook" =

1213− type$ "incollection" = % For Singer

1214− or or % in BS 1629.

1215− 'author.editor.sort

1216− { type$ "proceedings" =

1217− 'editor.sort

1218− 'author.sort

1219− if$

1220− }

1221− if$

1222− #1 entry.max$ substring$

1223− 'sort.label :=

1224− sort.label

1225− *

1226− " "

1227− *

1228− title field.or.null

1229− sort.format.title

1230− *

1231− #1 entry.max$ substring$

1232− 'sort.key$ :=

1233−}

1234−

1235−ITERATE {presort}

1236−

1237−SORT

1238−

1239−STRINGS { last.label next.extra }

1240−

1241−INTEGERS { last.extra.num }

1242−

1243−FUNCTION {initialize.extra.label.stuff}

1244−{ #0 int.to.chr$ 'last.label :=

1245− "" 'next.extra :=

1246− #0 'last.extra.num :=

1247−}

1248−

1249−FUNCTION {forward.pass}

1250−{ last.label label =

1251− { last.extra.num #1 + 'last.extra.num :=

1252− last.extra.num int.to.chr$ 'extra.label :=

1253− }

1254− { "a" chr.to.int$ 'last.extra.num :=

1255− "" 'extra.label :=

1256− label 'last.label :=

1257− }

1258− if$

1259−}

1260−

1261−FUNCTION {reverse.pass}

1262−{ next.extra "b" =

1263− { "a" 'extra.label := }

1264− 'skip$

1265− if$ % Code needed here

1266− % if \citeauthor

1267− % and \citeyear

1268− label extra.label * 'label := % were supported.

1269− extra.label 'next.extra :=

1270−}

1271−

1272−EXECUTE {initialize.extra.label.stuff}

1273−

1274−ITERATE {forward.pass}

1275−

1276−REVERSE {reverse.pass}

1277−

1278−FUNCTION {bib.sort.order}

1279−{ sort.label

1280− " "

1281− *

1282− year field.or.null sortify

1283− *

1284− " "

1285− *

1286− title field.or.null

1287− sort.format.title

1288− *

1289− #1 entry.max$ substring$

1290− 'sort.key$ :=

1291−}

1292−

1293−ITERATE {bib.sort.order}

1294−

1295−SORT

1296−

1297−FUNCTION {begin.bib}

1298−{ preamble$ empty$

1299− 'skip$

1300− { preamble$ write$ newline$ }

1301− if$

1302− "\begin{thebibliography}{}" write$ newline$

1303−}

1304−

1305−EXECUTE {begin.bib}

1306−

1307−EXECUTE {init.state.consts}

1308−

1309−ITERATE {call.type$}

1310−

1311−FUNCTION {end.bib}

1312−{ newline$

1313− "\end{thebibliography}" write$ newline$

1314−}

1315−

1316−EXECUTE {end.bib}

papers/impl-paper/jfp1.clsdeleted−1894

@@ -1,1894 +0,0 @@

1−%%

2−%% This is file `jfp.cls'

3−%%

4−%% CUP Journal of Functional Programming document class

6−%%

7−%% by Mark A. Reed

8−%% based on JFP.STY v1.24.

9−%%

10−%% Incorporating parts of authordate.sty

11−%% by David Rhead, Cripps Computing Centre (Feb 1990).

12−%%

13−%% Bugs (in the case of unchanged files) should be reported to

14−%% texline@cambridge.org

15−%%

16−%% This software may only be used in the preparation of journal articles

17−%% or books or parts of books to be published by Cambridge University Press.

18−%% Any other use constitutes an infringement of copyright.

19−%%

20−%% \CharacterTable

21−%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z

22−%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z

23−%% Digits \0\1\2\3\4\5\6\7\8\9

24−%% Exclamation \! Double quote \" Hash (number) \#

25−%% Dollar \$ Percent \% Ampersand \&

26−%% Acute accent \' Left paren $ Right paren $

27−%% Asterisk \* Plus \+ Comma \,

28−%% Minus \- Point \. Solidus \/

29−%% Colon \: Semicolon \; Less than \<

30−%% Equals \= Greater than \> Question mark \?

31−%% Commercial at \@ Left bracket \[ Backslash \\

32−%% Right bracket \] Circumflex \^ Underscore \_

33−%% Grave accent \` Left brace \{ Vertical bar \|

34−%% Right brace \} Tilde \~}

35−%%

36−

37−\NeedsTeXFormat{LaTeX2e}[1997/12/01]

38−\ProvidesClass{jfp}[2001/09/27 v1.02 Journal of Functional Programming

39− ^^Jdocument class]

40−

41−\newif\ifprodtf

42−\newif\ifonepage\global\onepagefalse%

43−\newif\ifonline

44−\onlinefalse

45−%

46−\newif\ifcompmod\global\compmodfalse

47−%

48−\newif\ifincremental\incrementalfalse

49−%%

50−\newif\ifindex

51−\newif\ifdraft

52−\newif\ifnoquery

53−\newif\ifbookreview

54−\newif\ifsptitle

55−%

56−\newif\ifsplissue

57−\global\splissuefalse

58−%

59−\newif\ifprinter

60−\newdimen\draftrule

61−\newdimen\trimrule

62−\global\draftrule0pt

63−\trimrule.1pt

64−%

65−\newdimen\trimwidth

66−\newdimen\trimheight

67−\newdimen\typewidth

68−\newdimen\typeheight

69−

70−\newdimen\tempdimen

71−\newdimen\normaltextheight

72−\newskip\normalbaselineskip

73−\newdimen\blindfoliodrop

74−\newif\ifprinter

75−\global\printerfalse

76−%%

77−\DeclareOption{compmod}{\compmodtrue}

78−%

79−\DeclareOption{splissue}{\splissuetrue}

80−%

81−%

82−\DeclareOption{incremental}{\incrementaltrue}

83−\DeclareOption{index}{\indextrue}

84−\DeclareOption{bookreview}{\bookreviewtrue}

85−\DeclareOption{noquery}{\noquerytrue}

86−\DeclareOption{oneside}{\relax}

87−\DeclareOption{twoside}{\@twosidetrue \@mparswitchtrue}

88−\DeclareOption{draft}{\draftrule.5pt\setlength\overfullrule{5\p@}}

89−\DeclareOption{final}{\setlength\overfullrule{\z@}}

90−\DeclareOption{onecolumn}{\@twocolumnfalse}

91−\DeclareOption{onepage}{\global\onepagetrue}

92−\DeclareOption{twocolumn}{\relax}

93−\DeclareOption{titlepage}{\relax}

94−\DeclareOption{notitlepage}{\relax}

95−\DeclareOption{leqno}{\relax}

96−\DeclareOption{fleqn}{\relax}

97−\DeclareOption{prodtf}{\prodtftrue}

98−\DeclareOption{sptitle}{\sptitletrue}

99−\DeclareOption{printer}{\printertrue}

100−\DeclareOption{online}{\onlinetrue}

101−%

102−\ExecuteOptions{twoside,final,onecolumn}

103−\ProcessOptions\relax

104−

105−\newif\ifCUPmtlplainloaded

106−%% \ifprodtf

107−%% \CUPmtlplainloadedtrue

108−%% \RequirePackage{CUPTimes,jfp2esym}

109−%% % \RequirePackage{Times,jfp2esym} %%% TB

110−%% \fi

111−%%%%%%%%%%%%%%%%

112−%

113−\def\trkdefault{trk}% All trk

114−\DeclareRobustCommand\trkshape

115− {\not@math@alphabet\trkshape\mathrm

116− \fontshape\trkdefault\selectfont}

117−%

118−\def\spchapterfont{\fontsize{18}{21}\selectfont}%\trkshape}

119−\def\subtitlefont{\normalfont\fontsize{12}{14}\selectfont\itshape}%

120−%

121−\def\splissuefont{\fontsize{12}{14}\itshape\selectfont}%\trkshape}

122−%

123−\DeclareFontFamily{OT1}{mtr}{}

124−\DeclareFontShape{OT1}{mtr}{m}{n}{<->mtr10}{}

125−\DeclareFontShape{OT1}{mtr}{m}{trk}{<->mtr10[track+140]}{}

126−\DeclareFontShape{OT1}{mtr}{m}{sl}{<->mtsl10}{}

127−\DeclareFontShape{OT1}{mtr}{m}{it}{<->mtti10}{}

128−\DeclareFontShape{OT1}{mtr}{m}{sc}{<->mtcsc10}{}

129−%

130−% Warning: please note that the upright shape below is

131−% used for the \pounds symbol of LaTeX. So this

132−% font definition shouldn't be removed.

133−%

134−\DeclareFontShape{OT1}{mtr}{m}{ui}{<->mtu10}{}

135−%

136−%%%%%%% bold series

137−\DeclareFontShape{OT1}{mtr}{b}{n}{<->sub * cmr/b/n}{}

138−%

139−%%%%%%%% bold extended series

140−\DeclareFontShape{OT1}{mtr}{bx}{n}{<->mtbx10}{}

141−\DeclareFontShape{OT1}{mtr}{bx}{sl}{<->mtbxsl10}{}

142−\DeclareFontShape{OT1}{mtr}{bx}{it}{<->mtbxti10}{}

143−%

144−% Again this is necessary for a correct \pounds symbol in

145−% the cmr fonts Hopefully the dc/ec font layout will take

146−% over soon.

147−%

148−\DeclareFontShape{OT1}{mtr}{bx}{ui}{<->ssub * mtr/m/ui}{}

149−%

150−%%%%% For mathfrak ... updated on 26th of April 2006

151−%

152−\DeclareFontFamily{U}{eufa}{}%

153−\DeclareFontShape{U}{eufa}{m}{n}{<-6>eufm5<6-8>eufm7<8->eufm10}{}%

154−\DeclareFontShape{U}{eufa}{b}{n}{<-6>eufb5<6-8>eufb7<8->eufb10}{}%

155−%

156−%%\newcommand{\mathfrak}[1]{{\protect\pmathfrak#1}}

157−%%\newcommand{\pmathfrak}{\@fontswitch{\relax}{\mfraknew}}

158−\DeclareMathAlphabet\mfraknew{U}{eufa}{m}{n}

159−\SetMathAlphabet\mfraknew{normal}{U}{eufa}{m}{n}

160−\SetMathAlphabet\mfraknew{bold}{U}{eufa}{b}{n}

161−%%%%

162−

163−%%%%%%%%%%%%%%%%

164−\setlength\lineskip{1\p@}

165−\setlength\normallineskip{1\p@}

166−\renewcommand\baselinestretch{}

167−

168−\renewcommand\normalsize{%

169−\ifbookreview

170−\@setfontsize\small\@ixpt{11}%

171−\else

172−\@setfontsize\normalsize\@xpt{13}%

173−\fi

174− \abovedisplayskip 6.5\p@ \@plus 1\p@ \@minus 1\p@

175− \belowdisplayskip \abovedisplayskip

176− \abovedisplayshortskip 3\p@ \@plus 1\p@

177− \belowdisplayshortskip \abovedisplayshortskip

178− \let\@listi\@listI}

179−

180−\normalsize

181−

182−\newcommand\small{%

183− \@setfontsize\small\@ixpt{11}%

184− \abovedisplayskip 6\p@ \@plus 1\p@ \@minus 1\p@

185− \belowdisplayskip \abovedisplayskip

186− \abovedisplayshortskip 3\p@ \@plus 1\p@

187− \belowdisplayshortskip \abovedisplayshortskip

188− \def\@listi{\leftmargin\leftmargini

189− \topsep 6\p@ \@plus 1\p@ \@minus 1\p@

190− \parsep \z@ \itemsep \parsep}%

191−}

192−

193−\newcommand\footnotesize{%

194− \@setfontsize\footnotesize\@ixpt\@xpt

195− \abovedisplayskip 5\p@ \@plus 1\p@ \@minus 1\p@

196− \belowdisplayskip \abovedisplayskip

197− \abovedisplayshortskip \z@ \@plus 1\p@

198− \belowdisplayshortskip \abovedisplayshortskip

199− \def\@listi{\leftmargin\leftmargini

200− \topsep 4.5\p@ \@plus 1\p@ \@minus 1\p@

201− \parsep \z@ \itemsep \parsep}%

202−}

203−

204−\newcommand\scriptsize{\@setfontsize\scriptsize\@viiipt\@ixpt}

205−\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}

206−\newcommand\large{\@setfontsize\large\@xiipt{14}}

207−\newcommand\Large{\@setfontsize\Large\@xvpt{18}}

208−\ifprodtf

209− \newcommand\LARGE{\@setfontsize\LARGE{19}{21}}%

210−\else

211− \newcommand\LARGE{\@setfontsize\LARGE{18}{21}}%

212−\fi

213−\newcommand\huge{\@setfontsize\huge\@xxpt{25}}

214−\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}

215−%

216−\def\sluglinefont{\fontsize{7.5}{10}\selectfont}

217−%

218−\newcommand\affilsize{\@setfontsize\affilsize\@viiipt\@xpt}

219−\newcommand\onlineaffilsize{\@setfontsize\affilsize\@viipt\@ixpt}

220−\let\authorsize\normalsize

221−

222−\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}

223−\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}

224−\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}

225−\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}

226−\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}

227−\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}

228−\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}

229−\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}

230−\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}

231−

232− \setlength\topmargin{11mm}

233−\setlength\trimheight{247mm}

234−\setlength\trimwidth{174mm}

235−%

236−\setlength\typeheight{50.5pc}

237−\setlength\typewidth{30pc}

238−

239−\setlength\marginparwidth{2.0cm}

240−\setlength\marginparsep{10\p@}

241−

242−\setlength\headheight{6\p@}

243−\setlength\headsep{18\p@}

244−\setlength\topskip{6\p@}

245−\setlength\footskip{26\p@}

246−

247−\setlength\textheight{48.5pc}

248−\addtolength\textheight{-8.8pt}

249−\addtolength\textheight{\topskip}

250−\setlength\normaltextheight{\textheight}

251−

252−\setlength\textwidth{30pc}

253−\setlength\columnsep{10\p@}

254−\setlength\columnseprule{\z@}

255−

256−\setlength\oddsidemargin{21mm}%5pc}

257−\setlength\evensidemargin\trimwidth

258−\addtolength\evensidemargin{-\textwidth}

259−\addtolength\evensidemargin{-\oddsidemargin}

260−

261−\setlength\footnotesep{\z@}

262−\setlength{\skip\footins}{19.5\p@ \@plus 12\p@ \@minus 1\p@}

263−

264−\setlength\floatsep{13\p@ \@plus 6.5\p@ \@minus 1\p@}

265−\setlength\textfloatsep{15\p@ \@plus 4.5\p@ \@minus 3\p@}

266−\setlength\intextsep{13\p@ \@plus 6.5\p@ \@minus 2\p@}

267−\setlength\dblfloatsep{13\p@ \@plus 6.5\p@ \@minus 2\p@}

268−\setlength\dbltextfloatsep{15\p@ \@plus 4.5\p@ \@minus 3\p@}

269−\setlength\@fptop{\z@ \@plus 0fil}

270−\setlength\@fpsep{13\p@ \@plus 0fil}

271−\setlength\@fpbot{\z@ \@plus 3fil}

272−\setlength\@dblfptop{\z@ \@plus 0fil}

273−\setlength\@dblfpsep{13\p@ \@plus 0fil}

274−\setlength\@dblfpbot{\z@ \@plus 3fil}

275−\setlength\marginparpush{5\p@}

276−

277−\setlength\parskip{\z@}% \@plus .3\p@}

278−\setlength\parindent{10pt}

279−\setlength\partopsep{\z@ \@plus 1\p@}

280−\@lowpenalty 51

281−\@medpenalty 151

282−\@highpenalty 301

283−\@beginparpenalty -\@lowpenalty

284−\@endparpenalty -\@lowpenalty

285−\@itempenalty -\@lowpenalty

286−\clubpenalty\@M%z@

287−\widowpenalty\@M

288−\hyphenpenalty8000

289−

290−%

291−\def\cleardoublepage{\clearpage\if@twoside \ifodd\c@page\else

292− \hbox{}\thispagestyle{empty}\newpage\if@twocolumn\hbox{}\newpage\fi\fi\fi}

293−%

294−\newcommand\partname{Part}

295−\newcommand\part{\par\addvspace{4ex}\@afterindentfalse \secdef\@part\@spart}

296−

297−\def\@part[#1]#2{%

298− \ifnum \c@secnumdepth >\m@ne

299− \refstepcounter{part}%

300− \addcontentsline{toc}{part}{\partname\ \thepart: #1}%

301− \else

302− \addcontentsline{toc}{part}{#1}%

303− \fi

304− {\parindent \z@ \centering

305− \ifnum \c@secnumdepth >\m@ne

306− \normalfont\large\rmfamily \MakeUppercase{\partname}\ %

307− \ifcase\thepart \or ONE \or TWO \or THREE \or FOUR \or FIVE

308− \or SIX \or SEVEN \or EIGHT \or NINE \or TEN \else \fi

309− \par \nobreak

310− \fi

311− \normalfont\LARGE\rmfamily #2 \markboth{}{}\par}%

312− \nobreak \vskip 3ex \@afterheading

313−}

314−

315−\def\@spart#1{%

316− {\parindent \z@ \centering\normalfont\LARGE\rmfamily #1\par}%

317− \nobreak \vskip 3ex \@afterheading

318−}

319−

320−\newcommand\section{%

321− \@startsection {section}{1}{\z@}%

322− {-19.5\p@ \@plus -6.5\p@ \@minus -3.25\p@}%

323− {6.5\p@ \@plus \z@ \@minus 1\p@}

324− {\normalfont\normalsize\bfseries\centering}%

325−}

326−

327−\newcommand\subsection{%

328− \@startsection{subsection}{2}{\z@}

329− {-19.5\p@ \@plus -3.25\p@ \@minus -3.25\p@}

330− {6.5\p@ \@plus \z@ \@minus 1\p@}

331− {\normalfont\normalsize\bfseries\itshape\centering}%

332−}

333−

334−\newcommand\subsubsection{%

335− \@startsection{subsubsection}{3}{\z@}

336− {-19.5\p@ \@plus -3.25\p@ \@minus -3.25\p@}

337− {6.5\p@ \@plus \z@ \@minus 1\p@}

338− {\normalfont\normalsize\itshape\centering}%

339−}

340−

341−\newcommand\paragraph{%

342− \@startsection{paragraph}{4}{\z@}

343− {-13\p@ \@plus -1.5\p@ \@minus -1.5\p@}

344− {-0.5em}

345− {\normalfont\normalsize\bfseries\raggedright}%

346−}

347−

348−\newcommand\subparagraph{%

349− \@startsection{subparagraph}{4}{\parindent}

350− {-13\p@ \@plus -3.25\p@ \@minus -3.25\p@}

351− {-0.5em}

352− {\normalfont\normalsize\rmfamily\raggedright}%

353−}

354−

355−\def\@seccntformat#1{\csname the#1\endcsname\hskip5pt}%

356−

357−\newcommand\appendixname{Appendix}

358−

359−\newcommand\appendix{\par

360− \@addtoreset{equation}{section}%

361− \@addtoreset{figure}{section}%

362− \@addtoreset{table}{section}%

363− \setcounter{section}\z@

364− \renewcommand\thesection{\@Alph\c@section}%

365− \renewcommand\theequation{\thesection\,\@arabic\c@equation}%

366− \renewcommand\thefigure{\thesection\,\@arabic\c@figure}%

367− \renewcommand\thetable{\thesection\,\@arabic\c@table}%

368−}

369−

370−\setcounter{secnumdepth}{3}

371−

372−\newcounter{part}

373−\newcounter{section}

374−\newcounter{subsection}[section]

375−\newcounter{subsubsection}[subsection]

376−\newcounter{paragraph}[subsubsection]

377−\newcounter{subparagraph}[paragraph]

378−\renewcommand\thepart {\@arabic\c@part}

379−\renewcommand\thesection {\@arabic\c@section}

380−\renewcommand\thesubsection {\thesection.\@arabic\c@subsection}

381−\renewcommand\thesubsubsection {\thesubsection.\@arabic\c@subsubsection}

382−\renewcommand\theparagraph {\thesubsubsection.\@arabic\c@paragraph}

383−\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph}

384−

385−\newskip\@leftskip \@leftskip=\z@

386−

387−\setlength\leftmargini {13pt}

388−\setlength\leftmarginii {15.2pt}

389−\setlength\leftmarginiii {1.5em}

390−\setlength\leftmarginiv {1.5em}

391−\setlength\leftmarginv {1em}

392−\setlength\leftmarginvi {1em}

393−\setlength\leftmargin {\leftmargini}

394−\setlength\labelsep {5\p@}

395−\setlength\labelwidth {\leftmargini}

396−\addtolength\labelwidth {-\labelsep}

397−

398−\newcommand\makeRLlabel[1]{\rlap{#1}\hss}

399−\newcommand\makeRRlabel[1]{\hss\llap{#1}}

400−

401−\def\@listI{\leftmargin\leftmargini\advance\leftmargin11.5pt

402− \parsep \z@ \topsep 6.5\p@ \@plus 3\p@ \@minus 3\p@

403− \itemsep \z@ \@plus 1\p@ \@minus 1\p@

404− \let\makelabel\makeRLlabel}

405−

406−\def\@listii{\leftmargin\leftmarginii

407− \labelwidth\leftmarginii

408− \advance\labelwidth-\labelsep

409− \topsep 3\p@ \@plus 1\p@ \@minus 1\p@

410− \parsep \z@ \itemsep \parsep

411− \let\makelabel\makeRLlabel}

412−

413−\def\@listiii{\leftmargin\leftmarginiii

414− \labelwidth\leftmarginiii

415− \advance\labelwidth-\labelsep

416− \topsep 3\p@ \@plus 1\p@ \@minus 1\p@

417− \parsep \z@ \partopsep \z@

418− \itemsep \topsep

419− \let\makelabel\makeRLlabel}

420−

421−\def\@listiv{\leftmargin\leftmarginiv

422− \labelwidth\leftmarginiv

423− \advance\labelwidth-\labelsep

424− \let\makelabel\makeRLlabel}

425−

426−\def\@listv{\leftmargin\leftmarginv

427− \labelwidth\leftmarginv

428− \advance\labelwidth-\labelsep

429− \let\makelabel\makeRLlabel}

430−

431−\def\@listvi{\leftmargin\leftmarginvi

432− \labelwidth\leftmarginvi

433− \advance\labelwidth-\labelsep

434− \let\makelabel\makeRLlabel}

435−

436−\let\@listi\@listI

437−\@listi

438−

439−\def\itemize{% FROM LATEX.LTX

440− \ifnum \@itemdepth >\thr@@ \@toodeep\else

441− \advance\@itemdepth \@ne

442− \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%

443− \expandafter

444− \list

445− \csname\@itemitem\endcsname

446− {\let\makelabel\makeRRlabel\advance\itemindent0pt\advance\leftmargin.5pt}%

447− \fi

448−}

449−

450−\newif\ifhyphen\global\hyphenfalse

451−

452−\newcommand\labelitemi{\ifhyphen \normalfont\bfseries ---\else

453−$\m@th\bullet$\fi}

454−

455−%\newcommand\labelitemi{$\m@th\bullet$}

456−\newcommand\labelitemii{\normalfont\bfseries ---}

457−\newcommand\labelitemiii{\normalfont\bfseries --}

458−\newcommand\labelitemiv{$\m@th\cdot$}

459−

460−%%%%%%%%%%%%%%%%%%%%%%%%%%%%% unnumlist %%%%%%%%%%%%%%%%%%%%%%%%%%%%% TB

461−%

462−\def\unnumlistfont{\fontsize{10}{13}\selectfont}

463−

464−\newenvironment{unnumlist}{\par%

465− \unnumlistfont%

466− \list{}{%

467− \topsep6pt plus2pt

468− \itemindent-10pt

469− \leftmargin10pt

470− \parsep0pt

471− \itemsep0pt

472− \partopsep0pt}

473− \def\makelable##1{##1}%

474−}{%

475− \endlist%

476−}%

477−%

478−%%%%%%%%%%%%%%%%%%%%%%%%%%%%% unnumlist %%%%%%%%%%%%%%%%%%%%%%%%%%%%%

479−

480−\def\enumerate{% FROM LATEX.LTX

481− \ifnum \@enumdepth >\thr@@ \@toodeep\else

482− \advance\@enumdepth \@ne

483− \edef\@enumctr{enum\romannumeral\the\@enumdepth}%

484− \fi

485− \@ifnextchar [{\@enumeratetwo}{\@enumerateone}%

486−}

487−

488−\def\@enumerateone{%

489− \expandafter

490− \list

491− \csname label\@enumctr\endcsname

492− {\usecounter{\@enumctr}%

493− \let\makelabel\makeRRlabel}%

494−}

495−

496−\def\@enumeratetwo[#1]{%

497− \expandafter

498− \list

499− \csname label\@enumctr\endcsname

500− {\usecounter{\@enumctr}%

501− \settowidth\labelwidth{\normalfont\rmfamily #1}%

502− \itemindent0pt\leftmargin\labelwidth\advance\leftmargin\labelsep\advance\leftmargin13pt

503− \let\makelabel\makeRRlabel}%

504−}

505−

506−\newcommand\labelenumi {{\normalfont\rmfamily\theenumi.}}

507−\newcommand\labelenumii {{\normalfont\rmfamily(\theenumii)}}

508−\newcommand\labelenumiii{{\normalfont\rmfamily\theenumiii}}

509−\newcommand\labelenumiv {{\normalfont\rmfamily\theenumiv}}

510−

511−\renewcommand\theenumi{\@arabic\c@enumi}

512−\renewcommand\theenumii{\@alph\c@enumii}

513−\renewcommand\theenumiii{\@roman\c@enumiii}

514−\renewcommand\theenumiv{\@Alph\c@enumiv}

515−

516−\renewcommand\p@enumii{\theenumi}

517−\renewcommand\p@enumiii{\theenumi(\theenumii)}

518−\renewcommand\p@enumiv{\p@enumiii\theenumiii}

519−

520−\newcommand*\descriptionlabel[1]{\hspace\labelsep \normalfont\bfseries #1}

521−

522−\newenvironment{description}

523− {\list{}{\leftmargin 1em \labelwidth\z@ \itemindent-\leftmargin

524− \let\makelabel\descriptionlabel}}

525− {\endlist}

526−

527−\newenvironment{verse}

528− {\let\\=\@centercr

529− \list{}{\itemsep\z@

530− \itemindent -2.5em%

531− \listparindent \itemindent

532− \rightmargin\leftmargin

533− \advance\leftmargin 2.5em}\item[]}

534− {\endlist}

535−

536−\newenvironment{extract} %quotation

537− {\list{}{\vskip6pt\listparindent\parindent

538− \topsep6pt\itemindent\listparindent

539− \leftmargin\z@ \rightmargin\leftmargin

540− \parsep \z@ \@plus 1\p@}\item[]%

541− \normalfont\small\rmfamily}

542− {\endlist}

543−

544−

545−\newenvironment{quote} %quotation

546− {\par\vskip5pt\itshape\leftskip0pt plus1fill\rightskip0pt plus 0fill}

547− {\par}

548−

549−\newenvironment{qtsource} %quotation source

550− {\par\leftskip0pt plus1fill\rightskip0pt plus 0fill}

551− {\par}

552−

553−\def\quotespace{\vspace*{6.5pt}}

554−

555−\newenvironment{letter} %quotation

556− {\list{}{\listparindent\z@

557− \topsep6pt\itemindent\listparindent

558− \leftmargin24pt \rightmargin\z@

559− \parsep \z@ \@plus 1\p@}\item[]%

560− \normalfont\itshape}

561− {\endlist}

562−

563−

564−\newif\ifrembrks

565−\newcommand\removebrackets{\rembrkstrue}

566−

567−\def\@begintheorem#1#2{% FROM LATEX.LTX

568− \normalfont\rmfamily

569− \trivlist

570− \item[\hskip \labelsep{\normalfont\itshape #1\ #2}]%

571− \item[]%

572−}

573−

574−\def\@opargbegintheorem#1#2#3{% FROM LATEX.LTX

575− \normalfont\rmfamily

576− \trivlist

577− \item[\hskip \labelsep{\normalfont\itshape #1\ #2\ %

578− \ifrembrks #3\/\global\rembrksfalse\else {\upshape(}#3\/{\upshape)}\fi}]%

579− \item[]%

580−}

581−

582−\newsavebox{\proofsavebox}

583−

584−

585−%% \newtheorem{lemma}{Lemma}[section]

586−%% \newtheorem{example}{Example}[section]

587−%% \newtheorem{theorem}{Theorem}[section]

588−%% \newtheorem{definition}{Definition}[section]

589−%% \newtheorem{corollary}{Corollary}[section]

590−

591−

592− \sbox{\proofsavebox}

593− {\unitlength 1pt\begin{picture}(6.5,6.5)%

594− \put(0,0){\framebox(6.5,6.5){}}\end{picture}}

595− \newcommand\proofbox{\usebox{\proofsavebox}\relax}

596−

597−\newcommand\mathproofbox{\rlap{\quad\proofbox}}

598−

599−\def\@nprf{\normalfont\rmfamily \trivlist

600− \item[\hskip \labelsep {\normalfont\itshape Proof}]%

601− \item[]}

602−

603−\def\@oprf[#1]{\normalfont\rmfamily \trivlist

604− \item[\hskip \labelsep {\normalfont\itshape #1\ }]%

605− \item[]}

606−

607−\newenvironment{proof}

608− {\@ifnextchar[{\@oprf}{\@nprf}}

609− {\hspace*{15pt}\hbox{\proofbox}\endtrivlist}

610−

611−\newenvironment{proof*}

612− {\proof}

613− {\endtrivlist}

614−

615−\renewcommand\theequation{\@arabic\c@equation}

616−

617−\setlength\arraycolsep{5\p@}

618−\setlength\tabcolsep{0\p@}

619−\setlength\arrayrulewidth{.5\p@}

620−\setlength\doublerulesep{1.5\p@}

621−\setlength\tabbingsep{\labelsep}

622−\setlength{\skip\@mpfootins}{\skip\footins}

623−\setlength\fboxsep{3\p@}

624−\setlength\fboxrule{.5\p@}

625−

626−\newcommand\maketitle{\@ifnextchar [{\m@ketitleone}{\m@ketitleone[n]}}

627−

628−\def\m@ketitleone[#1]{\par

629− \begingroup

630− \newpage

631− \global\@topnum\z@

632− \titlefntrue

633− \def\thefootnote{\@fnsymbol\c@footnote}%

634− \def\@makefnmark{\hbox{$\@thefnmark$}}%

635− \@maketitle{#1}%

636− \thispagestyle{titlepage}\@thanks

637− \endgroup

638− \global\let\@maketitle\relax

639− \global\let\@thanks\@empty

640− \global\let\@title\@empty

641− \global\let\@author\@empty

642− \global\let\maketitle\relax

643− \global\let\thanks\relax

644− \setcounter{footnote}\z@

645−}

646−

647−\def\pe@rl#1{%

648− \if t#1 {\tpe@rl}\else

649− \if T#1 {\Tpe@rl}\else

650− \if f#1 {\fpe@rl}\else

651− \if F#1 {\Fpe@rl}\else

652− \if e#1 {\edpe@rl}\else

653− \if E#1 {\Edpe@rl}\else

654− \if o#1 {\otherpearl}\else

655− \vspace*{32\p@}%

656− \fi

657− \fi

658− \fi

659− \fi

660− \fi

661− \fi

662− \fi

663−}

664−%

665−\newenvironment{bookrevauthor}{\par\vskip5pt\noindent\ignorespaces}{\par}

666−

667−\def\bookreventryfont{\fontsize{10}{13}\selectfont}

668−\newenvironment{bookreventry}{\par\bookreventryfont\noindent\leftskip18pt\rightskip18pt\ignorespaces}{\vskip7pt\@endparenv\@ignoretrue}

669−\newenvironment{question}{\par\vskip6.5pt\tablefont\noindent\ignorespaces}{\vskip6.5pt\@endparenv\@ignoretrue}

670−%

671−\def\spe@rl{\vspace*{32\p@}\normalfont\LARGE\rmfamily}

672−\def\epe@rl#1{\par\vspace*{6.5\p@}\xdef\@shorttitle{#1}}

673−

674−\def\tpe@rl{\spe@rl T\ls H\ls E\ls O\ls R\ls E\ls T\ls

675− I\ls C\ls A\ls L\ns P\ls E\ls A\ls R\ls L\ls S%

676− \epe@rl{Theoretical pearls}%

677−}

678−

679−\def\Tpe@rl{\spe@rl T\ls H\ls E\ls O\ls R\ls E\ls T\ls

680− I\ls C\ls A\ls L\ns P\ls E\ls A\ls R\ls L%

681− \epe@rl{Theoretical pearl}%

682−}

683−

684−\def\fpe@rl{\spe@rl F\ls U\ls N\ls C\ls T\ls I\ls O\ls

685− N\ls A\ls L\ns P\ls E\ls A\ls R\ls L\ls S%

686− \epe@rl{Functional pearls}%

687−}

688−

689−\def\Fpe@rl{\spe@rl F\ls U\ls N\ls C\ls T\ls I\ls O\ls

690− N\ls A\ls L\ns P\ls E\ls A\ls R\ls L%

691− \epe@rl{Functional pearl}%

692−}

693−

694−\def\edpe@rl{\spe@rl E\ls D\ls U\ls C\ls A\ls T\ls I\ls O\ls N\ls A\ls L\ns

695− P\ls E\ls A\ls R\ls L\ls S%

696− \epe@rl{Educational pearls}%

697−}

698−

699−\def\Edpe@rl{\spe@rl E\ls D\ls U\ls C\ls A\ls T\ls I\ls O\ls N\ls A\ls L\ns

700− P\ls E\ls A\ls R\ls L%

701− \epe@rl{Educational pearl}%

702−}

703−

704−\def\otherpearl{\spe@rl

705− \@ifundefined{othrpearl}

706− {Please define {\normalfont\ttfamily\char92 othrpearl} to obtain\\ the correct title!}

707− {\othrpearl}%

708− \epe@rl{Short title--please redefine with {\normalfont\ttfamily\char92 shorttitle}}%

709−}

710−

711−\def\authormark#1{\xdef\@authormark{#1}}

712−

713−\def\author{\@ifnextchar [{\@authortwo}{\@authorone}}

714−\def\@authortwo[#1]#2{\@author{#2}\xdef\@authormark{#1}}

715−\def\@authorone#1{\@author{#1}\xdef\@authormark{#1}}

716−%

717−%\def\@author#1{\global\advance\authorcount by 1

718−% \expandafter\xdef\csname author\romannumeral\the\authorcount\endcsname{#1}\affil{}}

719−%

720−\def\@author#1{\global\advance\authorcount by 1

721− \expandafter\gdef\csname author\romannumeral\the\authorcount\endcsname{#1}}

722−%

723−\def\affil#1{\expandafter\gdef\csname affil\romannumeral\the\authorcount\endcsname{#1}}

724−\def\email#1{\expandafter\gdef\csname email\romannumeral\the\authorcount\endcsname{\normalfont\rmfamily

725− \itshape\textup{(}e-mail: \textup{\texttt{#1})}}}

726−%

727−\def\and{{\reset@font and}}

728−%

729−\def\authorsep{\unskip, }

730−\newcount\authorcount\authorcount=0

731−\newcount\tempcount

732−\newcount\authortempcount

733−%

734−\def\@authors{%

735− \ifnum\authorcount>0% %%%% Authors available

736− \tempcount=1%

737− \loop%

738− \ifnum\authorcount>0%

739− \noindent{\reset@font\authorsize\csname author\romannumeral\the\tempcount \endcsname}\par\vskip3pt%

740− \noindent{\baselineskip10pt\normalfont\reset@font\affilsize\itshape\csname affil\romannumeral\the\tempcount \endcsname\par}%

741− \noindent{\baselineskip10pt\normalfont\affilsize\itshape\csname email\romannumeral\the\tempcount \endcsname\par}%

742−% \ifnum\authorcount>1\ifnum\authorcount>2\ \else \ \and\ \fi\fi%

743− \global\advance\authorcount by -1%

744− \advance\tempcount by 1 %

745− \vskip7pt

746− \repeat

747− \global\authortempcount\tempcount

748− \fi}%

749−%

750−\def\spchapter{\@ifnextchar[{\@@spchapter}{\@@spchapter[]}}

751−

752−\def\@@spchapter[#1]#2{\gdef\@spchapter{#2}}

753−\spchapter{}

754−%

755−\ifindex

756− \def\@maketitle#1{\cleardoublepage\bgroup%

757− {\vspace*{18pt}\indexheadfont

758−\indexname\par}\vskip43pt

759− \egroup

760− }%

761−\else

762−\def\@maketitle#1{%

763− \newpage\null

764− \ifbookreview\vskip-29pt\else\vskip-25\p@\fi%

765− {\centering \sloppy

766− \pe@rl{#1}%

767− \ifsptitle

768− \ifx\@spchapetr\@empty\else{\spchapterfont\@spchapter}\par\vskip7pt\fi%

769− \else

770− \ifsplissue

771− \ifx\@spchapetr\@empty\else{\splissuefont\@spchapter}\par\fi%

772− \else

773− \fi

774− \fi

775− {\normalfont\LARGE\itshape \@title\par}%

776− \ifx\@subtitle\@empty%

777− \else%

778− \vskip8pt%

779− {\subtitlefont \@subtitle\par}%

780−% \vskip4pt%

781− \fi%

782− \vskip 16\p@

783− {%

784− \@authors

785− \par}%

786− }%

787− \ifsptitle\vspace*{-4\p@}\else\vskip 13.5\p@ \fi\ifbookreview\vskip26.5pt\fi%\@plus 2\p@ \@minus 1\p@

788−}

789−\fi

790−\def\abs@header#1{%

791− \vbox{\hrule \@height .25pt \@width30.05pc

792− \vskip 8\p@ \@plus 3\p@ \@minus 1\p@

793− \centerline{\normalfont\normalsize\bfseries #1}}%

794−}

795−

796−\def\abs@body{%

797− \list{}{\leftmargin\z@ \rightmargin\leftmargin

798− \listparindent 1em \parsep \z@ \@plus 1\p@

799− \topsep 8\p@ %\@plus 3\p@ \@minus 1\p@

800− }%

801− \item[]\normalfont\small\rmfamily

802−}

803−

804−\newcommand\abstractname{Abstract}

805−\newenvironment{abstract}

806− {\ifsptitle\vspace*{17.3\p@}\else\fi\abs@header{\abstractname}\abs@body}

807− {\endlist\vbox{\hrule \@height .25pt \@width 30.05pc}%

808− \gdef\abs@header##1{\vskip 2\p@

809− \centerline{\normalfont\normalsize\bfseries ##1}}}

810−

811−\newcommand\capsulename{Capsule Review}

812−\newenvironment{capsule}

813− {\abs@header{\capsulename}\abs@body}

814− {\endabstract}

815−

816−

817−\mark{{}{}}

818−

819−\newcommand\shortauthor[1]{\gdef\@shortauthor{#1}}

820−\gdef\@shortauthor{}

821−

822−\renewcommand\title{\@ifnextchar [{\@titletwo}{\@titleone}}

823−\def\@titleone#1{\gdef\@title{#1}\xdef\@shorttitle{#1}}

824−\def\@titletwo[#1]#2{\gdef\@title{#2}\xdef\@shorttitle{#1}}

825−\gdef\@title{\mbox{}}

826−

827−\newcommand\subtitle[1]{\xdef\@subtitle{#1}}

828−\subtitle{}

829−

830−\newcommand\shorttitle[1]{\xdef\@shorttitle{#1}}

831−

832−\newcommand\volume[1]{\gdef\@volume{#1}}

833−\gdef\@volume{{\normalfont\bfseries 1} (1):}

834−

835−\newcommand\pagerange[1]{\gdef\@pagerange{#1}}

836−\gdef\@pagerange{1--000}

837−

838−\newcommand\pubyear[1]{\gdef\@year{#1}}

839−\gdef\@year{19XX}

840−

841−\newcommand\jdate[1]{\gdef\@jdate{#1}}

842−\gdef\@jdate{January \@year}

843−

844−\newcommand\doi[1]{\gdef\@doi{10.1017/#1}}

845−\gdef\@doi{10.1017/S0000000000000000}

846−

847−%% TB

848−

849−\def\Copyright{\raise.2pt\hbox{\fontsize{8}{8}\selectfont\ooalign{\hfil\raise.9pt\hbox{\hskip-.3pt{\normalfont\fontsize{7.5}{7.5}\selectfont

850−c}}%

851− \hfil\crcr\mathhexbox20D}}}

852−

853−\newcommand\journal[1]{\gdef\@journal{#1}}

854−%

855−\def\pubonline#1{\gdef\@pubonline{#1}}

856−\def\@pubonline{}

857−%

858−\ifonline

859− \def\@journal{%

860− \vbox to 8.6\p@{\noindent\parbox[t]{4.8in}{\normalfont\onlineaffilsize\rmfamily

861− {\itshape JFP\/}\ {\bf \@volume}\ (\@issue):\ \ifonepage\thepage\else\thepage--\pageref{lastpage}\fi* %

862− (First pubd online \@cpyyear)\hskip5pt \Copyright\

863− \@cpyyear\ Cambridge University Press\ doi:\@doi\\[2\p@]

864− *Provisional -- final page numbers to be inserted when paper edition is published}% published

865− \vss}}

866−\else

867− \ifincremental

868− \def\@journal{%

869− \vbox to 8.6\p@{\noindent\parbox[t]{4.8in}{\sluglinefont%

870− {\it JFP\kern-1pt{:}\/}\ page \ifonepage\thepage\else\thepage\ of\ \pageref{lastpage}\fi.\hskip7.5pt %

871− \Copyright\ \@cpyyear\ Cambridge University Press\\[2\p@]

872− doi:\@doi}%

873− \vss}}%

874−\else

875− \def\@journal{%

876− \vbox to 8.6\p@{\noindent\parbox[t]{4.8in}{\sluglinefont%

877− {\itshape JFP\/}\ {\bf \@volume}\ (\@issue):\ \ifonepage\thepage\else\thepage--\pageref{lastpage}\fi, %

878− \@pubyear.\hskip7.5pt \Copyright\

879− \@cpyyear\ Cambridge University Press\\[2\p@]

880− doi:\@doi\hskip5pt \ifx\@pubonline\empty\else First published online \@pubonline\fi\hskip5pt {Printed in the United Kingdom}}%{Printed in the United Kingdom}}%

881− \vss}%

882−}

883−\fi\fi

884−

885−\def\@underjournal{%

886− \vbox to 5.6\p@{\noindent\parbox[t]{4.8in}{\normalfont\affilsize\rmfamily

887− {\itshape Under consideration for publication in

888− J.\ Functional Programming\/}\\[2.5\p@]

889− \ }%

890− \vss}%

891−}

892−%%

893−\def\bookrevmark#1{\gdef\@bookrevmark{#1}}

894−\bookrevmark{Book review}

895−%

896−\def\rhfont{\fontsize{11}{11}\selectfont}

897−%%

898−\def\ps@headings{\let\@mkboth\markboth

899− \def\@oddhead{\hfil{\ifbookreview\fontsize{10}{13}\selectfont\fi\itshape\@shorttitle}\hfil \llap{\rhfont\thepage}}%

900− \def\@evenhead{\rlap{\rhfont\thepage}\hfil\ifbookreview{\fontsize{10}{13}\selectfont\itshape\@bookrevmark}\else\itshape\@authormark\fi\hfil}%

901− \let\@oddfoot\@empty

902− \let\@evenfoot\@oddfoot

903− \def\sectionmark##1{\markboth{##1}{}}%

904− \def\subsectionmark##1{\markright{##1}}%

905−}

906−

907−\def\ps@Empty{%

908− \def\@oddfoot{}%

909− \let\@evenfoot\@oddfoot

910− \def\@evenhead{}%

911− \def\@oddhead{}%

912− \let\@mkboth\markboth

913− \let\chaptermark\@gobble

914− \let\sectionmark\@gobble%

915−}

916−

917−\def\ps@myheadings{\let\@mkboth\@gobbletwo

918− \def\@oddhead{\hfil{\itshape\rightmark}\hfil \llap{\rhfont\thepage}}%

919− \def\@evenhead{\rlap{\rhfont\thepage}\hfil\itshape\leftmark\hfil}%

920− \let\@oddfoot\@empty

921− \let\@evenfoot\@oddfoot

922− \let\sectionmark\@gobble

923− \let\subsectionmark\@gobble

924−}

925−

926−\def\@indjournal{%

927− \vbox to 6.5\p@{\noindent\parbox[t]{4.8in}{\normalfont\affilsize\rmfamily

928− {\itshape J. Functional Programming\/}\ {\bf \@volume}\ (\@issue):\

929−\thepage--\pageref{lastpage}, \@pubyear\hskip7.5pt {Printed in

930−United Kingdom}}%

931− \vss}%

932−}

933−

934−\ifprodtf

935− \let\@j@urnal\@journal

936−\else

937− \let\@j@urnal\@underjournal

938−\fi

939−

940−\def\ps@titlepage{\leftskip\z@ \let\@mkboth\@gobbletwo

941− \def\@oddhead{\ifindex\@indjournal

942−\hfil\hbox{\llap{\rhfont\thepage}}\else\@j@urnal \hfil\raise1.6pt\hbox{\llap{\rhfont\thepage}}\fi}%

943− \let\@evenhead\@oddhead

944− \let\@oddfoot\@empty

945− \let\@evenfoot\@oddfoot

946− \let\sectionmark\@gobble

947− \let\subsectionmark\@gobble

948−}

949−

950−\def\@pnumwidth{1.55em}

951−\def\@tocrmarg {2.55em}

952−\def\@dotsep{4.5}

953−\setcounter{tocdepth}{2}

954−

955−\def\@dottedtocline#1#2#3#4#5{% FROM LATEX.LTX

956− \ifnum #1>\c@tocdepth \else

957− \vskip \z@ \@plus.2\p@

958− {\leftskip #2\relax \rightskip \@tocrmarg \parfillskip -\rightskip

959− \parindent #2\relax\@afterindenttrue

960− \interlinepenalty\@M

961− \leavevmode

962− \@tempdima #3\relax

963− \advance\leftskip \@tempdima \null\hskip -\leftskip

964− {#4}\nobreak

965− \leaders\hbox{$\m@th

966− \mkern \@dotsep mu\hbox{\phantom{.}}\mkern \@dotsep

967− mu$}\hfill

968− \nobreak

969− \hb@xt@\@pnumwidth{\hfil\normalfont \normalcolor #5}%

970− \par}%

971− \fi}

972−

973−\newcommand\contentsname{Contents}

974−

975−\newcommand\tableofcontents{%

976− \section*{\contentsname}%

977− \@starttoc{toc}\par

978− \vspace{13\p@}%

979−}

980−

981−\newcommand*\l@part[2]{%

982− \ifnum \c@tocdepth >-2\relax

983− \addpenalty{-\@highpenalty}%

984− \addvspace{.5\baselineskip \@plus 1\p@}%

985− \begingroup

986− \parindent \z@ \rightskip \@pnumwidth

987− \parfillskip -\@pnumwidth

988− {\leavevmode

989− \normalfont\rmfamily

990− #1\hfil \hb@xt@\@pnumwidth{\hfil}}\par

991− \nobreak

992− \if@compatibility

993− \global\@nobreaktrue

994− \everypar{\global\@nobreakfalse\everypar{}}%

995− \fi

996− \endgroup

997− \vskip .25\baselineskip \@plus 1\p@

998− \fi

999−}

1000−

1001−\newcommand*\l@section[2]{%

1002− \ifnum \c@tocdepth >\z@

1003− \addpenalty\@secpenalty

1004− \setlength\@tempdima{1.5em}%

1005− \begingroup

1006− \parindent \z@ \rightskip \@pnumwidth

1007− \parfillskip -\@pnumwidth

1008− \leavevmode \normalfont\rmfamily

1009− \advance\leftskip\@tempdima

1010− \hskip -\leftskip

1011− {\bfseries #1}\nobreak\hfil \nobreak\hb@xt@\@pnumwidth{\hss #2}\par

1012− \endgroup

1013− \fi}

1014−

1015−\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}

1016−\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}

1017−\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}

1018−\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}}

1019−

1020−\newcommand\listfigurename{List of Figures}

1021−\newcommand\listoffigures{%

1022− \section*{\listfigurename}%

1023− \@starttoc{lof}\par

1024− \vskip 13\p@

1025−}

1026−

1027−\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}

1028−

1029−\newcommand\listtablename{List of Tables}

1030−\newcommand\listoftables{%

1031− \section*{\listtablename}%

1032− \@starttoc{lot}\par

1033− \vskip 13\p@

1034−}

1035−

1036−\let\l@table\l@figure

1037−

1038−\renewcommand\footnoterule{%

1039− \kern-3\p@

1040− \hrule \@width .4\columnwidth height \z@

1041− \kern 3\p@}

1042−

1043−\newif\iftitlefn

1044−

1045−%%

1046−\newbox\tempbox

1047−\newdimen\@footmax

1048−\def\footmax#1{%

1049− \setbox\tempbox\hbox{\footnotesize$^{#1}$}%

1050− \global\@footmax\wd\tempbox\global\advance\@footmax.5em}

1051−%

1052−\footmax{0}

1053−%%

1054−\newcommand\@makefntext[1]{%

1055− \leavevmode\@hangfrom{\hb@xt@ \@footmax{\hss$\iftitlefn\else^\fi{\@thefnmark}\hskip.5em$}}#1}

1056−%%

1057−

1058−\ifprodtf \else \let\highast\ast\fi

1059−

1060−\def\@fnsymbol#1{\ensuremath{% FROM LATEX.LTX

1061− \ifcase#1\or \hbox{$\highast$}\or \dagger\or \ddagger\or

1062− \mathchar "278\or \mathchar "27B\or \|\or \hbox{$\highast\highast$}\or

1063− \dagger\dagger\or \ddagger\ddagger\or \mathchar "278\mathchar "278\or

1064− \mathchar "27B\mathchar "27B\or \|\|\or \else\@ctrerr\fi}%

1065−}

1066−

1067−\renewcommand\@makefnmark{\hbox{$^{\@thefnmark}$}}% FROM LATEX.LTX

1068−\renewcommand\thefootnote{\@arabic\c@footnote}% FROM LATEX.LTX

1069−\renewcommand\thempfootnote{\mathit{\@alph\c@mpfootnote}}% FROM LATEX.LTX

1070−

1071−\setcounter{topnumber}{2}

1072−\renewcommand\topfraction{.9}

1073−\setcounter{bottomnumber}{1}

1074−\renewcommand\bottomfraction{.9}

1075−\setcounter{totalnumber}{3}

1076−\renewcommand\textfraction{.1}

1077−\renewcommand\floatpagefraction{.9}

1078−\setcounter{dbltopnumber}{2}

1079−\renewcommand\dbltopfraction{.9}

1080−\renewcommand\dblfloatpagefraction{.5}

1081−

1082−\newcounter{table}

1083−\renewcommand\thetable{\@arabic\c@table}

1084−\def\fps@table{tbp}

1085−\def\ftype@table{1}

1086−\def\ext@table{lot}

1087−\newcommand\tablename{Table}

1088−\def\fnum@table{\tablename\ \thetable}

1089−

1090−\newenvironment{table}

1091− {\@float{table}}

1092− {\end@float}

1093−

1094−\newenvironment{table*}

1095− {\@dblfloat{table}}

1096− {\end@dblfloat}

1097−

1098−\def\fstyle@table{\normalfont\small\rmfamily}

1099−\def\fjust@table{\centering}

1100−\def\fcapjust@table{\centering}

1101−\def\fcapsize@table{\normalfont\normalsize\rmfamily}

1102−\def\fcapstyle@table{\normalfont\normalsize\itshape}

1103−

1104−\newcommand\contname{(cont.)}

1105−\newcommand\continuedfigure{%

1106− \addtocounter{figure}\m@ne

1107− \let\curr@thefigure\thefigure

1108− \def\thefigure{\curr@thefigure\ \contname}%

1109−}

1110−

1111−\newcommand\continuedtable{%

1112− \addtocounter{table}\m@ne

1113− \let\curr@thetable\thetable

1114− \def\thetable{\curr@thetable\ \contname}%

1115−}

1116−

1117−\newif\ifrem@fullpt

1118−\newcommand\removefullpoint{\global\rem@fullpttrue}

1119−

1120−\newif\ifbot@fig

1121−\newenvironment{bottomfigure}{\def\fps@figure{b}%

1122− \setcounter{bottomnumber}{1}%

1123− \global\bot@figtrue

1124− \@float{figure}\fstyle@figure}

1125− {\end@float}

1126−

1127−\newbox\@tempboxb

1128−

1129−\def\enskip{\hskip4.5pt}

1130−\long\def\@makecaption#1#2{%

1131− \ifbot@fig \rule{30.05pc}{.25\p@}\fi

1132− \vskip 0\p@ %\@plus .4\p@ \@minus .4\p@

1133− \begingroup

1134− \setbox\@tempboxb\hbox{#2}%

1135− \def\@xtra{\ifdim\wd\@tempboxb>\z@ \ifrem@fullpt\else .\enskip\fi\fi}%

1136− \setbox\@tempboxa\hbox{#1\@xtra #2}%

1137− \ifdim\wd\@tempboxa>\tw@\textwidth

1138− {\let\centering\relax #1\@xtra #2\par}%

1139− \else

1140− #1\@xtra #2\par

1141− \fi

1142− \endgroup

1143− \global\bot@figfalse

1144− \global\rem@fullptfalse

1145−}

1146−

1147−\newcounter{figure}

1148−\renewcommand\thefigure{\@arabic\c@figure}

1149−\def\fps@figure{tbp}

1150−\def\ftype@figure{2}

1151−\def\ext@figure{lof}

1152−\newcommand\figurename{Fig.}

1153−\def\fnum@figure{\figurename\ \thefigure}

1154−

1155−\newenvironment{figure}

1156− {\@float{figure}}

1157− {\end@float}

1158−

1159−\newenvironment{figure*}

1160− {\@dblfloat{figure}}

1161− {\end@dblfloat}

1162−

1163−\def\fstyle@figure{\normalfont\small\rmfamily}

1164−\def\fjust@figure{\centering}

1165−\def\fcapjust@figure{\centering}

1166−\def\fcapsize@figure{\normalfont\small\rmfamily}

1167−\def\fcapstyle@figure{\normalfont\small\rmfamily}

1168−

1169−\long\def\@caption#1[#2]#3{% FROM LATEX.LTX

1170− \par

1171− \addcontentsline{\csname ext@#1\endcsname}{#1}%

1172− {\protect\numberline{\csname the#1\endcsname}{\ignorespaces #2}}%

1173− \begingroup

1174− \@parboxrestore

1175− \if@minipage

1176− \@setminipage

1177− \fi

1178− \normalsize

1179− \@makecaption{\csname fcapjust@#1\endcsname

1180− \csname fcapsize@#1\endcsname

1181− \csname fnum@#1\endcsname}%

1182− {\csname fcapstyle@#1\endcsname \ignorespaces #3}\par

1183− \endgroup

1184−}

1185−

1186−\def\@xfloat #1[#2]{% FROM LATEX.LTX

1187− \@nodocument

1188− \def\@captype {#1}%

1189− \def\@fps {#2}%

1190− \@onelevel@sanitize \@fps

1191− \def \reserved@b {!}%

1192− \ifx \reserved@b \@fps

1193− \@fpsadddefault

1194− \else

1195− \ifx \@fps \@empty

1196− \@fpsadddefault

1197− \fi

1198− \fi

1199− \ifhmode

1200− \@bsphack

1201− \@floatpenalty-\@Mii

1202− \else

1203− \@floatpenalty-\@Miii

1204− \fi

1205− \ifinner

1206− \@parmoderr\@floatpenalty\z@

1207− \else

1208− \@next\@currbox\@freelist

1209− {%

1210− \@tempcnta \sixt@@n

1211− \expandafter \@tfor \expandafter \reserved@a

1212− \expandafter :\expandafter =\@fps

1213− \do

1214− {%

1215− \if \reserved@a h%

1216− \ifodd \@tempcnta

1217− \else

1218− \advance \@tempcnta \@ne

1219− \fi

1220− \fi

1221− \if \reserved@a t%

1222− \@setfpsbit \tw@

1223− \fi

1224− \if \reserved@a b%

1225− \@setfpsbit 4%

1226− \fi

1227− \if \reserved@a p%

1228− \@setfpsbit 8%

1229− \fi

1230− \if \reserved@a !%

1231− \ifnum \@tempcnta>15

1232− \advance\@tempcnta -\sixt@@n\relax

1233− \fi

1234− \fi

1235− }%

1236− \@tempcntb \csname ftype@\@captype \endcsname

1237− \multiply \@tempcntb \@xxxii

1238− \advance \@tempcnta \@tempcntb

1239− \global \count\@currbox \@tempcnta

1240− }%

1241− \@fltovf

1242− \fi

1243− \global \setbox\@currbox

1244− \color@vbox

1245− \normalcolor

1246− \vbox \bgroup

1247− \hsize\columnwidth

1248− \@parboxrestore

1249− \@floatboxreset

1250− \csname fstyle@\@captype\endcsname

1251− \csname fjust@\@captype\endcsname

1252−}

1253−

1254−\let\oldtabular\tabular

1255−\let\endoldtabular\endtabular

1256−

1257−\def\tabular{% FROM LATEX.LTX

1258− \def\@halignto{to \textwidth}\tabskip\tabcolsep \@plus 1fil\@ttabular

1259−}

1260−

1261−\def\@ttabular{\leavevmode \hbox \bgroup $\let\@acol\@tabacol

1262− \let\@classz\@tabclassz

1263− \let\@classiv\@tabclassiv \let\\\@tabularcr\@ttabarray}

1264−

1265−\def\@ttabarray{\m@th\@ifnextchar[\@tarray{\@ttarray}}

1266−

1267−\def\@tarray[#1]#2{\t@barray[#1]{@{\tabskip\tw@\tabcolsep \@plus 3\p@}#2}}

1268−\def\@ttarray#1{\t@barray[c]{@{\tabskip\tw@\tabcolsep \@plus 3\p@}#1}}

1269−

1270−\def\t@barray[#1]#2{%

1271− \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi\fi

1272− \bgroup

1273− \setbox\@arstrutbox\hbox{%

1274− \vrule \@height\arraystretch\ht\strutbox

1275− \@depth\arraystretch \dp\strutbox

1276− \@width\z@}%

1277− \@mkpream{#2}%

1278− \edef\@preamble{%

1279− \halign \noexpand\@halignto

1280− \bgroup \tabskip\z@skip \@arstrut \@preamble \tabskip\tabcolsep \@plus 1fil\cr}%

1281− \let\@startpbox\@@startpbox \let\@endpbox\@@endpbox

1282− \let\tabularnewline\\%

1283− \let\par\@empty

1284− \let\@sharp##%

1285− \set@typeset@protect

1286− \lineskip\z@skip\baselineskip\z@skip

1287− \@preamble}

1288−

1289−\newcommand\ls{\kern.15em\relax}

1290−\newcommand\ns{\kern.55em\relax}

1291−

1292−\def\hline{% FROM LATEX.LTX

1293− \noalign{\ifnum0=`}\fi \vskip 6\p@

1294− \hrule \@height \arrayrulewidth \vskip 6\p@

1295− \futurelet \reserved@a\@xhline}

1296−

1297−\def\@xhline{% FROM LATEX.LTX

1298− \ifx\reserved@a\hline

1299− \vskip -12\p@

1300− \vskip\doublerulesep

1301− \fi

1302− \ifnum0=`{\fi}}

1303−

1304−\newcommand\today{}

1305−\edef\today{\number\day\ \ifcase\month\or

1306− January\or February\or March\or April\or May\or June\or

1307− July\or August\or September\or October\or November\or December

1308− \fi \ \number\year}

1309−

1310−\renewcommand\@biblabel[1]{}% FROM LATEX.LTX

1311−\newcommand\newblock{\hskip .11em \@plus .33em \@minus .07em}

1312−

1313−\newcommand\refname{References}

1314−\newenvironment{thebibliography}[1]

1315− {\section*{\refname}%

1316− \normalfont\small\rmfamily

1317− \addcontentsline{toc}{section}{\refname}%

1318− \list{}{\usecounter{enumiv}\labelwidth\z@ \leftmargin 9pt \itemindent -9pt}%

1319− \parindent\z@

1320− \parskip 2\p@ \@plus .1\p@

1321− \sloppy\clubpenalty\z@ \widowpenalty\@M

1322− \sfcode`\.\@m\relax}

1323− {\def\@noitemerr

1324− {\@latex@warning{Empty `thebibliography' environment}}%

1325− \endlist}

1326−%

1327−%

1328−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End Bibliography Section %%%%%%%%%%%%%%%%

1329−\def\@citex[#1]#2{% FROM LATEX.LTX

1330− \let\@citea\@empty

1331− \@cite{\@for\@citeb:=#2\do

1332− {\@citea\def\@citea{; }%

1333− \edef\@citeb{\expandafter\@firstofone\@citeb}%

1334− \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi

1335− \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%

1336− \G@refundefinedtrue

1337− \@latex@warning

1338− {Citation `\@citeb' on page \thepage \space undefined}}%

1339− {\csname b@\@citeb\endcsname}}}{#1}}

1340−

1341−\def\@cite#1#2{{\if@tempswa #2\else (#1)\fi}}% FROM LATEX.LTX

1342−

1343−\let\@internalcite\cite

1344−\def\cite{\def\citename##1{##1}\@internalcite}

1345−\DeclareRobustCommand\shortcite{\def\citename##1{}\@internalcite}

1346−

1347−\newif\iffontfound

1348−\newcommand\checkfont[1]{%

1349− \batchmode

1350− \font\test=#1\relax

1351− \errorstopmode

1352− \fontfoundfalse

1353− \ifx\test\nullfont \else \fontfoundtrue\fi

1354−}

1355−%%%%%%%%%%%

1356−%

1357−\def\ct@indenttext#1{\parindent24pt{\par\hangindent48pt #1\par}}

1358−\def\ct@Indenttext#1{\parindent48pt{\par\hangindent48pt #1\par}}

1359−%

1360−%

1361−%

1362−\newcount\minute

1363−\newcount\hour

1364−\def\currenttime{%

1365− \minute\time

1366− \hour\minute

1367− \divide\hour60

1368− \the\hour:\multiply\hour60\advance\minute-\hour\the\minute}

1369−%%%%%

1370−\def\gray{\special{color CMYK 0 0 0 0.5}}

1371−\def\@questionmark{\vbox to 0pt{\vskip13pc\hskip-5pc

1372− \hbox to \textwidth{\special{color push}\gray\fontsize{270}{270}\selectfont ?

1373− \special{color pop}\hss}}}

1374−\def\questionmark#1{\xdef\@questionmark{#1}}%

1375−%

1376−\def\@TotalChars{}

1377−\def\TotalChars#1{\xdef\@TotalChars{#1}}%

1378−%%

1379−\def\document{\endgroup

1380− \ifx\@unusedoptionlist\@empty\else

1381− \@latex@warning@no@line{Unused global option(s):^^J%

1382− \@spaces[\@unusedoptionlist]}%

1383− \fi

1384− \@colht\textheight

1385− \@colroom\textheight \vsize\textheight

1386− \columnwidth\textwidth

1387− \@clubpenalty\clubpenalty

1388− \if@twocolumn

1389− \advance\columnwidth -\columnsep

1390− \divide\columnwidth\tw@ \hsize\columnwidth \@firstcolumntrue

1391− \fi

1392− \hsize\columnwidth \linewidth\hsize

1393− \begingroup\@floatplacement\@dblfloatplacement

1394− \makeatletter\let\@writefile\@gobbletwo

1395− \global \let \@multiplelabels \relax

1396− \@input{\jobname.aux}%

1397− \endgroup

1398− \if@filesw

1399− \immediate\openout\@mainaux=\jobname.aux

1400− \immediate\write\@mainaux{\relax}

1401− \fi

1402− \process@table

1403− \let\glb@currsize\@empty %% Force math initialization.

1404− \normalsize

1405− \everypar{}%

1406− \ifx\normalsfcodes\@empty

1407− \ifnum\sfcode`\.=\@m

1408− \let\normalsfcodes\frenchspacing

1409− \else

1410− \let\normalsfcodes\nonfrenchspacing

1411− \fi

1412− \fi

1413− \@noskipsecfalse

1414− \let \@refundefined \relax

1415− \let\AtBeginDocument\@firstofone

1416− \@begindocumenthook

1417− \ifdim\topskip<1sp\global\topskip 1sp\relax\fi

1418− \global\@maxdepth\maxdepth

1419− \global\let\@begindocumenthook\@undefined

1420− \ifx\@listfiles\@undefined

1421− \global\let\@filelist\relax

1422− \global\let\@addtofilelist\@gobble

1423− \fi

1424− \gdef\do##1{\global\let ##1\@notprerr}%

1425− \@preamblecmds

1426− \global\let \@nodocument \relax

1427− \global\let\do\noexpand

1428− \ignorespaces}

1429−%

1430−%%

1431−\def\enddocument{\label{lastpage}%

1432− \@checkend{document}%

1433− \@enddocumenthook

1434− \ifodd\c@page\cleardoublepage\else\clearpage\fi

1435− \begingroup

1436− \if@filesw

1437− \immediate\write\@mainaux{\string\questionmark{}}%

1438− \immediate\closeout\@mainaux

1439− \let\@setckpt\@gobbletwo

1440− \let\@newl@bel\@testdef

1441− \@tempswafalse

1442− \makeatletter

1443− \catcode`\\0

1444− \catcode`\{1

1445− \catcode`\}2

1446− \catcode`\^=7

1447− \catcode`\_=8

1448− \catcode`\&=4

1449− \catcode`\$=3

1450− \catcode`\@11

1451− \catcode`\#6

1452− \catcode`\"=12

1453− \input\jobname.aux

1454− \fi

1455− \@dofilelist

1456− \ifdim \font@submax >\fontsubfuzz\relax

1457− \@font@warning{Size substitutions with differences\MessageBreak

1458− up to \font@submax\space have occured.\@gobbletwo}%

1459− \fi

1460− \@defaultsubs

1461− \@refundefined

1462− \if@filesw

1463− \ifx \@multiplelabels \relax

1464− \if@tempswa

1465− \@latex@warning@no@line{Label(s) may have changed.

1466− Rerun to get cross-references right}%

1467− \fi

1468− \else

1469− \@multiplelabels

1470− \fi

1471− \fi

1472− \endgroup

1473− \deadcycles\z@\@@end}

1474−%%

1475−\def\@outputpage{%

1476−\begingroup % the \endgroup is put in by \aftergroup

1477− \let \protect \noexpand

1478− \@resetactivechars

1479− \@parboxrestore

1480− \shipout \vbox{%

1481− \set@typeset@protect

1482− \aftergroup \endgroup

1483− \aftergroup \set@typeset@protect

1484− % correct? or just restore by ending

1485− % the group?

1486− \if@specialpage

1487− \global\@specialpagefalse\@nameuse{ps@\@specialstyle}%

1488− \fi

1489− \if@twoside

1490− \ifodd\count\z@ \let\@thehead\@oddhead \let\@thefoot\@oddfoot

1491− \let\@themargin\oddsidemargin

1492− \else \let\@thehead\@evenhead

1493− \let\@thefoot\@evenfoot \let\@themargin\evensidemargin

1494− \fi

1495− \fi

1496− \reset@font

1497− \normalsize

1498− \normalsfcodes

1499− \let\label\@gobble

1500− \let\index\@gobble

1501− \let\glossary\@gobble

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1849−

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papers/impl-paper/library.bibdeleted−2295

@@ -1,2295 +0,0 @@

1−Automatically generated by Mendeley 1.6

2−Any changes to this file will be lost if it is regenerated by Mendeley.

3−

4−@article{McBride2007,

5−author = {McBride, Conor and Paterson, Ross},

6−file = {:Users/edwin/Documents/Mendeley Desktop/McBride, Paterson/Applicative programming with effects/McBride, Paterson - Applicative programming with effects - 2008.pdf:pdf},

7−journal = {Journal of functional programming},

8−number = {1},

9−pages = {1----13},

10−title = {{Applicative programming with effects}},

11−url = {http://journals.cambridge.org/abstract_S0956796807006326},

12−volume = {18},

13−year = {2008}

14−}

15−@inproceedings{McBride2006,

16−author = {McBride, C and Goguen, H and McKinna, J},

17−booktitle = {Types for Proofs and Programs {(TYPES 2006)}},

18−title = {{A few constructions on constructors}},

19−url = {http://www.springerlink.com/index/P4863U0M41396254.pdf},

20−year = {2006}

21−}

22−@article{McBride2005,

23−author = {McBride, Conor},

24−editor = {Vene, Varmo and Uustalu, Tarmo},

25−isbn = {3540285407},

26−journal = {Advanced Functional Programming},

27−keywords = {Dependent Types},

28−mendeley-tags = {Dependent Types},

29−pages = {130--170},

30−publisher = {Springer},

31−series = {Lecture Notes in Computer Science},

32−title = {{Epigram: Practical programming with dependent types}},

33−url = {http://www.springerlink.com/index/96j7v5vn8tyebeky.pdf},

34−volume = {3622},

35−year = {2005}

36−}

37−@article{Okasaki1993,

38−author = {Okasaki, Chris},

39−file = {:Users/edwin/Documents/Mendeley Desktop/Okasaki/Red-Black Trees in A Functional Setting/Okasaki - Red-Black Trees in A Functional Setting - 1993.pdf:pdf},

40−journal = {Journal of functional programming},

41−title = {{Red-Black Trees in A Functional Setting}},

42−year = {1993}

43−}

44−@inproceedings{Hancock2000,

45−author = {Hancock, Peter and Setzer, Anton},

46−booktitle = {{Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic}},

47−file = {:Users/edwin/Documents/Mendeley Desktop/Hancock, Setzer/Interactive Programs in Dependent Type Theory/Hancock, Setzer - Interactive Programs in Dependent Type Theory - 2000.pdf:pdf},

48−isbn = {3-540-67895-6},

49−month = aug,

50−pages = {317--331},

51−title = {{Interactive Programs in Dependent Type Theory}},

52−url = {http://dl.acm.org/citation.cfm?id=647850.737221},

53−year = {2000}

54−}

55−@article{Turner2004,

56−author = {Turner, D A},

57−file = {:Users/edwin/Documents/Mendeley Desktop/Turner/Total Functional Programming/Turner - Total Functional Programming - 2004.pdf:pdf},

58−journal = {Journal of Universal Computer Science},

59−keywords = {functional programming},

60−number = {7},

61−pages = {751----768},

62−title = {{Total Functional Programming}},

63−volume = {10},

64−year = {2004}

65−}

66−@phdthesis{norell2007thesis,

67−author = {Norell, Ulf},

68−file = {:Users/edwin/Documents/Mendeley Desktop/Norell/Towards a practical programming language based on dependent type theory/Norell - Towards a practical programming language based on dependent type theory - 2007.pdf:pdf},

69−keywords = {Dependent Types},

70−mendeley-tags = {Dependent Types},

71−publisher = {Citeseer},

72−school = {Chalmers University of Technology},

73−title = {{Towards a practical programming language based on dependent type theory}},

74−url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.65.7934&rep=rep1&type=pdf},

75−year = {2007}

76−}

77−@article{Wu,

78−annote = {1,3

79−

80−

81−This paper describes a solution, in Haskell, of the 2012 ICFP Programming Contest task, explaining in particular how Haskell's laziness and higher order functions helped to build a solution in limited time. I enjoyed reading this paper as an experience report - it provides evidence for the importance of high level features such as purity and laziness (for example when describing the GameTrie), and shows that Haskell can handle more realistic, practical, problems such as concurrency and exceptions (for example when dealing gracefully with timeout and communication between solving threads).

82−

83−

84−My main concern with the paper is that it reads as if the reader is already familiar with the contest task. It would be useful to be more precise about the task itself in the introduction, rather than by making it implicit from the code samples. Section 1.1 describes the problem, but only in general terms - I think it would be worth extending this, and correspondingly removing some of the code. In particular, 'stepRobot' and 'updRocks' would probably be fine just with their type signatures if the problem specification was more precise.

85−

86− },

87−author = {Wu, Nicolas and Magalh\~{a}es, Jos\'{e} Pedro and Bransen, Jeroen and Swierstra, Wouter},

88−file = {:Users/edwin/Documents/Mendeley Desktop/Wu et al/Pure and Lazy Lambda Mining/Wu et al. - Pure and Lazy Lambda Mining - Unknown.pdf:pdf},

89−title = {{Pure and Lazy Lambda Mining}}

90−}

91−@inproceedings{NanevskiAAMorrisett2008,

92−abstract = {We describe an axiomatic extension to the Coq proof assistant, that supports writing, reasoning about, and extracting higher-order, dependently-typed programs with side-effects. Coq already includes a powerful functional language that supports dependent types, but that language is limited to pure, total functions. The key contribution of our extension, which we call Ynot, is the added support for computations that may have effects such as non-termination, accessing a mutable store, and throwing/catching exceptions. The axioms of Ynot form a small trusted computing base which has been formally justified in our previous work on Hoare Type Theory (HTT). We show how these axioms can be combined with the powerful type and abstraction mechanisms of Coq to build higher-level reasoning mechanisms which in turn can be used to build realistic, verified software components. To substantiate this claim, we describe here a representative series of modules that implement imperative finite maps, including support for a higher-order (effectful) iterator. The implementations range from simple (e.g., association lists) to complex (e.g., hash tables) but share a common interface which, abstracts the implementation details and ensures that the modules properly implement the finite map abstraction. Copyright 2008 ACM.},

93−author = {{Nanevski A A Morrisett}, G B Shinnar A B Govereau P B Birkedal L C},

94−booktitle = {International Conference on Functional Programming},

95−doi = {10.1145/1411204.1411237},

96−file = {:Users/edwin/Documents/Mendeley Desktop/Nanevski A A Morrisett/Ynot Dependent types for imperative programs/Nanevski A A Morrisett - Ynot Dependent types for imperative programs - 2008.pdf:pdf},

97−isbn = {9781595939197},

98−issn = {15232867},

99−keywords = {Dependent Types},

100−mendeley-tags = {Dependent Types},

101−number = {9},

102−pages = {229--240},

103−title = {{Ynot: Dependent types for imperative programs}},

104−url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-67650032847&partnerID=40&md5=7a5be3083878399cebafda33b1affa6b},

105−volume = {43},

106−year = {2008}

107−}

108−@article{Walt,

109−annote = {-1, 5

110−

111−

112−This paper describes the use of Agda's reflection mechanism to help with proof automation, and gives some simple examples, including proving evenness of natural numbers and proving that a boolean formula is a tautology.

113−

114−

115−It seems that proof automation is important for a practical language with dependent types, and Agda's reflection mechanism as described is likely to help. However, this paper only really scratches the surface of what is possible - existing (unpublished, as far as I'm aware) examples such as the Ring solver go much further towards demonstrating its value.

116−

117−

118−The 'Evenness' example uses a lot of space for something pretty simple. An in practice, the number won't necessarily be known. What if you know "Even x" and need to prove "Even (x + 100)". Does it still work? Similarly for the tautology example - what if there is an unknown formula which is nevertheless known to be a tautology? It would be nice, therefore, to show how such proof obligations come up in practice and how the reflection techniques described help. Without this, it's not clear that the paper answers the given central question of whether Agda's reflective capabilities are sufficient and practically usable.

119−

120−

121−In summary: there's some nice tutorial material here describing reflection and its application, but I don't think there is enough depth for it to be really interesting.

122−

123−

124−Minor comments

125−

126−

127−The fonts and layout look wrong. Is this the proper LaTeX class? Also remember that the colour won't come out in print...

128−

129−

130−p2 "new" keywords seems wrong for a technique was has been aroundfor a couple of years. I know it hasn't been written up elsewhere, but I'd omit the word "new"

131−

132−

133−p3 "This is why we have decidable equality" - can you explain what you mean by this, for the non-Agda expert?

134−

135−

136−Vars are naturals - so they are de Bruijn indexed?

137−

138−

139−p5 "Other terms are rejected" - what does it mean for a term to be rejected? i.e. what is the effect? The text hints that this is a type error, since there is a suggestion that a proof is needed to show it is valid, but it would be good to be explicit.

140−

141−

142−p8 I'm not sure I'd go as far as to say it's "trivial" to show that (1) is a tautology, but I agree it should be easy, if tedious.},

143−author = {Walt, Paul Van Der and Swierstra, Wouter},

144−file = {:Users/edwin/Documents/Mendeley Desktop/Walt, Swierstra/Engineering Proof by Reflection in Agda/Walt, Swierstra - Engineering Proof by Reflection in Agda - Unknown.pdf:pdf},

145−title = {{Engineering Proof by Reflection in Agda}}

146−}

147−@misc{Haskell98,

148− author = {{Peyton-Jones}, Simon and Hughes, John and Augustsson, Lennart and Barton, Dave and Boutel, Brian and Burton, Warren and Fasel, Joseph and Hammond, Kevin and Hinze, Ralf and Hudak, Paul and Johnsson, Thomas and Jones, Mark and Launchbury, John and Meijer, Erik and Peterson, John and Reid, Alastair and Runciman, Colin and Wadler, Philip},

149− citeulike-article-id = {4034405},

150− comment = {Available from \url{http://www.haskell.org/onlinereport/}},

151− keywords = {file-import-09-02-11, postdoc\_bib},

152− posted-at = {2009-02-11 10:55:50},

153− priority = {2},

154− title = {{The Haskell 98 Report}},

155− year = {1999}

156−}

157−@inproceedings{madhavapeddy2007melange,

158−author = {Madhavapeddy, A. and Ho, A. and Deegan, T. and Scott, D. and Sohan, R.},

159−booktitle = {ACM SIGOPS Operating Systems Review},

160−file = {:Users/edwin/Documents/Mendeley Desktop/Madhavapeddy et al/Melange creating a functional internet/Madhavapeddy et al. - Melange creating a functional internet - 2007.pdf:pdf},

161−number = {3},

162−pages = {101--114},

163−publisher = {ACM},

164−title = {{Melange: creating a functional internet}},

165−url = {http://dl.acm.org/citation.cfm?id=1273009},

166−volume = {41},

167−year = {2007}

168−}

169−@inproceedings{czarnecki2004dsl,

170−author = {Czarnecki, K. and O’Donnell, J. and Striegnitz, J. and Taha, W.},

171−booktitle = {Domain-Specific Program Generation},

172−file = {:Users/edwin/Documents/Mendeley Desktop/Czarnecki et al/DSL implementation in MetaOCaml, Template Haskell, and C/Czarnecki et al. - DSL implementation in MetaOCaml, Template Haskell, and C - 2004.pdf:pdf},

173−pages = {51--72},

174−publisher = {Springer},

175−title = {{DSL implementation in MetaOCaml, Template Haskell, and C++}},

176−url = {http://www.springerlink.com/index/NL620EL7N94M161H.pdf},

177−year = {2004}

178−}

179−@article{Wadler2001,

180−abstract = {The use of monads to structure functional programs is described. Monads provide a convenient framework for simulating effects found in other languages, such as global state, exception handling, output, or non-determinism. Three case studies are looked at in detail: how monads ease the modification of a simple evaluator; how monads act as the basis of a datatype of arrays subject to in-place update; and how monads can be used to build parsers.},

181−author = {Wadler, Philip},

182−doi = {10.1007/3-540-59451-5_2},

183−editor = {Jeuring, Johan and Meijer, Erik},

184−file = {:Users/edwin/Documents/Mendeley Desktop/Wadler/Monads for functional programming/Wadler - Monads for functional programming - 2001.pdf:pdf},

185−isbn = {3540594515},

186−issn = {03029743},

187−journal = {Advanced Functional Programming},

188−number = {August 1992},

189−pages = {24--52},

190−publisher = {Springer},

191−series = {Lecture Notes in Computer Science},

192−title = {{Monads for functional programming}},

193−url = {http://www.springerlink.com/index/715264614rh13340.pdf},

194−volume = {925},

195−year = {2001}

196−}

197−@phdthesis{Boquist1999,

198−author = {Boquist, Urban},

199−file = {:Users/edwin/Documents/Mendeley Desktop/Boquist/Code optimisation techniques for lazy functional languages/Boquist - Code optimisation techniques for lazy functional languages - 1999.pdf:pdf},

200−title = {{Code optimisation techniques for lazy functional languages}},

201−url = {http://mirror.seize.it/papers/Code Optimization Techniques for Lazy Functional Languages.pdf},

202−year = {1999}

203−}

204−@inproceedings{Taha2003,

205−author = {Taha, Walid and Nielsson, Michael Florentin},

206−booktitle = {Principles of Programming Languages},

207−file = {:Users/edwin/Documents/Mendeley Desktop/Taha, Nielsson/Environment Classifiers/Taha, Nielsson - Environment Classifiers - 2003.pdf:pdf},

208−isbn = {1581136285},

209−keywords = {linear,modal logic,multi-stage programming,temporal logic,type safety,type systems},

210−title = {{Environment Classifiers}},

211−year = {2003}

212−}

213−@article{Brady2012a,

214−author = {{Peyton Jones}, S.L.},

215−doi = {10.1093/geront/gns026},

216−file = {:Users/edwin/Documents/Mendeley Desktop/Peyton Jones/Beautiful Code Chapter 24/Peyton Jones - Beautiful Code Chapter 24 - 2012.pdf:pdf},

217−isbn = {9780596510046},

218−issn = {1758-5341},

219−journal = {The Gerontologist},

220−month = dec,

221−number = {6},

222−pages = {NP},

223−pmid = {23150082},

224−title = {{Beautiful Code Chapter 24}},

225−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

226−volume = {52},

227−year = {2012}

228−}

229−@article{mcbride2010ornamental,

230−author = {McBride, Conor},

231−file = {:Users/edwin/Documents/Mendeley Desktop/McBride/Ornamental algebras, algebraic ornaments/McBride - Ornamental algebras, algebraic ornaments - 2010.pdf:pdf},

232−journal = {Journal of Functional Programming},

233−title = {{Ornamental algebras, algebraic ornaments}},

234−url = {http://personal.cis.strath.ac.uk/$\sim$conor/pub/OAAO/Ornament.pdf},

235−year = {2010}

236−}

237−@inproceedings{Gall2012,

238−author = {Gall, Yann Le and Lee, Adam J and Kapdia, Apu},

239−booktitle = {SCMAT},

240−file = {:Users/edwin/Documents/Mendeley Desktop/Gall, Lee, Kapdia/PlexC A Policy Language for Exposure Control/Gall, Lee, Kapdia - PlexC A Policy Language for Exposure Control - 2012.pdf:pdf},

241−isbn = {9781450312950},

242−keywords = {exposure,policy languages,privacy},

243−pages = {219--228},

244−title = {{PlexC : A Policy Language for Exposure Control}},

245−year = {2012}

246−}

247−@article{Campbell-moore,

248−author = {Campbell-moore, Catrin},

249−file = {:Users/edwin/Documents/Mendeley Desktop/Campbell-moore/A Computable Infinitary Logic/Campbell-moore - A Computable Infinitary Logic - Unknown.pdf:pdf},

250−pages = {1--10},

251−title = {{A Computable Infinitary Logic}}

252−}

253−@misc{Resolution2012a,

254−author = {Fall, Kevin R and Stevens, W. Richard},

255−doi = {10.1093/epirev/mxr031},

256−file = {:Users/edwin/Documents/Mendeley Desktop/Fall, Stevens/TCPIP Illustrated Volume 1 Chapter 11/Fall, Stevens - TCPIP Illustrated Volume 1 Chapter 11 - Unknown.pdf:pdf},

257−issn = {1478-6729},

258−pmid = {22215642},

259−title = {{TCP/IP Illustrated Volume 1 Chapter 11}}

260−}

261−@inproceedings{Pasalic2002,

262−author = {Pa\v{s}alic, Emir and Taha, Walid and Sheard, Tim},

263−booktitle = {International Conference on Functional Programming},

264−doi = {10.1145/583852.581499},

265−file = {:Users/edwin/Documents/Mendeley Desktop/Pa\v{s}alic, Taha, Sheard/Tagless staged interpreters for typed languages/Pa\v{s}alic, Taha, Sheard - Tagless staged interpreters for typed languages - 2002.pdf:pdf},

266−isbn = {1-58113-487-8},

267−issn = {03621340},

268−keywords = {calculus of constructions,definitional interpreters,domain-specific languages,multi-stage programming},

269−month = sep,

270−number = {9},

271−pages = {218--229},

272−title = {{Tagless staged interpreters for typed languages}},

273−url = {http://dl.acm.org/citation.cfm?id=583852.581499},

274−volume = {37},

275−year = {2002}

276−}

277−@book{Projects,

278−author = {Hunt, Andrew and Thomas, David},

279−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 8/Hunt, Thomas - The Pragmatic Programmer Chapter 8 - Unknown.pdf:pdf},

280−isbn = {020161622X},

281−title = {{The Pragmatic Programmer Chapter 8}}

282−}

283−@inproceedings{Wadler1989,

284−abstract = {From the type of a polymorphic function we can derive a theorem that it satisfies. Every function of the same type satisfies the same theorem. This provides a free source of useful theorems, courtesy of Reynolds' abstraction theorem for the polymorphic lambda calculus.},

285−author = {Wadler, Philip},

286−booktitle = {Proceedings of the fourth international conference on Functional programming languages and computer architecture},

287−doi = {10.1145/99370.99404},

288−file = {:Users/edwin/Documents/Mendeley Desktop/Wadler/Theorems for free!/Wadler - Theorems for free! - 1989.pdf:pdf},

289−isbn = {0897913280},

290−number = {June},

291−pages = {347--359},

292−publisher = {ACM},

293−series = {FPCA '89},

294−title = {{Theorems for free!}},

295−url = {http://portal.acm.org/citation.cfm?id=99404},

296−year = {1989}

297−}

298−@inproceedings{swierstra2007beauty,

299−author = {Swierstra, W. and Altenkirch, T.},

300−booktitle = {Proceedings of the ACM SIGPLAN workshop on Haskell workshop},

301−file = {:Users/edwin/Documents/Mendeley Desktop/Swierstra, Altenkirch/Beauty in the beast/Swierstra, Altenkirch - Beauty in the beast - 2007.pdf:pdf},

302−pages = {25--36},

303−publisher = {ACM},

304−title = {{Beauty in the beast}},

305−url = {http://dl.acm.org/citation.cfm?id=1291206},

306−year = {2007}

307−}

308−@inproceedings{Xi1999,

309−abstract = {Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.},

310−author = {Xi, Hongwei and Pfenning, Frank},

311−booktitle = {Proceedings of the 26th ACM SIGPLANSIGACT symposium on Principles of programming languages POPL 99},

312−doi = {10.1145/292540.292560},

313−file = {:Users/edwin/Documents/Mendeley Desktop/Xi, Pfenning/Dependent types in practical programming/Xi, Pfenning - Dependent types in practical programming - 1999.pdf:pdf},

314−isbn = {1581130953},

315−issn = {07439016},

316−keywords = {Dependent Types},

317−mendeley-tags = {Dependent Types},

318−organization = {Carnegie Mellon University},

319−pages = {214--227},

320−publisher = {ACM Press},

321−series = {POPL '99},

322−title = {{Dependent types in practical programming}},

323−url = {http://portal.acm.org/citation.cfm?doid=292540.292560},

324−volume = {26},

325−year = {1999}

326−}

327−@inproceedings{Kimmell2012,

328−author = {Kimmell, G and Stump, A and {Eades III}, HD and Fu, Peng and Sheard, Tim and Weirich, S and Casinghino, C and Sj\"{o}berg, V and Collins, N and Ahn, KY},

329−booktitle = {{Proceedings of the 6th {ACM} workshop on Programming Languages Meets Program Verification - PLPV '12}},

330−file = {:Users/edwin/Documents/Mendeley Desktop/Kimmell et al/Equational reasoning about programs with general recursion and call-by-value semantics/Kimmell et al. - Equational reasoning about programs with general recursion and call-by-value semantics - 2012.pdf:pdf},

331−title = {{Equational reasoning about programs with general recursion and call-by-value semantics}},

332−url = {http://dl.acm.org/citation.cfm?id=2103780},

333−year = {2012}

334−}

335−@article{mccann2000packet,

336−author = {McCann, P.J. and Chandra, S.},

337−journal = {ACM SIGCOMM Computer Communication Review},

338−number = {4},

339−pages = {321--333},

340−publisher = {ACM},

341−title = {{Packet types: abstract specification of network protocol messages}},

342−url = {http://dl.acm.org/citation.cfm?id=347563},

343−volume = {30},

344−year = {2000}

345−}

346−@misc{Ferreira2012,

347−annote = {This paper explains how to compile Beluga, a programming language with higher order abstract syntax which is specifically designed to support data structures with binders. In particular, it aims to make it easy to reason about metatheory of programming languages by supporting name generation, alpha conversion and capture avoiding substitution.

348−

349−

350−In general, I liked this paper, primarily because it tackles an underrepresented problem - namely, taking a high level language with support for theorem proving and dependent types, and generating efficient executable code. This is clearly important if such high level languages are to be useful in practice, and even to demonstrate the usefulness and power of the language on anything other than small scale examples.

351−

352−

353−I think this paper can be accepted, though I have some small comments and suggestions for improvements:

354−

355−

356−The introductory example in section 2 provides a generally clear introduction to contextual objects, motivating the problem with a well-understood example. However, it would be nice to say more here about what the target of the compilation is (otherwise I'm not sure what you mean by using "simple names" here). You say: "The output is a fully annotated program using a representation close to the one presented by Cave and Pientka" - as well as the reference it would be very useful here to summarise what that representation is. There are a couple of instances of this, where some background is assumed, which would be good to explain in a couple of sentences in the early sections - e.g. it would also be useful to say what you mean by "Fresh-Style" earlier on.

357−

358−

359−Section 4 - maybe give the informal description of fresh binders earlier?

360−

361−

362−p6-7 On dependency erasure - "The compiler keeps the simple types as a way of sanity check" - is this always true? It isn't true in general for dependent types (consider, for example, a function which computes a simple type) and certainly not with more aggressive dependency erasure such as forcing of constructor arguments which is implemented in Agda and Idris, for example.

363−

364−

365−p9 It seems that the type system is strong enough to support some optimisations on pattern match compilation - such as Epigram's detagging, where the result of a case split on one value informs what another value should be.

366−

367−

368−In related work, you don't mention any other compilers for dependently typed languages which have to tackle similar problems, though you do mention program extraction for Coq. There is also MAlonzo, which translates Agda to Haskell, and Epic (Trends in Functional Programming), used by Epigram, Agda and Idris, which deals with naming though in a much more limited way than this paper.},

369−author = {Ferreira, Francisco and Monnier, Stefan and Pientka, Brigitte},

370−file = {:Users/edwin/Documents/Mendeley Desktop/Ferreira, Monnier, Pientka/Compiling Contextual Objects Bringing Higher-Order Abstract Syntax to Programmers/Ferreira, Monnier, Pientka - Compiling Contextual Objects Bringing Higher-Order Abstract Syntax to Programmers - 2012.pdf:pdf},

371−keywords = {compilation,contextual objects,pattern matching},

372−title = {{Compiling Contextual Objects Bringing Higher-Order Abstract Syntax to Programmers}},

373−year = {2012}

374−}

375−@misc{The2012b,

376−author = {Brooks, Fred},

377−doi = {10.1093/epirev/mxr031},

378−file = {:Users/edwin/Documents/Mendeley Desktop/Brooks/The Design of Design Chapter 1/Brooks - The Design of Design Chapter 1 - Unknown.pdf:pdf},

379−isbn = {9780321702081},

380−issn = {1478-6729},

381−pmid = {22215642},

382−title = {{The Design of Design Chapter 1}}

383−}

384−@book{peyton1987implementation,

385−author = {{Peyton Jones}, S.L.},

386−publisher = {Prentice-Hall, Inc.},

387−title = {{The implementation of functional programming languages (prentice-hall international series in computer science)}},

388−url = {http://dl.acm.org/citation.cfm?id=1096899},

389−year = {1987}

390−}

391−@article{Miller1992,

392−author = {Miller, Dale},

393−file = {:Users/edwin/Documents/Mendeley Desktop/Miller/Unification under a mixed prefix/Miller - Unification under a mixed prefix - 1992.pdf:pdf},

394−journal = {Journal of Symbolic Computation},

395−title = {{Unification under a mixed prefix}},

396−url = {http://www.sciencedirect.com/science/article/pii/074771719290011R},

397−year = {1992},

398−volume = {14},

399−pages = {321--358}

400−}

401−@inproceedings{Danielsson2010,

402−author = {Danielsson, Nils Anders},

403−booktitle = {International Conference on Functional Programming},

404−doi = {10.1145/1932681.1863585},

405−file = {:Users/edwin/Documents/Mendeley Desktop/Danielsson/Total parser combinators/Danielsson - Total parser combinators - 2010.pdf:pdf},

406−isbn = {978-1-60558-794-3},

407−issn = {03621340},

408−keywords = {dependent types,mixed induction and coinduction,parser combinators,productivity,termination},

409−month = sep,

410−number = {9},

411−pages = {285},

412−title = {{Total parser combinators}},

413−url = {http://dl.acm.org/citation.cfm?id=1932681.1863585},

414−volume = {45},

415−year = {2010}

416−}

417−@inproceedings{augustsson1999exercise,

418−author = {Augustsson, L. and Carlsson, M.},

419−booktitle = {In Workshop on Dependent Types in Programming, Gothenburg},

420−keywords = {Depe},

421−mendeley-tags = {Depe},

422−publisher = {Citeseer},

423−title = {{An exercise in dependent types: A well-typed interpreter}},

424−url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.2895},

425−year = {1999}

426−}

427−@inproceedings{Sheard2005,

428−address = {New York, New York, USA},

429−author = {Sheard, Tim},

430−booktitle = {Proceedings of the 2005 ACM SIGPLAN workshop on Haskell - Haskell '05},

431−doi = {10.1145/1088348.1088356},

432−file = {:Users/edwin/Documents/Mendeley Desktop/Sheard/Putting curry-howard to work/Sheard - Putting curry-howard to work - 2005.pdf:pdf},

433−isbn = {159593071X},

434−keywords = {GADT,curry-howard isomorphism,extensional kind system,haskell,logic},

435−month = sep,

436−pages = {74--85},

437−publisher = {ACM Press},

438−title = {{Putting curry-howard to work}},

439−url = {http://dl.acm.org/citation.cfm?id=1088348.1088356},

440−year = {2005}

441−}

442−@phdthesis{McBride1999,

443−author = {McBride, Conor},

444−file = {:Users/edwin/Documents/Mendeley Desktop/McBride/Dependently typed functional programs and their proofs/McBride - Dependently typed functional programs and their proofs - 1999.pdf:pdf},

445−keywords = {Dependent Types},

446−mendeley-tags = {Dependent Types},

447−school = {University of Edinburgh},

448−title = {{Dependently typed functional programs and their proofs}},

449−url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.26.4785&rep=rep1&type=pdf},

450−year = {1999}

451−}

452−@article{The2012a,

453−author = {Bentley, Jon},

454−doi = {10.1093/geront/gns026},

455−file = {:Users/edwin/Documents/Mendeley Desktop/Bentley/Beautiful Code Chapter 3/Bentley - Beautiful Code Chapter 3 - 2012.pdf:pdf},

456−isbn = {9780596510046},

457−issn = {1758-5341},

458−month = dec,

459−number = {6},

460−pages = {NP},

461−pmid = {23150082},

462−title = {{Beautiful Code Chapter 3}},

463−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

464−volume = {52},

465−year = {2012}

466−}

467−@inproceedings{Fournet2011,

468−author = {Fournet, Cedric and Bhargavan, Karthikeyan and Gordon, Andrew D},

469−booktitle = {Foundations of security analysis and design {VI}},

470−file = {:Users/edwin/Documents/Mendeley Desktop/Fournet, Bhargavan, Gordon/Cryptographic verification by typing for a sample protocol implementation/Fournet, Bhargavan, Gordon - Cryptographic verification by typing for a sample protocol implementation - 2010.pdf:pdf},

471−title = {{Cryptographic verification by typing for a sample protocol implementation}},

472−url = {http://www.springerlink.com/index/V168041M46658R73.pdf},

473−year = {2010}

474−}

475−@inproceedings{chlipala2010ur,

476−author = {Chlipala, Adam},

477−booktitle = {ACM SIGPLAN Notices},

478−file = {:Users/edwin/Documents/Mendeley Desktop/Chlipala/Ur statically-typed metaprogramming with type-level record computation/Chlipala - Ur statically-typed metaprogramming with type-level record computation - 2010.pdf:pdf},

479−number = {6},

480−pages = {122--133},

481−publisher = {ACM},

482−title = {{Ur: statically-typed metaprogramming with type-level record computation}},

483−url = {http://dl.acm.org/citation.cfm?id=1806612},

484−volume = {45},

485−year = {2010}

486−}

487−@article{Fluet,

488−annote = {0,3

489−

490−

491−This paper gives a control flow analysis for polymorphic functional programs (specifically System F with recursion). Surprisingly (to me at least) this appears not to have been done before, with previous analyses targetting dynamically typed or simply typed languages, or handling polymorphism by explicitly eliminating it. It seems to be a worthwhile exercise: richer static type systems should give more information to support static analysis.

492−

493−

494−While I like what is achieved by this paper, I did find it rather hard going. The introduction feels laboured and then the paper covers a lot of detail (possibly too much) in quite a short space (though it still runs to 18 pages, two more than the limit!). I would suggest that the paper would be much improved, particularly to a non-expert reader, if it give one or more motivating examples in the introduction and showed how the analysis applied to these examples, when translated to ANF.

495−I think this would shorten the introduction and give a much better intuition for the rules.},

496−author = {Fluet, Matthew},

497−file = {:Users/edwin/Documents/Mendeley Desktop/Fluet/A Type- and Control-Flow Analysis for System F/Fluet - A Type- and Control-Flow Analysis for System F - Unknown.pdf:pdf},

498−pages = {1--18},

499−title = {{A Type- and Control-Flow Analysis for System F}}

500−}

501−@article{Vytiniotis2011,

502−author = {Vytiniotis, Dimitrios and {Peyton Jones}, Simon and Schrijvers, Tom and Sulzmann, Martin},

503−file = {:Users/edwin/Documents/Mendeley Desktop/Vytiniotis et al/textsc{OutsideIn}(X) Modular type inference with local assumptions/Vytiniotis et al. - textsc{OutsideIn}(X) Modular type inference with local assumptions - 2011.pdf:pdf;:Users/edwin/Documents/Mendeley Desktop/Vytiniotis et al/textsc{OutsideIn}(X) Modular type inference with local assumptions/Vytiniotis et al. - textsc{OutsideIn}(X) Modular type inference with local assumptions - 2011(2).pdf:pdf},

504−journal = {{Journal of Functional Programming}},

505−number = {4--5},

506−pages = {333----412},

507−title = {{\textsc{OutsideIn}(X) Modular type inference with local assumptions}},

508−url = {http://journals.cambridge.org/abstract_S0956796811000098},

509−volume = {21},

510−year = {2011}

511−}

512−@inproceedings{Gregoire2005,

513−author = {Gregoire, Benjamin and Mahboubi, Assia},

514−booktitle = {{Theorem Proving in Higher Order Logics (TPHOLS 2005)}},

515−file = {:Users/edwin/Documents/Mendeley Desktop/Gregoire, Mahboubi/Proving Equalities in a Commutative Ring Done Right in Coq/Gregoire, Mahboubi - Proving Equalities in a Commutative Ring Done Right in Coq - 2005.pdf:pdf},

516−pages = {98----113},

517−title = {{Proving Equalities in a Commutative Ring Done Right in Coq}},

518−url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.3041},

519−year = {2005}

520−}

521−@book{Cryptography2012,

522−author = {Anderson, Ross},

523−doi = {10.1093/intimm/dxs023},

524−file = {:Users/edwin/Documents/Mendeley Desktop/Anderson/Security Engineering Chapter 5/Anderson - Security Engineering Chapter 5 - Unknown.pdf:pdf},

525−isbn = {9780470068526},

526−issn = {1460-2377},

527−number = {4},

528−pmid = {22451589},

529−title = {{Security Engineering Chapter 5}},

530−url = {http://www.ncbi.nlm.nih.gov/pubmed/22451589},

531−volume = {24}

532−}

533−@article{Brady,

534−author = {Butenhof, David R.},

535−file = {:Users/edwin/Documents/Mendeley Desktop/Butenhof/Programming with POSIX Threads Chapter 8/Butenhof - Programming with POSIX Threads Chapter 8 - Unknown.pdf:pdf},

536−isbn = {0201633922},

537−title = {{Programming with POSIX Threads Chapter 8}}

538−}

539−@inproceedings{oury2008power,

540−author = {Oury, N. and Swierstra, W.},

541−booktitle = {International Conference on Functional Programming},

542−file = {:Users/edwin/Documents/Mendeley Desktop/Oury, Swierstra/The power of Pi/Oury, Swierstra - The power of Pi - 2008.pdf:pdf},

543−keywords = {Dependent Types},

544−mendeley-tags = {Dependent Types},

545−number = {9},

546−pages = {39--50},

547−publisher = {ACM},

548−title = {{The power of Pi}},

549−url = {http://dl.acm.org/citation.cfm?id=1411213},

550−volume = {43},

551−year = {2008}

552−}

553−@article{McBride2004a,

554−abstract = {ABSTRACT Pattern matching has proved an extremely powerful and durable notion in functional programming. This paper contributes a new programming notation for type theory which elaborates the notion in various ways. First, as is by now quite well-known in the type theory community, definition by pattern matching becomes a more discriminating tool in the presence of dependent types, since it refines the explanation of types as well as values. This becomes all the more true in the presence of the rich class of datatypes known as inductive families (Dybjer, 1991). Secondly, as proposed by Peyton Jones (1997) for Haskell, and independently rediscovered by us, subsidiary case analyses on the results of intermediate computations, which commonly take place on the right-hand side of definitions by pattern matching, should rather be handled on the left. In simply-typed languages, this subsumes the trivial case of Boolean guards; in our setting it becomes yet more powerful. Thirdly, elementary pattern matching decompositions have a well-defined interface given by a dependent type; they correspond to the statement of an induction principle for the datatype. More general, user-definable decompositions may be defined which also have types of the same general form. Elementary pattern matching may therefore be recast in abstract form, with a semantics given by translation. Such abstract decompositions of data generalize Wadler's (1987) notion of ‘view’. The programmer wishing to introduce a new view of a type mathitT, and exploit it directly in pattern matching, may do so via a standard programming idiom. The type theorist, looking through the Curry–Howard lens, may see this as proving a theorem, one which establishes the validity of a new induction principle for mathitT. We develop enough syntax and semantics to account for this high-level style of programming in dependent type theory. We close with the development of a typechecker for the simply-typed lambda calculus, which furnishes a view of raw terms as either being well-typed, or containing an error. The implementation of this view is ipso facto a proof that typechecking is decidable.},

555−author = {McBride, Conor and McKinna, James},

556−doi = {10.1017/S0956796803004829},

557−file = {:Users/edwin/Documents/Mendeley Desktop/McBride, McKinna/The view from the left/McBride, McKinna - The view from the left - 2004.pdf:pdf},

558−issn = {09567968},

559−journal = {Journal of Functional Programming},

560−keywords = {Dependent Types},

561−mendeley-tags = {Dependent Types},

562−number = {1},

563−pages = {69--111},

564−publisher = {Cambridge University Press},

565−title = {{The view from the left}},

566−url = {http://www.journals.cambridge.org/abstract_S0956796803004829},

567−volume = {14},

568−year = {2004}

569−}

570−@book{Cryptography2012a,

571−author = {Pfleeger, Charles P and Pfleeger, S. L.},

572−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

573−doi = {10.1093/ntr/nts035},

574−file = {:Users/edwin/Documents/Mendeley Desktop/Pfleeger, Pfleeger/Security in Computing Chapter 2/Pfleeger, Pfleeger - Security in Computing Chapter 2 - 2012.pdf:pdf},

575−isbn = {0132390779},

576−issn = {1469-994X},

577−month = oct,

578−number = {10},

579−pages = {NP},

580−pmid = {23012339},

581−title = {{Security in Computing Chapter 2}},

582−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

583−volume = {14},

584−year = {2012}

585−}

586−@phdthesis{Pretnar2010,

587−author = {Pretnar, Matija},

588−file = {:Users/edwin/Documents/Mendeley Desktop/Pretnar/The Logic and Handling of Algebraic Effects/Pretnar - The Logic and Handling of Algebraic Effects - 2010.pdf:pdf},

589−school = {University of Edinburgh},

590−title = {{The Logic and Handling of Algebraic Effects}},

591−year = {2010}

592−}

593−@inproceedings{Brady2010,

594−author = {Brady, Edwin and Hammond, Kevin},

595−booktitle = {Proceedings of the 15th ACM SIGPLAN international conference on Functional programming},

596−file = {:Users/edwin/Documents/Mendeley Desktop/Brady, Hammond/Scrapping your inefficient engine using partial evaluation to improve domain-specific language implementation/Brady, Hammond - Scrapping your inefficient engine using partial evaluation to improve domain-specific language implementation - 2010.pdf:pdf},

597−isbn = {9781605587943},

598−keywords = {Dependent Types,code generation gives,contrast,dependent types,efficient,harder,however,implementation,likely efficient,ness interpreter,partial evaluation,resulting implementation,un,verify its correctness},

599−mendeley-tags = {Dependent Types},

600−pages = {297--308},

601−publisher = {ACM},

602−title = {{Scrapping your inefficient engine: using partial evaluation to improve domain-specific language implementation}},

603−url = {http://portal.acm.org/citation.cfm?id=1863587},

604−year = {2010}

605−}

606−@misc{Danielsson2002,

607−author = {Danielsson, Nils Anders and Altenkirch, Thorsten},

608−file = {:Users/edwin/Documents/Mendeley Desktop/Danielsson, Altenkirch/Subtyping, Declaratively/Danielsson, Altenkirch - Subtyping, Declaratively - 2002.pdf:pdf},

609−title = {{Subtyping, Declaratively}},

610−year = {2002}

611−}

612−@book{Strings2012,

613−author = {Sedgewick, Robert and Wayne, Kevin},

614−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

615−doi = {10.1093/ntr/nts035},

616−file = {:Users/edwin/Documents/Mendeley Desktop/Sedgewick, Wayne/Algorithms Chapter 5/Sedgewick, Wayne - Algorithms Chapter 5 - 2012.pdf:pdf},

617−isbn = {9780132762571},

618−issn = {1469-994X},

619−month = oct,

620−number = {10},

621−pages = {NP},

622−pmid = {23012339},

623−title = {{Algorithms Chapter 5}},

624−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

625−volume = {14},

626−year = {2012}

627−}

628−@inproceedings{Augustsson1985,

629−address = {Berlin, Heidelberg},

630−author = {Augustsson, Lennart},

631−booktitle = {Functional Programming Languages and Computer Architecture},

632−doi = {10.1007/3-540-15975-4},

633−editor = {Jouannaud, Jean-Pierre},

634−isbn = {978-3-540-15975-9},

635−keywords = {Computer Science},

636−pages = {368----381},

637−publisher = {Springer Berlin Heidelberg},

638−series = {Lecture Notes in Computer Science},

639−title = {{Compiling Pattern Matching}},

640−url = {http://www.springerlink.com/content/y647423656557505/},

641−volume = {201},

642−year = {1985}

643−}

644−@misc{Abel1998,

645−author = {Abel, Andreas},

646−booktitle = {Language},

647−file = {:Users/edwin/Documents/Mendeley Desktop/Abel/foetus - Termination Checker for Simple Functional Programs/Abel - foetus - Termination Checker for Simple Functional Programs - 1998.pdf:pdf},

648−title = {{foetus - Termination Checker for Simple Functional Programs}},

649−year = {1998}

650−}

651−@article{Silkensen,

652−author = {Silkensen, Erik and Siek, Jeremy},

653−file = {:Users/edwin/Documents/Mendeley Desktop/Silkensen, Siek/Well-typed Islands Parse Faster/Silkensen, Siek - Well-typed Islands Parse Faster - Unknown.pdf:pdf},

654−title = {{Well-typed Islands Parse Faster}}

655−}

656−@misc{Svenningsson,

657−author = {Svenningsson, Josef and Axelsson, Emil},

658−booktitle = {Writing},

659−file = {:Users/edwin/Documents/Mendeley Desktop/Svenningsson, Axelsson/Combining Deep and Shallow Embedding for EDSL/Svenningsson, Axelsson - Combining Deep and Shallow Embedding for EDSL - Unknown.pdf:pdf},

660−title = {{Combining Deep and Shallow Embedding for EDSL}}

661−}

662−@misc{Bauer,

663−archivePrefix = {arXiv},

664−arxivId = {arXiv:1203.1539v1},

665−author = {Bauer, Andrej and Pretnar, Matija},

666−eprint = {arXiv:1203.1539v1},

667−file = {:Users/edwin/Documents/Mendeley Desktop/Bauer, Pretnar/Programming with Algebraic Effects and Handlers/Bauer, Pretnar - Programming with Algebraic Effects and Handlers - Unknown.pdf:pdf},

668−keywords = {()},

669−title = {{Programming with Algebraic Effects and Handlers}}

670−}

671−@misc{Krustev,

672−author = {Krustev, Dimitur},

673−booktitle = {Language},

674−file = {:Users/edwin/Documents/Mendeley Desktop/Krustev/Towards a Framework for Building Formally Verified Supercompilers in Coq/Krustev - Towards a Framework for Building Formally Verified Supercompilers in Coq - Unknown.pdf:pdf},

675−title = {{Towards a Framework for Building Formally Verified Supercompilers in Coq}}

676−}

677−@book{Graphs2012,

678−author = {Sedgewick, Robert and Wayne, Kevin},

679−booktitle = {The Gerontologist},

680−doi = {10.1093/geront/gns026},

681−file = {:Users/edwin/Documents/Mendeley Desktop/Sedgewick, Wayne/Algorithms Chapter 4/Sedgewick, Wayne - Algorithms Chapter 4 - 2012.pdf:pdf},

682−isbn = {9780132762571},

683−issn = {1758-5341},

684−month = dec,

685−number = {6},

686−pages = {NP},

687−pmid = {23150082},

688−title = {{Algorithms Chapter 4}},

689−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

690−volume = {52},

691−year = {2012}

692−}

693−@misc{Brady2012c,

694−author = {Brooks, Fred},

695−doi = {10.1093/epirev/mxr031},

696−file = {:Users/edwin/Documents/Mendeley Desktop/Brooks/The Design of Design Chapter 5/Brooks - The Design of Design Chapter 5 - Unknown.pdf:pdf},

697−isbn = {9780321702081},

698−issn = {1478-6729},

699−number = {1},

700−pages = {NP},

701−pmid = {22215642},

702−title = {{The Design of Design Chapter 5}},

703−volume = {34}

704−}

705−@inproceedings{coquand1986analysis,

706−author = {Coquand, T.},

707−booktitle = {{Proceedings of the First IEEE Symposium on Logic in Computer Science}},

708−file = {:Users/edwin/Documents/Mendeley Desktop/Coquand/An analysis of Girard's paradox/Coquand - An analysis of Girard's paradox - 1986.pdf:pdf},

709−pages = {227----246},

710−title = {{An analysis of Girard's paradox}},

711−url = {http://hal.inria.fr/docs/00/07/60/23/PDF/RR-0531.pdf},

712−year = {1986}

713−}

714−@book{Harper2012,

715−author = {Harper, Robert},

716−file = {:Users/edwin/Documents/Mendeley Desktop/Harper/Practical Foundations for Programming Languages/Harper - Practical Foundations for Programming Languages - 2012.pdf:pdf},

717−title = {{Practical Foundations for Programming Languages}},

718−year = {2012}

719−}

720−@misc{dagand2011transporting,

721−author = {Dagand, Pierre-Evariste and McBride, Conor},

722−file = {:Users/edwin/Documents/Mendeley Desktop/Dagand, McBride/Transporting Functions across Ornaments/Dagand, McBride - Transporting Functions across Ornaments - 2011.pdf:pdf},

723−title = {{Transporting Functions across Ornaments}},

724−url = {http://personal.cis.strath.ac.uk/$\sim$dagand/stuffs/paper-2011-patch/paper.pdf},

725−year = {2011}

726−}

727−@article{Abel2010,

728−abstract = {Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstractions like higher-order functions and polymorphism. To study the application of sized types to proof assistants and programming languages based on dependent type theory, we have implemented a core language, MiniAgda, with explicit handling of sizes. New considerations were necessary to soundly integrate sized types with dependencies and pattern matching, which was made possible by concepts such as inaccessible patterns and parametric function spaces. This paper provides an introduction to MiniAgda by example and informal explanations of the underlying principles.},

729−author = {Abel, Andreas},

730−file = {:Users/edwin/Documents/Mendeley Desktop/Abel/MiniAgda Integrating Sized and Dependent Types/Abel - MiniAgda Integrating Sized and Dependent Types - 2010.pdf:pdf},

731−journal = {EPTCS},

732−pages = {1--15},

733−title = {{MiniAgda: Integrating Sized and Dependent Types}},

734−url = {http://arxiv.org/abs/1012.4896},

735−volume = {43},

736−year = {2010}

737−}

738−@article{burrows1990,

739−author = {Burrows, Michael and Abadi, Martin and Needham, Roger},

740−file = {:Users/edwin/Documents/Mendeley Desktop/Burrows, Abadi, Needham/A logic of authentication/Burrows, Abadi, Needham - A logic of authentication - 1990.pdf:pdf},

741−journal = {ACM Transactions on Computer Systems},

742−pages = {18----36},

743−title = {{A logic of authentication}},

744−url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.3569},

745−volume = {8},

746−year = {1990}

747−}

748−@article{loh2010tutorial,

749−author = {L\"{o}h, A. and McBride, C. and Swierstra, W.},

750−file = {:Users/edwin/Documents/Mendeley Desktop/L\"{o}h, McBride, Swierstra/A tutorial implementation of a dependently typed lambda calculus/L\"{o}h, McBride, Swierstra - A tutorial implementation of a dependently typed lambda calculus - 2010.pdf:pdf},

751−journal = {Fundamenta Informaticae},

752−number = {2},

753−pages = {177--207},

754−publisher = {IOS Press},

755−title = {{A tutorial implementation of a dependently typed lambda calculus}},

756−url = {http://iospress.metapress.com/index/976W4716TM79M6U8.pdf},

757−volume = {102},

758−year = {2010}

759−}

760−@article{mcbride2008functional,

761−author = {McBride, C. and Paterson, R.},

762−file = {:Users/edwin/Documents/Mendeley Desktop/McBride, Paterson/Functional pearl Applicative programming with effects/McBride, Paterson - Functional pearl Applicative programming with effects - 2008.pdf:pdf},

763−journal = {Journal of functional programming},

764−number = {1},

765−pages = {1--13},

766−publisher = {Cambridge Univ Press},

767−title = {{Functional pearl: Applicative programming with effects}},

768−url = {http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=1457860},

769−volume = {18},

770−year = {2008}

771−}

772−@techreport{Cardelli1988,

773−author = {Cardelli, L},

774−file = {:Users/edwin/Documents/Mendeley Desktop/Cardelli/Phase distinctions in type theory/Cardelli - Phase distinctions in type theory - 1988.pdf:pdf},

775−title = {{Phase distinctions in type theory}},

776−year = {1988}

777−}

778−@misc{Abadi1997,

779−author = {Abadi, Martin and Gordon, Andrew D},

780−booktitle = {4TH ACM CONFERENCE ON COMPUTER AND COMMUNICATIONS SECURITY},

781−file = {:Users/edwin/Documents/Mendeley Desktop/Abadi, Gordon/A calculus for cryptographic protocols The spi calculus/Abadi, Gordon - A calculus for cryptographic protocols The spi calculus - 1997.pdf:pdf},

782−pages = {36 -- 47},

783−title = {{A calculus for cryptographic protocols: The spi calculus}},

784−url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.2176},

785−year = {1997}

786−}

787−@article{Haskell2012a,

788−author = {Biancuzzi, F and Warden, S},

789−doi = {10.1093/epirev/mxr031},

790−file = {:Users/edwin/Documents/Mendeley Desktop/Biancuzzi, Warden/Masterminds of Programming Chapter 8/Biancuzzi, Warden - Masterminds of Programming Chapter 8 - Unknown.pdf:pdf},

791−isbn = {9780596801670},

792−issn = {1478-6729},

793−pmid = {22215642},

794−title = {{Masterminds of Programming Chapter 8}}

795−}

796−@inproceedings{madhavapeddy2010turning,

797−author = {Madhavapeddy, A. and Mortier, R. and Sohan, R. and Gazagnaire, T. and Hand, S. and Deegan, T. and McAuley, D. and Crowcroft, J.},

798−booktitle = {Proceedings of the 2nd USENIX conference on Hot topics in cloud computing},

799−file = {:Users/edwin/Documents/Mendeley Desktop/Madhavapeddy et al/Turning down the LAMP software specialisation for the cloud/Madhavapeddy et al. - Turning down the LAMP software specialisation for the cloud - 2010.pdf:pdf},

800−publisher = {USENIX Association},

801−title = {{Turning down the LAMP: software specialisation for the cloud}},

802−url = {http://dl.acm.org/citation.cfm?id=1863114},

803−year = {2010}

804−}

805−@misc{Braßel,

806−annote = {New compilation system for Curry, a Haskell like language with equational constraints, making it a functional logic language.

807−

808−

809−What is the contribution of this paper? i.e. what is new about the compiler? Seems to be efficient implementation of equational constraints.

810−

811−

812−Nice introduction to the language, easy for a Haskell programmer to follow, and nice explanation of how it works motivating the problem. But I find it hard to tell what in the paper is already known and what is a specific contribution.

813−

814−

815−Functional patterns look nice, if hard to implement. Related to views? Limitations?

816−Could these techniques improve (compile-time) unification in dependently typed languages?

817−

818−

819−Not many results. Encouraging, but only 7 of various forms isn't conclusive. },

820−author = {Bra\ss el, Bernd and Hanus, Michael and Peem\"{o}ller, Bj\"{o}rn and Reck, Fabian},

821−file = {:Users/edwin/Documents/Mendeley Desktop/Bra\ss el et al/Implementing Equational Constraints in a Functional Language/Bra\ss el et al. - Implementing Equational Constraints in a Functional Language - Unknown.pdf:pdf},

822−keywords = {func-,functional logic programming,implementation,unification},

823−title = {{Implementing Equational Constraints in a Functional Language}}

824−}

825−@inproceedings{Brady2003,

826−author = {Brady, Edwin and McBride, Conor and McKinna, James},

827−booktitle = {Types for Proofs and Programs {(TYPES 2003)}},

828−file = {:Users/edwin/Documents/Mendeley Desktop/Brady, McBride, McKinna/Inductive families need not store their indices/Brady, McBride, McKinna - Inductive families need not store their indices - 2003.pdf:pdf},

829−keywords = {Dependent Types},

830−mendeley-tags = {Dependent Types},

831−title = {{Inductive families need not store their indices}},

832−year = {2003}

833−}

834−@book{An2012,

835−author = {Fowler, Martin},

836−booktitle = {Carcinogenesis},

837−doi = {10.1093/carcin/bgs054},

838−file = {:Users/edwin/Documents/Mendeley Desktop/Fowler/Domain Specific Languages Chapter 1/Fowler - Domain Specific Languages Chapter 1 - Unknown.pdf:pdf},

839−isbn = {9780132107549},

840−issn = {1460-2180},

841−number = {3},

842−pmid = {22383472},

843−title = {{Domain Specific Languages Chapter 1}},

844−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

845−volume = {33}

846−}

847−@book{Choosing2012,

848−author = {Fowler, Martin},

849−booktitle = {Carcinogenesis},

850−doi = {10.1093/carcin/bgs054},

851−file = {:Users/edwin/Documents/Mendeley Desktop/Fowler/Domain Specific Languages Chapter 6/Fowler - Domain Specific Languages Chapter 6 - Unknown.pdf:pdf},

852−isbn = {9780132107549},

853−issn = {1460-2180},

854−number = {3},

855−pmid = {22383472},

856−title = {{Domain Specific Languages Chapter 6}},

857−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

858−volume = {33}

859−}

860−@misc{altenkirch2008nσ,

861−author = {Altenkirch, T. and Oury, N.},

862−file = {:Users/edwin/Documents/Mendeley Desktop/Altenkirch, Oury/$Pi$$Sigma$ A Core Language for Dependently Typed Programming/Altenkirch, Oury - $Pi$$Sigma$ A Core Language for Dependently Typed Programming - 2008.pdf:pdf},

863−title = {{$\Pi$$\Sigma$: A Core Language for Dependently Typed Programming}},

864−url = {http://verse.aasemoon.com/images/6/6f/PiSigma.pdf},

865−year = {2008}

866−}

867−@misc{Silkensen2012,

868−annote = {This paper tackles an interesting problem, namely that of building DSLs independently which are nevertheless composable (at least as far as parsing goes). The claim is that the approach taken - using type based disambiguation - can combine the good features of internal and external DSLs - namely, that they become easier to implement, and have a nice syntax.

869−

870−

871−I found the paper interesting to read, the contribution worthwhile and the results convincing, though I have a few suggestions for preparing the paper for TFP submission, since it wouldn't be possible to accept it in its current form.

872−

873−

874−Perhaps most importantly, the draft submission is in the SIGPLAN format, which means you've used a lot more space than you have available. I find that 1 SIGPLAN page becomes at least 2 in Springer format because of font size and margins, so you'll need to think carefully about what you consider the most important contribution of the paper, how much detail you can go into, and how many examples to give.

875−If it helps, I think you could reduce section 5 to just a short sketch of Typed Racket and there'd be enough of a contribution to justify a TFP paper (though of course I can't speak for other potential referees!)

876−

877−

878−I found the paper a bit difficult to read at first since I don't have a detailed understand of parsing algorithms, and I suspect I won't be alone in this among the TFP readership. It would be useful to say more in the introduction about island parsing, and what a chart parsing strategy is. An intuitive explanation of the various parsing algorithms you give formally (Example 2.3, say) would be very useful for this (possibly even more useful than the formal descriptions...).

879−

880−

881−Another advantage of internal DSLs that I didn't see mentioned explicitly in the paper is that many features of the host language - syntax, code generation, type checking - are available for free, but have to be implemented explicitly for an external DSL. Maybe this is part of what you mean by interoperability. There is more than parsing needed for this though.

882−

883−

884−A question on contribution 1: how realistic is it to assume that nonterminals are largely disjoint? I could imagine, say, function calls or arithmetic being part of multiple DSLs if not factored out. Or have I misunderstood what you mean?

885−

886−

887−Some modern languages with dependent types have systems for syntax extension, e.g. Agda has mixfix declarations, Idris has syntax rules, type-directed elaboration and overloaded variable bindings. I wonder, therefore, if your approach to parsing could be better integrated into this kind of language, where embedded verifiable DSLs seem to be an obvious application. The Typed Racket example suggests to me that this would be an interesting thing to explore.},

888−author = {Silkensen, Erik and Siek, Jeremy},

889−file = {:Users/edwin/Documents/Mendeley Desktop/Silkensen, Siek/Well-typed Islands Parse Faster/Silkensen, Siek - Well-typed Islands Parse Faster - 2012.pdf:pdf},

890−pages = {1--12},

891−title = {{Well-typed Islands Parse Faster}},

892−year = {2012}

893−}

894−@misc{The2012c,

895−author = {Robbins, A and Hannah, E and Lamb, L},

896−doi = {10.1093/epirev/mxr031},

897−file = {:Users/edwin/Documents/Mendeley Desktop/Robbins, Hannah, Lamb/Learning the vi and Vim Editors/Robbins, Hannah, Lamb - Learning the vi and Vim Editors - Unknown.pdf:pdf},

898−isbn = {9780596529833},

899−issn = {1478-6729},

900−pmid = {22215642},

901−title = {{Learning the vi and Vim Editors}}

902−}

903−@misc{idristutorial,

904−author = {Brady, Edwin},

905−file = {:Users/edwin/Documents/Mendeley Desktop/Brady/Programming in Idris a tutorial/Brady - Programming in Idris a tutorial - 2012.pdf:pdf},

906−title = {{Programming in Idris : a tutorial}},

907−url = {http://idris-lang.org/tutorial},

908−year = {2013}

909−}

910−@book{Simon2012,

911−author = {Seibel, Peter},

912−booktitle = {The Gerontologist},

913−doi = {10.1093/geront/gns026},

914−file = {:Users/edwin/Documents/Mendeley Desktop/Seibel/Coders at Work Chapter 7/Seibel - Coders at Work Chapter 7 - 2012.pdf:pdf},

915−isbn = {9781430219484},

916−issn = {1758-5341},

917−month = dec,

918−number = {6},

919−pages = {NP},

920−pmid = {23150082},

921−title = {{Coders at Work Chapter 7}},

922−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

923−volume = {52},

924−year = {2012}

925−}

926−@misc{TheMendeleySupportTeam2011,

927−abstract = {A quick introduction to Mendeley. Learn how Mendeley creates your personal digital library, how to organize and annotate documents, how to collaborate and share with colleagues, and how to generate citations and bibliographies.},

928−address = {London},

929−author = {{The Mendeley Support Team}},

930−booktitle = {Mendeley Desktop},

931−file = {:Users/edwin/Documents/Mendeley Desktop/The Mendeley Support Team/Getting Started with Mendeley/The Mendeley Support Team - Getting Started with Mendeley - 2011.pdf:pdf},

932−keywords = {Mendeley,how-to,user manual},

933−pages = {1--16},

934−publisher = {Mendeley Ltd.},

935−title = {{Getting Started with Mendeley}},

936−url = {http://www.mendeley.com},

937−year = {2011}

938−}

939−@book{Brady2012d,

940−author = {Seibel, Peter},

941−booktitle = {The Gerontologist},

942−doi = {10.1093/geront/gns026},

943−file = {:Users/edwin/Documents/Mendeley Desktop/Seibel/Coders at Work Chapter 6/Seibel - Coders at Work Chapter 6 - 2012.pdf:pdf},

944−isbn = {9781430219484},

945−issn = {1758-5341},

946−month = dec,

947−number = {6},

948−pages = {NP},

949−pmid = {23150082},

950−title = {{Coders at Work Chapter 6}},

951−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

952−volume = {52},

953−year = {2012}

954−}

955−@inproceedings{l,

956−author = {L\"{a}mmel, R. and Jones, S.P.},

957−booktitle = {ACM SIGPLAN Notices},

958−file = {:Users/edwin/Documents/Mendeley Desktop/L\"{a}mmel, Jones/Scrap your boilerplate a practical design pattern for generic programming/L\"{a}mmel, Jones - Scrap your boilerplate a practical design pattern for generic programming - 2003.pdf:pdf},

959−number = {3},

960−pages = {26--37},

961−publisher = {ACM},

962−title = {{Scrap your boilerplate: a practical design pattern for generic programming}},

963−url = {http://dl.acm.org/citation.cfm?id=640136.604179},

964−volume = {38},

965−year = {2003}

966−}

967−@phdthesis{Okasaki1996,

968−author = {Okasaki, Chris},

969−file = {:Users/edwin/Documents/Mendeley Desktop/Okasaki/Purely Functional Data Structures/Okasaki - Purely Functional Data Structures - 1996.pdf:pdf},

970−school = {Carnegie Mellon University},

971−title = {{Purely Functional Data Structures}},

972−year = {1996}

973−}

974−@inproceedings{McBride2004b,

975−author = {McBride, Conor and McKinna, James},

976−booktitle = {Haskell Workshop},

977−file = {:Users/edwin/Documents/Mendeley Desktop/McBride, McKinna/I am not a number I am a free variable/McBride, McKinna - I am not a number I am a free variable - 2004.pdf:pdf},

978−title = {{I am not a number : I am a free variable}},

979−year = {2004}

980−}

981−@inproceedings{Brady2005a,

982−author = {Brady, E and Hammond, K},

983−booktitle = {Implementation and Application of Functional \ldots},

984−file = {:Users/edwin/Documents/Mendeley Desktop/Brady, Hammond/A dependently typed framework for static analysis of program execution costs/Brady, Hammond - A dependently typed framework for static analysis of program execution costs - 2005.pdf:pdf},

985−keywords = {Dependent Types},

986−mendeley-tags = {Dependent Types},

987−title = {{A dependently typed framework for static analysis of program execution costs}},

988−url = {http://www.springerlink.com/index/P446P2HH70107759.pdf},

989−year = {2005}

990−}

991−@misc{TMR13,

992−author = {Eidhof, Chris and Elkins, Derek and Hicks, Stephen},

993−file = {:Users/edwin/Documents/Mendeley Desktop/Eidhof, Elkins, Hicks/The Monad . Reader Issue 13/Eidhof, Elkins, Hicks - The Monad . Reader Issue 13 - 2009.pdf:pdf},

994−number = {13},

995−title = {{The Monad . Reader Issue 13}},

996−year = {2009}

997−}

998−@inproceedings{taha2004gentle,

999−author = {Taha, W.},

1000−booktitle = {Domain-Specific Program Generation},

1001−pages = {30--50},

1002−publisher = {Springer},

1003−title = {{A gentle introduction to multi-stage programming}},

1004−url = {http://www.springerlink.com/index/JEMT0D8VYN5JB2L8.pdf},

1005−year = {2004}

1006−}

1007−@article{Rose,

1008−annote = {This paper describes a language, Jeeves, for describing privacy policies and ensuring that they are automatically enforced. It gives the semantics of Jeeves in terms of a translation to a target language $\lambda_J$ and shows how to implement the privacy rules in a monadic style in Haskell which captures the constraint propagation.

1009−

1010−

1011−Capturing policy rules in this way is an interesting idea and the monadic definition of constraint propagation is natural, but unfortunately the paper itself only seems half-written. I found the website (https://sites.google.com/site/jeevesprogramming/) and the tutorial there much more enlightening! Perhaps relating the implementation to some more extensive examples would be helpful, illustrating how the Haskell code relates to Jeeves programs. This would be particularly valuable in sections 3 and 5, and there is plenty of space available for this.

1012−

1013−

1014−The paper could use a thorough proof read and spell check. For example:

1015−

1016−

1017−end of sec 1 - references for the report and web site would be useful here.

1018−End of sec 2: privacy politics? This is the only place this phrase is used.

1019−

1020−

1021−p2 etal => et al

1022−

1023−

1024−"The program read" => "The program reads"

1025−"Depending on what" => comma before this

1026−"bottem" => "bottom"

1027−

1028−

1029−p4 "Eventhough" => "Even though"

1030−"The program body, consist" => "The program body consists"

1031−

1032−

1033−"but without any substantial..." - there is a missing word here

1034−

1035−

1036−The presentation of Sec 5 is untidy - for example a section heading at the end of the page and bad spacing between subsections.

1037−

1038−

1039−Reference 1 is blank

1040−

1041−

1042−

1043− },

1044−author = {Rose, Eva},

1045−file = {:Users/edwin/Documents/Mendeley Desktop/Rose/Declarative implementation aspects of privacy policy effects/Rose - Declarative implementation aspects of privacy policy effects - Unknown.pdf:pdf},

1046−keywords = {constraints,language design,mon-,privacy policy,semantics},

1047−title = {{Declarative implementation aspects of privacy policy effects}}

1048−}

1049−@inproceedings{morris2006exploring,

1050−author = {Morris, P. and Altenkirch, T. and McBride, C.},

1051−booktitle = {Types for Proofs and Programs},

1052−file = {:Users/edwin/Documents/Mendeley Desktop/Morris, Altenkirch, McBride/Exploring the regular tree types/Morris, Altenkirch, McBride - Exploring the regular tree types - 2006.pdf:pdf},

1053−pages = {252--267},

1054−publisher = {Springer},

1055−title = {{Exploring the regular tree types}},

1056−url = {http://www.springerlink.com/index/f9p1317716614834.pdf},

1057−year = {2006}

1058−}

1059−@inproceedings{pj2006gadts,

1060−author = {{Peyton Jones}, S. and Vytiniotis, D. and Weirich, S. and Washburn, G.},

1061−booktitle = {{International Conference on Functional Programming} ({ICFP} '06)},

1062−file = {:Users/edwin/Documents/Mendeley Desktop/Peyton Jones et al/Simple unification-based type inference for GADTs/Peyton Jones et al. - Simple unification-based type inference for GADTs - 2006.pdf:pdf},

1063−number = {9},

1064−pages = {50--61},

1065−publisher = {ACM},

1066−title = {{Simple unification-based type inference for GADTs}},

1067−url = {http://dl.acm.org/citation.cfm?id=1159811},

1068−volume = {41},

1069−year = {2006}

1070−}

1071−@book{luo1994,

1072−author = {Luo, Z.},

1073−publisher = {Oxford University Press, Inc.},

1074−title = {{Computation and reasoning: a type theory for computer science}},

1075−url = {http://dl.acm.org/citation.cfm?id=SERIES9893.184757},

1076−year = {1994}

1077−}

1078−@misc{Hancock,

1079−author = {Hancock, Peter and Setzer, Anton},

1080−file = {:Users/edwin/Documents/Mendeley Desktop/Hancock, Setzer/Interactive Programs in Dependent Type Theory/Hancock, Setzer - Interactive Programs in Dependent Type Theory - 2000(2).pdf:pdf},

1081−keywords = {dependent types,functional programming,interac-,monadic i,o,reactive programming,refinement,repetition constructs,tion},

1082−title = {{Interactive Programs in Dependent Type Theory}},

1083−year = {2000}

1084−}

1085−@book{Chlipala2012,

1086−author = {Chlipala, Adam},

1087−file = {:Users/edwin/Documents/Mendeley Desktop/Chlipala/Certified Programming with Dependent Types/Chlipala - Certified Programming with Dependent Types - 2012.pdf:pdf},

1088−title = {{Certified Programming with Dependent Types}},

1089−year = {2012}

1090−}

1091−@article{Mandelbaum2007,

1092−abstract = {Massive amounts of useful data are stored and processed in ad hoc formats for which common tools like parsers, printers, query engines and format converters are not readily available. In this paper, we explain the design and implementation of PADS/ML , a new language and system that facilitates the generation of data processing tools for ad hoc formats. The PADS/ML design includes features such as dependent, polymorphic and recursive datatypes, which allow programmers to describe the syntax and semantics of ad hoc data in a concise, easy-to-read notation. The PADS/ML implementation compiles these descriptions into ml structures and functors that include types for parsed data, functions for parsing and printing, and auxiliary support for user-specified, format-dependent and format-independent tool generation.},

1093−author = {Mandelbaum, Yitzhak and Fisher, Kathleen and Walker, David and Fernandez, Mary and Gleyzer, Artem},

1094−doi = {10.1145/1190215.1190231},

1095−isbn = {1595935754},

1096−issn = {03621340},

1097−journal = {SIGPLAN Not},

1098−number = {1},

1099−pages = {77--83},

1100−publisher = {ACM},

1101−series = {POPL '07},

1102−title = {{PADS/ML: a functional data description language}},

1103−url = {http://doi.acm.org/10.1145/1190216.1190231},

1104−volume = {42},

1105−year = {2007}

1106−}

1107−@article{Nabais2008,

1108−author = {Nabais, Davide},

1109−file = {:Users/edwin/Documents/Mendeley Desktop/Nabais/DesCo a Web Based Information System for Descriptional Complexity of Formal Languages/Nabais - DesCo a Web Based Information System for Descriptional Complexity of Formal Languages - 2008.pdf:pdf},

1110−journal = {Most},

1111−pages = {1--5},

1112−title = {{DesCo : a Web Based Information System for Descriptional Complexity of Formal Languages}},

1113−year = {2008}

1114−}

1115−@book{Edition2012,

1116−author = {Pfleeger, Charles P and Pfleeger, S. L.},

1117−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

1118−doi = {10.1093/ntr/nts035},

1119−file = {:Users/edwin/Documents/Mendeley Desktop/Pfleeger, Pfleeger/Security in Computing Chapter 1/Pfleeger, Pfleeger - Security in Computing Chapter 1 - 2012.pdf:pdf},

1120−isbn = {0132390779},

1121−issn = {1469-994X},

1122−month = oct,

1123−number = {10},

1124−pages = {NP},

1125−pmid = {23012339},

1126−title = {{Security in Computing Chapter 1}},

1127−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

1128−volume = {14},

1129−year = {2012}

1130−}

1131−@book{Eap,

1132−author = {Fall, Kevin R and Stevens, W. Richard},

1133−file = {:Users/edwin/Documents/Mendeley Desktop/Fall, Stevens/TCPIP Illustrated Chapter 18/Fall, Stevens - TCPIP Illustrated Chapter 18 - Unknown.pdf:pdf},

1134−isbn = {9780132808200},

1135−title = {{TCP/IP Illustrated Chapter 18}}

1136−}

1137−@book{Fowler,

1138−author = {Fowler, Martin},

1139−booktitle = {Language},

1140−file = {:Users/edwin/Documents/Mendeley Desktop/Fowler/Domain Specific Languages Chapter 2/Fowler - Domain Specific Languages Chapter 2 - Unknown.pdf:pdf},

1141−isbn = {9780132107549},

1142−title = {{Domain Specific Languages Chapter 2}}

1143−}

1144−@book{Brady2012e,

1145−author = {Seibel, Peter},

1146−booktitle = {The Gerontologist},

1147−doi = {10.1093/geront/gns026},

1148−file = {:Users/edwin/Documents/Mendeley Desktop/Seibel/Coders at Work Chapter 9/Seibel - Coders at Work Chapter 9 - 2012.pdf:pdf},

1149−isbn = {9781430219484},

1150−issn = {1758-5341},

1151−month = dec,

1152−number = {6},

1153−pages = {NP},

1154−pmid = {23150082},

1155−title = {{Coders at Work Chapter 9}},

1156−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

1157−volume = {52},

1158−year = {2012}

1159−}

1160−@article{Regular2012,

1161−author = {Kernighan, Brian},

1162−doi = {10.1093/geront/gns026},

1163−file = {:Users/edwin/Documents/Mendeley Desktop/Kernighan/Beautiful Code Chapter 1/Kernighan - Beautiful Code Chapter 1 - 2012.pdf:pdf},

1164−isbn = {9780596510046},

1165−issn = {1758-5341},

1166−month = dec,

1167−number = {6},

1168−pages = {NP},

1169−pmid = {23150082},

1170−title = {{Beautiful Code Chapter 1}},

1171−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

1172−volume = {52},

1173−year = {2012}

1174−}

1175−@inproceedings{norell2009dependently,

1176−author = {Norell, Ulf},

1177−booktitle = {Advanced Functional Programming},

1178−file = {:Users/edwin/Documents/Mendeley Desktop/Norell/Dependently typed programming in Agda/Norell - Dependently typed programming in Agda - 2009.pdf:pdf},

1179−keywords = {Dependent Types},

1180−mendeley-tags = {Dependent Types},

1181−pages = {230--266},

1182−publisher = {Springer},

1183−title = {{Dependently typed programming in Agda}},

1184−url = {http://www.springerlink.com/index/8X0H38858233VN26.pdf},

1185−year = {2009}

1186−}

1187−@misc{Interface2012a,

1188−author = {Kreibich, Jay A.},

1189−doi = {10.1093/epirev/mxr031},

1190−file = {:Users/edwin/Documents/Mendeley Desktop/Kreibich/Using SQLite Chapter 7/Kreibich - Using SQLite Chapter 7 - Unknown.pdf:pdf},

1191−isbn = {9781449394592},

1192−issn = {1478-6729},

1193−pmid = {22215642},

1194−title = {{Using SQLite Chapter 7}}

1195−}

1196−@inproceedings{Augustsson1998,

1197−abstract = {Cayenne is a Haskell-like language. The main difference between Haskell and Cayenne is that Cayenne has dependent types, i.e., the result type of a function may depend on the argument value , and types of record components (which can be types or values) may depend on other components. Cayenne also combines the syntactic categories for value expressions and type expressions; thus reducing the number of language concepts. Having dependent types and combined type and value expressions makes the language very powerful. It is powerful enough that a special module concept is unnecessary; ordinary records suffice. It is also powerful enough to encode predicate logic at the type level, allowing types to be used as specifications of programs. However, this power comes at a cost: type checking of Cayenne is undecidable. While this may appear to be a steep price to pay, it seems to work well in practice.},

1198−author = {Augustsson, Lennart},

1199−booktitle = {International Conference on Functional Programming},

1200−doi = {10.1097/MEG.0b013e328342f213},

1201−file = {:Users/edwin/Documents/Mendeley Desktop/Augustsson/Cayenne - a language with dependent types/Augustsson - Cayenne - a language with dependent types - 1998.pdf:pdf},

1202−issn = {14735687},

1203−keywords = {Depe,Dependent Types},

1204−mendeley-tags = {Depe,Dependent Types},

1205−number = {1},

1206−pages = {239--250},

1207−pmid = {21139473},

1208−publisher = {ACM Press},

1209−title = {{Cayenne - a language with dependent types}},

1210−url = {http://www.cs.chalmers.se/$\sim$augustss/cayenne/paper.ps},

1211−volume = {23},

1212−year = {1998}

1213−}

1214−@article{OutsideIn,

1215−author = {Vytiniotis, D and {Peyton Jones}, Simon and Shrijvers, Tom and Sulzmann, Martin},

1216−file = {:Users/edwin/Documents/Mendeley Desktop/Vytiniotis et al/textsc{OutsideIn}(X) Modular type inference with local assumptions/Vytiniotis et al. - textsc{OutsideIn}(X) Modular type inference with local assumptions - 2011.pdf:pdf},

1217−journal = {Journal of Functional Programming},

1218−number = {4--5},

1219−pages = {333----412},

1220−title = {{OutsideIn (X) Modular type inference with local assumptions}},

1221−url = {http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=8274818},

1222−volume = {21},

1223−year = {2011}

1224−}

1225−@inproceedings{fisher2005pads,

1226−author = {Fisher, K. and Gruber, R.},

1227−booktitle = {ACM SIGPLAN Notices},

1228−number = {6},

1229−pages = {295--304},

1230−publisher = {ACM},

1231−title = {{PADS: a domain-specific language for processing ad hoc data}},

1232−url = {http://dl.acm.org/citation.cfm?id=1065046},

1233−volume = {40},

1234−year = {2005}

1235−}

1236−@inproceedings{Levitation2010,

1237−author = {Chapman, James and Dagand, Pierre-Evariste and McBride, Conor and Morris, Peter},

1238−booktitle = {{15th ACM SIGPLAN International Conference on Functional programming (ICFP '10)}},

1239−doi = {10.1145/1932681.1863547},

1240−file = {:Users/edwin/Documents/Mendeley Desktop/Chapman et al/The gentle art of levitation/Chapman et al. - The gentle art of levitation - 2010.pdf:pdf},

1241−isbn = {978-1-60558-794-3},

1242−issn = {03621340},

1243−keywords = {Dependent Types,data structure,metaprogramming,monads,proof assistants,type systems},

1244−mendeley-tags = {Dependent Types},

1245−month = sep,

1246−number = {9},

1247−title = {{The gentle art of levitation}},

1248−url = {http://dl.acm.org/citation.cfm?id=1932681.1863547},

1249−volume = {45},

1250−year = {2010}

1251−}

1252−@book{While2012,

1253−author = {Hunt, Andrew and Thomas, David},

1254−booktitle = {Carcinogenesis},

1255−doi = {10.1093/carcin/bgs054},

1256−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 6/Hunt, Thomas - The Pragmatic Programmer Chapter 6 - Unknown.pdf:pdf},

1257−isbn = {020161622X},

1258−issn = {1460-2180},

1259−number = {3},

1260−pmid = {22383472},

1261−title = {{The Pragmatic Programmer Chapter 6}},

1262−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

1263−volume = {33}

1264−}

1265−@article{Hughes1989,

1266−abstract = {As software becomes more and more complex, it is more and more important to structure it well. Well-structured software is easy to write, easy to debug, and provides a collection of modules that can be re-used to reduce future programming costs. Conventional languages place conceptual limits on the way problems can be modularised. Functional languages push those limits back. In this paper we show that two features of functional languages in particular, higher-order functions and lazy evaluation, can contribute greatly to modularity. As examples, we manipulate lists and trees, program several numerical algorithms, and implement the alpha-beta heuristic (an algorithm from Artificial Intelligence used in game-playing programs). Since modularity is the key to successful programming, functional languages are vitally important to the real world.},

1267−author = {Hughes, J},

1268−chapter = {2},

1269−doi = {10.1093/comjnl/32.2.98},

1270−editor = {Turner, David A},

1271−file = {:Users/edwin/Documents/Mendeley Desktop/Hughes/Why Functional Programming Matters/Hughes - Why Functional Programming Matters - 1989.pdf:pdf},

1272−institution = {Programming Methodology Group, University of {G\"{o}teborg} and Chalmers Institute of Technology, Sweden},

1273−isbn = {0201172364},

1274−issn = {00104620},

1275−journal = {The Computer Journal},

1276−number = {2},

1277−pages = {98--107},

1278−publisher = {Br Computer Soc},

1279−title = {{Why Functional Programming Matters}},

1280−url = {http://comjnl.oupjournals.org/cgi/doi/10.1093/comjnl/32.2.98},

1281−volume = {32},

1282−year = {1989}

1283−}

1284−@inproceedings{Asperti2011,

1285−author = {Asperti, Andrea and Ricciotti, Wilmer and Coen, Claudio Sacerdoti and Tassi, Enrico},

1286−booktitle = {{Automated Deduction --- CADE-23}},

1287−file = {:Users/edwin/Documents/Mendeley Desktop/Asperti et al/The Matita Interactive Theorem Prover/Asperti et al. - The Matita Interactive Theorem Prover - 2011.pdf:pdf},

1288−pages = {64----69},

1289−title = {{The Matita Interactive Theorem Prover}},

1290−year = {2011}

1291−}

1292−@article{Brady2006a,

1293−author = {Brady, E and Hammond, K},

1294−file = {:Users/edwin/Documents/Mendeley Desktop/Brady, Hammond/A verified staged interpreter is a verified compiler/Brady, Hammond - A verified staged interpreter is a verified compiler - 2006.pdf:pdf},

1295−journal = {\ldots of the 5th international conference on \ldots},

1296−keywords = {Dependent Types},

1297−mendeley-tags = {Dependent Types},

1298−title = {{A verified staged interpreter is a verified compiler}},

1299−url = {http://portal.acm.org/citation.cfm?id=1173706.1173724},

1300−year = {2006}

1301−}

1302−@article{Xi1998,

1303−abstract = {We present a type-based approach to eliminating array bound checking and list tag checking by conservatively extending Standard ML with a restricted form of dependent types. This enables the programmer to capture more invariants through types while type-checking remains decidable in theory and can still be performed efficiently in practice. We illustrate our approach through concrete examples and present the result of our preliminary experiments which support support the feasibility and effectiveness of our approach.},

1304−author = {Xi, Hongwei and Pfenning, Frank},

1305−doi = {10.1145/277652.277732},

1306−file = {:Users/edwin/Documents/Mendeley Desktop/Xi, Pfenning/Eliminating array bound checking through dependent types/Xi, Pfenning - Eliminating array bound checking through dependent types - 1998.pdf:pdf},

1307−isbn = {0897919874},

1308−issn = {03621340},

1309−journal = {ACM Sigplan Notices},

1310−keywords = {Dependent Types},

1311−mendeley-tags = {Dependent Types},

1312−number = {5},

1313−pages = {249--257},

1314−publisher = {ACM},

1315−series = {PLDI '98},

1316−title = {{Eliminating array bound checking through dependent types}},

1317−url = {http://portal.acm.org/citation.cfm?doid=277652.277732},

1318−volume = {33},

1319−year = {1998}

1320−}

1321−@inproceedings{Abel2013,

1322−author = {Abel, Andreas and Pientka, Brigitte and Thibodeau, David and Setzer, Anton},

1323−booktitle = {Principles of Programming Languages},

1324−file = {:Users/edwin/Documents/Mendeley Desktop/Abel et al/Copatterns Programming Infinite Structures by Observations/Abel et al. - Copatterns Programming Infinite Structures by Observations - 2013.pdf:pdf},

1325−isbn = {9781450318327},

1326−keywords = {2008,by the graduiertenkol-,coinduction,elimination,functional programming,introduction,leg programm und modellanalyse,message passing,of the deutsche,pattern matching,puma,thibodeau acknowledges financial support,vs},

1327−title = {{Copatterns: Programming Infinite Structures by Observations}},

1328−year = {2013}

1329−}

1330−@misc{pollack1997believe,

1331−author = {Pollack, R.},

1332−file = {:Users/edwin/Documents/Mendeley Desktop/Pollack/How to believe a machine-checked proof/Pollack - How to believe a machine-checked proof - 1997.pdf:pdf},

1333−title = {{How to believe a machine-checked proof}},

1334−url = {http://books.google.co.uk/books?hl=en&lr=&id=pLnKggT_In4C&oi=fnd&pg=PA205&dq=how+to+believe+a+machine+checked+proof&ots=c2OI8krqqA&sig=EF3QonGFVdOpYdKO1KmW6ljCkjY},

1335−year = {1997}

1336−}

1337−@book{Searching2012,

1338−author = {Sedgewick, Robert and Wayne, Kevin},

1339−booktitle = {The Gerontologist},

1340−doi = {10.1093/geront/gns026},

1341−file = {:Users/edwin/Documents/Mendeley Desktop/Sedgewick, Wayne/Algorithms Chapter 3/Sedgewick, Wayne - Algorithms Chapter 3 - 2012.pdf:pdf},

1342−isbn = {9780132762571},

1343−issn = {1758-5341},

1344−month = dec,

1345−number = {6},

1346−pages = {NP},

1347−pmid = {23150082},

1348−title = {{Algorithms Chapter 3}},

1349−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

1350−volume = {52},

1351−year = {2012}

1352−}

1353−@book{Philosophy2012,

1354−author = {Hunt, Andrew and Thomas, David},

1355−booktitle = {Carcinogenesis},

1356−doi = {10.1093/carcin/bgs054},

1357−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 1/Hunt, Thomas - The Pragmatic Programmer Chapter 1 - Unknown.pdf:pdf},

1358−isbn = {020161622X},

1359−issn = {1460-2180},

1360−number = {3},

1361−pmid = {22383472},

1362−title = {{The Pragmatic Programmer Chapter 1}},

1363−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

1364−volume = {33}

1365−}

1366−@article{Servers,

1367−author = {Totty, Brian and Gourley, David},

1368−file = {:Users/edwin/Documents/Mendeley Desktop/Totty, Gourley/HTTP The Definitive Guide Chapter 5/Totty, Gourley - HTTP The Definitive Guide Chapter 5 - Unknown.pdf:pdf},

1369−isbn = {1565925092},

1370−title = {{HTTP: The Definitive Guide Chapter 5}}

1371−}

1372−@article{Bird2012a,

1373−annote = {This new version of the paper is, I think, very clear and an entertaining read. It presents a neat example of program calculation and reasoning with each step in the calculation explained precisely - indeed the interesting thing to me is the calculation, rather than the problem itself, and it is nice that this works for an algorithm which requires in-place update (even if it does involve pretending // is in-place!).

1374−

1375−

1376−I'm not totally convinced about the condition of the algorithm being "discovered in a disciplined manner" since many of the steps in the calculation required some insight, but others will disagree and I don't think it really matters for the main point of this paper in any case - the point is the calculational development, which is sufficiently detailed that a careful reader should be able to develop that insight, with practice. I would recommend this paper for acceptance in its current form. },

1377−author = {Bird, Richard S},

1378−file = {:Users/edwin/Documents/Mendeley Desktop/Bird/An in-situ algorithm for expanding a graph/Bird - An in-situ algorithm for expanding a graph - 2012.pdf:pdf},

1379−keywords = {a href,journal of functional programming},

1380−title = {{An in-situ algorithm for expanding a graph}},

1381−year = {2012}

1382−}

1383−@inproceedings{Sculthorpe2009,

1384−author = {Sculthorpe, Neil and Nilsson, Henrik},

1385−booktitle = {International Conference on Functional Programming ({ICFP} '09)},

1386−file = {:Users/edwin/Documents/Mendeley Desktop/Sculthorpe, Nilsson/Safe functional reactive programming through dependent types/Sculthorpe, Nilsson - Safe functional reactive programming through dependent types - 2009.pdf:pdf;:Users/edwin/Documents/Mendeley Desktop/Sculthorpe, Nilsson/Safe functional reactive programming through dependent types/Sculthorpe, Nilsson - Safe functional reactive programming through dependent types - 2009(2).pdf:pdf},

1387−title = {{Safe functional reactive programming through dependent types}},

1388−url = {http://dl.acm.org/citation.cfm?id=1596558},

1389−year = {2009}

1390−}

1391−@article{landin1966next,

1392−author = {Landin, P.J.},

1393−file = {:Users/edwin/Documents/Mendeley Desktop/Landin/The next 700 programming languages/Landin - The next 700 programming languages - 1966.pdf:pdf},

1394−journal = {Communications of the ACM},

1395−number = {3},

1396−pages = {157--166},

1397−publisher = {ACM},

1398−title = {{The next 700 programming languages}},

1399−url = {http://dl.acm.org/citation.cfm?id=365257 )},

1400−volume = {9},

1401−year = {1966}

1402−}

1403−@inproceedings{Delahaye2000,

1404−author = {Delahaye, D},

1405−booktitle = {Logic for Programming and Automated Reasoning ({LPAR})},

1406−file = {:Users/edwin/Documents/Mendeley Desktop/Delahaye/A tactic language for the system Coq/Delahaye - A tactic language for the system Coq - 2000.pdf:pdf;:Users/edwin/Documents/Mendeley Desktop/Delahaye/A tactic language for the system Coq/Delahaye - A tactic language for the system Coq - 2000(2).pdf:pdf},

1407−pages = {85----95},

1408−publisher = {Springer},

1409−title = {{A tactic language for the system Coq}},

1410−url = {http://www.springerlink.com/index/EFQAH8J88K42VN8T.pdf},

1411−year = {2000}

1412−}

1413−@book{Messages,

1414−author = {Totty, Brian and Gourley, David},

1415−file = {:Users/edwin/Documents/Mendeley Desktop/Totty, Gourley/HTTP The Definitive Guide Chapter 3/Totty, Gourley - HTTP The Definitive Guide Chapter 3 - Unknown.pdf:pdf},

1416−isbn = {1565925092},

1417−title = {{HTTP: The Definitive Guide Chapter 3}}

1418−}

1419−@article{Asperti,

1420−author = {Asperti, Andrea and Ricciotti, Wilmer and Coen, Claudio Sacerdoti and Tassi, Enrico},

1421−doi = {10.2168/LMCS-},

1422−file = {:Users/edwin/Documents/Mendeley Desktop/Asperti et al/A bi-directional refinement algorithm for the calculus of (co)inductive constructions/Asperti et al. - A bi-directional refinement algorithm for the calculus of (co)inductive constructions - 2012.pdf:pdf},

1423−journal = {{Logical Methods in Computer Science}},

1424−keywords = {and phrases,calculus of inductive construc-,interactive theorem prover,refiner,type inference},

1425−pages = {1----49},

1426−title = {{A bi-directional refinement algorithm for the calculus of (co)inductive constructions}},

1427−volume = {8},

1428−year = {2012}

1429−}

1430−@inproceedings{Altenkirch2010,

1431−abstract = {The recent success of languages like Agda and Coq demonstrates the potential of using dependent types for programming. These systems rely on many high-level features like datatype definitions, pattern matching and implicit arguments to facilitate the use of the languages. However, these features complicate the metatheoretical study and are a potential source of bugs. To address these issues we introduce $\Pi$$\Sigma$, a dependently typed core language. It is small enough for metatheoretical study and the type checker is small enough to be formally verified. In this language there is only one mechanism for recursionused for types, functions and infinite objectsand an explicit mechanism to control unfolding, based on lifted types. Furthermore structural equality is used consistently for values and types; this is achieved by a new notion of $\alpha$-equality for recursive definitions. We show, by translating several high-level constructions, that $\Pi$$\Sigma$ is suitable as a core language for dependently typed programming.},

1432−author = {Altenkirch, Thorsten and Danielsson, Nils Anders and L\"{o}h, Andres and Oury, Nicolas},

1433−booktitle = {{FLOPS 2010}},

1434−doi = {10.1007/978-3-642-12251-4_5},

1435−editor = {Blume, Matthias and Kobayashi, Naoki and Vidal, Germ\'{a}n},

1436−file = {:Users/edwin/Documents/Mendeley Desktop/Altenkirch et al/Dependent Types without the Sugar/Altenkirch et al. - Dependent Types without the Sugar - 2010.pdf:pdf},

1437−isbn = {9783642122507},

1438−pages = {40----55},

1439−publisher = {Springer Berlin Heidelberg},

1440−series = {Lecture Notes in Computer Science},

1441−title = {{Dependent Types without the Sugar}},

1442−url = {http://www.springerlink.com/index/91W712G2806R575H.pdf},

1443−year = {2010}

1444−}

1445−@misc{Gobi2010,

1446−author = {Gobi, Attila and Shkaravska, Olha and {Van Eekelen}, Marko},

1447−booktitle = {Syntax},

1448−file = {:Users/edwin/Documents/Mendeley Desktop/Gobi, Shkaravska, Van Eekelen/Higher-Order Size Checking Without Subtyping/Gobi, Shkaravska, Van Eekelen - Higher-Order Size Checking Without Subtyping - 2010.pdf:pdf},

1449−number = {100039},

1450−title = {{Higher-Order Size Checking Without Subtyping}},

1451−year = {2010}

1452−}

1453−@book{Context2012,

1454−author = {Sedgewick, Robert and Wayne, Kevin},

1455−booktitle = {The Gerontologist},

1456−doi = {10.1093/geront/gns026},

1457−file = {:Users/edwin/Documents/Mendeley Desktop/Sedgewick, Wayne/Algorithms Chapter 6/Sedgewick, Wayne - Algorithms Chapter 6 - 2012.pdf:pdf},

1458−isbn = {9780132762571},

1459−issn = {1758-5341},

1460−month = dec,

1461−number = {6},

1462−pages = {NP},

1463−pmid = {23150082},

1464−title = {{Algorithms Chapter 6}},

1465−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

1466−volume = {52},

1467−year = {2012}

1468−}

1469−@misc{Protocols2012a,

1470−author = {Anderson, Ross},

1471−doi = {10.1093/epirev/mxr031},

1472−file = {:Users/edwin/Documents/Mendeley Desktop/Anderson/Security Engineering Chapter 3/Anderson - Security Engineering Chapter 3 - Unknown.pdf:pdf},

1473−isbn = {9780470068526},

1474−issn = {1478-6729},

1475−pmid = {22215642},

1476−title = {{Security Engineering Chapter 3}}

1477−}

1478−@inproceedings{Visser2008,

1479−author = {Visser, E},

1480−booktitle = {Generative and Transformational Techniques in Software Engineering},

1481−title = {{WebDSL: A case study in domain-specific language engineering}},

1482−url = {http://www.springerlink.com/index/A3213003X6268032.pdf},

1483−year = {2008}

1484−}

1485−@inproceedings{gibbons2011modularising,

1486−author = {Gibbons, J. and Ko, H.S. and Others},

1487−file = {:Users/edwin/Documents/Mendeley Desktop/Ko, Gibbons/Modularising inductive families/Ko, Gibbons - Modularising inductive families - 2011.pdf:pdf},

1488−title = {{Modularising inductive families}},

1489−url = {http://www.cs.ox.ac.uk/publications/publication5008-abstract.html},

1490−year = {2011}

1491−}

1492−@book{Synchronization2012,

1493−author = {Butenhof, David R.},

1494−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

1495−doi = {10.1093/ntr/nts035},

1496−file = {:Users/edwin/Documents/Mendeley Desktop/Butenhof/Programming with POSIX Threads Chapter 3/Butenhof - Programming with POSIX Threads Chapter 3 - Unknown.pdf:pdf},

1497−isbn = {0201633922},

1498−issn = {1469-994X},

1499−number = {10},

1500−pmid = {23012339},

1501−title = {{Programming with POSIX Threads Chapter 3}},

1502−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

1503−volume = {14}

1504−}

1505−@article{Pl,

1506−annote = {-2, 3

1507−

1508−

1509−This paper gives a type inference algorithm for Java extended with lambdas, extending earlier work on type inference for a small functional language with subtyping. It is interesting to see how this could work, and I'm sure this would be a welcome addition to Java. However, I didn't find the paper very well organised or presented so it was difficult to get very much from it. There is too much unnecessary detail (such as fragments of the parser or complete sets of coercions and substitutions) and not enough useful context such as syntax of Java_lambda with its typing rules.

1510−

1511−

1512−If there is an implementation, it would also be good to give a url to download it so that the reader can try out some of the ideas given in the paper, and try to reproduce your results!

1513−

1514−

1515−Other comments:

1516−

1517−

1518−p1 The opening sentences don't seem to make sense on their own. It would be useful to know what your language in [7] is.

1519−

1520−

1521−There are several typos which suggest that the paper could use a proof read and spell check. For example:

1522−p2 "The improvement is that, that" => remove a "that"

1523−"not necessary" => "not necessarily"

1524−"can also consists" => "can also consist"

1525−"remainig" => "remaining"

1526−

1527−

1528−p3 What does "The concrete syntax [...] is oriented at [3]" mean? Is the syntax defined in this reference? It would be better to give it explicitly to make the paper more self contained.

1529−

1530−

1531−p4 Is there some reason that you use tuples in the representation of classes, functions and expressions?

1532−

1533−

1534−p9 "Decomposition: ..." I don't understand this sentence.

1535−

1536−

1537−p10 "corecions" => "coercions" (several times)

1538−also "coersions" => "coercions"

1539−

1540−

1541−p14 (and other places similarly) I don't think it helps much to give the full set of substitutions here. A representative selection at most should be fine.

1542−

1543−

1544−

1545− },

1546−author = {Pl\"{u}micke, Martin},

1547−file = {:Users/edwin/Documents/Mendeley Desktop/Pl{u}micke/Functional implementation of well-typings in/Pl{u}micke - Functional implementation of well-typings in - Unknown.pdf:pdf},

1548−title = {{Functional implementation of well-typings in}}

1549−}

1550−@article{gordon2003authenticity,

1551−author = {Gordon, A.D. and Jeffrey, A.},

1552−file = {:Users/edwin/Documents/Mendeley Desktop/Gordon, Jeffrey/Authenticity by typing for security protocols/Gordon, Jeffrey - Authenticity by typing for security protocols - 2003.pdf:pdf},

1553−journal = {Journal of computer security},

1554−number = {4},

1555−pages = {451--520},

1556−publisher = {IOS Press},

1557−title = {{Authenticity by typing for security protocols}},

1558−url = {http://iospress.metapress.com/index/BHQQUFRA1C7W8TLY.pdf},

1559−volume = {11},

1560−year = {2003}

1561−}

1562−@book{Approach2012,

1563−author = {Hunt, Andrew and Thomas, David},

1564−booktitle = {Carcinogenesis},

1565−doi = {10.1093/carcin/bgs054},

1566−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 2/Hunt, Thomas - The Pragmatic Programmer Chapter 2 - Unknown.pdf:pdf},

1567−isbn = {020161622X},

1568−issn = {1460-2180},

1569−number = {3},

1570−pmid = {22383472},

1571−title = {{The Pragmatic Programmer Chapter 2}},

1572−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

1573−volume = {33}

1574−}

1575−@inproceedings{barras2008implicit,

1576−author = {Barras, B. and Bernardo, B.},

1577−booktitle = {Foundations of Software Science and Computational Structures},

1578−file = {:Users/edwin/Documents/Mendeley Desktop/Barras, Bernardo/The implicit calculus of constructions as a programming language with dependent types/Barras, Bernardo - The implicit calculus of constructions as a programming language with dependent types - 2008.pdf:pdf},

1579−pages = {365--379},

1580−publisher = {Springer},

1581−title = {{The implicit calculus of constructions as a programming language with dependent types}},

1582−url = {http://www.springerlink.com/index/m84h82904546l265.pdf},

1583−year = {2008}

1584−}

1585−@article{Zanasi,

1586−author = {Zanasi, Fabio},

1587−file = {:Users/edwin/Documents/Mendeley Desktop/Zanasi/On the Expressive Power of MSO and WMSO on Trees of Arbitrary Degree ( Extended abstract )/Zanasi - On the Expressive Power of MSO and WMSO on Trees of Arbitrary Degree ( Extended abstract ) - Unknown.pdf:pdf},

1588−pages = {1--6},

1589−title = {{On the Expressive Power of MSO and WMSO on Trees of Arbitrary Degree ( Extended abstract )}}

1590−}

1591−@article{Thiemann,

1592−annote = {1, 4

1593−

1594−

1595−This paper is a case study in dependently typed programming, investigating how an existing Haskell library (Accelerate) could benefit from dependent types by implementing a version of the library in Agda. The Haskell version is a generative library, meaning that programs are constructed as Haskell ADTs, then compiled to code which will run on a GPU. The authos observe that type correctness of Accelerate programs is checked statically, as far as possible, by using advanced features of the Haskell type system such as GADTs, and hypothesise that a language with a stronger type system such as Agda would increase the static guarantees which are expressible.

1596−

1597−

1598−This is an interesting question, well worth asking, and the paper presents mixed results. The presentation of the Agda version is clear, and the relationship with the Haskell version is easy to see. However, some properties which one might hope to express turn out to be difficult in the current form. One conclusion I would draw from this is that to use dependent types well involves more than simply annotating an existing program. The difficulties with filter and fold in particular show that care must be taken to preserve information required for checking later.

1599−

1600−

1601−I wonder if the work has become too constrained by porting directly from the Haskell implementation. Perhaps a question to ask in future work would be - what would a dependently typed API to GPUs look like? What properties do we want to capture, and how can we do so with minimal work for the programmer?

1602−

1603−

1604−Nevertheless, I enjoyed reading the paper and I think this is a good first step towards data parallel programming with dependent types.

1605−

1606−

1607−Minor comments:

1608−

1609−

1610−p3 Given that proceedings are in black and white, maybe it'd be more distinctive to put the Haskell code in a box rather than just a vertical bar?

1611−

1612−

1613−p8 It would be useful to see the type of the zipWith function which corresponds to the Haskell version, if not the implementation (which I suspect is a little tricky).

1614−

1615−

1616−p9 Probably not relevant to this paper, but this comment about properties of floating point arithmetic makes me wonder if it'd be possible to represent floating point error bounds in the type to recover these properties.

1617−

1618−

1619−p10 Another alternative for the type of filter could be a type level function to calculate the length. However, this would probably make proofs even harder. I think this is evidence that dependently typed programming is more than Haskell plus extra type annotations!

1620−

1621−

1622−p14 "We have build" => "We have built"},

1623−author = {Thiemann, Peter and Chakravarty, Manuel M T},

1624−file = {:Users/edwin/Documents/Mendeley Desktop/Thiemann, Chakravarty/Agda Meets Accelerate/Thiemann, Chakravarty - Agda Meets Accelerate - Unknown.pdf:pdf},

1625−keywords = {data parallelism,programming with dependent types},

1626−pages = {1--16},

1627−title = {{Agda Meets Accelerate}}

1628−}

1629−@inproceedings{Delahaye,

1630−author = {Delahaye, David},

1631−booktitle = {Proceedings of Logic for Programming and Automated Reasoning ({LPAR})},

1632−file = {:Users/edwin/Documents/Mendeley Desktop/Delahaye/A Tactic Language for the System Coq/Delahaye - A Tactic Language for the System Coq - 2000(3).pdf:pdf},

1633−title = {{A Tactic Language for the System Coq}},

1634−url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.9062},

1635−year = {2000}

1636−}

1637−@inproceedings{atkey2009unembedding,

1638−author = {Atkey, R. and Lindley, S. and Yallop, J.},

1639−booktitle = {Proceedings of the 2nd ACM SIGPLAN symposium on Haskell},

1640−pages = {37--48},

1641−publisher = {ACM},

1642−title = {{Unembedding domain-specific languages}},

1643−url = {http://dl.acm.org/citation.cfm?id=1596644},

1644−year = {2009}

1645−}

1646−@inproceedings{ko2011modularising,

1647−author = {Ko, H.S. and Gibbons, J.},

1648−booktitle = {Proceedings of the seventh ACM SIGPLAN workshop on Generic programming},

1649−file = {:Users/edwin/Documents/Mendeley Desktop/Ko, Gibbons/Modularising inductive families/Ko, Gibbons - Modularising inductive families - 2011.pdf:pdf},

1650−pages = {13--24},

1651−publisher = {ACM},

1652−title = {{Modularising inductive families}},

1653−url = {http://www.cs.ox.ac.uk/publications/publication5008-abstract.html http://dl.acm.org/citation.cfm?id=2036921},

1654−year = {2011}

1655−}

1656−@article{Chapman2005epigram,

1657−author = {Chapman, James and Altenkirch, Thorsten and McBride, Conor},

1658−file = {:Users/edwin/Documents/Mendeley Desktop/Chapman, Altenkirch, McBride/Epigram Reloaded A Standalone Typechecker for {ETT}/Chapman, Altenkirch, McBride - Epigram Reloaded A Standalone Typechecker for {ETT} - 2005.pdf:pdf},

1659−journal = {Trends in Functional Programming},

1660−publisher = {Intellect Books},

1661−title = {{Epigram Reloaded: A Standalone Typechecker for {ETT}}},

1662−url = {http://books.google.co.uk/books?hl=en&lr=&id=p0yV1sHLubcC&oi=fnd&pg=PA79&dq=epigram+reloaded&ots=x50ou0VMsm&sig=7TjAGohIatNLTWsHcuNcK5hEGGY},

1663−year = {2005}

1664−}

1665−@article{Hutton,

1666−author = {Hutton, Graham and Fulger, Diana},

1667−file = {:Users/edwin/Documents/Mendeley Desktop/Hutton, Fulger/Reasoning About Effects Seeing the Wood Through the Trees/Hutton, Fulger - Reasoning About Effects Seeing the Wood Through the Trees - Unknown.pdf:pdf},

1668−title = {{Reasoning About Effects : Seeing the Wood Through the Trees}}

1669−}

1670−@article{dybjer1994inductive,

1671−author = {Dybjer, P.},

1672−journal = {Formal aspects of computing},

1673−number = {4},

1674−pages = {440--465},

1675−publisher = {Springer},

1676−title = {{Inductive families}},

1677−url = {http://www.springerlink.com/index/J17824H467X6J288.pdf},

1678−volume = {6},

1679−year = {1994}

1680−}

1681−@misc{TheMendeleySupportTeam2011a,

1682−abstract = {A quick introduction to Mendeley. Learn how Mendeley creates your personal digital library, how to organize and annotate documents, how to collaborate and share with colleagues, and how to generate citations and bibliographies.},

1683−address = {London},

1684−author = {{The Mendeley Support Team}},

1685−booktitle = {Mendeley Desktop},

1686−file = {:Users/edwin/Documents/Mendeley Desktop/The Mendeley Support Team/Getting Started with Mendeley/The Mendeley Support Team - Getting Started with Mendeley - 2011.pdf:pdf},

1687−keywords = {Mendeley,how-to,user manual},

1688−pages = {1--16},

1689−publisher = {Mendeley Ltd.},

1690−title = {{Getting Started with Mendeley}},

1691−url = {http://www.mendeley.com},

1692−year = {2011}

1693−}

1694−@misc{Brady2012b,

1695−author = {Brooks, Fred},

1696−doi = {10.1093/epirev/mxr031},

1697−file = {:Users/edwin/Documents/Mendeley Desktop/Brooks/The Design of Design Chapter 2/Brooks - The Design of Design Chapter 2 - Unknown.pdf:pdf},

1698−isbn = {9780321702081},

1699−issn = {1478-6729},

1700−pmid = {22215642},

1701−title = {{The Design of Design Chapter 2}}

1702−}

1703−@misc{Bove2008,

1704−abstract = {In these lecture notes we give an introduction to functional programming with dependent types. We use the dependently typed programming language Agda which is based on ideas in Martin-L\"{o}f type theory and Martin-L\"{o}fs logical framework. We begin by showing how to do simply typed functional programming, and discuss the differences between Agdas type system and the Hindley-Milner type system, which underlies mainstream typed functional programming languages like Haskell and ML. We then show how to employ dependent types for programming with functional data structures such as vectors and binary search trees. We go on to explain the Curry-Howard identification of propositions and types, and how it makes Agda not only a programming language but also a programming logic. According to Curry-Howard, we also identify programs and proofs, something which is possible only by requiring that all program terminate. However, we show in the final section a method for encoding general and possibly partial recursive functions as total functions using dependent types.},

1705−author = {Bove, Ana and Dybjer, Peter},

1706−booktitle = {Notes},

1707−doi = {10.1007/978-3-642-03153-3_2},

1708−file = {:Users/edwin/Documents/Mendeley Desktop/Bove, Dybjer/Dependent Types at Work/Bove, Dybjer - Dependent Types at Work - 2008.pdf:pdf},

1709−number = {February},

1710−pages = {57--99},

1711−publisher = {Springer},

1712−title = {{Dependent Types at Work}},

1713−url = {http://www.springerlink.com/index/1039q8qk71257677.pdf},

1714−volume = {5520},

1715−year = {2008}

1716−}

1717−@article{In2012,

1718−author = {Gulhati, Ashish},

1719−doi = {10.1093/geront/gns026},

1720−file = {:Users/edwin/Documents/Mendeley Desktop/Gulhati/Beautiful Code Chapter 11/Gulhati - Beautiful Code Chapter 11 - 2012.pdf:pdf},

1721−isbn = {9780596510046},

1722−issn = {1758-5341},

1723−month = dec,

1724−number = {6},

1725−pages = {NP},

1726−pmid = {23150082},

1727−title = {{Beautiful Code Chapter 11}},

1728−url = {http://www.ncbi.nlm.nih.gov/pubmed/23150082},

1729−volume = {52},

1730−year = {2012}

1731−}

1732−@article{McBride2002,

1733−author = {McBride, C},

1734−file = {:Users/edwin/Documents/Mendeley Desktop/McBride/Elimination with a Motive/McBride - Elimination with a Motive - 2000.pdf:pdf},

1735−journal = {Types for proofs and programs ({TYPES 2000})},

1736−title = {{Elimination with a Motive}},

1737−url = {http://www.springerlink.com/index/vbpg19305t46f6dm.pdf},

1738−year = {2000}

1739−}

1740−@inproceedings{lempsink2009type,

1741−author = {Lempsink, E. and Leather, S. and L\"{o}h, A.},

1742−booktitle = {Proceedings of the 2009 ACM SIGPLAN workshop on Generic programming},

1743−file = {:Users/edwin/Documents/Mendeley Desktop/Lempsink, Leather, L\"{o}h/Type-safe diff for families of datatypes/Lempsink, Leather, L\"{o}h - Type-safe diff for families of datatypes - 2009.pdf:pdf},

1744−pages = {61--72},

1745−publisher = {ACM},

1746−title = {{Type-safe diff for families of datatypes}},

1747−url = {http://dl.acm.org/citation.cfm?id=1596624},

1748−year = {2009}

1749−}

1750−@inproceedings{Brady2011a,

1751−address = {New York, New York, USA},

1752−author = {Brady, Edwin},

1753−booktitle = {{Proceedings of the 5th {ACM} workshop on Programming Languages Meets Program Verification - PLPV '11}},

1754−doi = {10.1145/1929529.1929536},

1755−file = {:Users/edwin/Documents/Mendeley Desktop/Brady/Idris --- Systems Programming Meets Full Dependent Types/Brady - Idris --- Systems Programming Meets Full Dependent Types - 2011.pdf:pdf},

1756−isbn = {9781450304870},

1757−keywords = {Dependent Types,data description,dependent types},

1758−mendeley-tags = {Dependent Types},

1759−month = jan,

1760−publisher = {ACM Press},

1761−title = {{Idris --- Systems Programming Meets Full Dependent Types}},

1762−url = {http://dl.acm.org/citation.cfm?id=1929529.1929536},

1763−year = {2011}

1764−}

1765−@misc{altenkirch2005dependent,

1766−author = {Altenkirch, T. and McBride, C. and McKinna, J.},

1767−booktitle = {Manuscript, available online},

1768−file = {:Users/edwin/Documents/Mendeley Desktop/Altenkirch, McBride, McKinna/Why dependent types matter/Altenkirch, McBride, McKinna - Why dependent types matter - 2005.pdf:pdf},

1769−title = {{Why dependent types matter}},

1770−url = {http://www.cs.nott.ac.uk/$\sim$txa/talks/splst11.pdf},

1771−year = {2005}

1772−}

1773−@misc{Nodes2012a,

1774−author = {Brooks, Fred},

1775−doi = {10.1093/epirev/mxr031},

1776−file = {:Users/edwin/Documents/Mendeley Desktop/Brooks/The Design of Design Chapter 3/Brooks - The Design of Design Chapter 3 - Unknown.pdf:pdf},

1777−isbn = {9780321702081},

1778−issn = {1478-6729},

1779−pmid = {22215642},

1780−title = {{The Design of Design Chapter 3}}

1781−}

1782−@article{danielsson2011parsing,

1783−author = {Danielsson, N. and Norell, U.},

1784−journal = {Implementation and Application of Functional Languages},

1785−pages = {80--99},

1786−publisher = {Springer},

1787−title = {{Parsing mixfix operators}},

1788−url = {http://www.springerlink.com/index/386243257W504252.pdf},

1789−year = {2011}

1790−}

1791−@book{Bird2010,

1792−author = {Bird, Richard},

1793−file = {:Users/edwin/Documents/Mendeley Desktop/Bird/Pearls of Functional Algorithm Design/Bird - Pearls of Functional Algorithm Design - 2010.pdf:pdf},

1794−isbn = {9780521513388},

1795−title = {{Pearls of Functional Algorithm Design}},

1796−year = {2010}

1797−}

1798−@article{Jones1999,

1799−abstract = {Haskell benefits from a sophisticated type system, but implementors, programmers, and researchers suffer because it has no formal description. To remedy this shortcoming, we present a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a notation that is familiar to Haskell users. We expect this program to fill a serious gap in current descriptions of Haskell, both as a starting point for discussions about existing features of the type system, and as a platform from which to explore new proposals.},

1800−author = {Jones, Mark P},

1801−file = {:Users/edwin/Documents/Mendeley Desktop/Jones/Typing Haskell in Haskell/Jones - Typing Haskell in Haskell - 1999.pdf:pdf},

1802−journal = {October},

1803−publisher = {Citeseer},

1804−title = {{Typing Haskell in Haskell}},

1805−url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.134.7274&rep=rep1&type=pdf},

1806−year = {1999}

1807−}

1808−@book{Security2012,

1809−author = {Pfleeger, Charles P and Pfleeger, S. L.},

1810−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

1811−doi = {10.1093/ntr/nts035},

1812−file = {:Users/edwin/Documents/Mendeley Desktop/Pfleeger, Pfleeger/Security in Computing Chapter 3/Pfleeger, Pfleeger - Security in Computing Chapter 3 - 2012.pdf:pdf},

1813−isbn = {0132390779},

1814−issn = {1469-994X},

1815−month = oct,

1816−number = {10},

1817−pages = {NP},

1818−pmid = {23012339},

1819−title = {{Security in Computing Chapter 3}},

1820−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

1821−volume = {14},

1822−year = {2012}

1823−}

1824−@article{Steiner1988,

1825−author = {Steiner, JG},

1826−file = {:Users/edwin/Documents/Mendeley Desktop/Steiner/Kerberos An authentication service for open network systems/Steiner - Kerberos An authentication service for open network systems - 1988.pdf:pdf},

1827−journal = {Proc. Winter USENIX Conference},

1828−title = {{Kerberos: An authentication service for open network systems}},

1829−url = {http://www.cse.nd.edu/$\sim$dthain/courses/cse598z/fall2004/papers/kerberos.pdf},

1830−year = {1988}

1831−}

1832−@inproceedings{stump2010resource,

1833−author = {Stump, A. and Austin, E.},

1834−booktitle = {Proceedings of the 4th ACM SIGPLAN workshop on Programming languages meets program verification},

1835−file = {:Users/edwin/Documents/Mendeley Desktop/Stump, Austin/Resource typing in Guru/Stump, Austin - Resource typing in Guru - 2010.pdf:pdf},

1836−pages = {27--38},

1837−publisher = {ACM},

1838−title = {{Resource typing in Guru}},

1839−url = {http://dl.acm.org/citation.cfm?id=1707796},

1840−year = {2010}

1841−}

1842−@article{fisher2006next,

1843−author = {Fisher, K. and Mandelbaum, Y. and Walker, D.},

1844−file = {:Users/edwin/Documents/Mendeley Desktop/Fisher, Mandelbaum, Walker/The next 700 data description languages/Fisher, Mandelbaum, Walker - The next 700 data description languages - 2010.pdf:pdf},

1845−journal = {Journal of the ACM},

1846−number = {2},

1847−pages = {1--51},

1848−publisher = {ACM},

1849−title = {{The next 700 data description languages}},

1850−url = {http://dl.acm.org/citation.cfm?id=1111039},

1851−volume = {15},

1852−year = {2010}

1853−}

1854−@inproceedings{brady2011epic,

1855−author = {Brady, Edwin},

1856−booktitle = {Trends in Functional Programming ({TFP}’11)},

1857−file = {:Users/edwin/Documents/Mendeley Desktop/Brady/Epic --- A Library for Generating Compilers/Brady - Epic --- A Library for Generating Compilers - 2011.pdf:pdf},

1858−title = {{Epic --- A Library for Generating Compilers}},

1859−url = {http://scholar.google.co.uk/scholar?cites=2588300990390214449&as_sdt=2005&sciodt=0,5&hl=en#1},

1860−year = {2011}

1861−}

1862−@inproceedings{Brady2006b,

1863−author = {Brady, Edwin},

1864−booktitle = {Implementation and Application of Functional Languages ({IFL}'06)},

1865−file = {:Users/edwin/Documents/Mendeley Desktop/Brady/Ivor, a proof engine/Brady - Ivor, a proof engine - 2006.pdf:pdf},

1866−isbn = {978-3-540-74129-9},

1867−month = sep,

1868−pages = {145----162},

1869−title = {{Ivor, a proof engine}},

1870−url = {http://dl.acm.org/citation.cfm?id=1757028.1757037},

1871−year = {2006}

1872−}

1873−@article{Reynolds1972,

1874−abstract = {Higher-order programming languages (i.e., languages in which procedures or labels can occur as values) are usually defined by interpreters which are themselves written in a programming language based on the lambda calculus (i.e., an applicative language such as pure LISP). Examples include McCarthy's definition of LISP, Landin's SECD machine, the Vienna definition of PL/I, Reynolds' definitions of GEDANKEN, and recent unpublished work by L. Morris and C. Wadsworth. Such definitions can be classified according to whether the interpreter contains higher-order functions, and whether the order of application (i.e., call-by-value versus call-by-name) in the defined language depends upon the order of application in the defining language. As an example, we consider the definition of a simple applicative programming language by means of an interpreter written in a similar language. Definitions in each of the above classifications are derived from one another by informal but constructive methods. The treatment of imperative features such as jumps and assignment is also discussed.},

1875−author = {Reynolds, John C},

1876−file = {:Users/edwin/Documents/Mendeley Desktop/Reynolds/Definitional interpreters for higher-order programming languages/Reynolds - Definitional interpreters for higher-order programming languages - 1972.pdf:pdf},

1877−journal = {Proceedings of the ACM annual conference on ACM 72},

1878−keywords = {applicative language,closure,continuation,gedanken,higher order function,interpreter,j operator,lambda calculus,language definition,lisp,order application,pal,programming language,reference,secd machine},

1879−number = {30602},

1880−pages = {717--740},

1881−publisher = {ACM Press},

1882−title = {{Definitional interpreters for higher-order programming languages}},

1883−volume = {2},

1884−year = {1972}

1885−}

1886−@book{Hunt,

1887−author = {Hunt, Andrew and Thomas, David},

1888−booktitle = {Design},

1889−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 4/Hunt, Thomas - The Pragmatic Programmer Chapter 4 - Unknown.pdf:pdf},

1890−isbn = {020161622X},

1891−title = {{The Pragmatic Programmer Chapter 4}}

1892−}

1893−@article{Epstein2011,

1894−author = {Epstein, Jeff and Black, Andrew P and Peyton-jones, Simon},

1895−institution = {Microsoft Research},

1896−journal = {researchmicrosoftcom},

1897−number = {Section 8},

1898−pages = {1--12},

1899−title = {{Haskell for the cloud}},

1900−url = {http://research.microsoft.com/en-us/um/people/simonpj/papers/parallel/remote.pdf},

1901−year = {2011}

1902−}

1903−@book{Bertot2004,

1904−author = {Bertot, Yves and Cast\'{e}ran, Pierre},

1905−publisher = {Springer},

1906−title = {{Interactive theorem proving and program development: {Coq'Art}: the {Calculus of Inductive Constructions}}},

1907−url = {http://books.google.co.uk/books?hl=en&lr=&id=m5w5PRj5Nj4C&oi=fnd&pg=PA1&dq=coq+theorem+prover&ots=VHny1IYV0h&sig=-K0FC67cdkhMDkAocFla8cZyRT4},

1908−year = {2004}

1909−}

1910−@article{Swierstra2011,

1911−author = {Swierstra, W},

1912−file = {:Users/edwin/Documents/Mendeley Desktop/Swierstra/Sorted Verifying the Problem of the {Dutch National} Flag in {Agda}/Swierstra - Sorted Verifying the Problem of the {Dutch National} Flag in {Agda} - 2011.pdf:pdf},

1913−journal = {Journal of Functional Programming},

1914−number = {6},

1915−pages = {575----583},

1916−title = {{Sorted: Verifying the Problem of the {Dutch National} Flag in {Agda}}},

1917−url = {http://journals.cambridge.org/abstract_S0956796811000207},

1918−volume = {21},

1919−year = {2011}

1920−}

1921−@misc{Casinghino2012,

1922−author = {Casinghino, Chris and Sj\"{o}berg, Vilhelm and Weirich, Stephanie},

1923−file = {:Users/edwin/Documents/Mendeley Desktop/Casinghino, Sj{o}berg, Weirich/Combining Proofs and Programs in a Dependently Typed Language/Casinghino, Sj{o}berg, Weirich - Combining Proofs and Programs in a Dependently Typed Language - 2012.pdf:pdf},

1924−keywords = {dependent types,general recursion,termination},

1925−pages = {1--12},

1926−title = {{Combining Proofs and Programs in a Dependently Typed Language}},

1927−year = {2012}

1928−}

1929−@article{Huet1997,

1930−author = {Huet, G},

1931−file = {:Users/edwin/Documents/Mendeley Desktop/Huet/The zipper/Huet - The zipper - 1997.pdf:pdf},

1932−journal = {{Journal of Functional Programming}},

1933−number = {5},

1934−pages = {549----554},

1935−title = {{The zipper}},

1936−url = {http://journals.cambridge.org/abstract_S0956796897002864},

1937−volume = {7},

1938−year = {1997}

1939−}

1940−@inproceedings{bradyresource,

1941−author = {Brady, Edwin and Hammond, Kevin},

1942−booktitle = {Practical Applications of Declarative Languages ({PADL} 2012)},

1943−file = {:Users/edwin/Documents/Mendeley Desktop/Brady, Hammond/Resource-safe Systems Programming with Embedded Domain Specific Languages/Brady, Hammond - Resource-safe Systems Programming with Embedded Domain Specific Languages - 2012.pdf:pdf},

1944−pages = {242----257},

1945−title = {{Resource-safe Systems Programming with Embedded Domain Specific Languages}},

1946−url = {http://www.cs.st-andrews.ac.uk/$\sim$eb/drafts/dsl-idris.pdf},

1947−year = {2012}

1948−}

1949−@book{Management,

1950−author = {Totty, Brian and Gourley, David},

1951−file = {:Users/edwin/Documents/Mendeley Desktop/Totty, Gourley/HTTP The Definitive Guide Chapter 4/Totty, Gourley - HTTP The Definitive Guide Chapter 4 - Unknown.pdf:pdf},

1952−isbn = {1565925092},

1953−title = {{HTTP: The Definitive Guide Chapter 4}}

1954−}

1955−@phdthesis{Brady2005,

1956−author = {Brady, Edwin},

1957−file = {:Users/edwin/Documents/Mendeley Desktop/Brady/Practical Implementation of a Dependently Typed Functional Programming Language/Brady - Practical Implementation of a Dependently Typed Functional Programming Language - 2005.pdf:pdf},

1958−keywords = {Dependent Types},

1959−mendeley-tags = {Dependent Types},

1960−school = {University of Durham},

1961−title = {{Practical Implementation of a Dependently Typed Functional Programming Language}},

1962−year = {2005}

1963−}

1964−@article{Lee2001,

1965−author = {Lee, Chin Soon and Jones, Neil D. and Ben-Amram, Amir M.},

1966−doi = {10.1145/373243.360210},

1967−file = {:Users/edwin/Documents/Mendeley Desktop/Lee, Jones, Ben-Amram/The size-change principle for program termination/Lee, Jones, Ben-Amram - The size-change principle for program termination - 2001.pdf:pdf},

1968−isbn = {1-58113-336-7},

1969−issn = {03621340},

1970−journal = {{ACM SIGPLAN Notices}},

1971−keywords = {PSPACE-completeness,omega automaton,partial evaluation,program analysis,termination},

1972−month = mar,

1973−number = {3},

1974−pages = {81--92},

1975−title = {{The size-change principle for program termination}},

1976−url = {http://dl.acm.org/citation.cfm?id=373243.360210},

1977−volume = {36},

1978−year = {2001}

1979−}

1980−@misc{Bloat,

1981−author = {Brooks, Fred},

1982−file = {:Users/edwin/Documents/Mendeley Desktop/Brooks/The Design of Design Chapter 4/Brooks - The Design of Design Chapter 4 - Unknown.pdf:pdf},

1983−isbn = {9780321702081},

1984−title = {{The Design of Design Chapter 4}}

1985−}

1986−@misc{Caldwell,

1987−author = {Caldwell, James and Roan, Ryan},

1988−file = {:Users/edwin/Documents/Mendeley Desktop/Caldwell, Roan/Type Checking SQL for Secure Database Access/Caldwell, Roan - Type Checking SQL for Secure Database Access - Unknown.pdf:pdf},

1989−title = {{Type Checking SQL for Secure Database Access}}

1990−}

1991−@inproceedings{Peterson1993,

1992−address = {New York, New York, USA},

1993−author = {Peterson, John and Jones, Mark},

1994−booktitle = {Proceedings of the ACM SIGPLAN 1993 conference on Programming Language Design and Implementation - PLDI '93},

1995−doi = {10.1145/155090.155112},

1996−file = {:Users/edwin/Documents/Mendeley Desktop/Peterson, Jones/Implementing type classes/Peterson, Jones - Implementing type classes - 1993.pdf:pdf},

1997−isbn = {0897915984},

1998−issn = {0362-1340},

1999−month = aug,

2000−number = {6},

2001−pages = {227--236},

2002−publisher = {ACM Press},

2003−title = {{Implementing type classes}},

2004−url = {http://dl.acm.org/citation.cfm?id=155090.155112},

2005−volume = {28},

2006−year = {1993}

2007−}

2008−@misc{Attacks2012a,

2009−author = {Anderson, Ross},

2010−doi = {10.1093/epirev/mxr031},

2011−file = {:Users/edwin/Documents/Mendeley Desktop/Anderson/Security Engineering Chapter 18/Anderson - Security Engineering Chapter 18 - Unknown.pdf:pdf},

2012−isbn = {9780470068526},

2013−issn = {1478-6729},

2014−number = {1},

2015−pages = {NP},

2016−pmid = {22215642},

2017−title = {{Security Engineering Chapter 18}},

2018−volume = {34}

2019−}

2020−@inproceedings{bhargavan2010modular,

2021−author = {Bhargavan, K. and Fournet, C. and Gordon, A.D.},

2022−booktitle = {ACM Sigplan Notices},

2023−number = {1},

2024−pages = {445--456},

2025−publisher = {ACM},

2026−title = {{Modular verification of security protocol code by typing}},

2027−url = {http://dl.acm.org/citation.cfm?id=1707801.1706350},

2028−volume = {45},

2029−year = {2010}

2030−}

2031−@article{Hoare1978,

2032−abstract = {This paper suggests that input and output are basic primitives of programming and that parallel composition of communicating sequential processes is a fundamental program structuring method. When combined with a development of Dijkstra's guarded command, these concepts are surprisingly versatile. Their use is illustrated by sample solutions of a variety of a familiar programming exercises.},

2033−author = {Hoare, C A R},

2034−doi = {10.1016/0167-6423(87)90028-1},

2035−editor = {McKeag, R M and Macnaghten, A M},

2036−file = {:Users/edwin/Documents/Mendeley Desktop/Hoare/Communicating sequential processes/Hoare - Communicating sequential processes - 1978.pdf:pdf},

2037−isbn = {0131532715},

2038−issn = {01676423},

2039−journal = {Communications of the ACM},

2040−number = {8},

2041−pages = {666--677},

2042−pmid = {2142694823583477576},

2043−publisher = {ACM},

2044−series = {International Series in Computer Science},

2045−title = {{Communicating sequential processes}},

2046−url = {http://linkinghub.elsevier.com/retrieve/pii/0167642387900281},

2047−volume = {21},

2048−year = {1978}

2049−}

2050−@article{Overview,

2051−author = {Totty, Brian and Gourley, David},

2052−file = {:Users/edwin/Documents/Mendeley Desktop/Totty, Gourley/HTTP The Definitive Guide Chapter 1/Totty, Gourley - HTTP The Definitive Guide Chapter 1 - Unknown.pdf:pdf},

2053−isbn = {1565925092},

2054−title = {{HTTP: The Definitive Guide Chapter 1}}

2055−}

2056−@inproceedings{Sozeau2008,

2057−author = {Sozeau, Matthieu and Oury, Nicolas},

2058−booktitle = {Theorem Proving in Higher Order Logics ({TPHOLs 2008})},

2059−file = {:Users/edwin/Documents/Mendeley Desktop/Sozeau, Oury/First-Class Type Classes/Sozeau, Oury - First-Class Type Classes - 2008.pdf:pdf},

2060−pages = {278----293},

2061−title = {{First-Class Type Classes}},

2062−year = {2008}

2063−}

2064−@book{Fogel,

2065−author = {Fogel, Karl},

2066−file = {:Users/edwin/Documents/Mendeley Desktop/Fogel/Producing Open Source Software How to Run a Successful Free Software Project/Fogel - Producing Open Source Software How to Run a Successful Free Software Project - Unknown.pdf:pdf},

2067−title = {{Producing Open Source Software: How to Run a Successful Free Software Project}}

2068−}

2069−@book{Brady2012,

2070−author = {Hunt, Andrew and Thomas, David},

2071−booktitle = {Carcinogenesis},

2072−doi = {10.1093/carcin/bgs054},

2073−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 5/Hunt, Thomas - The Pragmatic Programmer Chapter 5 - Unknown.pdf:pdf},

2074−isbn = {020161622X},

2075−issn = {1460-2180},

2076−number = {3},

2077−pmid = {22383472},

2078−title = {{The Pragmatic Programmer Chapter 5}},

2079−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

2080−volume = {33}

2081−}

2082−@inproceedings{augustsson2008paradise,

2083−author = {Augustsson, L. and Mansell, H. and Sittampalam, G.},

2084−booktitle = {International Conference on Functional Programming},

2085−file = {:Users/edwin/Documents/Mendeley Desktop/Augustsson, Mansell, Sittampalam/Paradise a two-stage DSL embedded in Haskell/Augustsson, Mansell, Sittampalam - Paradise a two-stage DSL embedded in Haskell - 2008.pdf:pdf},

2086−number = {9},

2087−pages = {225--228},

2088−publisher = {ACM},

2089−title = {{Paradise: a two-stage DSL embedded in Haskell}},

2090−url = {http://dl.acm.org/citation.cfm?id=1411203.1411236},

2091−volume = {43},

2092−year = {2008}

2093−}

2094−@article{marlow2006making,

2095−author = {Marlow, S. and {Peyton Jones}, S.},

2096−file = {:Users/edwin/Documents/Mendeley Desktop/Marlow, Peyton Jones/Making a fast curry pushenter vs. evalapply for higher-order languages/Marlow, Peyton Jones - Making a fast curry pushenter vs. evalapply for higher-order languages - 2006.pdf:pdf},

2097−journal = {Journal of Functional Programming},

2098−number = {4-5},

2099−pages = {415--449},

2100−publisher = {Cambridge University Press},

2101−title = {{Making a fast curry: push/enter vs. eval/apply for higher-order languages}},

2102−url = {http://dl.acm.org/citation.cfm?id=1166018},

2103−volume = {16},

2104−year = {2006}

2105−}

2106−@misc{TheMendeleySupportTeam2011b,

2107−abstract = {A quick introduction to Mendeley. Learn how Mendeley creates your personal digital library, how to organize and annotate documents, how to collaborate and share with colleagues, and how to generate citations and bibliographies.},

2108−address = {London},

2109−author = {{The Mendeley Support Team}},

2110−booktitle = {Mendeley Desktop},

2111−file = {:Users/edwin/Documents/Mendeley Desktop/The Mendeley Support Team/Getting Started with Mendeley/The Mendeley Support Team - Getting Started with Mendeley - 2011.pdf:pdf},

2112−keywords = {Mendeley,how-to,user manual},

2113−pages = {1--16},

2114−publisher = {Mendeley Ltd.},

2115−title = {{Getting Started with Mendeley}},

2116−url = {http://www.mendeley.com},

2117−year = {2011}

2118−}

2119−@inproceedings{ko2011modularising,

2120−author = {Ko, H.S. and Gibbons, J.},

2121−booktitle = {Proceedings of the seventh ACM SIGPLAN workshop on Generic programming},

2122−pages = {13--24},

2123−publisher = {ACM},

2124−title = {{Modularising inductive families}},

2125−url = {http://dl.acm.org/citation.cfm?id=2036921},

2126−year = {2011}

2127−}

2128−@book{Fry1985,

2129−author = {Abelson, Harold and Sussman, Gerald and Sussman, Julie},

2130−booktitle = {Computer Music Journal},

2131−doi = {10.2307/3679579},

2132−file = {:Users/edwin/Documents/Mendeley Desktop/Abelson, Sussman, Sussman/Structure and Interpretation of Computer Programs/Abelson, Sussman, Sussman - Structure and Interpretation of Computer Programs - 1985.pdf:pdf},

2133−isbn = {0262011530},

2134−issn = {01489267},

2135−month = jan,

2136−number = {3},

2137−title = {{Structure and Interpretation of Computer Programs}},

2138−url = {http://www.jstor.org/stable/3679579?origin=crossref},

2139−volume = {9},

2140−year = {1985}

2141−}

2142−@article{Bird2012,

2143−annote = {I enjoyed reading this pearl. It describes, clearly and concisely, the calculation of a program for changing the way of representing a graph in response to a challenge of Donald Knuth's, who asked whether such an algorithm could be discovered in a "disciplined manner". The paper describes that disciplined manner.

2144−

2145−

2146−

2147−

2148−In general, I found the paper easy to follow. Section 2 sets up the problem, giving a purely functional representation of graphs and the definitions of some basic, important functions, in particular encode and decode. Section 3 gives a first example of program calculation, assuming the existence of a function 'lengthen' corresponding to 'shorten' and deriving an implementation from its required properties. Later, we see a definition using arrays rather than lists in order to improve the complexity to linear time. Section 4 addresses a condition Knuth imposes, namely that update must be in place and gives an imperative translation.

2149−

2150−

2151−I think this paper gives a nice example of program calculation leading from a functional specification to an imperative program. I do have a few suggestions though which I think would improve the paper:

2152−

2153−

2154−In the introduction, you say there is a reason why the code cannot be purely functional, but I don't see an explicit explanation of why this is. In place update perhaps? Can this be clarified?

2155−

2156−

2157−The equation numbering, e.g. (1) at the bottom of p1 - some equations are clearly important and referred to elsewhere, such as this one. Is it possible to make these stand out more? e.g. with an explicit heading "Equation 1"?

2158−

2159−

2160−p3 In the first examples of program calculation, it is easy to follow the reasoning of why the calculation is correct, but it is not so obvious what the insight was that led to the calculation. Is this simply a matter of experience?

2161−

2162−

2163−p6 I'm surprised to read that // updates an array in place. Is this really what is happening or is there a clever representation of Data.Array.Diff? It appears to use IO operations internally. So it might be nice to say a little more about what is really going on.

2164−

2165−

2166−p7 "...an observation that could have been made earlier" seems an odd thing to say. Why not either make it earlier, or just make it here where it is used?

2167−

2168−

2169−p9 There is no need to give the translation rules to the imperative code in detail, but it would still be useful to sketch what is going on. It seems that the foldr becomes the outer for loop, and apply the inner for loop. It would also be useful, in Figs 1-4 to give the functional code alongside the imperative versions. It is interesting to examine how the mapping works and I think an important point made by the paper (as indeed you say in the conclusion).

2170−

2171−

2172−p14 The last paragraph appears to be largely a comment to the present referees!

2173−

2174− },

2175−author = {Bird, Richard S},

2176−file = {:Users/edwin/Documents/Mendeley Desktop/Bird/An in-situ algorithm for expanding a graph/Bird - An in-situ algorithm for expanding a graph - 2012(2).pdf:pdf},

2177−journal = {Journal of Functional Programming},

2178−keywords = {a href,journal of functional programming},

2179−title = {{An in-situ algorithm for expanding a graph}},

2180−year = {2012}

2181−}

2182−@article{Ahn,

2183−annote = {-1,5

2184−

2185−

2186−The paper describes Nax, a new functional programming language with term indices which supports logical consistency and Hindley-Milner style type inference. The authors give four key features of Nax (1: strong normalization, 2: type inference, 3: expressivity and 4: support for term indices) and give several examples to demonstrate the simplicity of programming in Nax as compared with Haskell and Agda. Three examples are given, in each language: a type preserving evaluator for an expression language, a generic Path datatype which describes a path through an index type, and a stack safe compiler for the expression language.

2187−

2188−

2189−Presenting examples in this way gives a nice introduction to Nax, in that they are well understood examples already and it is easy to relate them to implementations with which the reader is already familiar. On the other hand, this leads to my main problem with this paper: it doesn't really tell us anything we don't already know, and the promising things about Nax which *would* be an interesting contribution are left out of the paper.

2190−

2191−

2192−Of the four features of Nax given above, 1 and 2 are described as "beyond the scope of this paper" which is a shame because these are the things I'm most interested in hearing about! Existing dependently typed languages lack type inference, and whlie I would argue that it is usually best to write types first in any case, there are still many situations where recovering type inference would be useful - typically small or simply typed helper functions. So this would have been a very nice technical contribution.

2193−

2194−

2195−The third feature (expressivity) is one that the authors claim as a contribution of the paper. They claim that programming in Nax is as "simple" as programming in Haskell or Agda. However, I think this is a strong claim to make given the available evidence - it is quite subjective. I agree that the programs are quite easy to read, but to say that *programming* is as simple really requires some externally verified evidence from other programmers! It seems to me that programming with Mendler-style combinators may take some practice, for example.

2196−

2197−

2198−In summary, I do like the idea behind Nax and some of its features sound as if they could be interesting, and I think this latest contribution to the design space of dependently typed functional programming is welcome. But this paper does not really provide any new insights as it stands.

2199−

2200−

2201−Minor comments:

2202−

2203−

2204−Fig 1,2 and 3 - I'm not sure I would like the rotation of these in print (it's pretty awkward on screen too).},

2205−author = {Ahn, Ki Yung and Sheard, Tim and Fiore, Marcelo and Pitts, Andrew M},

2206−file = {:Users/edwin/Documents/Mendeley Desktop/Ahn et al/Programming with Term-Indexed Types in Nax/Ahn et al. - Programming with Term-Indexed Types in Nax - Unknown.pdf:pdf},

2207−keywords = {gadts,indexed datatypes,lightweight dependent types,term-indexed types,universe polymorphism,universe subtyping},

2208−title = {{Programming with Term-Indexed Types in Nax}}

2209−}

2210−@article{Morrisett1999,

2211−author = {Morrisett, G and Walker, D},

2212−file = {:Users/edwin/Documents/Mendeley Desktop/Morrisett, Walker/From System F to typed assembly language/Morrisett, Walker - From System F to typed assembly language - 1999.pdf:pdf},

2213−journal = {ACM Transactions on \ldots},

2214−title = {{From System F to typed assembly language}},

2215−url = {http://dl.acm.org/citation.cfm?id=319345},

2216−year = {1999}

2217−}

2218−@article{Altenkirch2010a,

2219−abstract = {We begin by revisiting the idea of using a universe of types to write generic programs in a dependently typed setting by constructing a universe for Strictly Positive Types (SPTs). Here we extend this construction to cover dependent types, i.e. Strictly Positive Families (SPFs), thereby fixing a gap left open in previous work. Using the approach presented here we are able to represent all of Epigrams datatypes within Epigram including the universe of datatypes itself.},

2220−author = {Altenkirch, Thorsten and Mcbride, Conor and Morris, Peter},

2221−file = {:Users/edwin/Documents/Mendeley Desktop/Altenkirch, Mcbride, Morris/Generic Programming with Dependent Types/Altenkirch, Mcbride, Morris - Generic Programming with Dependent Types - 2010.pdf:pdf},

2222−journal = {Citeseer},

2223−publisher = {Citeseer},

2224−title = {{Generic Programming with Dependent Types}},

2225−url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.129.2926&rep=rep1&type=pdf},

2226−year = {2010}

2227−}

2228−@book{Edition2012a,

2229−author = {Pfleeger, Charles P and Pfleeger, S. L.},

2230−booktitle = {Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco},

2231−doi = {10.1093/ntr/nts035},

2232−file = {:Users/edwin/Documents/Mendeley Desktop/Pfleeger, Pfleeger/Security in Computer Chapter 12/Pfleeger, Pfleeger - Security in Computer Chapter 12 - 2012.pdf:pdf},

2233−isbn = {0132390779},

2234−issn = {1469-994X},

2235−month = oct,

2236−number = {10},

2237−pages = {NP},

2238−pmid = {23012339},

2239−title = {{Security in Computer Chapter 12}},

2240−url = {http://www.ncbi.nlm.nih.gov/pubmed/23012339},

2241−volume = {14},

2242−year = {2012}

2243−}

2244−@book{Pierce2004,

2245−author = {Pierce, Benjamin},

2246−editor = {Pierce, Benjamin},

2247−file = {:Users/edwin/Documents/Mendeley Desktop/Pierce/Advanced topics in types and programming languages/Pierce - Advanced topics in types and programming languages - 2004.pdf:pdf},

2248−publisher = {MIT Press},

2249−title = {{Advanced topics in types and programming languages}},

2250−year = {2004}

2251−}

2252−@inproceedings{taha1997multi,

2253−author = {Taha, W. and Sheard, T.},

2254−booktitle = {ACM SIGPLAN Notices},

2255−number = {12},

2256−pages = {203--217},

2257−publisher = {ACM},

2258−title = {{Multi-stage programming with explicit annotations}},

2259−url = {http://dl.acm.org/citation.cfm?id=259019},

2260−volume = {32},

2261−year = {1997}

2262−}

2263−@misc{Lorenzen,

2264−author = {Lorenzen, Florian},

2265−file = {:Users/edwin/Documents/Mendeley Desktop/Lorenzen/A Statically Typed Functional Language With Programmable Binders/Lorenzen - A Statically Typed Functional Language With Programmable Binders - Unknown.pdf:pdf},

2266−title = {{A Statically Typed Functional Language With Programmable Binders}}

2267−}

2268−@book{The2012,

2269−author = {Hunt, Andrew and Thomas, David},

2270−booktitle = {Carcinogenesis},

2271−doi = {10.1093/carcin/bgs054},

2272−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 3/Hunt, Thomas - The Pragmatic Programmer Chapter 3 - Unknown.pdf:pdf},

2273−isbn = {020161622X},

2274−issn = {1460-2180},

2275−number = {3},

2276−pmid = {22383472},

2277−title = {{The Pragmatic Programmer Chapter 3}},

2278−url = {http://www.ncbi.nlm.nih.gov/pubmed/22383472},

2279−volume = {33}

2280−}

2281−@inproceedings{pollack1990implicit,

2282−author = {Pollack, R.},

2283−booktitle = {{Informal Proceedings of First Workshop on Logical Frameworks, Antibes}},

2284−file = {:Users/edwin/Documents/Mendeley Desktop/Pollack/Implicit syntax/Pollack - Implicit syntax - 1990.pdf:pdf},

2285−publisher = {Citeseer},

2286−title = {{Implicit syntax}},

2287−url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.30.7361&rep=rep1&type=pdf},

2288−year = {1990}

2289−}

2290−@article{Bradya,

2291−author = {Hunt, Andrew and Thomas, David},

2292−file = {:Users/edwin/Documents/Mendeley Desktop/Hunt, Thomas/The Pragmatic Programmer Chapter 7/Hunt, Thomas - The Pragmatic Programmer Chapter 7 - Unknown.pdf:pdf},

2293−isbn = {020161622X},

2294−title = {{The Pragmatic Programmer Chapter 7}}

2295−}

papers/impl-paper/library.ltxdeleted−325

@@ -1,325 +0,0 @@

1−%%%%%%%%%%%%%%% library file for datatypes etc.

2−

3−%%% Identifiers

4−

5−\newcommand{\va}{\VV{a}}

6−\newcommand{\vb}{\VV{b}}

7−\newcommand{\vc}{\VV{c}}

8−\newcommand{\vd}{\VV{d}}

9−\newcommand{\ve}{\VV{e}}

10−\newcommand{\vf}{\VV{f}}

11−\newcommand{\vg}{\VV{g}}

12−\newcommand{\vh}{\VV{h}}

13−\newcommand{\vi}{\VV{i}}

14−\newcommand{\vj}{\VV{j}}

15−\newcommand{\vk}{\VV{k}}

16−\newcommand{\vl}{\VV{l}}

17−\newcommand{\vm}{\VV{m}}

18−\newcommand{\vn}{\VV{n}}

19−\newcommand{\vo}{\VV{o}}

20−\newcommand{\vp}{\VV{p}}

21−\newcommand{\vq}{\VV{q}}

22−\newcommand{\vr}{\VV{r}}

23−\newcommand{\vs}{\VV{s}}

24−\newcommand{\vt}{\VV{t}}

25−\newcommand{\vu}{\VV{u}}

26−\newcommand{\vv}{\VV{v}}

27−\newcommand{\vw}{\VV{w}}

28−\newcommand{\vx}{\VV{x}}

29−\newcommand{\vy}{\VV{y}}

30−\newcommand{\vz}{\VV{z}}

31−\newcommand{\vA}{\VV{A}}

32−\newcommand{\vB}{\VV{B}}

33−\newcommand{\vC}{\VV{C}}

34−\newcommand{\vD}{\VV{D}}

35−\newcommand{\vE}{\VV{E}}

36−\newcommand{\vF}{\VV{F}}

37−\newcommand{\vG}{\VV{G}}

38−\newcommand{\vH}{\VV{H}}

39−\newcommand{\vI}{\VV{I}}

40−\newcommand{\vJ}{\VV{J}}

41−\newcommand{\vK}{\VV{K}}

42−\newcommand{\vL}{\VV{L}}

43−\newcommand{\vM}{\VV{M}}

44−\newcommand{\vN}{\VV{N}}

45−\newcommand{\vO}{\VV{O}}

46−\newcommand{\vP}{\VV{P}}

47−\newcommand{\vQ}{\VV{Q}}

48−\newcommand{\vR}{\VV{R}}

49−\newcommand{\vS}{\VV{S}}

50−\newcommand{\vT}{\VV{T}}

51−\newcommand{\vU}{\VV{U}}

52−\newcommand{\vV}{\VV{V}}

53−\newcommand{\vW}{\VV{W}}

54−\newcommand{\vX}{\VV{X}}

55−\newcommand{\vY}{\VV{Y}}

56−\newcommand{\vZ}{\VV{Z}}

57−\newcommand{\vas}{\VV{as}}

58−\newcommand{\vbs}{\VV{bs}}

59−\newcommand{\vcs}{\VV{cs}}

60−\newcommand{\vds}{\VV{ds}}

61−\newcommand{\ves}{\VV{es}}

62−\newcommand{\vfs}{\VV{fs}}

63−\newcommand{\vgs}{\VV{gs}}

64−\newcommand{\vhs}{\VV{hs}}

65−\newcommand{\vis}{\VV{is}}

66−\newcommand{\vjs}{\VV{js}}

67−\newcommand{\vks}{\VV{ks}}

68−\newcommand{\vls}{\VV{ls}}

69−\newcommand{\vms}{\VV{ms}}

70−\newcommand{\vns}{\VV{ns}}

71−\newcommand{\vos}{\VV{os}}

72−\newcommand{\vps}{\VV{ps}}

73−\newcommand{\vqs}{\VV{qs}}

74−\newcommand{\vrs}{\VV{rs}}

75−%\newcommand{\vss}{\VV{ss}}

76−\newcommand{\vts}{\VV{ts}}

77−\newcommand{\vus}{\VV{us}}

78−\newcommand{\vvs}{\VV{vs}}

79−\newcommand{\vws}{\VV{ws}}

80−\newcommand{\vxs}{\VV{xs}}

81−\newcommand{\vys}{\VV{ys}}

82−\newcommand{\vzs}{\VV{zs}}

83−

84−%%% Telescope Identifiers

85−

86−\newcommand{\ta}{\vec{\VV{a}}}

87−\newcommand{\tb}{\vec{\VV{b}}}

88−\newcommand{\tc}{\vec{\VV{c}}}

89−\newcommand{\td}{\vec{\VV{d}}}

90−\newcommand{\te}{\vec{\VV{e}}}

91−\newcommand{\tf}{\vec{\VV{f}}}

92−\newcommand{\tg}{\vec{\VV{g}}}

93−%\newcommand{\th}{\vec{\VV{h}}}

94−\newcommand{\ti}{\vec{\VV{i}}}

95−\newcommand{\tj}{\vec{\VV{j}}}

96−\newcommand{\tk}{\vec{\VV{k}}}

97−\newcommand{\tl}{\vec{\VV{l}}}

98−\newcommand{\tm}{\vec{\VV{m}}}

99−\newcommand{\tn}{\vec{\VV{n}}}

100−%\newcommand{\to}{\vec{\VV{o}}}

101−\newcommand{\tp}{\vec{\VV{p}}}

102−\newcommand{\tq}{\vec{\VV{q}}}

103−\newcommand{\tr}{\vec{\VV{r}}}

104−\newcommand{\tts}{\vec{\VV{s}}}

105−\newcommand{\ttt}{\vec{\VV{t}}}

106−\newcommand{\tu}{\vec{\VV{u}}}

107−\newcommand{\tv}{\vec{\VV{v}}}

108−\newcommand{\tw}{\vec{\VV{w}}}

109−\newcommand{\tx}{\vec{\VV{x}}}

110−\newcommand{\ty}{\vec{\VV{y}}}

111−\newcommand{\tz}{\vec{\VV{z}}}

112−\newcommand{\tA}{\vec{\VV{A}}}

113−\newcommand{\tB}{\vec{\VV{B}}}

114−\newcommand{\tC}{\vec{\VV{C}}}

115−\newcommand{\tD}{\vec{\VV{D}}}

116−\newcommand{\tE}{\vec{\VV{E}}}

117−\newcommand{\tF}{\vec{\VV{F}}}

118−\newcommand{\tG}{\vec{\VV{G}}}

119−\newcommand{\tH}{\vec{\VV{H}}}

120−\newcommand{\tI}{\vec{\VV{I}}}

121−\newcommand{\tJ}{\vec{\VV{J}}}

122−\newcommand{\tK}{\vec{\VV{K}}}

123−\newcommand{\tL}{\vec{\VV{L}}}

124−\newcommand{\tM}{\vec{\VV{M}}}

125−\newcommand{\tN}{\vec{\VV{N}}}

126−\newcommand{\tO}{\vec{\VV{O}}}

127−\newcommand{\tP}{\vec{\VV{P}}}

128−\newcommand{\tQ}{\vec{\VV{Q}}}

129−\newcommand{\tR}{\vec{\VV{R}}}

130−\newcommand{\tS}{\vec{\VV{S}}}

131−\newcommand{\tT}{\vec{\VV{T}}}

132−\newcommand{\tU}{\vec{\VV{U}}}

133−\newcommand{\tV}{\vec{\VV{V}}}

134−\newcommand{\tW}{\vec{\VV{W}}}

135−\newcommand{\tX}{\vec{\VV{X}}}

136−\newcommand{\tY}{\vec{\VV{Y}}}

137−\newcommand{\tZ}{\vec{\VV{Z}}}

138−

139−

140−

141−%%% Nat

142−

143−\newcommand{\NatPackage}{

144− \newcommand{\Nat}{\TC{Nat}}

145− \newcommand{\Z}{\DC{Z}}

146− \newcommand{\suc}{\DC{S}}

147− \newcommand{\NatDecl}{

148− \Data \hg

149− \Axiom{\Nat\Hab\Type} \hg

150− \Where \hg

151− \Axiom{\Z\Hab\Nat} \hg

152− \Rule{\vn\Hab\Nat}

153− {\suc\:\vn\Hab\Nat}

154−}}

155−

156−%%% Bool

157−

158−\newcommand{\BoolPackage}{

159− \newcommand{\Bool}{\TC{Bool}}

160− \newcommand{\true}{\DC{true}}

161− \newcommand{\false}{\DC{false}}

162− \newcommand{\BoolDecl}{

163− \Data \hg

164− \Axiom{\Bool\Hab\Type} \hg

165− \Where \hg

166− \Axiom{\true\Hab\Bool} \hg

167− \Axiom{\false\Hab\Bool}

168−}}

169−

170−%%% So

171−

172−\newcommand{\SoPackage}{

173− \newcommand{\So}{\TC{So}}

174− \newcommand{\oh}{\DC{oh}}

175− \newcommand{\SoDecl}{

176− \Data \hg

177− \Rule{\vb\Hab\Bool}

178− {\So\:\vb\Hab\Type} \hg

179− \Where \hg

180− \Axiom{\oh\Hab\So\:\true}

181−}}

182−

183−%%% Unit

184−

185−\newcommand{\UnitPackage}{

186− \newcommand{\Unit}{\TC{Unit}}

187− \newcommand{\void}{\DC{void}}

188− \newcommand{\UnitDecl}{

189− \Data \hg

190− \Axiom{\Unit\Hab\Type} \hg

191− \Where \hg

192− \Axiom{\void\Hab\Unit}

193−}}

194−

195−%%% Maybe

196−

197−\newcommand{\MaybePackage}{

198− \newcommand{\Maybe}{\TC{Maybe}}

199− \newcommand{\yes}{\DC{yes}}

200− \newcommand{\no}{\DC{no}}

201− \newcommand{\MaybeDecl}{

202− \Data \hg

203− \Rule{\vA\Hab\Type}

204− {\Maybe\:\vA\Hab\Type} \hg

205− \Where \hg

206− \Rule{\va \Hab \vA}

207− {\yes\:\va\Hab\Maybe\:\vA} \hg

208− \Axiom{\no\Hab\Maybe\:\vA}

209−}}

210−

211−%%% Cross

212−

213−\newcommand{\pr}[2]{(#1\DC{,}#2)} %grrrr

214−\newcommand{\CrossPackage}{

215− \newcommand{\Cross}{\times}

216− \newcommand{\CrossDecl}{

217− \Data \hg

218− \Rule{\vA,\vB\Hab\Type}

219− {\vA\Cross\vB\Hab\Type} \hg

220− \Where \hg

221− \Rule{\va \Hab \vA \hg \vb\Hab\vB}

222− {\pr{\va}{\vb}\Hab\vA\Cross\vB}

223−}}

224−

225−%%% Fin

226−

227−\newcommand{\FinPackage}{

228− \newcommand{\Fin}{\TC{Fin}}

229− \newcommand{\fz}{\DC{f0}}

230− \newcommand{\fs}{\DC{fs}}

231− \newcommand{\FinDecl}{

232− \AR{

233− \Data \hg

234− \Rule{\vn\Hab\Nat}

235− {\Fin\:\vn\Hab\Type} \hg \\

236− \Where \hg

237− \begin{array}[t]{c}

238− \Axiom{\fz\Hab\Fin\:(\suc\:\vn)} \hg

239− \Rule{\vi\Hab\Fin\:\vn}

240− {\fs\:\vi\Hab\Fin\:(\suc\:\vn)}

241− \end{array}

242− }

243−}}

244−

245−%%% Vect

246−

247−\newcommand{\VectPackage}{

248− \newcommand{\Vect}{\TC{Vect}}

249− \newcommand{\vnil}{\DC{Nil}}

250− \newcommand{\vcons}{\,\dcolon\,}

251− \newcommand{\vsnoc}{\,\dcolon\,}

252− \newcommand{\VectConsDecl}{

253− \Data \hg

254− \Rule{\vA \Hab \Type \hg \vn\Hab\Nat}

255− {\Vect\:\vA\:\vn\Hab\Type} \hg

256− \Where \hg \begin{array}[t]{c}

257− \Axiom{\vnil \Hab \Vect\:\vA\:\Z} \\

258− \Rule{\vx\Hab\vA \hg \vxs\Hab \Vect\:\vA\:\vn }

259− {\vx\vcons\vxs\Hab\Vect\:\vA\:(\suc\vn)}

260− \end{array}

261−}

262− \newcommand{\VectSnocDecl}{

263− \Data \hg

264− \Rule{\vA \Hab \Type \hg \vn\Hab\Nat}

265− {\Vect\:\vA\:\vn\Hab\Type} \hg

266− \Where \hg \begin{array}[t]{c}

267− \Axiom{\vnil \Hab \Vect\:\vA\:\Z} \\

268− \Rule{\vxs\Hab \Vect\:\vA\:\vn \hg \vx\Hab\vA}

269− {\vxs\vsnoc\vx\Hab\Vect\:\vA\:(\suc\vn)}

270− \end{array}

271−}

272−}

273−

274−%%% Compare

275−

276−%Data Compare : (x:nat)(y:nat)Type

277−% = lt : (x:nat)(y:nat)(Compare x (plus (S y) x))

278−% | eq : (x:nat)(Compare x x)

279−% | gt : (x:nat)(y:nat)(Compare (plus (S x) y) y);

280−

281−

282−\newcommand{\ComparePackage}{

283− \newcommand{\Compare}{\TC{Compare}}

284− \newcommand{\ltComp}{\DC{lt}}

285− \newcommand{\eqComp}{\DC{eq}}

286− \newcommand{\gtComp}{\DC{gt}}

287− \newcommand{\CompareDecl}{

288− \Data \hg

289− \Rule{\vm\Hab\Nat\hg\vn\Hab\Nat}

290− {\Compare\:\vm\:\vn\Hab\Type} \\

291− \Where \hg\begin{array}[t]{c}

292− \Rule{\vx\Hab\Nat\hg\vy\Hab\Nat}

293− {\ltComp_{\vx}\:\vy\Hab\Compare\:\vx\:(\FN{plus}\:\vx\:(\suc\:\vy))} \\

294− \Rule{\vx\Hab\Nat}

295− {\eqComp_{\vx}\Hab\Compare\:\vx\:\vx}\\

296− \Rule{\vx\Hab\Nat\hg\vy\Hab\Nat}

297− {\gtComp_{\vy}\:\vx\Hab\Compare\:(\FN{plus}\:\vy\:(\suc\:\vx))\:\vy} \\

298− \end{array}

299− }

300−

301−%Data CompareM : Type

302−% = ltM : (ydiff:nat)CompareM

303−% | eqM : CompareM

304−% | gtM : (xdiff:nat)CompareM;

305−

306− \newcommand{\CompareM}{\TC{Compare^-}}

307− \newcommand{\ltCompM}{\DC{lt^-}}

308− \newcommand{\eqCompM}{\DC{eq^-}}

309− \newcommand{\gtCompM}{\DC{gt^-}}

310− \newcommand{\CompareMDecl}{

311−

312− \Data \hg

313− \Axiom{\CompareM\Hab\Type} \\

314− \Where \hg\begin{array}[t]{c}

315− \Rule{\vy\Hab\Nat}

316− {\ltCompM\:\vy\Hab\CompareM} \\

317− \Axiom{\eqCompM\Hab\CompareM}\\

318− \Rule{\vx\Hab\Nat}

319− {\gtCompM\:\vx\Hab\CompareM} \\

320− \end{array}

321− }

322− \newcommand{\CompareRec}{\FN{CompareRec}}

323− \newcommand{\CompareRecM}{\FN{CompareRec^-}}

324−

325−}

papers/impl-paper/literature.bibdeleted−3846

@@ -1,3846 +0,0 @@

1−@article{lambdapi,

2− author = {Andres L\"{o}h and Conor McBride and Wouter Swierstra},

3− title = {A tutorial implementation of a dependently typed lambda calculus},

4− year = 2010,

5− journal = {Fundamenta Informaticae},

6− volume = 102,

7− number = 2

8−}

9−

10−@article{idioms,

11− author = {McBride, Conor and Paterson, Ross},

12− title = {Applicative programming with effects},

13− journal = {J. Funct. Program.},

14− volume = {18},

15− issue = {1},

16− month = {January},

17− year = {2008},

18− issn = {0956-7968},

19− pages = {1--13},

20− numpages = {13},

21− url = {http://portal.acm.org/citation.cfm?id=1348940.1348941},

22− doi = {10.1017/S0956796807006326},

23− acmid = {1348941},

24− publisher = {Cambridge University Press},

25− address = {New York, NY, USA},

26−}

27−

28−@inproceedings{lava,

29− author = {Bjesse, Per and Claessen, Koen and Sheeran, Mary and Singh, Satnam},

30− title = {Lava: hardware design in {Haskell}},

31− booktitle = {Proceedings of the third ACM SIGPLAN international conference on Functional programming},

32− series = {ICFP '98},

33− year = {1998},

34− isbn = {1-58113-024-4},

35− location = {Baltimore, Maryland, United States},

36− pages = {174--184},

37− numpages = {11},

38− url = {http://doi.acm.org/10.1145/289423.289440},

39− doi = {http://doi.acm.org/10.1145/289423.289440},

40− acmid = {289440},

41− publisher = {ACM},

42− address = {New York, NY, USA},

43−}

44−

45−@inproceedings{plpv11,

46− author = {Edwin Brady},

47− title = {Idris --- Systems programming meets full dependent types},

48− booktitle = {Programming Languages meets Program Verification {(PLPV 2011)}},

49− year = {2011},

50− pages = {43--54},

51− ee = {http://doi.acm.org/10.1145/1929529.1929536},

52− bibsource = {DBLP, http://dblp.uni-trier.de}

53−}

54−

55−@inproceedings{epic-tfp,

56− author = {Edwin Brady},

57− title = {Epic --- a library for generating compilers},

58− year = 2011,

59− booktitle = {{Trends in Functional Programming} ({TFP} '11)},

60− note = {To appear}

61−}

62−

63−@inproceedings{ynot08,

64− author = {Nanevski,, Aleksandar and Morrisett,, Greg and

65− Shinnar,, Avraham and Govereau,, Paul and Birkedal,,

66− Lars},

67− title = {Ynot: reasoning with the awkward squad},

68− booktitle = {{ICFP} '08: Proceeding of the 13th {ACM SIGPLAN}

69− international conference on Functional programming},

70− year = {2008},

71− isbn = {978-1-59593-919-7},

72− pages = {229--240},

73− location = {Victoria, BC, Canada},

74− doi = {http://doi.acm.org/10.1145/1411204.1411237},

75− publisher = {ACM},

76− address = {New York, NY, USA},

77−}

78−

79−@article{cbconc-fi,

80− author = {Edwin Brady and Kevin Hammond},

81− title = {Correct-by-Construction Concurrency: Using Dependent Types to Verify Implementations of Effectful Resource Usage Protocols},

82− year = 2010,

83− journal = {Fundamenta Informaticae},

84− volume = 102,

85− number = 2,

86− pages = {145--176}

87−}

88−

89−@inproceedings{devil-osdi00,

90− author = {Fabrice M{\'e}rillon and

91− Laurent R{\'e}veill{\`e}re and

92− Charles Consel and

93− Renaud Marlet and

94− Gilles Muller},

95− title = {Devil: An IDL for Hardware Programming},

96− booktitle = {4th USENIX Symposium on Operating Systems Design and Implementation (OSDI 2000)},

97− year = {2000}

98−}

99−

100−

101−@INPROCEEDINGS{device-osdi08,

102− author = {Dan Williams and Patrick Reynolds and Kevin Walsh and Emin Gün Sirer and Fred B. Schneider},

103− title = {Device driver safety through a reference validation mechanism},

104− booktitle = {8th USENIX Symposium on Operating Systems Design and Implementation (OSDI 2008)},

105− year = {2008}

106−}

107−

108−@inproceedings{sozeau-equations,

109− author = {Matthieu Sozeau},

110− title = {Equations: A Dependent Pattern-Matching Compiler},

111− booktitle = {First International Conference on Interactive Theorem Proving (ITP 2010)},

112− year = {2010},

113− pages = {419--434},

114− ee = {http://dx.doi.org/10.1007/978-3-642-14052-5_29},

115− crossref = {DBLP:conf/itp/2010},

116− bibsource = {DBLP, http://dblp.uni-trier.de}

117−}

118−

119−

120−@inproceedings{packet-type,

121− author = "Peter J. McCann and Satish Chandra",

122− title = "Packet Types: Abstract Specification of Network Protocol Messages",

123− year = 2000,

124− booktitle = "SIGCOMM '00",

125− publisher = {{ACM}}

126−}

127−

128−@inproceedings{qs-types,

129− author = {Eelis {van der Weegen} and James McKinna},

130−

131− title={A Machine-checked Proof of the Average-case Complexity of Quicksort in Coq},

132− year={2009},

133− pages={256--271},

134− series = {Lecture Notes in Computer Science},

135− publisher = {Springer}

136−

137−}

138−

139−@inproceedings{totalparser,

140− author = {Nils Anders Danielsson},

141− title = {Total Parser Combinators},

142− booktitle = {{ICFP} '10: Proceedings of the 15th {ACM} {SIGPLAN} International Conference on Functional Programming},

143− year = {2010},

144− isbn = {978-1-60558-794-3},

145− pages = {285--296},

146− location = {Baltimore, Maryland, USA},

147− doi = {http://doi.{ACM}.org/10.1145/1863543.1863587},

148− publisher = {{ACM}},

149− address = {New York, NY, USA},

150− }

151−

152−@misc{rfc791,

153− author="J. Postel",

154− title="{Internet Protocol}",

155− series="Request for Comments",

156− number="791",

157− howpublished="RFC 791 (Standard)",

158− publisher="IETF",

159− organization="Internet Engineering Task Force",

160− year=1981,

161− month=sep,

162− note="Updated by RFC 1349",

163− url="http://www.ietf.org/rfc/rfc791.txt",

164−}

165−

166−

167−@misc{rfc792,

168− author="J. Postel",

169− title="{Internet Control Message Protocol}",

170− series="Request for Comments",

171− number="792",

172− howpublished="RFC 792 (Standard)",

173− publisher="IETF",

174− organization="Internet Engineering Task Force",

175− year=1981,

176− month=sep,

177− note="Updated by RFCs 950, 4884",

178− url="http://www.ietf.org/rfc/rfc792.txt",

179−}

180−

181−@INPROCEEDINGS{Dybjer-indrec,

182− author = {Peter Dybjer and Anton Setzer},

183− title = {A Finite Axiomatization of Inductive-Recursive Definitions},

184− booktitle = {Tyed Lambda Calculi and Applications},

185− volume = {1581},

186− series = {Lecture Notes in Computer Science},

187− year = {1998},

188− pages = {129--146},

189− publisher = {Springer}

190−}

191−

192−@book{stevenstcpip,

193− author = {W. Richard Stevens},

194− title = {{TCP/IP} Illustrated Volume 1: The Protocols},

195− year = 1994,

196− publisher = {Addison Wesley},

197− isbn = {0-201-63346-9}

198−}

199−

200−@inproceedings{coqtypeclasses,

201− author = {Sozeau, Matthieu and Oury, Nicolas},

202− title = {First-Class Type Classes},

203− booktitle = {TPHOLs '08: Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics},

204− year = {2008},

205− isbn = {978-3-540-71065-3},

206− pages = {278--293},

207− location = {Montreal, P.Q., Canada},

208− doi = {http://dx.doi.org/10.1007/978-3-540-71067-7_23},

209− publisher = {Springer-Verlag},

210− address = {Berlin, Heidelberg},

211− }

212−

213−

214−@inproceedings{kipling,

215− author = {McBride, Conor},

216− title = {Outrageous but meaningful coincidences: dependent type-safe syntax and evaluation},

217− booktitle = {WGP '10: Proceedings of the 6th {ACM} {SIGPLAN} workshop on Generic programming},

218− year = {2010},

219− isbn = {978-1-4503-0251-7},

220− pages = {1--12},

221− location = {Baltimore, Maryland, USA},

222− doi = {http://doi.{ACM}.org/10.1145/1863495.1863497},

223− publisher = {{ACM}},

224− address = {New York, NY, USA},

225− }

226−

227−@inproceedings{padsml,

228− author = {Yitzhak Mandelbaum and

229− Kathleen Fisher and

230− David Walker and

231− Mary F. Fern{\'a}ndez and

232− Artem Gleyzer},

233− title = {{PADS/ML}: a functional data description language},

234− booktitle = {POPL '07: Proceedings of the 34th {ACM} {SIGPLAN}-SIGACT Symposium on

235− Principles of Programming Languages, POPL 2007, Nice, France,

236− January 17-19, 2007},

237− year = {2007},

238− pages = {77-83},

239− ee = {http://doi.{ACM}.org/10.1145/1190216.1190231},

240− crossref = {DBLP:conf/popl/2007},

241− bibsource = {DBLP, http://dblp.uni-trier.de}

242−}

243−

244−@proceedings{DBLP:conf/popl/2007,

245− editor = {Martin Hofmann and

246− Matthias Felleisen},

247− title = {Proceedings of the 34th {ACM} {SIGPLAN}-SIGACT Symposium on

248− Principles of Programming Languages, POPL 2007, Nice, France,

249− January 17-19, 2007},

250− booktitle = {POPL},

251− publisher = {{ACM}},

252− year = {2007},

253− isbn = {1-59593-575-4},

254− bibsource = {DBLP, http://dblp.uni-trier.de}

255−}

256−

257−@inproceedings{melange,

258− author = {Madhavapeddy, Anil and Ho, Alex and Deegan, Tim and Scott, David and Sohan, Ripduman},

259− title = {Melange: creating a "functional" internet},

260− booktitle = {EuroSys '07: Proceedings of the 2nd {ACM} SIGOPS/EuroSys European Conference on Computer Systems 2007},

261− year = {2007},

262− isbn = {978-1-59593-636-3},

263− location = {Lisbon, Portugal},

264− doi = {http://doi.{ACM}.org/10.1145/1272996.1273009},

265− publisher = {{ACM}},

266− address = {New York, NY, USA},

267− }

268−

269−

270−

271−@article{next700data,

272− author = {Fisher, Kathleen and Mandelbaum, Yitzhak and Walker, David},

273− title = {The next 700 data description languages},

274− journal = {{SIGPLAN} Not.},

275− volume = {41},

276− number = {1},

277− year = {2006},

278− issn = {0362-1340},

279− pages = {2--15},

280− doi = {http://doi.{ACM}.org/10.1145/1111320.1111039},

281− publisher = {{ACM}},

282− address = {New York, NY, USA},

283− }

284−

285−

286−@INPROCEEDINGS{xi-ats,

287− author = {Hongwei Xi},

288− title = {{Applied Type System} (extended abstract)},

289− booktitle = {Types for Proofs and Programs 2003},

290− editor = {Stefano Berardi and Mario Coppo and Ferruccio Damiani},

291− publisher = {Springer},

292− series = {Lecture Notes in Computer Science},

293− volume = {3085},

294− year = {2004},

295− pages = {394--408}

296−}

297−

298−@inproceedings{powerpi,

299− author = {Nicolas Oury and

300− Wouter Swierstra},

301− title = {The power of {Pi}},

302− booktitle = {{ICFP} '08: Proceedings of the 13th {ACM} {SIGPLAN} International Conference

303− on Functional Programming, {ICFP} 2008, Victoria, BC, Canada,

304− September 20-28, 2008},

305− year = {2008},

306− pages = {39--50},

307− ee = {http://doi.{ACM}.org/10.1145/1411204.1411213},

308− crossref = {DBLP:conf/{ICFP}/2008},

309− bibsource = {DBLP, http://dblp.uni-trier.de}

310−}

311−

312−@proceedings{DBLP:conf/{ICFP}/2008,

313− editor = {James Hook and

314− Peter Thiemann},

315− title = {Proceeding of the 13th {ACM} {SIGPLAN} international conference

316− on Functional programming, {ICFP} 2008, Victoria, BC, Canada,

317− September 20-28, 2008},

318− booktitle = {{ICFP}},

319− publisher = {{ACM}},

320− year = {2008},

321− isbn = {978-1-59593-919-7},

322− bibsource = {DBLP, http://dblp.uni-trier.de}

323−}

324−

325−

326−@inproceedings{security-types,

327− author = {Morgenstern, Jamie and Licata, Daniel R.},

328− title = {Security-typed programming within dependently typed programming},

329− booktitle = {{ICFP} '10: Proceedings of the 15th {ACM} {SIGPLAN} International Conference on Functional Programming},

330− year = {2010},

331− isbn = {978-1-60558-794-3},

332− pages = {169--180},

333− location = {Baltimore, Maryland, USA},

334− doi = {http://doi.{ACM}.org/10.1145/1863543.1863569},

335− publisher = {{ACM}},

336− address = {New York, NY, USA},

337− }

338−

339−@inproceedings{levitation,

340− author = {Chapman, James and Dagand, Pierre-\'{E}variste and McBride, Conor and Morris, Peter},

341− title = {The gentle art of levitation},

342− booktitle = {{ICFP} '10: Proceedings of the 15th {ACM} {SIGPLAN} International Conference on Functional Programming},

343− year = {2010},

344− isbn = {978-1-60558-794-3},

345− pages = {3--14},

346− location = {Baltimore, Maryland, USA},

347− doi = {http://doi.{ACM}.org/10.1145/1863543.1863547},

348− publisher = {{ACM}},

349− address = {New York, NY, USA},

350− }

351−

352−

353−

354−@INPROCEEDINGS{awkward,

355− author = {Simon {Peyton Jones}},

356− title = {Tackling the awkward squad: monadic input/output, concurrency, exceptions, and foreign-language calls in {Haskell}},

357− booktitle = {Engineering theories of software construction},

358− year = {2001},

359− pages = {47--96}

360−}

361−

362−@inproceedings{scrap-engine,

363− author = {Brady, Edwin and Hammond, Kevin},

364− title = {Scrapping your inefficient engine: using partial evaluation to improve domain-specific language implementation},

365− booktitle = {{ICFP} '10: Proceedings of the 15th {ACM} {SIGPLAN} International Conference on Functional Programming},

366− year = {2010},

367− isbn = {978-1-60558-794-3},

368− pages = {297--308},

369− location = {Baltimore, Maryland, USA},

370− doi = {http://doi.{ACM}.org/10.1145/1863543.1863587},

371− publisher = {{ACM}},

372− address = {New York, NY, USA},

373− }

374−

375−@article{urweb,

376− author = {Chlipala, Adam},

377− title = {Ur: statically-typed metaprogramming with type-level record computation},

378− journal = {{SIGPLAN} Not.},

379− volume = {45},

380− number = {6},

381− year = {2010},

382− issn = {0362-1340},

383− pages = {122--133},

384− doi = {http://doi.{ACM}.org/10.1145/1809028.1806612},

385− publisher = {{ACM}},

386− address = {New York, NY, USA},

387− }

388−

389−

390−

391−@phdthesis{norell-thesis,

392− author = {Ulf Norell},

393− title = {Towards a practical programming language based on dependent type

394− theory},

395− school = {Chalmers University of Technology},

396− year = 2007,

397− month = {September},

398−}

399−

400−@inproceedings{open-type,

401− author = {Schrijvers, Tom and Peyton Jones, Simon and Chakravarty, Manuel and Sulzmann, Martin},

402− title = {Type checking with open type functions},

403− booktitle = {International Conf. on Functional Programming ({ICFP} 2008)},

404− year = {2008},

405− pages = {51--62},

406− doi = {http://doi.{ACM}.org/10.1145/1411203.1411215},

407− publisher = {{ACM}},

408− address = {New York, NY, USA},

409− }

410−

411−@inproceedings{ngna-dsl,

412− title = {Domain Specific Languages ({DSL}s) for Network Protocols},

413− author = {Saleem Bhatti and Edwin Brady and Kevin Hammond and James McKinna},

414− year = {2009},

415− booktitle = {International Workshop on Next Generation Network Architecture ({NGNA} 2009)}

416−}

417−

418−@phdthesis{gill-thesis,

419− title = {Cheap deforestation for non-strict functional languages},

420− author = {A Gill},

421− institution = {University of Glasgow},

422− month = {January},

423− year = 1996

424−}

425−

426−@misc{llvm-haskell,

427− title = {Low Level Virtual Machine for {Glasgow Haskell Compiler}},

428− author = {David Terei},

429− year = 2009,

430− howpublished = {Bachelor's Thesis, Computer Science and Engineering Dept., The University of New South Wales, Sydney, Australia}

431−}

432−

433−@mastersthesis{llvm,

434− title = {{LLVM}: An Infrastructure for Multi-Stage Optimization},

435− author = {Chris Lattner},

436− year = 2002,

437− month = {December},

438− institution = {Computer Science Dept., University of Illinois at Urbana-Champaign}

439−}

440−

441−@inproceedings{gpu-arrays,

442− title = {GPU Kernels as Data-Parallel Array Computations in Haskell},

443− author = {Sean Lee and Manuel M. T. Chakravarty and Vinod Grover and Gabriele Keller.},

444− year = 2009,

445− booktitle = {Workshop on Exploiting Parallelism using GPUs and other Hardware-Assisted Methods (EPAHM 2009)}

446−}

447−

448−@misc{cryptol,

449− author = {Galois, Inc.},

450− title = {Cryptol},

451− year = {2009},

452− howpublished = {\url{http://cryptol.net/}}

453−}

454−

455−@inproceedings{paradise-dsl,

456− author = {Lennart Augustsson and Howard Mansell and Ganesh Sittampalam},

457− title = {{Paradise: a two-stage DSL embedded in Haskell}},

458− booktitle = {International Conf. on Functional Programming ({ICFP} 2008)},

459− year = {2008},

460− publisher = {{ACM}},

461− pages = {225--228}

462− }

463−

464−@misc{dsl-bib,

465− author = {Arie {van Deursen} and Paul Klint and Joost Visser},

466− title = {Domain-Specific Languages --- an annotated bibliography},

467− year = 2000,

468− howpublished = {\url{http://homepages.cwi.nl/~arie/papers/dslbib/}}

469−}

470−

471−@inproceedings{imperative-pe,

472− author = {Debois, S{\o}ren},

473− title = {Imperative program optimization by partial evaluation},

474− booktitle = {PEPM '04: Proceedings of the 2004 {ACM} {SIGPLAN} symposium on Partial evaluation and semantics-based program manipulation},

475− year = {2004},

476− isbn = {1-58113-835-0},

477− pages = {113--122},

478− location = {Verona, Italy},

479− doi = {http://doi.{ACM}.org/10.1145/1014007.1014019},

480− publisher = {{ACM}},

481− address = {New York, NY, USA},

482− }

483−

484−

485−@inproceedings{offline-pe-termination,

486− author = {Andersen, Peter Holst and Holst, Carsten Kehler},

487− title = {Termination Analysis for Offline Partial Evaluation of a Higher Order Functional Language},

488− booktitle = {Proc. SAS '96: Intl. Symp. on Static Analysis},

489− year = {1996},

490− isbn = {3-540-61739-6},

491− pages = {67--82},

492− publisher = {Springer},

493− notaddress = {London, UK},

494− }

495−

496−

497−@inproceedings{stage-duplication,

498− author = {Swadi, Kedar and Taha, Walid and Kiselyov, Oleg and Pasalic, Emir},

499− title = {A monadic approach for avoiding code duplication when staging memoized functions},

500− notbooktitle = {PEPM '06: Proceedings of the 2006 {ACM} {SIGPLAN} symposium on Partial evaluation and semantics-based program manipulation},

501− booktitle = {Proc. PEPM '06:{ACM} Symp. on Partial Evaluation and Semantics-based Program Manipulation},

502− year = {2006},

503− isbn = {1-59593-196-1},

504− pages = {160--169},

505− location = {Charleston, South Carolina},

506− doi = {http://doi.{ACM}.org/10.1145/1111542.1111570},

507− notpublisher = {{ACM}},

508− notaddress = {New York, NY, USA},

509− }

510−

511−

512−@inproceedings{concoqtion,

513− author = {Fogarty, Seth and Pasalic, Emir and Siek, Jeremy and Taha, Walid},

514− title = {Concoqtion: indexed types now!},

515− booktitle = {PEPM '07: Proceedings of the 2007 {ACM} {SIGPLAN} symposium on Partial evaluation and semantics-based program manipulation},

516− year = {2007},

517− isbn = {978-1-59593-620-2},

518− pages = {112--121},

519− location = {Nice, France},

520− doi = {http://doi.{ACM}.org/10.1145/1244381.1244400},

521− publisher = {{ACM}},

522− address = {New York, NY, USA},

523− }

524−

525−@inproceedings{metahaskell,

526− author = "Tim Sheard and Simon {Peyton Jones}",

527− title = "Template metaprogramming for {Haskell}",

528− booktitle = "{ACM} Haskell Workshop",

529− year = 2002,

530− month = oct,

531− pages = "1-16",

532− noteditor = "Manuel M. T. Chakravarty",

533− notpublisher = "{ACM} Press"

534−}

535−

536−@misc{shark-profiler,

537− title = {Optimizing your application with {Shark 4}},

538− year = 2009,

539− howpublished = {\url{http://developer.apple.com/tools/sharkoptimize.html}}

540−}

541−

542−@misc{shootout,

543− title = {The Computer Language Benchmark Game},

544− year = {2009},

545− howpublished = {\url{http://shootout.alioth.debian.org/}}

546−}

547−

548−@article{futamura,

549− author = {Yoshihiko Futamura},

550− year = 1971,

551− title = "Partial Evaluation of Computation Process --– An Approach to a Compiler-Compiler",

552− journal = {Systems, Comps., Controls},

553− volume = 2,

554− number = 5,

555− pages = {45-–50}

556−}

557−

558−@book{pebook,

559− title = {Partial Evaluation and Automatic Program Generation},

560− author = {N.D. Jones and C.K. Gomard and P. Sestoft},

561− year = 1993,

562− publisher = {Prentice Hall International}

563−}

564−

565−@inproceedings{pantheon,

566− author = {Sean Seefried and Manuel Chakravarty and Gabriele Keller},

567− title = {Optimising Embedded {DSLs} using {Template Haskell}},

568− year = {2004},

569− booktitle = {{Proc. GPCE~'04: Conf. Generative Prog. and Component Eng.}},

570− publisher = {Springer},

571− series = {LNCS}

572−}

573−

574−@article{pan,

575− author = {Elliott, Conal and Finne, Sigbj\orn and De Moor, Oege},

576− title = {Compiling embedded languages},

577− journal = {J. Funct. Program.},

578− volume = {13},

579− number = {3},

580− year = {2003},

581− issn = {0956-7968},

582− pages = {455--481},

583− doi = {http://dx.doi.org/10.1017/S0956796802004574},

584− publisher = {Cambridge University Press},

585− address = {New York, NY, USA},

586− }

587−

588−

589−@inproceedings{russell,

590− author = {Sozeau, Matthieu},

591− title = {Program-ing finger trees in Coq},

592− booktitle = {{ICFP} '07: Proceedings of the 12th {ACM} {SIGPLAN} international conference on Functional programming},

593− year = {2007},

594− isbn = {978-1-59593-815-2},

595− pages = {13--24},

596− location = {Freiburg, Germany},

597− doi = {http://doi.{ACM}.org/10.1145/1291151.1291156},

598− publisher = {{ACM}},

599− address = {New York, NY, USA},

600− }

601−

602−@inproceedings{turner-total,

603− author = {D. A. Turner},

604− title = {Elementary Strong Functional Programming},

605− year = 1995,

606− booktitle = "First International Symposium on Functional Programming Languages in Education",

607− publisher = {Springer},

608− series = {LNCS},

609− volume = {1022},

610− pages = {1--13}

611−}

612−

613−@incollection{free-theorems,

614− author = "P. Wadler",

615− title = "Theorems for Free!",

616− booktitle = "{Proc. 4th Int.\ Conf.\ on Funct.\ Prog.\ Languages and Computer Arch., {FPCA}'89, London, {UK}, 11--13 Sept 1989}",

617− publisher = "{ACM} Press",

618− address = "New York",

619− pages = "347--359",

620− year = "1989",

621− url = "citeseer.ist.psu.edu/wadler89theorems.html"

622−}

623−

624−@inproceedings{TrulyConcurrent,

625− author = {Naiyong Jin and Jifeng He},

626− title = {Towards A Truly Concurrent Model for Processes Sharing Resources},

627− booktitle = {Proc. 3rd {IEEE} International Conf. on Soft. Eng. and Formal Methods},

628− year = {2005},

629− isbn = {0-7695-2435-4},

630− pages = {231--239},

631− doi = {http://dx.doi.org/10.1109/SEFM.2005.50},

632− publisher = {{IEEE} Computer Society},

633− address = {Washington, DC, USA},

634− }

635−

636−@misc{GPCE2006,

637− note = {Omitted to preserve anonymity, contact PC chair for details}

638−}

639−

640−@misc{IFL2006,

641− note = {Omitted to preserve anonymity, contact PC chair for details}

642−}

643−

644−@misc{ivor-anon,

645− note = {Omitted to preserve anonymity, contact PC chair for details}

646−}

647−

648−@inproceedings{HaskellIO,

649− author = {Simon L. {Peyton Jones} and Philip Wadler},

650− title = {Imperative functional programming},

651− booktitle = {Proc. 20th {ACM} Symposium on Principles of programming languages},

652− year = {1993},

653− isbn = {0-89791-560-7},

654− pages = {71--84},

655− location = {Charleston, South Carolina, United States},

656− doi = {http://doi.{ACM}.org/10.1145/158511.158524},

657− publisher = {{ACM}},

658− address = {New York, NY, USA},

659− }

660−

661−@article{CorrectnessConstruction,

662−author = "P. Amey",

663−title = "{Correctness by Construction: Better can also be Cheaper}",

664−journal = "{CrossTalk: the Journal of Defense Software Engineering}",

665−month = mar,

666−year = 2002,

667−pages = "24--28"

668−}

669−

670−

671−

672−@INPROCEEDINGS{hj:popl03,

673− AUTHOR = {M. Hofmann and S. Jost},

674− TITLE = {Static Prediction of Heap Space Usage for First-Order Function

675−al Programs},

676−booktitle = "Proc. {POPL 2003 --- 2003 {ACM} Symp. on Principles of Programming La

677−nguages}",

678− KEY = {HJ_POPL03},

679− PAGES = {185--197},

680− YEAR = {2003},

681− ORGANIZATION = {{ACM}}

682−}

683−

684−

685−@article{kobayashi-lock,

686− author = {Naoki Kobayashi},

687− title = {A type system for lock-free processes},

688− journal = {Inf. Comput.},

689− volume = {177},

690− number = {2},

691− year = {2002},

692− issn = {0890-5401},

693− pages = {122--159},

694− doi = {http://dx.doi.org/10.1016/S0890-5401(02)93171-8},

695− publisher = {Academic Press, Inc.},

696− address = {Duluth, MN, USA},

697− }

698−

699−@techreport{linear-alias,

700− title = {Linear types for aliased resources},

701− author = {Chris Hawblitzel},

702− year = {2005},

703− institution = {Microsoft Research},

704− number = {MSR-TR-2005-141}

705−}

706−

707−@article{kobayashi-esop,

708− title = {Type-Based Analysis of Deadlock fora Concurrent Calculus with Interrupts},

709− author = {Kohei Suenaga and Naoki Kobayashi},

710− year = {2007},

711− booktitle = {ESOP}

712−}

713−

714−@inproceedings{res-c,

715− title = {A Path Sensitive Type System for Resource Usage Verification of C Like Languages},

716− author = {Hyun-Goo Kang and Youil Kim and Taisook Han and Hwansoo Han},

717− year = 2005,

718− publisher = {Springer-Verlag},

719− booktitle = {Programming Languages and Systems},

720− pages = {264--280},

721− series = {LNCS},

722− volume = {3780}

723−}

724−

725−@miscs{lsr,

726− title = {Lightweight static resources: Sexy types for embedded and systems programming},

727− author = {Oleg Kiselyov and Chung-Chieh Shan},

728− year = 2007,

729− note = {Draft}

730−}

731−

732−@inproceedings{scoped-res,

733− title = {Resource Usage Analysis Via Scoped Methods},

734− author = {Gang Tan and Xinming Ou and David Walker},

735− booktitle = {Foundations of Object-Oriented Languages},

736− year = {2003}

737−}

738−

739−@article{igarashi-res,

740− author = {Igarashi, Atsushi and Kobayashi, Naoki},

741− title = {Resource usage analysis},

742− journal = {ACM Trans. Program. Lang. Syst.},

743− volume = {27},

744− issue = {2},

745− month = {March},

746− year = {2005},

747− issn = {0164-0925},

748− pages = {264--313},

749− numpages = {50},

750− url = {http://doi.acm.org/10.1145/1057387.1057390},

751− doi = {http://doi.acm.org/10.1145/1057387.1057390},

752− acmid = {1057390},

753− publisher = {ACM},

754− address = {New York, NY, USA},

755− keywords = {Resource usage, type inference},

756−}

757−

758−@phdthesis{monitoring,

759− title = {Policy Enforcement via Program Monitoring},

760− author = {Jarred Adam Ligatti},

761− year = 2006,

762− month = {May}

763−}

764−

765−@inproceedings{sec-policy,

766− title = {A Type System for Expressive Security Policies},

767− author = {David Walker},

768− booktitle = {Twenty-Seventh {ACM} {SIGPLAN} Symposium on Principles of Programming Languages},

769− pages = {254--267},

770− year = 2000}

771−

772−@inproceedings{res-dfa,

773− author = {K. Marriott and P.J. Stuckey and M. Sulzmann},

774− title = {Resource Usage Verification},

775− year = 2003,

776− booktitle = {In Proc. of First Asian Symposium, APLAS 2003},

777− pages = {212--229},

778− publisher = {Springer-Verlag}

779−}

780−

781−@incollection{ hancock-interactive,

782− author = "Peter Hancock and Anton Setzer",

783− title = "Interactive Programs in Dependent Type Theory",

784− booktitle = "Proc.\ of 14th Ann.\ Conf.\ of {EACSL}, {CSL}'00, Fischbau, Germany, 21--26 Aug 2000",

785− volume = "1862",

786− publisher = "Springer-Verlag",

787− address = "Berlin",

788− editor = "P. Clote and H. Schwichtenberg",

789− pages = "317--331",

790− year = "2000",

791− url = "citeseer.ist.psu.edu/hancock00interactive.html" }

792−

793−@inproceedings{popeea-resources,

794− author = {Corneliu Popeea and Wei-Ngan Chin},

795− title = {A type system for resource protocol verification and its correctness proof},

796− booktitle = {PEPM '04: Proceedings of the 2004 {ACM} {SIGPLAN} symposium on Partial evaluation and semantics-based program manipulation},

797− year = {2004},

798− isbn = {1-58113-835-0},

799− pages = {135--146},

800− location = {Verona, Italy},

801− doi = {http://doi.{ACM}.org/10.1145/1014007.1014021},

802− publisher = {{ACM} Press},

803− address = {New York, NY, USA},

804− }

805−

806−@inproceedings{sheard-langfuture,

807− author = {Tim Sheard},

808− title = "Languages of the future",

809− booktitle = "{ACM} Conference on Object Orientated Programming Systems, Languages and Applicatioons (OOPSLA'04)",

810− year = "2004"

811−}

812−

813−@inproceedings{ivor,

814− author = {Edwin Brady},

815− title = {{Ivor}, a proof engine},

816− year = {2007},

817− publisher = {Springer-Verlag},

818− series = {LNCS},

819− booktitle = {Implementation and Application of Functional Languages 2006}

820−}

821−

822−@misc{coq-in-coq,

823− author = {Bruno Barras and Benjamin Werner},

824− year = 1997,

825− title = {{Coq} in {Coq}}

826−}

827−

828−@article{hudak-edsl,

829− author = {Paul Hudak},

830− title = {Building Domain-Specific Embedded Languages},

831− year = {1996},

832− month = {December},

833− journal = {{ACM} Computing Surveys},

834− volume = {28A},

835− number = {4}

836−}

837−

838−@inproceedings{concon,

839− author = {Conor McBride and Healfdene Goguen and James McKinna},

840− title = {Some Constructions On Constructors},

841− year = 2005,

842− booktitle = {TYPES 2004},

843− publisher = {Springer},

844− series = {LNCS},

845− volume = {3839}

846−}

847−

848−@InProceedings{Hume-GPCE,

849−author = {K. Hammond and G.J. Michaelson},

850−title = {{Hume: a Domain-Specific Language for Real-Time Embedded Systems}},

851−booktitle = {{Proc. Conf. Generative Programming and Component Engineering (GPCE~'03)}},

852−publisher = {Springer-Verlag},

853−series = {Lecture Notes in Computer Science},

854−year = {2003},

855−}

856−

857−@inproceedings{lcf-milner,

858− author = {Robin Milner},

859− title = {{LCF}: A Way of Doing Proofs with a Machine},

860− booktitle = {Mathematical Foundations of Computer Science 1978},

861− pages = {146-159},

862− year = 1979,

863− series = {LNCS},

864− volume = {64}

865−}

866−

867−

868−@inproceedings{epireloaded,

869− title = {Epigram Reloaded: A Standalone Typechecker for {ETT}},

870− author = {James Chapman and Thorsten Altenkirch and Conor McBride},

871− year = 2006,

872− booktitle = {Trends in Functional Programming 2005},

873− note = {To appear}

874−}

875−

876−@TECHREPORT{why-tool,

877− AUTHOR = {J.-C. Filli\^atre},

878− TITLE = {{Why: a multi-language multi-prover verification tool}},

879− INSTITUTION = {{LRI, Universit\'e Paris Sud}},

880− TYPE = {{Research Report}},

881− NUMBER = {1366},

882− MONTH = {March},

883− YEAR = 2003,

884− URL = {http://www.lri.fr/~filliatr/ftp/publis/why-tool.ps.gz}

885−}

886−

887−@misc{ large-extraction,

888− author = "Lu\'iz Cruz-Filipe and Bas Spitters",

889− title = "Program Extraction from Large Proof Developments",

890− year = 2003,

891− url = "citeseer.ist.psu.edu/cruz-filipe03program.html" }

892−

893−@inproceedings{ fta,

894− author = "Herman Geuvers and Freek Wiedijk and Jan Zwanenburg",

895− title = "A Constructive Proof of the Fundamental Theorem of Algebra without Using the Rationals",

896− booktitle = "{TYPES 2000}",

897− pages = "96--111",

898− year = "2000",

899− url = "citeseer.ist.psu.edu/geuvers01constructive.html" }

900−

901−@article{mckinna-expr,

902− title = {A type-correct, stack-safe, provably correct, expression compiler in {Epigram}},

903− author = {James McKinna and Joel Wright},

904− year = 2007,

905− journal = {Journal of Functional Programming},

906− note = {To appear}

907−}

908−

909−@article{pugh-omega,

910− title = "The {Omega} {Test}: a fast and practical integer programming algorithm for dependence analysis",

911− author = "William Pugh",

912− journal = "Communication of the {ACM}",

913− year = 1992,

914− pages = {102--114}

915−}

916−

917−@misc{four-colour,

918− author = "Georges Gonthier",

919− title = "A computer-checked proof of the {Four Colour Theorem}",

920− year = 2005,

921− howpublished = {\url{http://research.microsoft.com/~gonthier/4colproof.pdf}}}

922−

923−@inproceedings{sparkle,

924− author = "Maarten {de Mol} and Marko {van Eekelen} and Rinus Plasmeijer",

925− title = "Theorem Proving for Functional Programmers",

926− url = "citeseer.ist.psu.edu/654423.html",

927− BOOKTITLE = {Proc. Implementation of Functional Languages (IFL 2002)},

928− publisher = {Springer},

929− series = {LNCS},

930− volume = {2312},

931− year = 2002

932− }

933−

934−@misc{agda,

935− title = {Agda},

936− author = {Catarina Coquand},

937− howpublished= {\url{http://agda.sourceforge.net/}},

938− year = 2005

939−}

940−

941−@misc{cover,

942− title = {Cover Translator},

943− howpublished = {\url{http://coverproject.org/CoverTranslator/}}

944−}

945−

946−@misc{parsec,

947− title = {Parsec, a fast combinator parser},

948− author = {Daan Leijen},

949− year = {2001},

950− howpublished = {\url{http://www.cs.uu.nl/~daan/parsec.html}}

951−}

952−

953−@inproceedings{dtpmsp-gpce,

954− author = {Edwin Brady and Kevin Hammond},

955− title = {A Verified Staged Interpreter is a Verified Compiler},

956− booktitle = {{Proc. Conf. Generative Programming and Component Engineering (GPCE~'06)}},

957− year = 2006

958−}

959−

960−@misc{haddock,

961− title = {Haddock: A {Haskell} Documentation Tool},

962− howpublished = {\url{http://www.haskell.org/haddock/}}

963−}

964−

965−@inproceedings{offshoring,

966− title = {Implicitly Heterogeneous Multi-Stage Programming},

967− author = {Jason Eckhardt and Roumen Kaibachev and Emir Pa\v{s}al\'{i}c and Kedar Swadi and Walid Taha},

968− booktitle = {Proc. 2005 Conf. on Generative Programming and Component Engineering (GPCE 2005)},

969− publisher = {Springer},

970− series = {LNCS},

971− volume = {3676},

972− year = 2005

973−}

974−

975−@misc{alti-partial,

976− title = {Stop thinking about bottoms when writing programs},

977− author = {Thorsten Altenkirch},

978− year = 2006,

979− note = {Talk at BCTCS 2006}

980−}

981−

982−@misc{tarmo-partial,

983− title = {Partiality is an Effect},

984− author = {Tarmo Uustalu},

985− year = 2004,

986− note = {Talk at Dagstuhl workshop on Dependently Typed Progamming}

987−}

988−

989−@inproceedings{McKinnaPOPL06,

990− author = {James McKinna},

991− title = {Why dependent types matter},

992− booktitle = {Proc. {ACM} Symp. on Principles of Programming Languages (POPL 2006)},

993− year = {2006},

994− issn = {0362-1340},

995− pages = {1--1},

996− doi = {http://doi.{ACM}.org/10.1145/1111320.1111038},

997−}

998−

999−

1000−@inproceedings{leroy-compiler,

1001− title = {Formal Certification of a Compiler Back-end},

1002− author = {Xavier Leroy},

1003− year = 2006,

1004− booktitle = {Principles of Programming Languages 2006},

1005− pages = {42--54},

1006− publisher = {{ACM} Press}

1007−}

1008−

1009−@inproceedings{hutton-exceptions,

1010− title = {Compiling Exceptions Correctly},

1011− year = 2004,

1012− author = {Graham Hutton and Joel Wright},

1013− booktitle = {Mathematics of Program Construction},

1014− publisher = {Springer},

1015− series = {LNCS},

1016− volume = {3125}

1017−}

1018−

1019−@inproceedings{tagless-staged,

1020− title = {Tagless Staged Interpreters for Typed Languages},

1021− year = {2002},

1022− booktitle = {Proc. 2002 International Conf. on Functional Programming ({ICFP} 2002)},

1023− author = {Emir Pa\v{s}al\'{i}c and Walid Taha and Tim Sheard},

1024− publisher = {{ACM}}

1025−}

1026−

1027−@inproceedings{env-classifiers,

1028− title = {Environment Classifiers},

1029− year = 2003,

1030− author = {Walid Taha},

1031− booktitle = {Proc. {ACM} Symp. on Principles of Programming Languages (POPL 2003)},

1032− pages = {26--37},

1033−}

1034−

1035−@inproceedings{dsl-msp,

1036− title = {{DSL} Implementation in {MetaOCaml}, {Template Haskell}, {and C++}},

1037− booktitle = {Domain Specific Program Genearation 2004},

1038− author = {Krzysztof Czarnecki and John O'Donnell and J\"{o}rg Striegnitz and Walid Taha},

1039− publisher = {Springer},

1040− series = {LNCS},

1041− volume = {3016},

1042− year = 2004

1043−}

1044−

1045−@misc{ gadt-extk,

1046− author = {Tim Sheard and James Hook and Nathan Linger},

1047− title = {{GADTs} + Extensible Kinds = Dependent Programming},

1048− year = 2005,

1049− misc = {Submitted to {ICFP} '05}

1050−}

1051−

1052−@INPROCEEDINGS{dt-framework,

1053− TITLE = {A Dependently Typed Framework for Static Analysis of Program Execution Costs},

1054− YEAR = {2006},

1055− BOOKTITLE = {Proc. Implementation of Functional Languages (IFL 2005)},

1056− AUTHOR = {Edwin Brady and Kevin Hammond},

1057− VOLUME = {4015},

1058− SERIES = {LNCS},

1059− PAGES = {74--90},

1060− PUBLISHER = {Springer}

1061−}

1062−

1063−@INPROCEEDINGS{step-counting,

1064− TITLE = {Accurate Step Counting},

1065− YEAR = {2006},

1066− BOOKTITLE = {Proc. Implementation of Functional Languages (IFL 2005)},

1067− AUTHOR = {Catherine Hope and Graham Hutton},

1068− PUBLISHER = {Springer}

1069−}

1070−

1071−@misc{multi-taha,

1072− author = {Walid Taha},

1073− title = {{A Gentle Introduction to Multi-stage Programming}},

1074− year = {2003},

1075− note = {Available from \url{http://www.cs.rice.edu/~taha}},

1076− notnote = {Available from \url{http://www.cs.rice.edu/~taha/publications/journal/dspg04a.pdf}}

1077−}

1078−

1079−@misc{mckinnabrady-phase,

1080− title = {Phase Distinctions in the Compilation of {Epigram}},

1081− year = 2005,

1082− author = {James McKinna and Edwin Brady},

1083− note = {Draft}

1084−}

1085−

1086−@phdthesis{ brady-thesis,

1087− author = {Edwin Brady},

1088− title = {Practical Implementation of a Dependently Typed Functional Programming Language},

1089− year = 2005,

1090− school = {University of Durham}

1091−}

1092−

1093−@phdthesis{ taha-thesis,

1094− author = {Walid Taha},

1095− title = {Multi-stage Programming: Its Theory and Applications},

1096− year = 1999,

1097− school = {Oregon Graduate Inst. of Science and Technology}

1098−}

1099−

1100−@phdthesis{ pasalic-thesis,

1101− author = {Emir Pa\v{s}al\'{i}c},

1102− title = {The Role of Type-Equality in Meta-programming},

1103− year = 2004,

1104− school = {OGI School of Science and Engineering}

1105−}

1106−

1107−@misc{ydtm,

1108− author = {Thorsten Altenkirch and Conor McBride and James McKinna},

1109− title = {Why Dependent Types Matter},

1110− note = {Draft},

1111− year = 2005}

1112−

1113−

1114−@inproceedings { wadler-listless,

1115− author = {Philip Wadler},

1116− title = {Listlessness is better than laziness: {Lazy} evaluation and garbage collection at compile-time},

1117− booktitle = {Proceedings of the 1984 {ACM} Symposium on LISP and functional programming},

1118− year = 1984,

1119− pages = {45--52}

1120−}

1121−

1122−@techreport { gofer-impl,

1123− author = {Mark P. Jones},

1124− title = {The implementation of the Gofer functional programming system},

1125− month = {May},

1126− year = {1994},

1127− number = {YALEU/DCS/RR-1030},

1128− institution = {Yale University}

1129−}

1130−

1131−@techreport { pm-opt1,

1132− author = {Kevin Scott and Norman Ramsey},

1133− title = {When do match-compilation heuristics matter?},

1134− month = {May},

1135− year = {2000},

1136− number = {CS-2000-13},

1137− institution = {Department of Computer Science, University of Virginia}

1138−}

1139−

1140−@inproceedings{ pm-opt2,

1141− author = "Fabrice Le Fessant and Luc Maranget",

1142− title = "Optimizing Pattern Matching",

1143− booktitle = "International Conference on Functional Programming",

1144− pages = "26-37",

1145− year = "2001",

1146− url = "citeseer.ist.psu.edu/lefessant01optimizing.html" }

1147−

1148−@incollection{con-engine,

1149− author = {G\'{e}rard Huet},

1150− title = {The constructive engine},

1151− booktitle = {A Perspective in Theoreticak Computer Science},

1152− publisher = {World Scientific Publishing},

1153− year = {1989},

1154− editor = {R. Narasimhan},

1155− note = {Commemorative Volume for Gift Siromoney},

1156− pages = {38--69}

1157−}

1158−

1159−@inproceedings{gadts,

1160− title = {Simple unification-based type inference for {GADTs}},

1161− author = {Simon {Peyton Jones} and Dimitrios Vytiniotis and Stephanie Weirich and Geoffrey Washburn},

1162− year = {2006},

1163− booktitle = {Proc. 2006 International Conf. on Functional Programming ({ICFP} 2006)}

1164−}

1165−

1166−@misc{wobbly,

1167− author = {Simon {Peyton Jones} and Geoffrey Washburn and Stephanie Weirich},

1168− title = {Wobbly types: type inference for generalised algebraic data types},

1169− year = {2004},

1170− note = {Submitted to POPL 2005}

1171−}

1172−

1173−@misc{epigram-afp,

1174− author = {Conor McBride},

1175− title = {Epigram: Practical Programming with Dependent Types},

1176− year = {2004},

1177− howpublished = {Lecture Notes, International Summer School on Advanced Functional Programming}

1178−}

1179−

1180−@book{ml85,

1181− author = {Per Martin-L\"{o}f},

1182− title = "Intuitionistic Type Theory",

1183− year = "1985",

1184− publisher = "Bibliopolis"

1185−}

1186−

1187−@article{modular-fulllazy,

1188− title = {A Modular Fully Lazy Lambda Lifter in {Haskell}},

1189− author = {Simon {Peyton Jones} and David Lester},

1190− year = {1991},

1191− month = {May},

1192− journal = {Software Practice and Experience},

1193− volume = {21},

1194− number = {5},

1195− pages = {479--506}

1196−}

1197−

1198−@article{ghani-jay95,

1199− author = {Barry Jay and Neil Ghani},

1200− title = {The Virtues of Eta-Expansion},

1201− journal = {Journal of Functional Programming},

1202− year = {1995},

1203− volume = {5},

1204− number = {2},

1205− pages = {135-154},

1206−}

1207−

1208−@misc{nkpat,

1209− author = {Lennart Augustsson},

1210− title = {n+k patterns},

1211− year = {1993},

1212− howpublished = {Message to the haskell mailing list, Mon, 17 May 93}

1213−}

1214−

1215−@article{ danvy98functional,

1216− author = "Olivier Danvy",

1217− title = "Functional Unparsing",

1218− journal = "Journal of Functional Programming",

1219− volume = "8",

1220− number = "6",

1221− pages = "621-625",

1222− year = "1998",

1223− url = "citeseer.ist.psu.edu/danvy98functional.html" }

1224−

1225−@inproceedings{SeveriPoll94,

1226− author = {Paula Severi and Erik Poll},

1227− booktitle = {Logical Foundations of Computing Science, LFCS'94},

1228− editor = {A. Nerode and Yu. V. Matiyasevich},

1229− number = {813},

1230− pages = {316--328},

1231− publisher = {Springer},

1232− series = {LNCS},

1233− title = {{P}ure {T}ype {S}ystems with {D}efinitions},

1234− year = {1994}

1235−}

1236−

1237−@inproceedings{coinductive,

1238− title = {An Application of Co-Inductive Types in Coq: Verification of the Alternating Bit Protocol},

1239− booktitle = {Proceedings of the 1995 Workshop on Types for Proofs and Programs},

1240− series = {LNCS},

1241− year = {1995},

1242− volume = {1158},

1243− pages = {135-152},

1244− publisher = {Springer-Verlag},

1245− author = {Eduardo Gim\'{e}nez}

1246−}

1247−

1248−@book{erlang,

1249− author = "Joe Armstrong and Robert Virding and Claes Wikstr{\"o}m and Mike Williams",

1250− title = "Concurrent Programming in Erlang",

1251− edition = "Second",

1252− publisher = "Prentice-Hall",

1253− year = "1996",

1254− url = "citeseer.ist.psu.edu/armstrong93concurrent.html"

1255−}

1256−

1257−@PhdThesis{alti:phd93,

1258− author = "Thorsten Altenkirch",

1259− title = "Constructions, Inductive Types and Strong Normalization",

1260− school = "University of Edinburgh",

1261− year = "1993",

1262− month = "November",

1263−}

1264−

1265−@inproceedings{coq-modules,

1266− author = "Jacek Chrzaszcz",

1267− title = "Modules in {Coq} Are and Will Be Correct",

1268− year = {2004},

1269− booktitle = {Types for Proofs and Programs 2003},

1270− editor = {Stefano Berardi and Mario Coppo and Ferruccio Damiani},

1271− publisher = {Springer},

1272− volume = {3085}

1273−}

1274−

1275−@inproceedings{comp-polymorphism,

1276− author = "Robert Harper and Greg Morrisett",

1277− title = "Compiling Polymorphism Using Intensional Type Analysis",

1278− year = "1995",

1279− booktitle = "Proceedings of the 22nd {ACM} {SIGPLAN}-SIGACT symposium on Principles of programming languages",

1280− pages = "130 -- 141"

1281−}

1282−

1283−@misc{runtime-loader,

1284− author = "Andre Pang",

1285− title = "{GHC} Runtime Loading",

1286− year = "2004",

1287− howpublished = {Available from \verb+http://www.algorithm.com.au/wiki/hacking/haskell.ghc_runtime_loading+}

1288−}

1289−

1290−@article{mccarthy-lisp,

1291− author = "John McCarthy",

1292− title = "Recursive Functions of Symbolic Expressions and Their Computation By Machine",

1293− year = "1960",

1294− journal = "Communications of the {ACM}",

1295− volume = "3",

1296− number = "4",

1297− pages = "184--195"

1298−}

1299−

1300−@book{stl,

1301− author = " David R. Musser and Atul Saini and Gillmer J. Derge",

1302− title= "The {STL} Tutorial and Reference Guide: {C++} Programming with the Standard Template Library",

1303− year = "2001",

1304− publisher = "Addison Wesley"

1305−}

1306−

1307−@misc{ phase-distinction,

1308− author = "Luca Cardelli",

1309− title = "Phase Distinctions in Type Theory",

1310− howpublished = "Manuscript",

1311− year = "1988",

1312− url = "citeseer.ist.psu.edu/cardelli88phase.html" }

1313−

1314−@book {pierce-types,

1315− author = "Benjamin C. Pierce",

1316− title = "Type and Programming Languages",

1317− year = "2002",

1318− publisher = "MIT Press"

1319−}

1320−

1321−@article{ coqcc,

1322− Author = "Thierry Coquand and G\'{e}rard Huet",

1323− title = "The calculus of constructions",

1324− year = "1988",

1325− journal = "Information and Computation",

1326− volume = "76",

1327− pages = "95--120"

1328−}

1329−

1330−@article{ miller91jlc,

1331− Author = "Dale Miller",

1332− Title = "A Logic Programming Language with Lambda-Abstraction,

1333− Function Variables, and Simple Unification",

1334− Journal = "Journal of Logic and Computation",

1335− Volume = "1",

1336− Number = "4",

1337− Pages = "497-536",

1338− Year = "1991",

1339− URL = "citeseer.ist.psu.edu/miller91logic.html",

1340− URL = "file://ftp.cis.upenn.edu/pub/papers/miller/jlc91.dvi.Z" }

1341−

1342−@article{miller-unity,

1343− author = "Dale Miller",

1344− title = "Unification Under a Mixed Prefix",

1345− journal = "Journal of Symbolic Computation",

1346− volume = "14",

1347− pages = "321--358",

1348− year = 1992

1349−}

1350−

1351−@inproceedings{ cynthia,

1352− author = "Jon Whittle and Alan Bundy and Richard J. Boulton and Helen Lowe",

1353− title = "An {ML} Editor Based on Proofs-As-Programs",

1354− booktitle = "Automated Software Engineering",

1355− pages = "166-173",

1356− year = "1999",

1357− url = "citeseer.ist.psu.edu/whittle99ml.html" }

1358−

1359−

1360−@misc{ewd340,

1361− title={The Humble Programmer},

1362− author={Edsger Dijkstra},

1363− year={1972},

1364− note={Turing Award Lecture, EWD 340}

1365−}

1366−

1367−@misc{fortran,

1368− title={Specifications for the {IBM} Mathematical FORmula TRANslating System, {FORTRAN}},

1369− author={{IBM Applied Science Division}},

1370− key={IBM},

1371− year={1954},

1372− month={November}

1373−}

1374−

1375−@inproceedings{quickcheck,

1376− title = {{QuickCheck}: A Lightweight Tool For Random Testing Of {Haskell} Programs},

1377− author = {Koen Claessen and John Hughes},

1378− year = {2000},

1379− booktitle = {International Conference on Functional Programming}

1380−}

1381−

1382−@inproceedings{currylam,

1383− title = {Functionality in Combinatory Logic},

1384− author = {Haskell Curry},

1385− year = {1934},

1386− booktitle = {Proc. Nat. Acad. Sci, USA},

1387− volume = {20},

1388− pages = {584--590}

1389−}

1390−

1391−@article{churchsimplelam1,

1392− title = {A set of postulates for the foundation of logic},

1393− author = {Alonzo Church},

1394− year = {1932},

1395− journal = {Annals of Mathematics},

1396− volume = {2},

1397− number = {33},

1398− pages = {346--366}

1399−}

1400−

1401−@article{churchsimplelam2,

1402− title = {A set of postulates for the foundation of logic},

1403− author = {Alonzo Church},

1404− year = {1933},

1405− journal = {Annals of Mathematics},

1406− volume = {2},

1407− number = {34},

1408− pages = {839--864}

1409−}

1410−

1411−@article{churchlam,

1412− title = {A Formulation of the Simple Theory of Types},

1413− author = {Alonzo Church},

1414− year = {1940},

1415− journal = {Journal of Symbolic Logic},

1416− volume = {5},

1417− pages = {56--58}

1418−}

1419−

1420−@book{mitchell,

1421− title = {Concepts in Programming Languages},

1422− author = {John C. Mitchell},

1423− year = {2003},

1424− publisher = {Cambridge University Press}

1425−}

1426−

1427−@inproceedings{harrison-hol99,

1428− title = {A Machine-Checked Theory of Floating Point Arithmetic},

1429− year = {1999},

1430− booktitle = {Theorem Proving in Higher Order Logics: 12th International Conference, TP},

1431− pages = {113--130},

1432− author = {John Harrison},

1433− crossref = {hol99}

1434−}

1435−

1436−@inproceedings{c--,

1437− title = {C--: A portable assembly language},

1438− year = {1997},

1439− booktitle = {Workshop on Implementing Functional Languages, St Andrews},

1440− author = {Simon {Peyton Jones} and Thomas Nordin and Dino Oliva},

1441− crossref = {func-imp97}

1442−}

1443−

1444−@proceedings{func-imp97,

1445− title = {Workshop on Implementing Functional Languages, St Andrews},

1446− year = {1997},

1447− editor = {C Clack},

1448− publisher = {Springer-Verlag}

1449−}

1450−

1451−@proceedings{hol99,

1452− volume = {1690},

1453− title = {Theorem Proving in Higher Order Logics: 12th International Conference, TPHOLs'99},

1454− year = {1999},

1455− editor = {Yves Bertot and Gilles Dowek and Andr{\'e} Hirschowitz and Christine Paul},

1456− publisher = {Springer-Verlag},

1457− address = {Nice, France},

1458− series = {LNCS}

1459−}

1460−

1461−@book{mathlogic,

1462− title = {Mathematical Logic and Programming Languages},

1463− year = {1985},

1464− editor = {C.A.R. Hoare and J.C. Shepherdson},

1465− publisher = {Prentice-Hall}

1466−}

1467−

1468−@book{automath,

1469− title = {Selected Papers on Automath},

1470− year = {1994},

1471− editor = {S. Abramsky and J. Barwise and K. Fine and H.J. Keisler and A.S. Troelstr},

1472− publisher = {North-Holland}

1473−}

1474−

1475−@misc{gimps,

1476− howpublished = {http://www.mersenne.org/prime.htm},

1477− title = {Great Internet Mersenne Prime Search}

1478−}

1479−

1480−@misc{haskell-report,

1481− title = {Haskell 98 Language and Libraries --- The Revised Report},

1482− year = {2002},

1483− month = {December},

1484− author = {Simon {Peyton Jones} and others},

1485− howpublished = {Available from \verb+http://www.haskell.org/+}

1486−}

1487−

1488−@inproceedings{cayenne-{ICFP},

1489− author = "Lennart Augustsson",

1490− title = "Cayenne - a Language with Dependent Types",

1491− booktitle = "Proc. 1998 International Conf. on Functional Programming ({ICFP} '98)",

1492− pages = "239--250",

1493− year = "1998",

1494− url = "citeseer.nj.nec.com/augustsson98cayenne.html"

1495−}

1496−

1497−

1498−@misc{equality-cayenne,

1499− howpublished = {\verb+http://www.cs.chalmers.se/~augustss/cayenne/+},

1500− title = {Equality Proofs in Cayenne},

1501− year = {1999},

1502− author = {Lennart Augustsson}

1503−}

1504−

1505−@misc{interp-cayenne,

1506− title = {An exercise in dependent types: A well-typed interpreter},

1507− year = {1999},

1508− author = {Lennart Augustsson and Magnus Carlsson}

1509−}

1510−

1511−@inproceedings{balaa00fixpoint,

1512− title = {Fix-Point Equations for Well-Founded Recursion in Type Theory},

1513− year = {2000},

1514− booktitle = {Theorem Proving in Higher Order Logics},

1515− pages = {1-16},

1516− author = {Antonia Balaa and Yves Bertot}

1517−}

1518−

1519−@inproceedings{isabelle-maple,

1520− title = {Theorems and algorithms: An interface between Isabelle and Maple},

1521− year = {1995},

1522− booktitle = {International Symposium on Symbolic and Algebraic Computation},

1523− author = {Ballarin, C. and Homann, K., and Calmet, J.}

1524−}

1525−

1526−@book{barendregt-num,

1527− title = {The Lambda Calculus, Its Syntax and Semantics},

1528− year = {1984},

1529− publisher = {North-Holland},

1530− author = {Henk Barendregt}

1531−}

1532−

1533−@book{beiler,

1534− title = {Recreations in the Theory of Numbers},

1535− year = {1964},

1536− publisher = {Dover},

1537− author = {Albert H. Beiler}

1538−}

1539−

1540−@article{multidigit,

1541− journal = {Advances in Applied Mathematics},

1542− title = {Multidigit Multiplication for Mathematicians},

1543− year = {1998},

1544− author = {Daniel J. Bernstein}

1545−}

1546−

1547−@article{buhler-fox,

1548− journal = {{ACM} Crossroads 2.1.},

1549− month = {September},

1550− title = {The Fox project: A language-structured approach to networking software.},

1551− year = {1995},

1552− author = {Buhler, J.},

1553− note = {Available at http://www.{ACM}.org/crossroads/xrds2-1/foxnet.html}

1554−}

1555−

1556−@techreport{burstall91,

1557− title = {Computer Assisted Proof for Mathematics: an Introduction Using the \textsc{Lego} Proof System},

1558− year = {1991},

1559− institution = {University of Edinburgh},

1560− author = {Rod Burstall}

1561−}

1562−

1563−@article{plastic,

1564− title = {An Implementation of {LF} with Coercive Subtyping and Universes},

1565− author = {Paul Callaghan and Zhaohui Luo},

1566− journal = {Journal of Automated Reasoning},

1567− volume = {27},

1568− number = {1},

1569− pages = {3--27},

1570− year = {2001}

1571−}

1572−

1573−@article{coercive,

1574− title = {Coercive subtyping},

1575− author = {Zhaohui Luo},

1576− journal = {J. Logic Comput.},

1577− volume = {9},

1578− number = {1},

1579− year = {1991},

1580− pages = {105--130}

1581−}

1582−

1583−@inproceedings{calmet-homann,

1584− title = {Classification of communication and cooperation mechanisms for logical and symbolic computation systems},

1585− year = {1996},

1586− booktitle = {Proceedings of the First International Workshop 'Frontiers of Combining S},

1587− pages = {133-146},

1588− publisher = {Kluwer},

1589− author = {J. Calmet and K. Homann}

1590−}

1591−

1592−@techreport{comm-proofs,

1593− title = {On Communicating Proofs in Interactive Mathematical Documents},

1594− year = {2000},

1595− institution = {Eindhoven University of Technology},

1596− author = {Olga Caprotti and Martijn Oostdijk}

1597−}

1598−

1599−@article{prime2999,

1600− title = {How to formally and efficiently prove Prime(2999)},

1601− year = {2001},

1602− author = {Olga Caprotti and Martijn Oostdijk},

1603− journal = {Symbolic Computation and Automated Reasoning},

1604− pages = {114--125}

1605−}

1606−

1607−@book{church-num,

1608− title = {The Calculi of Lambda-Conversion},

1609− year = {1941},

1610− publisher = {Princeton University Press},

1611− author = {Alonzo Church}

1612−}

1613−

1614−@book{nuprl86,

1615− title = {Implementing Mathematics with the NuPrl Proof Development System},

1616− year = {1986},

1617− publisher = {Prentice-Hall},

1618− address = {NJ},

1619− author = {Constable, Robert L. and others}

1620−}

1621−

1622−@book{conway,

1623− title = {On Numbers and Games},

1624− year = {1976},

1625− publisher = {Academic Press},

1626− author = {J.H. Conway}

1627−}

1628−

1629−@misc{coq-manual,

1630− howpublished = {\verb+http://coq.inria.fr/+},

1631− title = {The {Coq} Proof Assistant --- Reference Manual},

1632− year = {2009},

1633− author = {{Coq Development Team}}

1634−}

1635−

1636−@misc{tt-prog,

1637− month = {June},

1638− title = {Type Theory and Programming},

1639− year = {1994},

1640− author = {Thierry Coquand and Bengt Nordstr\"{o}m and Jan M. Smith and Bj\"{o}rn von Sydow}

1641−}

1642−

1643−@book{func-appr,

1644− title = {The Functional Approach to Programming},

1645− year = {1998},

1646− publisher = {Cambridge University Press},

1647− author = {Guy Cousineau and Michel Mauny}

1648−}

1649−

1650−@misc{ibmspec,

1651− howpublished = {http://www2.hursley.ibm.com/decimal/},

1652− month = {January},

1653− title = {Standard Decimal Arithmetic Specification},

1654− year = {2001},

1655− author = {Mike Cowlishaw},

1656− note = {\copyright IBM Corporation 2001}

1657−}

1658−

1659−@book{dummett,

1660− title = {Elements of Intuitionism},

1661− year = {2000},

1662− edition = {2nd},

1663− publisher = {Oxford: Clarendon},

1664− author = {Michael A.E. Dummet}

1665−}

1666−

1667−@article{dybjer94,

1668− title = {Inductive Families},

1669− year = {1994},

1670− author = {Peter Dybjer},

1671− journal = {Formal Aspects Of Computing},

1672− volume = {6},

1673− pages = {440--465}

1674−}

1675−

1676−@misc{octave,

1677− howpublished = {http://www.octave.org/},

1678− month = {February},

1679− title = {GNU Octave -- A high-level interactive language for numerical computations},

1680− year = {1997},

1681− author = {John W. Eaton}

1682−}

1683−

1684−@book{comp-methods,

1685− title = {Computing methods for scientists and engineers},

1686− year = {1968},

1687− publisher = {Oxford : Clarendon Press},

1688− author = {L. Fox and D.F. Mayers}

1689−}

1690−

1691−@misc{guile,

1692− howpublished = {http://www.gnu.org/software/guile/guile.html},

1693− title = {Guile -- Project GNU's extension language},

1694− year = {2001},

1695− author = {{Free Software Foundation}}

1696−}

1697−

1698−@article{need-dep,

1699− journal = {Journal of Functional Programming},

1700− number = {4},

1701− volume = {10},

1702− title = {Do we need dependent types?},

1703− year = {2000},

1704− pages = {409-415},

1705− author = {Daniel Fridlender and Mia Indrika}

1706−}

1707−

1708−@book{primes-programming,

1709− title = {Primes and Programming -- An Introduction to Number Theory with Computing},

1710− year = {1993},

1711− publisher = {Cambridge University Press},

1712− author = {Peter Giblin}

1713−}

1714−

1715−@misc{rec-coq,

1716− month = {May},

1717− title = {A Tutorial on Recursive Types in \textsc{Coq}},

1718− year = {1998},

1719− author = {Eduardo Gim\'{e}nez}

1720−}

1721−

1722−@article{goldberg91,

1723− journal = {{ACM} Computing Surveys},

1724− number = {1},

1725− volume = {23},

1726− title = {What every computer scientist should know about floating point arithmetic},

1727− year = {1991},

1728− pages = {5-48},

1729− author = {D. Goldberg}

1730−}

1731−

1732−@article{binary-lambda,

1733− journal = {Journal of Functional Programming},

1734− number = {6},

1735− volume = {10},

1736− title = {An adequate and efficient left associated binary numeral system in the $\lambda$-calculus},

1737− year = {2000},

1738− author = {Mayer Goldberg}

1739−}

1740−

1741−@book{hol,

1742− title = {Introduction to HOL},

1743− year = {1993},

1744− publisher = {Cambridge University Press},

1745− author = {M. Gordon and T. Melham}

1746−}

1747−

1748−@misc{gmp,

1749− howpublished = {Available from \verb+http://www.swox.com/gmp/manual/+},

1750− title = {The {GNU Multiple Precision} Arithmetic Library 4.1.3 --- Manual},

1751− year = {2004},

1752− author = {Torbj\"{o}rn Granlund and others}

1753−}

1754−

1755−@article{harrison-fmsd94,

1756− journal = {Formal Methods in System Design},

1757− volume = {5},

1758− title = {Constructing the Real Numbers in {HOL}},

1759− year = {1994},

1760− pages = {35--59},

1761− author = {John Harrison}

1762−}

1763−

1764−@book{harrison-thesis,

1765− title = {Theorem Proving with the Real Numbers},

1766− year = {1998},

1767− publisher = {Springer-Verlag},

1768− author = {John Harrison}

1769−}

1770−

1771−@techreport{hol-maple,

1772− title = {Reasing about the Reals: the marriage of HOL and Maple},

1773− year = {1993},

1774− institution = {University of Cambridge Computer Laboratory},

1775− author = {John Harrison and Laurent Th\'{e}ry}

1776−}

1777−

1778−@misc{coq-tutorial,

1779− howpublished = {http://pauillac.inria.fr/coq},

1780− title = {The \textsc{Coq} Proof Assistant - A Tutorial},

1781− author = {G\'{e}rard Huet and Gilles Kahn and Christine Paulin-Mohring}

1782−}

1783−

1784−@misc{restr-haskell,

1785− howpublished = {http://citeseer.nj.nec.com/253599.html},

1786− month = {September},

1787− title = {Restricted Data Types in Haskell},

1788− year = {1999},

1789− author = {John Hughes}

1790−}

1791−

1792−@misc{javadec,

1793− howpublished = {http://www2.hursley.ibm.com/decimalj/decimald.html},

1794− month = {September},

1795− title = {Decimal Arithmetic for Java -- a Proposal},

1796− year = {2000},

1797− author = {{IBM Corporation}}

1798−}

1799−

1800−@misc{ieee754,

1801− title = {{IEEE} Standard for Binary Floating Point Arithmetic},

1802− year = {1985},

1803− author = {{IEEE Standard 754}}

1804−}

1805−

1806−@misc{ieee854,

1807− title = {IEEE Standard for Radix-Independent Floating-Point Arithmetic},

1808− year = {1987},

1809− author = {{IEEE Standard 854}}

1810−}

1811−

1812−@inproceedings{jon91,

1813− title = {Completing the Rational and Metric Spaces in \textsc{Lego}},

1814− year = {1991},

1815− booktitle = {Proceedings of the Second Workshop on Logical Frameworks},

1816− author = {Claire Jones}

1817−}

1818−

1819−@misc{ typinghaskell,

1820− author = "Mark Jones",

1821− title = "Typing {Haskell} in {Haskell}",

1822− howpublished = "In Haskell Workshop, September 1999.",

1823− year = "1999",

1824− url = "citeseer.ist.psu.edu/article/jones99typing.html" }

1825−

1826−@article{karatsuba,

1827− journal = {Soviet Physics-Doklady},

1828− volume = {7},

1829− title = {Multiplication of multidigit numbers by automata},

1830− year = {1963},

1831− pages = {595--596},

1832− author = {A. Karatsuba and Y. Ofman}

1833−}

1834−

1835−@book{knuth2,

1836− volume = {2},

1837− title = {The Art of Computer Programming - Seminumerical Algorithms},

1838− year = {1969},

1839− publisher = {Addison Wesley},

1840− author = {Donald E. Knuth}

1841−}

1842−

1843−@article{next700,

1844− journal = {Communications of the {ACM}},

1845− number = {3},

1846− month = {March},

1847− volume = {9},

1848− title = {The next 700 programming languages},

1849− year = {1966},

1850− author = {P.J. Landin}

1851−}

1852−

1853−@techreport{luo-spec,

1854− month = {January},

1855− title = {Program Specification and Data Refinement in Type Theory},

1856− year = {1993},

1857− institution = {Department of Computer Science, University of Edinburgh},

1858− author = {Zhaohui Luo}

1859−}

1860−

1861−@phdthesis{luo90,

1862− school = {University of Edinburgh},

1863− title = {An Extended Calculus Of Constructions},

1864− year = {1990},

1865− author = {Zhaohui Luo}

1866−}

1867−

1868−@techreport{lego-manual,

1869− title = {\textsc{Lego} Proof Development System: User's Manual},

1870− year = {1992},

1871− institution = {Department of Computer Science, University of Edinburgh},

1872− author = {Zhaohui Luo and Robert Pollack}

1873−}

1874−

1875−@inproceedings{alf,

1876− title = {The {ALF} proof editor and its proof engine},

1877− year = {1994},

1878− booktitle = {Formal Proceeding of the 1993 Workshop on Types for Proofs and Programs},

1879− author = {Lena Magnusson and Bengt N\"{o}rdstrom}

1880−}

1881−

1882−@misc{happy,

1883− howpublished = {http://www.haskell.org/happy/},

1884− title = {Happy User Guide},

1885− year = {2001},

1886− author = {Simon Marlow and Andy Gill}

1887−}

1888−

1889−@inproceedings{generic-haskell,

1890− title = {Generic Haskell, Specifically},

1891− author = {Dave Clarke and Andres L\"{o}h},

1892− editor = {Jeremy Gibbons and Johan Jeuring},

1893− booktitle = {Proceedings of the IFIP TC2 Working Conference on Generic Programming},

1894− year = {2002},

1895− publisher = {Kluwer Academic Publishers},

1896− pages = {21--48}

1897−}

1898−

1899−@article{faking-it,

1900− title = {Faking It -- Simulating Dependent Types in {Haskell}},

1901− year = {2002},

1902− author = {Conor McBride},

1903− journal = {Journal of Functional Programming},

1904− volume = {12},

1905− number = {4+5},

1906− pages = {375--392}

1907−}

1908−

1909−@misc{mcbride-inverting,

1910− title = {Inverting Inductively Defined Relations in \textsc{Lego}},

1911− year = {1996},

1912− author = {Conor McBride}

1913−}

1914−

1915−@phdthesis{mcbride-thesis,

1916− month = {May},

1917− school = {University of Edinburgh},

1918− title = {Dependently Typed Functional Programs and their proofs},

1919− year = {2000},

1920− author = {Conor McBride}

1921−}

1922−

1923−@article{mcbride-unification,

1924− title = {First-Order Unification by Structural Recursion},

1925− year = {2003},

1926− author = {Conor McBride},

1927− journal = {Journal of Functional Programming},

1928− volume = {13},

1929− number = {6},

1930− pages = {1061--1075}

1931−}

1932−

1933−@misc{mckinna-pollack,

1934− howpublished = {Kluwer Academic Publishers},

1935− title = {Some Lambda Calculus and Type Theory formalized},

1936− year = {1998},

1937− author = {James McKinna and Robert Pollack}

1938−}

1939−

1940−@book{num-theory,

1941− title = {An Introduction to the Theory of Numbers},

1942− year = {1980},

1943− publisher = {John Wiley and Sons},

1944− author = {Ivan Niven and Herbert S. Zuckerman}

1945−}

1946−

1947−@book{prog-mltt,

1948− title = {Programming in Martin-L\"{o}f's Type Theory -- An Introduction},

1949− year = {1990},

1950− publisher = {Oxford University Press},

1951− author = {Bengt Nordstr\"{o}m and Kent Petersson and Jan M. Smith},

1952− note = {Out of print. Available from http://www.cs.chalmers.se/Cs/Research/Logic}

1953−}

1954−

1955−@book{okasaki,

1956− title = {Purely Functional Data Structures},

1957− year = {1998},

1958− publisher = {Cambridge University Press},

1959− author = {Chris Okasaki}

1960−}

1961−

1962−@book{arith-systems,

1963− title = {Computer Arithmetic Systems},

1964− year = {1994},

1965− publisher = {Prentice-Hall},

1966− author = {Amos R. Omondi}

1967−}

1968−

1969−@book{pj-imp,

1970− title = {The Implementation of Functional Programming Languages},

1971− year = {1987},

1972− publisher = {Prentice-Hall},

1973− author = {Simon {Peyton Jones}}

1974−}

1975−

1976−@book{cp-bjc,

1977− title = {Computational Numerical Methods},

1978− year = {1986},

1979− publisher = {John Wiley and Sons},

1980− author = {C. Phillips and B. Cornelius}

1981−}

1982−

1983−@book{nag,

1984− title = {The NAG Library: a beginner's guide},

1985− year = {1986},

1986− publisher = {Oxford : Clarendon Press},

1987− author = {Jen Phillips}

1988−}

1989−

1990−@misc{believe,

1991− month = {September},

1992− title = {How to Believe a Machine-Checked Proof},

1993− year = {1996},

1994− author = {Robert Pollack}

1995−}

1996−

1997−@phdthesis{pollack94,

1998− school = {University of Edinburgh},

1999− title = {The Theory of LEGO -- A Proof Checker for the Extended Calculus of Constructions},

2000− year = {1994},

2001− author = {Robert Pollack}

2002−}

2003−

2004−@inproceedings{intel-bug,

2005− series = {LNCS},

2006− volume = {915},

2007− title = {Anatomy of the Pentium Bug},

2008− publisher = {Springer-Verlag},

2009− year = {1995},

2010− pages = {97--107},

2011− author = {V.R. Pratt}

2012−}

2013−

2014−@book{maple,

2015− title = {The Maple Handbook: Maple V Release 4},

2016− year = {1996},

2017− publisher = {Springer},

2018− author = {Darren Redfern}

2019−}

2020−

2021−@book{crypto,

2022− title = {Applied Cryptography: protocols, algorithms and source code in C.},

2023− year = {1996},

2024− publisher = {Wiley},

2025− author = {Bruce Schneier}

2026−}

2027−

2028−@article{adts,

2029− journal = {Mathematical Structures in Computer Science},

2030− number = {2},

2031− volume = {10},

2032− title = {On lists and other abstract data types in the calculus of construction},

2033− year = {2000},

2034− pages = {261-276},

2035− author = {Jonathan P. Seldin}

2036−}

2037−

2038−@article{seldin97,

2039− journal = {Annals of Pure and Applied Logic},

2040− number = {1},

2041− month = {January},

2042− volume = {83},

2043− title = {On the proof theory of Coquand's calculus of constructions},

2044− year = {1997},

2045− pages = {23--101},

2046− author = {Jonathan P. Seldin}

2047−}

2048−

2049−@article{wichmann,

2050− journal = {The Computer Journal},

2051− volume = {32},

2052− title = {Towards a Formal Specification of Floating Point},

2053− year = {1989},

2054− pages = {432-436},

2055− author = {B.A. Wichmann}

2056−}

2057−

2058−@book{mathematica,

2059− title = {Mathematica : a system for doing mathematics by computer},

2060− year = {1991},

2061− publisher = {Addison Wesley},

2062− author = {Stephen Wolfram}

2063−}

2064−

2065−@inproceedings{xi-imp,

2066−author = "Hongwei Xi",

2067−title = {{Imperative Programming with Dependent Types}},

2068−booktitle = "Proceedings of 15th {IEEE} Symposium on Logic in Computer Science",

2069−year = 2000,

2070−month = "June",

2071−address = "Santa Barbara",

2072−pages = "375--387"

2073−}

2074−

2075−@phdthesis{xi-thesis,

2076− month = {December},

2077− school = {Department of Mathematical Sciences, Carnegie Mellon University},

2078− title = {Dependent Types in Practical Programming},

2079− year = {1998},

2080− author = {Hongwei Xi}

2081−}

2082−

2083−

2084−@techreport{dtal,

2085−author = {Hongwei Xi and Robert Harper},

2086−title = {A Dependently Typed Assembly Language},

2087−institution = {Computer Science and Engineering Department, Oregon Graduate Institute},

2088−year = 1999,

2089−number = {OGI-CSE-99-008},

2090−month = {July},

2091−}

2092−

2093−@misc{bignum-cmp,

2094− month = {February},

2095− title = {Comparison of three public-domain multiprecision libraries: BigNum, Gmp and Pari},

2096− year = {1998},

2097− author = {Paul Zimmerman}

2098−}

2099−

2100−@book{perl,

2101− title = {Programming Perl},

2102− author = {Larry Wall and Tom Christiansen and Jon Orwant},

2103− year = {2000},

2104− edition = {3rd},

2105− publisher = {O'Reilly}

2106−}

2107−

2108−@misc{python,

2109− howpublished = {http://www.python.org/doc/current/tut/tut.html},

2110− month = {April},

2111− title = {Python Tutorial},

2112− year = {2001},

2113− author = {Guido van {Rossum} and Fred L. {Drake, Jr}}

2114−}

2115−

2116−@book{logic,

2117− title = {The Language of First Order Logic},

2118− year = {1992},

2119− publisher = {CSLI Lecture Notes},

2120− author = {Jon Barwise and John Etchemendy}

2121−}

2122−

2123−@book{haskell,

2124− title = {Haskell -- The Craft of Functional Programming},

2125− year = {1999},

2126− publisher = {Addison Wesley},

2127− author = {Simon Thompson}

2128−}

2129−

2130−@inproceedings{coq-hol,

2131− title = {A Comparative Study of Coq and HOL},

2132− year = {1997},

2133− booktitle = {Theorem Proving in Higher Order Logics},

2134− pages = {323-337},

2135− author = {Vincent Zammit}

2136−}

2137−

2138−@misc{gay90,

2139− month = {November},

2140− title = {Correctly Rounded Binary-Decimal and Decimal-Binary Conversions},

2141− year = {1990},

2142− author = {David M. Gay},

2143− note = {AT&T Bell Laboratories, Numerical Analysis Manuscript 90-10}

2144−}

2145−

2146−@article{hughes-matters,

2147− journal = {Computer Journal},

2148− number = {2},

2149− volume = {32},

2150− title = {Why Functional Programming Matters},

2151− year = {1989},

2152− pages = {98--107},

2153− author = {J. Hughes}

2154−}

2155−

2156−@inproceedings{proofpointing,

2157− title = {Proof by Pointing},

2158− year = {1994},

2159− booktitle = {Proceedings of the International Symposium on Theoretical Aspects of Computer So},

2160− pages = {141--160},

2161− editor = {M. Hagiya and J. C. Mitchell},

2162− publisher = {Springer-Verlag},

2163− series = {LNCS},

2164− volume = {789},

2165− address = {Sendai, Japan},

2166− author = {Yves Bertot and Gilles Kahn and Laurent Th{\'e}ry}

2167−}

2168−

2169−@misc{inductive-coq,

2170− month = {December},

2171− title = {Inductive Definitions in the System Coq -- Rules and Properties},

2172− year = {1992},

2173− author = {Christine Paulin-Mohring}

2174−}

2175−

2176−@misc{leiserson98,

2177− month = {July},

2178− title = {Using de Bruijn Sequences to Index a 1 in a Computer Word},

2179− year = {1998},

2180− author = {{Charles E. Leiserson} and {Harald Prokop} and {Keith H. Randall}}

2181−}

2182−

2183−@inproceedings{proofchecking,

2184− title = {A two-level approach towards lean proof-checking},

2185− year = {1996},

2186− booktitle = {TYPES},

2187− pages = {16--35},

2188− author = {G. Barthe and M.P.J. Ruys and H.P. Barendregt}

2189−}

2190−

2191−@inproceedings{congruence,

2192− title = {Congruence Types},

2193− year = {1995},

2194− booktitle = {CSL},

2195− pages = {36--51},

2196− author = {Gilles Barthe and Herman Geuvers}

2197−}

2198−

2199−@phdthesis{geuvers-thesis,

2200− title = {Logic and Type Systems},

2201− author = {Herman Geuvers},

2202− year = 1993,

2203− school = {Katholieke Universiteit Nijmegen}

2204−}

2205−

2206−@techreport{multiple-values,

2207− title = {Multiple Values in {Standard ML}},

2208− year = {1994},

2209− number = {94-312},

2210− institution = {LFCS, Dept of Computer Science, University of Edinburgh},

2211− author = {Kevin Mitchell}

2212−}

2213−

2214−@inproceedings{oracle-checking,

2215− month = {January},

2216− title = {Oracle-Based Checking of Untrusted Software},

2217− year = {2001},

2218− booktitle = {Proceedings of the 28th {ACM} Symposium on Principles of Programming Languages},

2219− pages = {142--154},

2220− author = {{George C. Necula} and {S.P. Rahul}}

2221−}

2222−

2223−@article{adams93jfp,

2224− journal = {Journal of Functional Programming},

2225− number = {4},

2226− volume = {3},

2227− title = {Efficient Sets -- A Balancing Act},

2228− year = {1993},

2229− pages = {553--561},

2230− author = {Stephen Adams}

2231−}

2232−

2233−@inproceedings{hughes-sized,

2234− title = {Proving the Correctness of Reactive Systems Using Sized Types},

2235− year = {1996},

2236− booktitle = {Proceedings of the 23rd {ACM} {SIGPLAN}-SIGACT symposium on Principles of programmin},

2237− pages = {410--423},

2238− author = {John Hughes and Lars Pareto and Amr Sabry}

2239−}

2240−

2241−@inproceedings{whittle99ml,

2242− title = {An {ML} Editor Based on Proofs-As-Programs},

2243− year = {1999},

2244− booktitle = {Automated Software Engineering},

2245− pages = {166--173},

2246− author = {Jon Whittle and Alan Bundy and Richard J. Boulton and Helen Lowe}

2247−}

2248−

2249−@book{efp-typeinf,

2250− title = {Elements of Functional Programming},

2251− year = {1989},

2252− publisher = {Addison-Wesley},

2253− author = {Chris Reade},

2254− series = {International Computer Science Series}

2255−}

2256−

2257−@incollection{ wadler-views,

2258− author = "Philip Wadler",

2259− title = "Views: {A} Way for Pattern Matching to Cohabit with Data Abstraction",

2260− booktitle = "Proceedings, 14th Symposium on Principles of Programming Languages",

2261− publisher = "Association for Computing Machinery",

2262− editor = "Steve Munchnik",

2263− pages = "307--312",

2264− year = "1987",

2265− url = "citeseer.nj.nec.com/wadler87views.html" }

2266−

2267−@article{ coquand-checking,

2268− author = "Thierry Coquand",

2269− title = "An Algorithm for Type-Checking Dependent Types",

2270− journal = "Science of Computer Programming",

2271− volume = "26",

2272− number = "1-3",

2273− pages = "167-177",

2274− year = "1996",

2275− url = "citeseer.nj.nec.com/coquand96algorithm.html" }

2276−

2277−@misc{coquand-pm,

2278− author = "Thierry Coquand",

2279− title = "Pattern Matching with Dependent Types",

2280− year = "1992",

2281− howpublished = "Available from \verb+http://www.cs.chalmers.se/~coquand/type.html+"

2282−}

2283−

2284−@misc{pollack-records,

2285− month = {August},

2286− title = {Dependently Typed Records for Representing Mathematical Structure},

2287− year = {2000},

2288− author = {Robert Pollack}

2289−}

2290−

2291−@article{checking-betarte,

2292− journal = {Journal of Functional Programming},

2293− number = {2},

2294− month = {March},

2295− volume = {10},

2296− title = {Type checking dependent (record) types and subtyping},

2297− year = {2000},

2298− pages = {137--166},

2299− author = {Gustavo Betarte}

2300−}

2301−

2302−

2303−@article{ gcode,

2304− author = "Thomas Johnsson",

2305− title = "Efficient Compilation of Lazy Evaluation",

2306− booktitle = "Proceedings of the {{ACM}} {{SIGPLAN}}'84 Symposium on Compiler Con struction",

2307− journal = "{SIGPLAN} Notices",

2308− volume = "19",

2309− number = "6",

2310− month = "June",

2311− publisher = "{ACM} Press",

2312− pages = "58--69",

2313− year = "1984",

2314− url = "citeseer.nj.nec.com/johnsson84efficient.html" }

2315−

2316−@misc{kamareddine01,

2317− month = {February},

2318− title = {Reviewing the classical and the de Bruijn notation for $\lambda$-calculus and pure type systems},

2319− year = {2001},

2320− author = {Fairouz Kamareddine}

2321−}

2322−

2323−@book{prooftheory,

2324− title = {Basic Proof Theory},

2325− year = {1996},

2326− publisher = {Cambridge University Press},

2327− author = {A.S. Troelstra and H. Schwichtenberg},

2328− series = {Cambridge Tracts in Theoretical Computer Science}

2329−}

2330−

2331−@misc{nbe_staged,

2332− title = {Integrating Normalization-by-Evaluation into a Staged Programming Language},

2333− year = {1998},

2334− author = {Tim Sheard}

2335−}

2336−

2337−@inproceedings{nbe2,

2338− title = {Normalization by evaluation},

2339− year = {1998},

2340− author = {Ulrich Berger and Matthias Eberl and Helmut Schwichtenberg},

2341− booktitle = {Prospects for Hardware Foundations 1998},

2342− pages = {117--137},

2343− series = {LNCS}

2344−}

2345−

2346−

2347−

2348−@misc{rtcg_jfp,

2349− title = {Compiling for Run-time Code Generation},

2350− year = {2000},

2351− author = {Frederick Smith and Dan Grossman and Greg Morrisett and Luke Hornof and Trevor J},

2352− note = {Under consideration for J. Functional Programming}

2353−}

2354−

2355−@phdthesis{fredsmith_thesis,

2356− month = {January},

2357− school = {Cornell University},

2358− title = {Certified Run-time Code Generation},

2359− year = {2002},

2360− author = {Frederick Smith}

2361−}

2362−

2363−@inproceedings{xi_arraybounds,

2364−author = "Hongwei Xi and Frank Pfenning",

2365−title = {Eliminating Array Bound Checking through Dependent Types},

2366−booktitle = "Proceedings of {ACM} {SIGPLAN} Conference on Programming Language Design and Implementation",

2367−year = 1998,

2368−month = "June",

2369−address = "Montreal",

2370−pages = "249--257",

2371−}

2372−

2373−@inproceedings{xi_deadcode,

2374−author = "Hongwei Xi",

2375−title = {Dead Code Elimination through Dependent Types},

2376−booktitle = "The First International Workshop on Practical Aspects of Declarative Languages",

2377−year = 1999,

2378−month = "January",

2379−address = "San Antonio",

2380−pages = "228--242"

2381−}

2382−

2383−@book{compilers,

2384− title = {Compilers --- Principles, Techniques and Tools},

2385− year = {1986},

2386− publisher = {Addison-Wesley},

2387− author = {Alfred Aho and Ravi Sethi and Jeffrey Ullman}

2388−}

2389−

2390−@inproceedings{nhc,

2391− title = {Highlights from nhc: A space efficient {Haskell} Compiler},

2392− year = {1995},

2393− author = "Niklas R{\"o}jemo",

2394− booktitle = "Functional Programming Languages and Computer Architecture",

2395− pages = "282--292"

2396−}

2397−

2398−

2399−@misc{mlmatch,

2400− title = {SML/NJ Match Compiler Notes},

2401− year = {1992},

2402− author = {William Aitken}

2403−}

2404−

2405−@misc{mlmatch_sestoft,

2406− title = {ML pattern match compilation and partial evaluation},

2407− year = {1992},

2408− author = {Peter Sestoft}

2409−}

2410−

2411−@inproceedings{compiledstrongreduction,

2412− title = {A Compiled Implementation of Strong Reduction},

2413− year = {2002},

2414− author = {Benjamin Gr\'{e}goire and Xavier Leroy},

2415− booktitle = {Proc. 2002 International Conf. on Functional Programming ({ICFP} 2002)},

2416− pages = {235--246}

2417−}

2418−

2419−@misc{tclhaskell,

2420− howpublished = {http://www.dcs.gla.ac.uk/~meurig/TclHaskell/usermanual.html},

2421− month = {August},

2422− title = {TclHaskell - User Manual},

2423− year = {1999},

2424− author = {Meurig Sage}

2425−}

2426−

2427−

2428−@InProceedings{nbe-cat,

2429− author = "Thorsten Altenkirch and Martin Hofmann and Thomas Streicher",

2430− title = "Categorical reconstruction of a reduction free

2431− normalization proof",

2432− year = "1995",

2433− booktitle = "Category Theory and Computer Science",

2434− editor = {David Pitt and David E. Rydeheard and Peter Johnstone},

2435− series = {LNCS},

2436− volume = {953},

2437− pages = {182-199}

2438−}

2439−

2440−@inproceedings{presburgerEFSM,

2441− title = {A Comparison of Presburger Engines for EFSM Reachability},

2442− year = {1998},

2443− booktitle = {Computer Aided Verification '98},

2444− pages = {280--292},

2445− author = {Thomas R. Shiple and James H. Kukula and Rajeev K. Ranjan}

2446−}

2447−

2448−@misc{typesafecast,

2449− title = {Type-Safe Cast},

2450− year = {2000},

2451− author = {Stephanie Weirich}

2452−}

2453−

2454−@phdthesis{grobauer-thesis,

2455− school = {University of Aarhus},

2456− title = {Topics in Semantics Based Program Manipulation},

2457− year = {2001},

2458− author = {Bernd Grobauer}

2459−}

2460−

2461−@misc{monads-moggi,

2462− title = {Computational Lambda Calculus and Monads},

2463− year = {1989},

2464− author = {Eugenio Moggi}

2465−}

2466−

2467−@article{gmp-proof,

2468− title = {A proof of {GMP} square root},

2469− year = {2002},

2470− journal = {Journal of Automated Reasoning},

2471− volume = {29},

2472− pages = {225--252},

2473− author = {Yves Bertot and Nicolas Magaud and Paul Zimmerman}

2474−}

2475−

2476−@article{F-tal,

2477− journal = {{ACM} Transactions on Programming Languages and Systems},

2478− number = {3},

2479− month = {May},

2480− volume = {21},

2481− title = {From {System F} to Typed Assembly Language},

2482− year = {1999},

2483− pages = {528--569},

2484− author = {Greg Morrisett and David Walker and Karl Crary and Neal Glew}

2485−}

2486−

2487−@techreport{nbe-rtcg,

2488− month = {December},

2489− title = {Strong Normalization by Type-Directed Partial Evaluation and Run-Time Code Generation},

2490− year = {1997},

2491− institution = {BRICS},

2492− author = {Vincent Balat and Oliver Danvy}

2493−}

2494−

2495−@misc{yong-schemata,

2496− howpublished = {http://www.dur.ac.uk/yong.luo/},

2497− title = {A Methodology for Implementing Inductive Schemata},

2498− year = {2002},

2499− author = {Yong Luo and Zhaohui Luo}

2500−}

2501−

2502−@inproceedings{harper93,

2503− title = {Explicit Polymorphism and CPS Conversion},

2504− year = {1993},

2505− booktitle = {20th {ACM} {SIGPLAN}-SIGACT Symposium on Principles of Programming Languages},

2506− pages = {206--219},

2507− publisher = {{ACM} Press, New York, NY, USA},

2508− author = {Robert Harper and Mark Lillibridge}

2509−}

2510−

2511−@techreport{backends,

2512− month = {November},

2513− title = {Functional Back-Ends within the Lambda-Sigma Calculus},

2514− year = {1996},

2515− institution = {INRIA},

2516− author = {Th\'{e}r\`{e}se Hardin and Luc Maranget and Bruno Pagano}

2517−}

2518−

2519−@article{stg,

2520− title = {Implementing lazy functional languages on stock hardware -- the {Spineless Tagless G-machine}},

2521− year = {1992},

2522− journal = {Journal of Functional Programming},

2523− volume = {2},

2524− number = {2},

2525− pages = {127--202},

2526− month = {April},

2527− author = {Simon {Peyton Jones}}

2528−}

2529−

2530−@article{debruijn,

2531− journal = {Indagationes Mathematicae},

2532− volume = {34},

2533− title = {Lambda calculus notation with nameless dummies},

2534− year = {1972},

2535− pages = {381--392},

2536− author = {N.G. de Bruijn}

2537−}

2538−

2539−@book{assembly,

2540− month = {January},

2541− title = {PC Assembly Language},

2542− year = {2002},

2543− publisher = {http://www.drpaulcarter.com/},

2544− author = {Paul A. Carter}

2545−}

2546−

2547−@inproceedings{poly99,

2548− title = {Once Upon A Polymorphic Type},

2549− year = {1999},

2550− booktitle = {26th {ACM} {SIGPLAN}-SIGACT Symposium on Principles of Programming Languages},

2551− publisher = {{ACM}},

2552− author = {Keith Wansbrough and Simon {Peyton Jones}}

2553−}

2554−

2555−@misc{lazy_intro,

2556− title = {Compiling Lazy Functional Languages: An introduction},

2557− year = {1986},

2558− author = {Thomas Johnsson}

2559−}

2560−

2561−@inproceedings{unboxed-fp,

2562− month = {Sept},

2563− title = {Unboxed Values as First Class Citizens in a Non-Strict Functional Language},

2564− year = {1991},

2565− author = {Simon {Peyton Jones} and John Launchbury},

2566− booktitle = {Functional Programming Languages and Computer Architecture (FPCA'91)},

2567− crossref = {fplca91},

2568− pages = {636--666}

2569−}

2570−

2571−@inproceedings{abc-machine,

2572− author = {Sjaak Smetsers and Eric N{\"{o}}cker and John {van Groningen} and Rinus Plasmeijer},

2573− title = {Generating efficient code for lazy functional languages},

2574− booktitle = {Functional programming Languages and Computer Architecture},

2575− year = {1991},

2576− pages = {592--617},

2577− crossref = {fplca91}

2578−}

2579−

2580−@proceedings{fplca91,

2581− title = {Functional programming Languages and Computer Architecture},

2582− year = {1991},

2583− volume = {523},

2584− series = {LNCS},

2585− publisher = {Springer-Verlag},

2586− editor = {John Hughes}

2587−}

2588−

2589−

2590−

2591−@inproceedings{nbe,

2592− title = {An inverse of the evaluation functional for typed $\lambda$-calculus},

2593− year = {1991},

2594− booktitle = {Proc. 1991 {IEEE} Symp. on Logic in Comp. Sci.},

2595− pages = {203--211},

2596− editor = {R. Vemuri},

2597− author = {Ulrich Berger and Helmut Schwichtenberg}

2598−}

2599−

2600−@inproceedings{typed-closure,

2601− title = {Typed Closure Conversion},

2602− year = {1996},

2603− booktitle = {Symposium on Principles of Programming Languages},

2604− pages = {271--283},

2605− author = {Yasuhiko Minamide and J. Gregory Morrisett and Robert Harper}

2606−}

2607−

2608−@misc{ghc-commentary,

2609− howpublished = {http://www.cse.unsw.edu.au/~chak/haskell/ghc/comm/},

2610− title = {The Glasgow Haskell Compiler (GHC) Commentary},

2611− year = {2002},

2612− author = {Manuel M. T. Chakravarty and Sigbjorn Finne and Simon Marlow and Simon {Peyton Jones} and Julian Seward and Reuben Thomas},

2613− note = {Available from GHC CVS repository}

2614−}

2615−

2616−@inproceedings{lambdalift,

2617− month = {September},

2618− title = {Lambda Lifting: Transforming Programs to Recursive Equations},

2619− year = {1985},

2620− booktitle = {Functional Programming Languages and Computer Architecture},

2621− pages = {190--203},

2622− editor = {Jean-Pierre Jouannaud},

2623− publisher = {Springer-Verlag},

2624− author = {Thomas Johnsson}

2625−}

2626−

2627−@inproceedings{til,

2628− title = {TIL: A Type-Directed Optimizing Compiler for ML},

2629− year = {1996},

2630− booktitle = {Proc. {{ACM}} {{SIGPLAN}} '96 Conference on Programming Language Design and Implementation},

2631− pages = {181--192},

2632− author = {D. Tarditi and G. Morrisett and P. Cheng and C. Stone and R. Harper and P. Lee}

2633−}

2634−

2635−@phdthesis{shao94,

2636− school = {Princeton University},

2637− title = {Compiling Standard {ML} for Efficient Execution on Modern Machines},

2638− year = {1994},

2639− author = {Zhong Shao}

2640−}

2641−

2642−@inproceedings{gmachine,

2643− month = {September},

2644− title = {The {G-Machine}: A fast, graph-reduction evaluator},

2645− year = {1985},

2646− booktitle = {Functional Programming Languages and Computer Architecture},

2647− pages = {400--413},

2648− editor = {Jean-Pierre Jouannaud},

2649− publisher = {Springer-Verlag},

2650− author = {R.B. Kieburtz}

2651−}

2652−

2653−@inproceedings{strictness,

2654− month = {September},

2655− title = {Strictness Analysis - A practical approach},

2656− year = {1985},

2657− booktitle = {Functional Programming Languages and Computer Hardware},

2658− pages = {35--49},

2659− editor = {Jean-Pierre Jouannaud},

2660− publisher = {Springer-Verlag},

2661− author = {Chris Clack and Simon {Peyton Jones}}

2662−}

2663−

2664−@book{fl-impl,

2665− title = {Implementing Functional Languages - A Tutorial},

2666− year = {1992},

2667− publisher = {Prentice Hall International},

2668− author = {Simon {Peyton Jones} and David Lester}

2669−}

2670−

2671−@phdthesis{capretta-thesis,

2672− school = {Katholieke Universiteit Nijmegen},

2673− title = {Abstraction and Computation},

2674− year = {2002},

2675− author = {Venanzio Capretta}

2676−}

2677−

2678−@article{bird-pointer,

2679− journal = {Journal of Functional Programming},

2680− number = {3},

2681− month = {May},

2682− volume = {11},

2683− title = {Unfolding Pointer Algorithms},

2684− year = {2001},

2685− pages = {347--358},

2686− author = {Richard S. Bird}

2687−}

2688−

2689−@article{impl-tp,

2690− journal = {Journal of Functional Programming},

2691− number = {2},

2692− month = {March},

2693− volume = {9},

2694− title = {Implementing Theorem Provers in a Purely Functional Style},

2695− year = {1999},

2696− pages = {147--166},

2697− author = {Keith Hanna}

2698−}

2699−

2700−@article{shrink-lambda,

2701− journal = {Journal of Functional Programming},

2702− number = {5},

2703− month = {September},

2704− volume = {7},

2705− title = {Shrinking Lambda Expressions in Linear Time},

2706− year = {1997},

2707− pages = {515--540},

2708− author = {Andrew W. Appel and Trevor Jim}

2709−}

2710−

2711−@article{stack-tal,

2712− journal = {Journal of Functional Programming},

2713− number = {1},

2714− month = {January},

2715− volume = {12},

2716− title = {Stack-based Typed Assembly Language},

2717− year = {2002},

2718− pages = {43--88},

2719− author = {Greg Morrisset and Karl Crart and Neal Glew and David Walker}

2720−}

2721−

2722−@article{runtime-lamsig,

2723− journal = {Journal of Functional Programming},

2724− number = {2},

2725− month = {March},

2726− volume = {8},

2727− title = {Functional Runtime Systems within the lambda-sigma Calculus},

2728− year = {1998},

2729− pages = {131--176},

2730− author = {Th\'{e}r\`{e}se Hardin and Luc Maranget and Bruno Pagano}

2731−}

2732−

2733−@article{busylazy,

2734− journal = {Journal of Functional Programming},

2735− number = {6},

2736− month = {November},

2737− volume = {11},

2738− title = {How to look busy while being as lazy as ever: the Implementation of a lazy functional debugger},

2739− year = {2001},

2740− pages = {629--671},

2741− author = {Henrik Nilsson}

2742−}

2743−

2744−@article{lazyveager,

2745− journal = {Journal of Functional Programming},

2746− number = {5},

2747− month = {September},

2748− volume = {7},

2749− title = {More haste, less speed: lazy versus eager evaluation},

2750− year = {1997},

2751− pages = {541--547},

2752− author = {Richard Bird and Geraint Jones and Oege {de Moor}}

2753−}

2754−

2755−@article{jvm-fp,

2756− journal = {Journal of Functional Programming},

2757− number = {6},

2758− month = {November},

2759− volume = {9},

2760− title = {Compiling lazy functional programs for the Java Virtual Machine},

2761− year = {1999},

2762− pages = {579--603},

2763− author = {David Wakeling}

2764−}

2765−

2766−@book{isabelle,

2767− publisher = {Springer-Verlag},

2768− series = {LNCS},

2769− volume = {2283},

2770− month = {March},

2771− title = {Isabelle/HOL - A proof assistant for higher order logic},

2772− year = {2002},

2773− author = {Tobias Nipkow and Lawrence C. Paulson and Markus Wenzel}

2774−}

2775−

2776−@article{ghc-inliner,

2777− journal = {Journal of Functional Programming},

2778− number = {4},

2779− month = {September},

2780− volume = {12},

2781− title = {Secrets of the {Glasgow Haskell Compiler} inliner},

2782− year = {2002},

2783− pages = {393--434},

2784− author = {Simon {Peyton Jones} and Simon Marlow}

2785−}

2786−

2787−@article{dynamic-fp,

2788− journal = {Journal of Functional Programming},

2789− number = {1},

2790− month = {January},

2791− volume = {8},

2792− title = {The dynamic compiliation of lazy functional programs},

2793− year = {1998},

2794− pages = {61--81},

2795− author = {David Wakeling}

2796−}

2797−

2798−@misc{isabelle-ref,

2799− month = {March},

2800− title = {Isabelle Reference Manual},

2801− year = {2002},

2802− author = {Lawrence C. Paulson}

2803−}

2804−

2805−@article{debruijn-nested,

2806− journal = {Journal of Functional Programming},

2807− number = {1},

2808− month = {January},

2809− volume = {9},

2810− title = {de Bruijn notation as a nested datatype},

2811− year = {1999},

2812− pages = {77--91},

2813− author = {Richard S. Bird and Ross Paterson}

2814−}

2815−

2816−@article{perfect-trees,

2817− journal = {Journal of Functional Programming},

2818− number = {3},

2819− month = {May},

2820− volume = {10},

2821− title = {Perfect trees and bit-reversal permutations},

2822− year = {2000},

2823− pages = {305--317},

2824− author = {Ralf Hinze}

2825−}

2826−

2827−@phdthesis{paulin-extraction,

2828− school = {Paris 7},

2829− title = {Extraction de programmes dans le Calcul des Constructions},

2830− year = {1989},

2831− author = {Christine Paulin-Mohring}

2832−}

2833−

2834−@phdthesis{santos95,

2835− school = {University of Glasgow},

2836− title = {Compilation By Transformation In Non-Strict Functional Languages},

2837− year = {1995},

2838− author = {{Andr\'{e} Lu\'{i}s de Medeiros} Santos}

2839−}

2840−

2841−@book{cps,

2842− title = {Compiling With Continuations},

2843− year = {1992},

2844− publisher = {Cambridge University Press},

2845− author = {Andrew W. Appel}

2846−}

2847−

2848−@techreport{SKIM,

2849− number = {31},

2850− title = {The {SKIM} microprogrammer's guide},

2851− year = {1983},

2852− institution = {University of Cambridge},

2853− author = {W.R. Stoye}

2854−}

2855−

2856−@misc{NORMA,

2857− title = {An Overview of Burroughs {NORMA}},

2858− year = {1985},

2859− author = {H. Richards}

2860−}

2861−

2862−@book{ml,

2863− title = {The Definition of Standard ML --- Revised},

2864− year = {1997},

2865− publisher = {MIT Press},

2866− author = {Robin Milner and Mads Tofte and Robert Harper and David MacQueen}

2867−}

2868−

2869−@misc{ml71,

2870− title = {An intuitionistic theory of types},

2871− year = {1971},

2872− author = {Per Martin-L\"{o}f}

2873−}

2874−

2875−@phdthesis{girard-thesis,

2876− school = {Universit\'{e} Paris VII},

2877− title = {Interpr\'{e}tation fonctionelle et \'{e}limination des coupures de l'arithm\'{e}tique d'ordre sup\'{e}rieur},

2878− year = {1972},

2879− author = {Jean-Yves Girard}

2880−}

2881−

2882−@inproceedings{ml75,

2883− title = {An intuitionistic theory of types: predicative part},

2884− year = {1975},

2885− booktitle = {Logic Colloquium '73},

2886− editor = {H. Rose and J.C. Shepherdson},

2887− publisher = {North-Holland},

2888− author = {Per Martin-L\"{o}f}

2889−}

2890−

2891−@inproceedings{cpm90,

2892− title = {Inductively defined types},

2893− year = {1990},

2894− author = {Thierry Coquand and Christine Paulin-Mohring},

2895− series = {LNCS},

2896− volume = {417},

2897− publusher = {Springer-Verlag}

2898−}

2899−

2900−@phdthesis{fpcustom,

2901− month = {May},

2902− school = {Computer Lab, University of Cambridge},

2903− title = {The Implementation of Functional Languages using Custom Hardware},

2904− year = {1985},

2905− author = {W.R. Stoye}

2906−}

2907−

2908−@phdthesis{hughesthesis,

2909− month = {September},

2910− school = {Programming Research Group, Oxford},

2911− title = {The design and implementation of programming languages},

2912− year = {1984},

2913− author = {John Hughes}

2914−}

2915−

2916−@inproceedings{tim,

2917− volume = {274},

2918− title = {{TIM} -- A simple lazy abstract machine to execute supercombinators},

2919− year = {1987},

2920− booktitle = {Functional Programming Languages and Computer Architecture},

2921− publisher = {Springer-Verlag},

2922− author = {John Fairbairn and Stuart Wray},

2923− pages = {34--45},

2924− series = {LNCS}

2925−}

2926−

2927−@techreport{abc,

2928− title = {The {ABC} machine -- A Sequential Stack-based Abstract Machine For Graph Rewriting},

2929− year = {1990},

2930− institution = {University of Nijmegen},

2931− author = {P.W.M. Koopman and M.C.J.D. van {Eekelen} and E.G.J.M.H. Ncker and J.E.W. Smetsers and M.J. Plasmeijer}

2932−}

2933−

2934−@techreport{implicit,

2935− title = {On Implicit Arguments},

2936− year = {1994},

2937− institution = {Faculty of Science, University of Tokyo},

2938− author = {Masami Hagiya and Yozo Toda}

2939−}

2940−

2941−@book{semantics,

2942− title = {Denotational Semantics},

2943− year = {1986},

2944− publisher = {Wm. C. Brown},

2945− author = {David A. Schmidt}

2946−}

2947−

2948−@inproceedings{lazyml,

2949− month = {August},

2950− title = {A compiler for {Lazy} {ML}},

2951− year = {1984},

2952− booktitle = {Proceedings of the {{ACM}} Symposium on Lisp and Functional Programming},

2953− pages = {218--227},

2954− author = {Lennart Augustsson}

2955−}

2956−

2957−@inproceedings{nu-g,

2958− title = {Parallel graph reduction with the $\langle\nu,G\rangle$-machine},

2959− year = {1989},

2960− booktitle = {Functional Programming Languages and Computer Architecture},

2961− publisher = {{ACM} Press},

2962− author = {Lennart Augustsson and Thomas Johnsson}

2963−}

2964−

2965−@book{k&r,

2966− title = {The C programming language},

2967− year = {1988},

2968− publisher = {Prentice-Hall},

2969− author = {Brian W. Kernighan and Dennis M. Ritchie}

2970−}

2971−

2972−@misc{c--garbage,

2973− title = {C--: a portable assembly language that supports garbage collection},

2974− year = {1999},

2975− author = {Simon {Peyton Jones} and Norman Ramsey and Fermin Reig},

2976− note = {Invited talk at PPDP'99}

2977−}

2978−

2979−@misc{epigram,

2980− howpublished = {http://www.dur.ac.uk/CARG/epigram.html},

2981− title = {Project Proposal: {Epigram}: Innovative Programming via Inductive Families},

2982− year = {2002},

2983− author = {Zhaohui Luo and James McKinna and Paul Callaghan and Conor McBride}

2984−}

2985−

2986−@misc{ghc-rewrite,

2987− title = {Playing by the Rules: Rewriting as a practical optimisation technique in {GHC}},

2988− year = {2001},

2989− author = {Simon {Peyton Jones} and Andrew Tolmach and Tony Hoare}

2990−}

2991−

2992−@UNPUBLISHED{implicit-pollack,

2993− AUTHOR = {Robert Pollack},

2994− TITLE = {Implicit Syntax},

2995− NOTE = {Informal Proceedings of First Workshop on

2996− Logical Frameworks, Antibes},

2997− YEAR = {1990},

2998− MONTH = MAY

2999−}

3000−

3001−

3002−@article{transform-haskell,

3003− journal = {Science of Computer Programming},

3004− volume = {32},

3005− title = {A transformation-based optimiser for {Haskell}},

3006− year = {1998},

3007− pages = {3--47},

3008− author = {Simon {Peyton Jones} and Andr\'{e} L. M. Santos}

3009−}

3010−

3011−@inproceedings{knuth-bendix,

3012− title = {Simple Word Problems in Universal Algebras},

3013− year = {1970},

3014− booktitle = {Computational Problems in Abstract Algebra},

3015− pages = {263--298},

3016− editor = {John Leech},

3017− publisher = {Pergamon Press},

3018− author = {Donald E. Knuth and Peter B. Bendix}

3019−}

3020−

3021−@inproceedings{phantomfun,

3022− title = {Fun With Phantom Types},

3023− author = {Ralf Hinze},

3024− pages = {245--262},

3025− year = {2003},

3026− crossref = {funprogramming},

3027− booktitle = {The Fun Of Programming},

3028− publisher = {Palgrave}

3029−}

3030−

3031−@book{funprogramming,

3032− month = {March},

3033− title = {The Fun Of Programming},

3034− year = {2003},

3035− editor = {Jeremy Gibbons and Oege {de Moor}},

3036− publisher = {Palgrave},

3037− series = {Cornerstones of Computing}

3038−}

3039−

3040−@inproceedings{anderson-proof,

3041− title = {Representing Proof Transformations For Program Optimization},

3042− year = {1994},

3043− booktitle = {International Conference On Automated Deduction},

3044− publisher = {Springer Verlag},

3045− author = {Penny Anderson}

3046−}

3047−

3048−@phdthesis{daria-thesis,

3049− month = {April},

3050− school = {Institute of Informatics, Warsaw University},

3051− title = {Termination of Rewriting in the Calculus of Constructions},

3052− year = {2003},

3053− author = {Daria Walukiewicz-Chrzaszcz}

3054−}

3055−

3056−@inproceedings{change-data,

3057− title = {Changing Data Structures In Type Theory: A Study Of Natural Numbers},

3058− year = {2001},

3059− booktitle = {Types For Proofs And Programs 2000},

3060− pages = {181--196},

3061− editor = {Paul Callaghan and Zhaohui Luo and James McKinna and Robert Pollack},

3062− publisher = {Springer},

3063− author = {Nicolas Magaud and Yves Bertot}

3064−}

3065−

3066−@phdthesis{nico-thesis,

3067− title = {Changement de Representation des donn\'{e}es dans le Calcul de Constructions},

3068− author = {Nicolas Magaud},

3069− year = {2003},

3070− month = {October},

3071− school = {Universit\'{e} de Nice - Sophia Antipolis}

3072−}

3073−

3074−

3075−@book{patterns,

3076− title = {Design Patterns},

3077− year = {1995},

3078− publisher = {Addison Wesley},

3079− author = {Erich Gamma and Richard Helm and Ralph Johnson and John Vlissides}

3080−}

3081−

3082−@misc{ghchugs,

3083− month = {August},

3084− title = {The New {GHC}/{Hugs} Runtime System},

3085− year = {1998},

3086− author = {Simon Marlow and Simon {Peyton Jones}}

3087−}

3088−

3089−@misc{stgrevised,

3090− month = {February},

3091− title = {The {STG} runtime system (revised)},

3092− year = {1999},

3093− author = {Simon {Peyton Jones} and Simon Marlow and Alastair Reid},

3094− howpublished = {Available from \verb+http://www.haskell.org/ghc/documentation.html+}

3095−}

3096−

3097−@inproceedings{optimistic,

3098− month = {March},

3099− title = {Optimistic Evaluation --- an adaptive evaluation strategy for non-strict programs},

3100− year = {2003},

3101− author = {Robert Ennals and Simon {Peyton Jones}},

3102− booktitle = {International Conference on Functional Programming},

3103− pages = {287--298}

3104−}

3105−

3106−@phdthesis{ennals-thesis,

3107− title = {Adaptive Evaluation of Non-Strict Programs},

3108− author = {Robert Ennals},

3109− year = {2003},

3110− month = {December},

3111− school = {King's College, University of Cambridge}

3112−}

3113−

3114−@article{garbage,

3115− journal = {{ACM} Computing Surveys},

3116− number = {3},

3117− volume = {13},

3118− title = {Garbage Collection of Linked Data Structures},

3119− year = {1981},

3120− pages = {341--367},

3121− author = {Jacques Cohen}

3122−}

3123−

3124−@article{baker-gc,

3125− journal = {Communications of the {ACM}},

3126− number = {4},

3127− month = {April},

3128− volume = {21},

3129− title = {List Processing In Real Time On A Serial Computer},

3130− year = {1978},

3131− pages = {280--294},

3132− author = {Henry G. {Baker Jr}}

3133−}

3134−

3135−@misc{bc-rec,

3136− month = {February},

3137− title = {Modelling General Recursion in Type Theory},

3138− year = {2003},

3139− note = {Under consideration for publication in Math. Struct. in Comp. Science. Draft, DCS, CTH --- INRIA, Sophia Antipolis, France},

3140− author = {Ana Bove and Venanzio Capretta}

3141−}

3142−

3143−@misc{global-tag,

3144− title = {Global Tagging Optimization by Type Inference},

3145− year = {1992},

3146− author = {Fritz Henglein}

3147−}

3148−

3149−@book{esr,

3150− month = {October},

3151− title = {The Cathedral And The Bazaar},

3152− year = {1999},

3153− publisher = {O'Reilly},

3154− author = {Eric Raymond}

3155−}

3156−

3157−@book{manmonth,

3158− title = {The Mythical Man-month: Essays on Software Engineering},

3159− year = {1975},

3160− publisher = {Addison Wesley},

3161− author = {Frederick P. Brooks}

3162−}

3163−

3164−@inproceedings{evalpush,

3165− title = {How to make a fast curry: push/enter vs eval/apply},

3166− year = {2004},

3167− author = {Simon Marlow and Simon {Peyton Jones}},

3168− booktitle = {International Conference on Functional Programming, Snowbird},

3169− pages = {4--15}

3170−}

3171−

3172−@phdthesis{boquist-thesis,

3173− month = {April},

3174− school = {Chalmers University of Technology},

3175− title = {Code Optimisation Techniques for Lazy Functional Languages},

3176− year = {1999},

3177− author = {Urban Boquist}

3178−}

3179−

3180−@book{formal-spec,

3181− title = {Formal Specification Of Programming Languages},

3182− year = {1981},

3183− publisher = {Prentice-Hall},

3184− author = {Frank G. Pagan}

3185−}

3186−

3187−@inproceedings{elim-motive,

3188− title = {Elimination With A Motive},

3189− year = {2000},

3190− booktitle = {Types for Proofs and Programs},

3191− pages = {197--216},

3192− editor = {Paul Callaghan and Zhaohui Luo and James McKinna and Robert Pollack},

3193− publisher = {Springer},

3194− author = {Conor McBride}

3195−}

3196−

3197−@article{telescope,

3198− journal = {Information and Computation},

3199− number = {2},

3200− month = {April},

3201− volume = {91},

3202− title = {Telescoping Mappings in Typed Lambda Calculus},

3203− year = {1991},

3204− pages = {189--204},

3205− author = {N.G. de Bruijn}

3206−}

3207−

3208−@misc{typeintype,

3209− title = {Typechecking is undecidable when 'type' is a type},

3210− year = {1989},

3211− author = {Mark B. Reinhold}

3212−}

3213−

3214−@misc{core,

3215− month = {September},

3216− title = {An External Representation for the {GHC} Core Language},

3217− year = {2001},

3218− author = {Andrew Tolmach and {The GHC Team}}

3219−}

3220−

3221−@article{deforestation,

3222− journal = {Theoretical Computer Science},

3223− volume = {73},

3224− title = {Deforestation: Transforming programs to eliminate trees},

3225− year = {1990},

3226− pages = {231--248},

3227− author = {Philip Wadler}

3228−}

3229−

3230−@misc{hep,

3231− month = {July},

3232− title = {Architecture of the {Haskell} Execution Platform},

3233− year = {1999},

3234− author = {Julian Seward and Simon Marlow and Andy Gill and Sigbjorn Finne and Simon {Peyton Jones} },

3235− note = {Version 6},

3236− howpublished = {Available from \verb+http://www.haskell.org/ghc/documentation.html+}

3237−}

3238−

3239−@mastersthesis{wahlstedt-thesis,

3240− month = {October},

3241− school = {Chalmers University Of Technology},

3242− title = {Detecting Termination Using Size Change In Parameter Values},

3243− year = {2000},

3244− author = {David Wahlstedt}

3245−}

3246−

3247−@inproceedings{size-change,

3248− title = {The size-change principle for program termination},

3249− year = {2001},

3250− booktitle = {Proceedings of the 28th Annual {ACM} {SIGPLAN}-SIGACT Symposium on Principles of Programming Languages},

3251− author = {Chin Soon Lee and Neil D. Jones and Amir Ben-Amram. }

3252−}

3253−

3254−@article{ski-turner,

3255− journal = {Software -- Practice and Experience},

3256− volume = {9},

3257− title = {A new implementation technique for applicative languages},

3258− year = {1979},

3259− pages = {31--49},

3260− author = {David Turner}

3261−}

3262−

3263−@inproceedings{turner-strong,

3264− number = {1022},

3265− title = {Elementary Strong Functional Programming},

3266− year = {1996},

3267− booktitle = {First International Symposium on Functional Programming Languages in Education, Nijmegen, Netherlands, December 1995.},

3268− pages = {1--13},

3269− publisher = {Springer},

3270− author = {David Turner},

3271− series = {LNCS}

3272−}

3273−

3274−@misc{clean,

3275− title = {The {Concurrent CLEAN} Language Report (draft)},

3276− year = {2003},

3277− author = {Rinus Plasmeijer and Marko van Eekelen},

3278− howpublished = {Available from \verb+http://www.cs.kun.nl/~clean/+}

3279−}

3280−

3281−@article{burstall-struct,

3282− journal = {Computer Journal},

3283− number = {1},

3284− volume = {12},

3285− title = {Proving Properties of Programs By Structural Induction},

3286− year = {1969},

3287− pages = {41--48},

3288− author = {Rod Burstall}

3289−}

3290−

3291−@incollection{ barendregt-types,

3292− author = "Henk Barendregt",

3293− title = "Lambda Calculi with Types",

3294− booktitle = "Handbook of Logic in Computer Science, Volumes 1 (Background: Mathematical Structures) and 2 (Background: Computational Structures), Abramsky \& Gabbay \& Maibaum (Eds.)",

3295− publisher = "Clarendon",

3296− volume = "2",

3297− year = "1992",

3298− url = "citeseer.nj.nec.com/barendregt92lambda.html" }

3299−

3300−@book{curry-feys,

3301− title = {Combinatory Logic, volume 1},

3302− year = {1958},

3303− publisher = {North Holland},

3304− author = {Haskell B. Curry and Robert Feys}

3305−}

3306−

3307−@phdthesis{bove-thesis,

3308− month = {November},

3309− school = {Chalmers University of Technology},

3310− title = {General Recursion in Type Theory},

3311− year = {2002},

3312− author = {Ana Bove}

3313−}

3314−

3315−@inbook{ml-cm,

3316− title = {Constructive Mathematics and Computer Programming},

3317− year = {1985},

3318− booktitle = {Mathematical Logic and Programming Languages},

3319− publisher = {Prentice Hall},

3320− author = {Per Martin-L\"{o}f}

3321−}

3322−

3323−@inproceedings{howard,

3324− title = {The formulae-as-types notion of construction},

3325− year = {1980},

3326− booktitle = {To H.B.Curry: Essays on combinatory logic, lambda calculus and formalism},

3327− editor = {Jonathan P. Seldin and J. Roger Hindley},

3328− publisher = {Academic Press},

3329− author = {William A. Howard},

3330− note = {A reprint of an unpublished manuscript from 1969}

3331−}

3332−

3333−@inproceedings{talx86,

3334− title = {TALx86: A Realistic Typed Assembly Language},

3335− year = {1999},

3336− booktitle = {{ACM} {SIGPLAN} Workshop on Compiler Support for System Software},

3337− pages = {25--35},

3338− author = {Greg Morrisett and Karl Crary and Neal Glew and Dan Grossman and Richard Samuels and Frederick Smith and David Walker and Stephanie Weirich and Steve Zdancewic}

3339−}

3340−

3341−@inproceedings{bove-capretta,

3342− volume = {2152},

3343− title = {Nested General Recursion and Partiality in Type Theory},

3344− year = {2001},

3345− booktitle = {Theorem Proving in Higher Order Logics, 14th International Conference, TPHOLS 2001},

3346− pages = {121--135},

3347− editor = {Richard J. Boulton and Paul B. Jackson},

3348− publisher = {Springer-Verlag},

3349− author = {Ana Bove and Venanzio Capretta},

3350− series = {LNCS}

3351−}

3352−

3353−@misc{lvm,

3354− month = {November},

3355− title = {LVM, the lazy virtual machine},

3356− year = {2002},

3357− author = {Daan Leijen}

3358−}

3359−

3360−@misc{ocaml,

3361− howpublished = {\verb+http://caml.inria.fr/ocaml/htmlman/+},

3362− month = {August},

3363− title = {The {Objective Caml} system release 3.06},

3364− year = {2002},

3365− author = {Xavier Leroy}

3366−}

3367−

3368−@misc{lambdagoto,

3369− title = {Lambda : The Ultimate Goto},

3370− year = {1977},

3371− author = {Guy L. {Steele Jr}},

3372− note = {MIT AI Memo 443}

3373−}

3374−

3375−@inproceedings{ liu-tail,

3376− author = "Yanhong A. Liu and Scott D. Stoller",

3377− title = "From Recursion to Iteration: What are the Optimizations?",

3378− booktitle = "Partial Evaluation and Semantic-Based Program Manipulation",

3379− pages = "73-82",

3380− year = "2000",

3381− url = "citeseer.nj.nec.com/liu00from.html" }

3382−

3383−@inproceedings{aczel77,

3384− title = {An Introduction To Inductive Definitions},

3385− year = {1977},

3386− booktitle = {Handbook of Mathematical Logic},

3387− editor = {J. Barwise},

3388− publisher = {North Holland},

3389− author = {Peter Aczel}

3390−}

3391−

3392−@inproceedings{inductive-plastic,

3393− volume = {1956},

3394− title = {Implementation Techniques for Inductive Types in {Plastic}},

3395− year = {1999},

3396− booktitle = {Types for Proofs and Programs},

3397− pages = {94--113},

3398− editor = {Thierry Coquand and Peter Dybjer and Bengt Nordstr\"{o}m and Jan Smith},

3399− publisher = {Springer-Verlag},

3400− author = {Paul Callaghan and Zhaohui Luo},

3401− series = {LNCS}

3402−}

3403−

3404−@misc{graham,

3405− howpublished = {Available from \verb+http://www.paulgraham.com/+},

3406− month = {April},

3407− title = {The Hundred Year Language},

3408− year = {2003},

3409− author = {Paul Graham},

3410− note = {Keynote address at PyCon 2003}

3411−}

3412−

3413−@inproceedings{gimenez98,

3414− volume = {1443},

3415− title = {Structural Recursive Definitions in Type Theory},

3416− year = {1998},

3417− booktitle = {Proceedings of ICALP '98},

3418− publisher = {Springer-Verlag},

3419− author = {Eduardo Gim\'{e}nez},

3420− series = {LNCS}

3421−}

3422−

3423−@article{quicksort,

3424− journal = {Computer Journal},

3425− number = {1},

3426− volume = {5},

3427− title = {Quicksort},

3428− year = {1962},

3429− pages = {10--15},

3430− author = {C.A.R. Hoare}

3431−}

3432−

3433−@phdthesis{goguen-thesis,

3434− school = {University of Edinburgh},

3435− title = {A Typed Operational Semantics for Type Theory},

3436− year = {1994},

3437− author = {Healfdene Goguen}

3438−}

3439−

3440−@article{ph-universes,

3441− journal = {Theoretical Computer Science},

3442− number = {1},

3443− volume = {89},

3444− title = {Type Checking With Universes},

3445− year = {1991},

3446− pages = {107--136},

3447− author = {Robert Harper and Randy Pollack}

3448−}

3449−

3450−@inproceedings{pm-compile,

3451− month = {September},

3452− title = {Compiling Pattern Matching},

3453− year = {1985},

3454− booktitle = {Functional Programming Languages and Computer Architecture},

3455− pages = {368--381},

3456− editor = {Jean-Pierre Jouannaud},

3457− publisher = {Springer-Verlag},

3458− author = {Lennart Augustsson}

3459−}

3460−

3461−@phdthesis{lena-thesis,

3462− school = {Chalmers University of Technology, G\"{o}teborg},

3463− title = {The implementation of {ALF} -- A Proof Editor based on {Martin-L\"{o}f}'s Monomorphic Type Theory with Explicit Substitutions},

3464− year = {1994},

3465− author = {Lena Magnusson}

3466−}

3467−

3468−@article{view-left,

3469− journal = {Journal of Functional Programming},

3470− number = {1},

3471− volume = {14},

3472− title = {The View From The Left},

3473− year = {2004},

3474− author = {Conor McBride and James McKinna},

3475− pages = {69--111}

3476−}

3477−

3478−@inproceedings{not-a-number,

3479− author = {Conor McBride and James McKinna},

3480− title = {I am not a number, {I} am a free variable},

3481− year = {2004},

3482− booktitle = {Proceedings of the {ACM} {SIGPLAN} Haskell Workshop}

3483−}

3484−

3485−

3486−@misc{profiling,

3487− title = {Time and Space Profiling for Non-Strict, Higher Order Functional Languages},

3488− year = {1995},

3489− author = {Patrick M. Sansom and Simon {Peyton Jones}}

3490−}

3491−

3492−@inbook{pattern-matching,

3493− title = {The Implementation of Functional Programming Languages},

3494− year = {1987},

3495− booktitle = {The Implementation of Functional Programming Languages},

3496− pages = {78--103},

3497− editor = {Simon {Peyton Jones}},

3498− chapter = {5},

3499− publisher = {Prentice Hall},

3500− author = {Philip Wadler},

3501− crossref = {pj-imp}

3502−}

3503−

3504−@article{pe-problems,

3505− author = {Jones, N. D.},

3506− title = {Challenging problems in partial evaluation and mixed computation},

3507− journal = {New Gen. Comput.},

3508− volume = {6},

3509− number = {2-3},

3510− year = {1988},

3511− issn = {0288-3635},

3512− pages = {291--302},

3513− doi = {http://dx.doi.org/10.1007/BF03037143},

3514− publisher = {Ohmsha},

3515− address = {Tokyo, Japan, Japan},

3516− }

3517−

3518−@inproceedings{tag-elim,

3519− title = {Tag Elimination -- or -- Type Specialisation is a Type Indexed Effect},

3520− year = {2000},

3521− booktitle = {Subtyping and Dependent Types in Programming, APPSEM Workshop},

3522− author = {Walid Taha and Henning Makholm}

3523−}

3524−

3525−@inproceedings{extraction-coq,

3526− title = {A New Extraction for {Coq}},

3527− year = {2002},

3528− booktitle = {Types for proofs and programs},

3529− editor = {Herman Geuvers and Freek Wiedijk},

3530− publisher = {Springer},

3531− author = {Pierre Letouzey},

3532− series = {LNCS}

3533−}

3534−

3535−@phdthesis{mcbride-snr-thesis,

3536− school = {Queen's University of Belfast},

3537− title = {Computer Aided Manipulation of Symbols},

3538− year = {1970},

3539− author = {Fred McBride}

3540−}

3541−

3542−@article{ho-strictness,

3543− journal = {Science of Computer Programming},

3544− volume = {7},

3545− title = {Strictness analysis for higher-order functions},

3546− year = {1986},

3547− pages = {249--278},

3548− author = { Geoffrey L. Burn and Chris Hankin and Samson Abramsky}

3549−}

3550−

3551−@phdthesis{mycroft-thesis,

3552− school = {Dept Computer Science, University of Edinburgh},

3553− title = {Abstract interpretation and optimising transformations for applicative programs},

3554− year = {1981},

3555− author = {A. Mycroft}

3556−}

3557−

3558−@inproceedings{bc-nested,

3559− month = {September},

3560− volume = {2152},

3561− title = {Nested General Recursion and Partiality in Type Theory},

3562− year = {2001},

3563− booktitle = {Theorem Proving In Higher Order Logics: 14th International Conferences, TPHOLS 2001},

3564− pages = {121--135},

3565− publisher = {Springer--Verlag},

3566− author = {Ana Bove and Venanzio Capretta},

3567− series = {LNCS}

3568−}

3569−

3570−@techreport{bove-mutual,

3571− month = {May},

3572− title = {Mutual General Recursion in Type Theory},

3573− year = {2002},

3574− institution = {Department of Computing Science, Chalmers University of Technology},

3575− author = {Ana Bove}

3576−}

3577−

3578−@article{berardi-pruning,

3579− journal = {Journal of Logic and Computation},

3580− number = {5},

3581− volume = {6},

3582− title = {Pruning Simply Typed Lambda Terms},

3583− year = {1996},

3584− pages = {663--681},

3585− author = {Stefano Berardi}

3586−}

3587−

3588−@article{milner-tc,

3589− journal = {Journal of Computer and System Science},

3590− volume = {17},

3591− title = {A Theory of Type Polymorphism in Programming},

3592− year = {1978},

3593− pages = {348--75},

3594− author = {R. Milner}

3595−}

3596−

3597−@inproceedings{extt,

3598− title = {Inductive Families Need Not Store Their Indices},

3599− year = {2004},

3600− booktitle = {Types for Proofs and Programs 2003},

3601− author = {Edwin Brady and Conor McBride and James McKinna},

3602− editor = {Stefano Berardi and Mario Coppo and Ferruccio Damiani},

3603− series = {Lecture Notes in Computer Science},

3604− publisher = {Springer},

3605− volume = {3085},

3606− pages = {115--129}

3607−}

3608−

3609−@book{luo94,

3610− title = {Computation and Reasoning -- A Type Theory for Computer Science},

3611− year = {1994},

3612− publisher = {OUP},

3613− author = {Zhaohui Luo},

3614− series = {Intl. Series of Monographs on Comp. Sci.}

3615−}

3616−

3617−@article{backus78,

3618− journal = {Communications of the {ACM}},

3619− month = {August},

3620− volume = {21},

3621− title = {Can Programming Be Liberated From the {Von Neumann} Style?},

3622− year = {1978},

3623− pages = {280--294},

3624− author = {John Backus}

3625−}

3626−

3627−@misc{henk,

3628− month = {May},

3629− title = {Henk: A Typed Intermediate Language},

3630− year = {1997},

3631− author = {Simon {Peyton Jones} and Erik Meijer}

3632−}

3633−

3634−@article{thunks,

3635− journal = {Journal of Functional Programming},

3636− number = {3},

3637− month = {May},

3638− volume = {7},

3639− title = {Thunks and the $\lambda$-calculus},

3640− year = {1997},

3641− pages = {303--319},

3642− author = {John Hatcliff and Olivier Danvy}

3643−}

3644−

3645−@inproceedings{grin-project,

3646− author = "Urban Boquist and Thomas Johnsson",

3647− title = "The {GRIN} Project: A Highly Optimising Back End for Lazy Functional Languages",

3648− booktitle = "Implementation of Functional Languages",

3649− pages = "58--84",

3650− year = "1996",

3651− url = "citeseer.ist.psu.edu/boquist96grin.html" }

3652−

3653−@misc{boehm-gc,

3654− nothowpublished = {\url{http://www.hpl.hp.com/personal/Hans_Boehm/gc/}},

3655− title = {A garbage collector for {C} and {C++}},

3656− year = {2001},

3657− author = {Hans-J. Boehm and Alan J. Demers and {Xerox Corporation Silicon Graphic} and {Hewlett-Packard Company}}

3658−}

3659−

3660−@misc{art-interpreter,

3661− month = {May},

3662− title = {The Art of the Interpreter or, the Modularity Complex (Parts Zero, One, and Two)},

3663− year = {1978},

3664− author = {Guy Lewis {Steele, Jr.} and Gerald Jay Sussman},

3665− note = {MIT AI Lab. AI Lab Memo AIM-453}

3666−}

3667−

3668−@inproceedings{gimenez,

3669− title = {Codifying Guarded Definitions With Recursive Schemes},

3670− year = {1994},

3671− booktitle = {Proceedings of TYPES 1994},

3672− pages = {39--59},

3673− author = {Eduardo Gim\'{e}nez}

3674−}

3675−

3676−@manual{ghc-manual,

3677− title = {The Glasgow Haskell Compiler User's Guide, Version 6.0},

3678− year = {2003},

3679− author = {The {GHC Team}}

3680−}

3681−

3682−@article{rbtree,

3683− journal = {Journal of Functional Programming},

3684− number = {4},

3685− month = {May},

3686− volume = {9},

3687− title = {Red-Black Trees In A Functional Setting},

3688− year = {1999},

3689− pages = {471--477},

3690− author = {Chris Okasaki}

3691−}

3692−

3693−@inproceedings{dt-data,

3694−author = "Hongwei Xi",

3695−title = {{Dependently Typed Data Structures}},

3696−booktitle = "Proceedings of Workshop of Algorithmic Aspects of Advanced Programming Languages (WAAAPL '99)",

3697−year = 1999,

3698−month = "September",

3699−pages = "17--32",

3700−address = "Paris",

3701−}

3702−

3703−@misc{krivine,

3704− title = {On the Correctness and Efficiency of the {Krivine} Machine},

3705− year = {2003},

3706− month = {October},

3707− author = {Mitchell Wand and Daniel P. Friedman},

3708− howpublished = {Submitted for publication}

3709− }

3710−

3711−@inproceedings{nbe-filinski,

3712− title = {Normalization by Evaluation for the Computational Lambda-Calculus},

3713− year = {2001},

3714− month = {May},

3715− booktitle = {Typed Lambda Calculi and Applications: 5th International Conference, TLCA 2001},

3716− author = {Andrzej Filinski},

3717− pages = {151--165},

3718− publisher = {Springer-Verlag},

3719− series = {LNCS},

3720− volume = {2044}

3721−}

3722−

3723−@inproceedings{filinski-nbesem,

3724− title = {A semantic account of type-directed partial evaluation},

3725− year = {1999},

3726− author = {Andrzej Filinski},

3727− editor = {G. Nadathur},

3728− booktitle = {International Conference on Principles and Practice of Declarative Programming},

3729− volume = {1702},

3730− series = {LNCS},

3731− pages = {378--395},

3732− publisher = {Springer-Verlag}

3733−}

3734−

3735−@article{secd,

3736− title = {The mechanical evaluation of expressions},

3737− author = {P.J. Landin},

3738− year = {1964},

3739− journal = {Computer Journal},

3740− volume = {6},

3741− pages = {308--320}

3742−}

3743−

3744−@misc{lispkit,

3745− title = {The {LispKit} Manual},

3746− author = {Peter Henderson and Geraint Jones and Simon Jones},

3747− year = {1982},

3748− howpublished = {Oxford University Computing Laboratory}

3749−}

3750−

3751−@inproceedings{wells-undecidable,

3752− title = {Typability and Type Checking in the Second-order $\lambda$-calculus are equivalent and undecidable},

3753− author = {J. Wells},

3754− year = {1994},

3755− month = {July},

3756− booktitle = {Proc. 9th Ann. {IEEE} Symp. Logic Comput. Sci.}

3757−}

3758−

3759−@misc{patguards,

3760− title = {Pattern Guards and Transformational Patterns},

3761− author = {Martin Erwig and Simon {Peyton Jones}},

3762− year = {2000},

3763− howpublished = {Haskell Workshop}

3764−}

3765−

3766−@misc{alfa-manual,

3767− title = {Alfa Users' Guide},

3768− author = {Thomas Hallgren},

3769− year = {2001},

3770− howpublished = {Available from \verb+http://www.cs.chalmers.se/~hallgren/Alfa/+}

3771−}

3772−

3773−@inproceedings{nofib,

3774− title = {The nofib Benchmark Suite of {Haskell} Programs},

3775− author = {Will Partain},

3776− year = {1992},

3777− booktitle = {Functional Programming},

3778− editor = {J. Launchbury and P.L. Sansom},

3779− series = {Workshops in Computing},

3780− publisher = {Springer Verlag}

3781−}

3782−

3783−@article{shape,

3784− title = {Shape in Computing},

3785− author = {Barry Jay},

3786− journal = "{{ACM}} Computing Surveys",

3787− year = "1996",

3788− volume = "28",

3789− number = "2",

3790− pages = "355--357",

3791−}

3792−

3793−@misc{ffi,

3794− title = {The {Haskell 98} Foreign Function Interface 1.0: An Addendum to the {Haskell 98} Report},

3795− editor = {Manuel Chakravarty},

3796− key = {FFI},

3797− year = {2002},

3798− month = {December},

3799− howpublished = {Available from \verb+http://www.haskell.org/+}

3800−}

3801−

3802−@misc{perlxs,

3803− title = {Perl {XS} Reference Manual},

3804− author = {Dean Roehrich and {The Perl Porters}},

3805− year = {1996},

3806− howpublished = {\verb+http://www.perldoc.com/perl5.6/pod/perlxs.html+}

3807−}

3808−

3809−@misc{swig,

3810− title = {{SWIG} : An Easy to Use Tool for Integrating Scripting Languages with {C} and {C++}},

3811− author = {David M. Beazley},

3812− year = {1996},

3813− howpublished = {\verb+http://www.swig.org/papers/Tcl96/tcl96.html+}

3814−}

3815−

3816−@inproceedings{types-prog,

3817− title = {Type Systems for Programming Languages},

3818− booktitle = {Handbook of Theoretical Computer Science},

3819− author = {John C. Mitchell},

3820− pages = {365--458},

3821− year = {1990},

3822− crossref = {htcs}

3823−}

3824−

3825−@book{htcs,

3826− title = {Handbook of Theoretical Computer Science},

3827− editor = {J. van Leeuwen},

3828− publisher = {Elsevier Science},

3829− year = {1990}

3830−}

3831−

3832−@misc{r5rs,

3833− title = {Revised$^5$ Report on the Algorithmic Language Scheme},

3834− author = {Richard Kelsey and William Clinger and Jonathan Rees},

3835− year = {1998},

3836− month = {February},

3837− howpublished = {Available from \verb+http://www.schemers.org/+}

3838− }

3839−

3840−@misc{gmail-outage,

3841− title = {Update on today's {Gmail} Outage},

3842− author = {{Official Gmail Blog}},

3843− howpublished = {\url{http://gmailblog.blogspot.com/2009/02/update-on-todays-gmail-outage.html}},

3844− note = {Retrieved 26th February 2009},

3845− year = 2009

3846−}

papers/impl-paper/macros.ltxdeleted−1066

@@ -1,1066 +0,0 @@

1−%\usepackage{amstex}

2−\usepackage{amssymb}

3−\usepackage{latexsym}

4−\usepackage{eepic}

5−

6−

7−%%%%%%%%% INFERENCE RULES

8−

9−\newlength{\rulevgap}

10−\setlength{\rulevgap}{0.05in}

11−\newlength{\ruleheight}

12−\newlength{\ruledepth}

13−\newsavebox{\rulebox}

14−\newlength{\GapLength}

15−\newcommand{\gap}[1]{\settowidth{\GapLength}{#1} \hspace*{\GapLength}}

16−\newcommand{\dotstep}[2]{\begin{tabular}[b]{@{}c@{}}

17− #1\\$\vdots$\\#2

18− \end{tabular}}

19−\newlength{\fracwid}

20−\newcommand{\dotfrac}[2]{\settowidth{\fracwid}{$\frac{#1}{#2}$}

21− \addtolength{\fracwid}{0.1in}

22− \begin{tabular}[b]{@{}c@{}}

23− $#1$\\

24− \parbox[c][0.02in][t]{\fracwid}{\dotfill} \\

25− $#2$\\

26− \end{tabular}}

27−\newcommand{\Rule}[2]{\savebox{\rulebox}[\width][b] %

28− {$ \frac{\raisebox{0in} {\( #1 $}} %

29− {\raisebox{-0.03in}{$ #2 $}} \)} %

30− \settoheight{\ruleheight}{\usebox{\rulebox}} %

31− \addtolength{\ruleheight}{\rulevgap} %

32− \settodepth{\ruledepth}{\usebox{\rulebox}} %

33− \addtolength{\ruledepth}{\rulevgap} %

34− \raisebox{0in}[\ruleheight][\ruledepth] %

35− {\usebox{\rulebox}}}

36−\newcommand{\Case}[2]{\savebox{\rulebox}[\width][b] %

37− {$ \dotfrac{\raisebox{0in} {\( #1 $}} %

38− {\raisebox{-0.03in}{$ #2 $}} \)} %

39− \settoheight{\ruleheight}{\usebox{\rulebox}} %

40− \addtolength{\ruleheight}{\rulevgap} %

41− \settodepth{\ruledepth}{\usebox{\rulebox}} %

42− \addtolength{\ruledepth}{\rulevgap} %

43− \raisebox{0in}[\ruleheight][\ruledepth] %

44− {\usebox{\rulebox}}}

45−\newcommand{\Axiom}[1]{\savebox{\rulebox}[\width][b] %

46− {$\frac{}{\raisebox{-0.03in}{$#1$}}$} %

47− \settoheight{\ruleheight}{\usebox{\rulebox}} %

48− \addtolength{\ruleheight}{\rulevgap} %

49− \settodepth{\ruledepth}{\usebox{\rulebox}} %

50− \addtolength{\ruledepth}{\rulevgap} %

51− \raisebox{0in}[\ruleheight][\ruledepth] %

52− {\usebox{\rulebox}}}

53−\newcommand{\RuleSide}[3]{\gap{$#2$} \hspace*{0.1in} %

54− \Rule{#1}{#3} %

55− \hspace*{0.1in}$#2$}

56−\newcommand{\AxiomSide}[2]{\gap{$#1$} \hspace*{0.1in} %

57− \Axiom{#2} %

58− \hspace*{0.1in}$#1$}

59−\newcommand{\RULE}[1]{\textbf{#1}}

60−\newcommand{\hg}{\hspace{0.2in}}

61−

62−\newcommand{\ProofState}

63− [2]{\parbox{10cm}{\AR{\hg\AR{#1}\\\Axiom{\hg#2\hg}}}}

64−

65−%%%%%%%%%%%% TRISTUFF

66−

67−\newcommand{\btr}{

68−\setlength{\unitlength}{0.0005in}

69−\begin{picture}(69,180)(0,12)

70−\blacken\path(57,192)(57,12)(12,102)

71− (57,192)(57,192)

72−\path(57,192)(57,12)(12,102)

73− (57,192)(57,192)

74−\end{picture}

75−}

76−

77−\newcommand{\btl}{

78−\setlength{\unitlength}{0.0005in}

79−\begin{picture}(69,180)(0,12)

80−\blacken\path(12,192)(12,12)(57,102)

81− (12,192)(12,192)

82−\path(12,192)(12,12)(57,102)

83− (12,192)(12,192)

84−\end{picture}

85−}

86−

87−\newcommand{\wtr}{

88−\setlength{\unitlength}{0.0005in}

89−\begin{picture}(69,180)(0,12)

90−%\blacken\path(57,192)(57,12)(12,102)

91−% (57,192)(57,192)

92−\path(57,192)(57,12)(12,102)

93− (57,192)(57,192)

94−\end{picture}

95−}

96−

97−\newcommand{\wtl}{

98−\setlength{\unitlength}{0.0005in}

99−\begin{picture}(69,180)(0,12)

100−%\blacken\path(12,192)(12,12)(57,102)

101−% (12,192)(12,192)

102−\path(12,192)(12,12)(57,102)

103− (12,192)(12,192)

104−\end{picture}

105−}

106−

107−

108−

109−%%%%%%%%%%%% FONTS

110−

111−\newcommand{\TC}[1]{\mathtt{#1}}

112−\newcommand{\DC}[1]{\mathtt{#1}}

113−\newcommand{\VV}[1]{\mathit{#1}}

114−\newcommand{\FN}[1]{\mathtt{#1}}

115−\newcommand{\HFN}[1]{\mathtt{#1}}

116−\newcommand{\RW}[1]{\underline{\textrm{#1}}}

117−\newcommand{\MO}[1]{\mbox{\textsc{#1}}}

118−

119−\newcommand{\tTC}[1]{\texttt{#1}}

120−\newcommand{\tDC}[1]{\texttt{#1}}

121−\newcommand{\tFN}[1]{\texttt{#1}}

122−

123−\newcommand{\HF}[1]{\mathtt{#1}}

124−

125−\newcommand{\MV}[1]{\nhole\mathit{#1}}

126−\newcommand{\Lang}[1]{\mathsf{#1}}

127−\newcommand{\Name}[1]{\mathit{#1}}

128−

129−\newcommand{\demph}[1]{\textbf{#1}}

130−\newcommand{\remph}[1]{\emph{#1}}

131−

132−%%%% Keywords for meta operations

133−\newcommand{\IF}{\;\RW{if}\;\;}

134−\newcommand{\THEN}{\RW{then}}

135−\newcommand{\ELSE}{\RW{else}}

136−\newcommand{\AND}{\RW{and}}

137−\newcommand{\Otherwise}{\RW{otherwise}}

138−\newcommand{\Do}{\RW{do}}

139−\newcommand{\Return}{\RW{return}}

140−

141−\newcommand{\CASE}{\RW{case}}

142−\newcommand{\LET}{\RW{let}}

143−\newcommand{\IN}{\RW{in}}

144−\newcommand{\of}{\RW{of}}

145−

146−\newcommand{\CLASS}{\mathtt{class}}

147−\newcommand{\INSTANCE}{\mathtt{instance}}

148−

149−%%%%%%%%%%%% GROUPING

150−

151−\newcommand{\G}{

152−\setlength{\unitlength}{1pt}

153−\begin{picture}(4,10)(0,0)

154−\path(2,10)(2,-10)

155−\end{picture}

156−}

157−

158−\newcommand{\E}{

159−\setlength{\unitlength}{1pt}

160−\begin{picture}(4,10)(0,0)

161−\path(2,10)(2,-2)(4,-2)

162−\end{picture}

163−}

164−

165−%\newcommand{\C}{

166−%\setlength{\unitlength}{1pt}

167−%\begin{picture}(4,10)(0,0)

168−%\path(4,8)(2,8)(2,-2)(4,-2)

169−%\end{picture}

170−%}

171−

172−\newcommand{\M}{

173−\setlength{\unitlength}{1pt}

174−\begin{picture}(4,10)(0,0)

175−\path(2,10)(2,-2)(6,-2)

176−\end{picture}

177−}

178−

179−\newcommand{\F}{

180−\setlength{\unitlength}{1pt}

181−\begin{picture}(4,10)(0,0)

182−\path(4,8)(2,8)(2,-6)

183−\end{picture}

184−}

185−

186−\newcommand{\K}{

187−\setlength{\unitlength}{1pt}

188−\begin{picture}(4,10)(0,0)

189−\path(0,8)(4,8)

190−\end{picture}

191−}

192−

193−\newcommand{\J}{

194−\setlength{\unitlength}{1pt}

195−\begin{picture}(4,10)(0,0)

196−\path(0,-2)(4,-2)

197−\end{picture}

198−}

199−

200−\newcommand{\W}{

201−\setlength{\unitlength}{1pt}

202−\begin{picture}(4,10)(0,0)

203−\end{picture}

204−}

205−

206−

207−

208−%%%%%%%%%%%% GUBBINS

209−

210−\newcommand{\mathskip}{\medskip}

211−

212−\newcommand{\fbx}[1]{\fbox{$#1$}}

213−\newcommand{\stk}[1]{\begin{array}{c}#1\end{array}}

214−%\newcommand{\DM}[1]{\hg\mbox{$#1$}}

215−\newcommand{\DM}[1]{\mathskip\par$#1$\mathskip}

216−\newcommand{\mbx}[1]{\mathskip\par\noindent$#1$\mathskip}

217−\newcommand{\AR}[1]{\begin{array}[t]{@{}l}#1\end{array}}

218−\newcommand{\ARt}[1]{\begin{array}[t]{@{}l@{}cl}#1\end{array}}

219−\newcommand{\ARc}[1]{\begin{array}{@{}l}#1\end{array}}

220−\newcommand{\ARd}[1]{\begin{array}[t]{cl}#1\end{array}}

221−\newcommand{\DAR}[1]{\begin{array}{ll}\hg & #1\end{array}}

222−\newcommand{\Dor}{\\ \hg\mid & }

223−\newcommand{\EA}[1]{\begin{array}[t]{r@{}c@{}l}#1\end{array}}

224−\newcommand{\A}{@{\:}c}

225−%\newcommand{\R}{@{\:}r}

226−\newcommand{\CA}{c}

227−\newcommand{\LA}{l}

228−\newcommand{\PAc}[2]{\begin{array}{l#1@{}r@{}l}#2\end{array}}

229−\newcommand{\PA}[2]{\begin{array}[t]{l@{\:}l#1@{}r@{\:}l}#2\end{array}}

230−\newcommand{\DTREE}[3]{\begin{array}[t]{l#1@{}r@{\:}l#2}#3\end{array}}

231−\newcommand{\IDTREE}[2]{%

232− \begin{array}[t]{l@{\:}c@{\:}l@{\:}r@{\:}l#1}#2\end{array}}

233−\newcommand{\IA}[2]

234− {\begin{array}[t]{l@{\:}r@{\:}c@{\:}l@{\:}#1@{\:}r@{\:}l}#2\end{array}}

235−\newcommand{\IAc}[2]

236− {\begin{array}[c]{r@{\:}c@{\:}l@{\:}#1@{}r@{}l}#2\end{array}}

237−\newcommand{\CS}[1]{\left\lfloor\begin{array}{@{}l}#1\end{array}\right.}

238−\newcommand{\BY}[3]{\multicolumn{2}{l}{\;\RW{by}\; #1} \\ %

239− \multicolumn{#2}{l}{\CS{#3}} }

240−\newcommand{\WITH}[3]{\multicolumn{2}{l}{\;\RW{with}\; #1} \\ %

241− \multicolumn{#2}{l}{\CS{#3}} }

242−\newcommand{\WithBy}{\RW{with-by}}

243−\newcommand{\Wb}[1]{\WithBy& #1}

244−\newcommand{\By}[1]{\multicolumn{2}{l}{\Leftarrow #1}}

245−\newcommand{\andby}{\Leftarrow}

246−\newcommand{\MyWith}[1]{\multicolumn{2}{l}{|\;#1}}

247−\newcommand{\Byr}[1]{\;\RW{by}\; #1}

248−

249−\renewcommand{\Bar}{|}

250−\newcommand{\Bart}{\settowidth{\GapLength}{$\Bar$}%

251− \raisebox{6pt}[0pt][0pt]{$\Bar$}%

252− \hspace*{-1\GapLength}%

253− \Bar}

254−\newcommand{\With}[1]{\Bar & #1}

255−\newcommand{\Witt}[1]{\Bart & #1}

256−

257−\newcommand{\B}{@{\:}r@{\:}c}

258−\newcommand{\Ret}[1]{\multicolumn{2}{l}{\cq #1}}

259−\newcommand{\MRet}[2]{\multicolumn{#1}{l}{\cq #2}}

260−\newcommand{\HRet}[1]{\multicolumn{2}{l}{\hq #1}}

261−\newcommand{\MHRet}[2]{\multicolumn{#1}{l}{\hq #2}}

262−\newcommand{\IRet}[1]{\multicolumn{2}{l}{\iq #1}}

263−\newcommand{\IMRet}[2]{\multicolumn{#1}{l}{\iq #2}}

264−\newcommand{\MoRet}[1]{\multicolumn{2}{l}{= #1}}

265−\newcommand{\MMoRet}[2]{\multicolumn{#1}{l}{\mq #2}}

266−\newcommand{\Data}{\RW{data}}

267−\newcommand{\Codata}{\RW{codata}}

268−\newcommand{\Where}{\RW{where}}

269−\newcommand{\Let}{\RW{let}}

270−\newcommand{\Fact}{\RW{fact}}

271−\newcommand{\Rec}[1]{#1\textbf{-Rec}}

272−\newcommand{\Memo}[1]{#1\textbf{-Memo}}

273−\newcommand{\Elim}[1]{#1\textbf{-Elim}}

274−\newcommand{\Cases}[1]{#1\textbf{-Case}}

275−\newcommand{\View}[1]{#1\textbf{-View}}

276−\newcommand{\As}[2]{#1 \:\RW{as}\: #2}

277−\newcommand{\nhole}{\Box}

278−\newcommand{\turq}{\:\vdash_?\:}

279−\renewcommand{\split}{\;\lhd\;}

280−\newcommand{\CType}[2]{\{#1 \split\; #2\}}

281−\newcommand{\CC}[2]{(#1)\:#2}

282−\newcommand{\UP}[2]{#1 | \{#2\}}

283−\newcommand{\Ured}{\:\Downarrow\:}

284−\newcommand{\gdd}{\prec}

285−\newcommand{\HC}[1]{\left<#1\right>}

286−\newcommand{\HT}[2]{\left<#1 \hab #2\right>}

287−

288−\newcommand{\view}{\RW{view}}

289−\newcommand{\ecase}{\RW{case}}

290−\newcommand{\rec}{\RW{rec}}

291−

292−\newcommand{\If}{\mathsf{if}}

293−\newcommand{\Then}{\mathsf{then}}

294−\newcommand{\Else}{\mathsf{else}}

295−\newcommand{\elim}{\RW{elim}}

296−

297−\newcommand{\Payload}{\mathsf{type}}

298−\newcommand{\Any}{\mathsf{Some}}

299−

300−\newcommand{\lbl}[2]{\langle #1 \Hab #2 \rangle}

301−\newcommand{\call}[2]{\RW{call}\:\langle#1\rangle\:#2}

302−\newcommand{\return}[1]{\RW{return}\:#1}

303−

304−\newcommand{\Remark}[1]{\noindent\textbf{Remark:} #1}

305−

306−\newcommand{\DBOX}[2]{\fbox{\parbox{#1}{\textbf{Definition:}#2}}}

307−

308−\newcommand{\useverbtb}[1]{\begin{tiny}\BUseVerbatim{#1}\end{tiny}}

309−\newcommand{\useverb}[1]{\begin{small}\BUseVerbatim{#1}\end{small}}

310−\newcommand{\useverbb}[1]{\begin{small}\BUseVerbatim{#1}\end{small}}

311−

312−\newcommand{\diagfig}[3]{\begin{figure}[h]\begin{center}\includegraphics[width=#1]{#2}\end{center}

313−\caption{#3}\label{#2}\end{figure}}

314−\newcommand{\codefig}[2]{\begin{figure}[h]\useverb{#1}\caption{#2}\label{#1}\end{figure}}

315−\newcommand{\codefigt}[2]{\begin{figure}[t]\useverb{#1}\caption{#2}\label{#1}\end{figure}}

316−\newcommand{\codefigb}[2]{\begin{figure}[b]\useverb{#1}\caption{#2}\label{#1}\end{figure}}

317−\newcommand{\codefigtc}[2]{\begin{figure*}[t]\useverb{#1}\caption{#2}\label{#1}\end{figure}}

318−\newcommand{\diagfigtc}[3]{\begin{figure*}[t]\begin{center}\includegraphics[width=#1]{#2}\end{center}

319−\caption{#3}\label{#2}\end{figure*}}

320−

321−\newcommand{\FIG}[3]{\begin{figure}[h]\DM{#1}\caption{#2}\label{#3}\end{figure}}

322−\newcommand{\FFIG}[3]{\begin{figure}\begin{center}\DM{#1}\end{center}\caption{#2}\label{#3}\end{figure}}

323−\newcommand{\FFIGB}[3]{\begin{figure}[b]\begin{center}\DM{#1}\end{center}\caption{#2}\label{#3}\end{figure}}

324−\newcommand{\FFIGTC}[3]{\begin{figure*}[t]\begin{center}\DM{#1}\end{center}\caption{#2}\label{#3}\end{figure*}}

325−\newcommand{\VFIG}[3]{\begin{figure}[h]\begin{boxedverbatim}#1\end{boxedverbatim}\caption{#2}\label{#3}\end{figure}}

326−\newcommand{\PFIG}[3]{\begin{figure}[p]\begin{center}\fbox{\DM{#1}}\end{center}\caption{#2}\label{#3}\end{figure}}

327−\newcommand{\CFIG}[3]{\begin{figure}[h]\begin{center}\DM{#1}\end{center}\caption{#2}\label{#3}\end{figure}}

328−

329−\newcommand{\TFIG}[4]{\begin{figure}[h]\begin{center}\begin{tabular}{#1}#2\end{tabular}\end{center}\caption{#3}\label{#4}\end{figure}}

330−\newcommand{\TFIGTC}[4]{\begin{figure*}[t]\begin{center}\begin{tabular}{#1}#2\end{tabular}\end{center}\caption{#3}\label{#4}\end{figure*}}

331−

332−\newcommand{\RESFIG}[3]{

333−\TFIG{|l|c|c|c|c|c|c|c|c|}{

334−\hline

335− & \multicolumn{4}{c|}{\Naive{} compilation} &

336− \multicolumn{4}{|c|}{Optimised compilation} \\

337−\cline{2-9}

338−\raisebox{1.5ex}[0pt]{Program} & Instrs & Thunks & Cells &

339−Accesses & Instructions & Thunks & Cells & Accesses \\

340−%\raisebox{1.5ex}[0pt]{Program} & I & T & C & M & I & T & C & M \\

341−\hline

342−#1

343−\hline

344−}{#2}{#3}}

345−

346−\newcommand{\NEWRESFIG}[3]{

347−\TFIG{|l|l|c|c|c|c|}{

348−\hline

349−% & \multicolumn{4}{c|}{\Naive{} compilation} &

350−% \multicolumn{4}{|c|}{Optimised compilation} \\

351−%\cline{2-9}

352−Program & Version & Instructions & Thunks & Memory Accesses & Cells \\

353−%\raisebox{1.5ex}[0pt]{Program} & I & T & C & M & I & T & C & M \\

354−\hline

355−#1

356−}{#2}{#3}}

357−

358−\newcommand{\NEWRESFIGTC}[3]{

359−\TFIGTC{|l|l|c|c|c|c|}{

360−\hline

361−% & \multicolumn{4}{c|}{\Naive{} compilation} &

362−% \multicolumn{4}{|c|}{Optimised compilation} \\

363−%\cline{2-9}

364−Program & Version & Instructions & Thunks & Memory Accesses & Cells \\

365−%\raisebox{1.5ex}[0pt]{Program} & I & T & C & M & I & T & C & M \\

366−\hline

367−#1

368−}{#2}{#3}}

369−

370−\newcommand{\RESLINE}[9]{

371−& \Naive{} & #2 & #3 & #5 & #4 \\

372−#1

373−& Optimised & #6 & #7 & #9 & #8 \\

374−}

375−\newcommand{\RESCHANGE}[4]{

376−& Change & \textbf{#1} & \textbf{#2} & \textbf{#4} & \textbf{#3} \\

377−\hline

378−}

379−\newcommand{\RESCHANGEa}[5]{

380−#5 & Change & \textbf{#1} & \textbf{#2} & \textbf{#4} & \textbf{#3} \\

381−\hline

382−}

383−

384−%%%%%%%%%%%% PUNCTUATION

385−

386−\newcommand{\pad}[2]{#1#2#1}

387−

388−\newcommand{\hab}{\pad{\,}{:}}

389−\newcommand{\Hab}{\pad{\;}{:}}

390−\newcommand{\HHab}{\pad{\;}{::}}

391−

392−%%%%%%%%%%%% TYPE

393−

394−\newcommand{\Type}{\mbox{\texttt{Type}}} %\star}

395−

396−

397−%%%%%%%%%%%%% ARROWS

398−

399−\newcommand{\To}{\pad{\:}{\rightarrow}}

400−\newcommand{\Gets}{\leftarrow}

401−%\newcommand{\car}{\vartriangleright}

402−

403−%%%%%%%%%%%%% QUANTIFIERS

404−

405−\newcommand{\lam}[2]{\lambda#1\pad{\!}{:}#2}

406−\newcommand{\fbind}[3]{(#1\Hab#2)\to#3}

407−\newcommand{\all}[2]{\forall#1\pad{\!}{:}#2}

408−\newcommand{\pat}[2]{\RW{var}\:#1\pad{\!}{:}#2}

409−\newcommand{\pty}[2]{\RW{pty}\:#1\pad{\!}{:}#2}

410−\newcommand{\hole}[2]{?#1\pad{\!}{:}#2}

411−\newcommand{\guess}[3]{?#1\pad{\!}\approx#3{:}#2}

412−\newcommand{\remlam}[2]{\lambda\{#1\pad{\!}{:}#2\}}

413−\newcommand{\remall}[2]{\forall\{#1\pad{\!}{:}#2\}}

414−\newcommand{\allpi}[2]{\Pi#1\pad{\!}{:}#2}

415−\newcommand{\ali}[2]{\forall#1|#2}

416−\newcommand{\exi}[2]{\exists#1\pad{\!}{:}#2}

417−\newcommand{\wit}[2]{\ang{#1,#2}}

418−\newcommand{\X}{\times}

419−\newcommand{\sig}[2]{\Sigma#1\pad{\!}{:}#2}

420−

421−\newcommand{\SC}{.\:}

422−

423−\newcommand{\letbind}[3]{\mathsf{let}\:#1{:}#2\:=\:#3\:\mathsf{in}}

424−\newcommand{\ifthen}[3]{\mathsf{if}\:#1\:\mathsf{then}\:#2\:\mathsf{else}\:#3}

425−

426−%%%%%%%%%%%%% EQUALITIES

427−

428−\newcommand{\cq}{\pad{\:}{\mapsto}}

429−\newcommand{\xq}{\pad{}{\doteq}}

430−\newcommand{\pq}{\pad{\:}{=}}

431−\newcommand{\dq}{\pad{\:}{:=}}

432−\newcommand{\iq}{\pad{\:}{\leadsto}}

433−\newcommand{\mq}{=} %\Longrightarrow}

434−\newcommand{\retq}{\Rightarrow}

435−\newcommand{\hq}{\pad{\:}{=}}

436−\newcommand{\defq}{\mapsto}

437−

438−\newcommand{\refl}{\TC{refl}}

439−

440−

441−

442−

443−%%%%%%%%%%%%% CATSTUFF

444−

445−\newlength{\Lwibrs}

446−\newlength{\Lwobrs}

447−\newsavebox{\Bwibrs}

448−\newsavebox{\Bwobrs}

449−\newcommand{\Db}[5]{%

450− \savebox{\Bwobrs}[\width][b]{$#5$}%

451− \savebox{\Bwibrs}[\width][b]{$\left#2\usebox{\Bwobrs}\right#3$}%

452− \settowidth{\Lwobrs}{\usebox{\Bwobrs}}%

453− \settowidth{\Lwibrs}{\usebox{\Bwibrs}}%

454− \addtolength{\Lwibrs}{-\Lwobrs}%

455− \left#1\pad{\hspace*{-0.25\Lwibrs}}{\usebox{\Bwibrs}}\right#4}

456−\newcommand{\LDb}[3]{%

457− \savebox{\Bwobrs}[\width][b]{$#3$}%

458− \savebox{\Bwibrs}[\width][b]{$\left#2\usebox{\Bwobrs}\right.$}%

459− \settowidth{\Lwobrs}{\usebox{\Bwobrs}}%

460− \settowidth{\Lwibrs}{\usebox{\Bwibrs}}%

461− \addtolength{\Lwibrs}{-\Lwobrs}%

462− \left#1\hspace*{-0.4\Lwibrs}\usebox{\Bwibrs}\right.}

463−\newcommand{\RDb}[3]{%

464− \savebox{\Bwobrs}[\width][b]{$#3$}%

465− \savebox{\Bwibrs}[\width][b]{$\left.\usebox{\Bwobrs}\right#1$}%

466− \settowidth{\Lwobrs}{\usebox{\Bwobrs}}%

467− \settowidth{\Lwibrs}{\usebox{\Bwibrs}}%

468− \addtolength{\Lwibrs}{-\Lwobrs}%

469− \left.\usebox{\Bwibrs}\hspace*{-0.4\Lwibrs}\right#2}

470−\newcommand{\Sc}{\Db{[}{[}{]}{]}}

471−\newcommand{\Mo}{\Db{|}{>}{<}{|}}

472−\newcommand{\MoL}{\LDb{|}{>}}

473−\newcommand{\MoR}{\RDb{<}{|}}

474−

475−\newcommand{\car}{\mbox{$-\!\triangleright$}}

476−\newcommand{\io}[1]{\iota_{#1}}

477−\newcommand{\cc}{\diamond}

478−

479−

480−%%%%%%%%%%%%% FNS

481−

482−\newcommand{\Wk}{\Uparrow}

483−

484−%%%%%%%%%%%%% Transformation

485−

486−\newcommand{\Transform}[3]{\textsc{Trans}\:_{\Name{#1}}

487− \interp{#2}\:\mq\:#3}

488−%\:[\:#2\:\Longrightarrow\:#3\:]}

489−\newcommand{\Morphism}[2]{\textsc{Morphism}\:#1\:\Longrightarrow\:#2}

490−\newcommand{\MI}[1]{\begin{array}{ll} #1 \end{array}\\}

491−\newcommand{\MorphItem}[2]{& #1 \:\Longrightarrow\: #2}

492−

493−%%%%%%%%%%%%% Stuff

494−

495−% Motive and methods

496−

497−\newcommand{\motive}{\vP}

498−\newcommand{\meth}[1]{\vm_{#1}}

499−

500−% Tuples

501−\newcommand{\tuple}[1]{\langle#1\rangle}

502−\newcommand{\Tuple}[1]{\mathsf{Tuple}}

503−\newcommand{\proj}{\mathsf{proj}}

504−\newcommand{\app}{\mathrm{+\!+}}

505−

506−% Commenting out

507−\newcommand{\ig}[1]{[#1]}

508−\newcommand{\rem}[1]{\{\!#1\!\}}

509−\newcommand{\igc}[1]{[#1]}

510−\newcommand{\remc}[1]{\{\!#1\!\}}

511−

512−

513−\newcommand{\ind}{\hspace*{0.1cm}}

514−

515−% Content free type

516−\newcommand{\CF}{\TC{CF}}

517−\newcommand{\cf}{\DC{cf}}

518−

519−% Error token

520−\newcommand{\error}{\DC{error}}

521−\newcommand{\fail}{\perp}

522−

523−% Constructor stripping

524−\newcommand{\conarg}[2]{#1!#2}

525−

526−\newcommand{\Vect}{\TC{Vect}}

527−\newcommand{\VectM}{\TC{Vect^-}}

528−\newcommand{\Vnil}{\DC{\epsilon}}

529−\newcommand{\Vcons}{\DC{::}}

530−

531−\newcommand{\Vsnoc}{\DC{::}}

532−

533−\newcommand{\VnilM}{\DC{\epsilon^-}}

534−\newcommand{\VconsM}{\DC{::^-}}

535−

536−\newcommand{\Vnilcase}{\VV{vNilCase}}

537−\newcommand{\Vconscase}{\VV{vConsCase}}

538−

539−\newcommand{\DSigma}{\TC{Sigma}}

540−\newcommand{\Exists}{\DC{Exists}}

541−

542−\newcommand{\ListPair}[2]{\sig{#1}{\List\:\vA}.#2 = \FN{length}\:#1}

543−\newcommand{\lpNilDef}{\lpNil{\FN{refl}\:\Z}}

544−\newcommand{\lpNil}[1]{(\nil\:\vA,#1)}

545−\newcommand{\lpConsDef}[3]{\lpCons{#1}{(\FN{fst\:#2})}{\FN{resp}\:(\FN{snd}\:#2)}}

546−\newcommand{\lpCons}[3]{(\cons\:#1\:#2,#3)}

547−\newcommand{\lp}[2]{(#1, #2)}

548−

549−\newcommand{\VnilTop}{\DC{vNil}^\ast}

550−\newcommand{\VconsTop}{\DC{vCons}^\ast}

551−

552−\newcommand{\VnilBot}{\DC{\epsilon}^-}

553−\newcommand{\VconsBot}{\DC{::}^-}

554−

555−\newcommand{\VectTop}{\TC{Vect}^\ast}

556−\newcommand{\VectBot}{\TC{Vect}^-}

557−

558−\newcommand{\VectDrop}{\FN{vectDropIdx}}

559−\newcommand{\VectRebuild}{\FN{vectRebuild}}

560−

561−\newcommand{\Prop}{\TC{Prop}}

562−\newcommand{\Set}{\TC{Type}}

563−\newcommand{\CoqType}{\TC{Type}}

564−

565−\newcommand{\List}{\TC{List}}

566−\newcommand{\nil}{\DC{Nil}}

567−\newcommand{\cons}{\DC{::}}

568−

569−\newcommand{\Zip}{\TC{Tsil}}

570−\newcommand{\zip}{\FN{tsil}}

571−\newcommand{\zipcons}{\FN{tsilcons}}

572−\newcommand{\snoc}{\DC{Snoc}}

573−\newcommand{\lin}{\DC{Empty}}

574−

575−\newcommand{\BigInt}{\TC{BigInt}}

576−\newcommand{\False}{\TC{False}}

577−\newcommand{\Unit}{\TC{Unit}}

578−\newcommand{\UnitI}{\DC{unit}}

579−

580−\newcommand{\genType}{\TC{X}}

581−\newcommand{\genIndicesDec}{\tb\Hab\tB}

582−\newcommand{\genIndices}{\tb}

583−\newcommand{\genConArgsDec}[1]{\vec{\VV{a_#1}}\Hab\vec{\VV{A_#1}}}

584−\newcommand{\genConArgs}[1]{\vec{\VV{a_#1}}}

585−\newcommand{\genConIndicesDec}[1]{\vec{\VV{b_#1}}\Hab\vec{\VV{B_#1}}}

586−\newcommand{\genConIndices}[1]{\vec{\VV{b_#1}}}

587−\newcommand{\genCon}[1]{\DC{x}_#1}

588−

589−\newcommand{\genTypeTop}{\TC{X^\ast}}

590−\newcommand{\genTypeBot}{\TC{X^-}}

591−

592−\newcommand{\genTypeDrop}{\FN{XDropIdx}}

593−\newcommand{\genTypeRebuild}{\FN{XRebuild}}

594−

595−\newcommand{\HTerm}{\texttt{Term}}

596−\newcommand{\Term}{\TC{Term}}

597−\newcommand{\Var}{\DC{var}}

598−\newcommand{\Lam}{\DC{lam}}

599−\newcommand{\App}{\DC{app}}

600−\newcommand{\TermM}{\TC{Term^-}}

601−\newcommand{\VarM}{\DC{var^-}}

602−\newcommand{\LamM}{\DC{lam^-}}

603−\newcommand{\AppM}{\DC{app^-}}

604−\newcommand{\Env}{\TC{Env}}

605−\newcommand{\SType}{\TC{STy}}

606−\newcommand{\farrow}{\Rightarrow}

607−\newcommand{\lookup}{\FN{lookup}}

608−

609−\newcommand{\source}{\Lang{TT}}

610−%\newcommand{\source}{\textbf{DT-Res}}

611−\newcommand{\target}{\Lang{ExTT}}

612−\newcommand{\runtime}{\Lang{RunTT}}

613−

614−\newcommand{\lt}{\TC{<}}

615−\newcommand{\ltO}{\DC{ltO}}

616−\newcommand{\ltS}{\DC{ltS}}

617−

618−\newcommand{\interp}[1]{\llbracket #1 \rrbracket}

619−\newcommand{\inferrable}[2]{\FN{inferrable}(#1,#2)}

620−\newcommand{\mkPat}{\FN{mkPat}}

621−

622−\newcommand{\FinM}{\TC{Fin^-}}

623−\newcommand{\fzM}{\DC{f0^-}}

624−\newcommand{\fsM}{\DC{fs^-}}

625−

626−\newcommand{\concat}{\mathrm{++}}

627−

628−%\newcommand{\bottom}{\perp}

629−

630−% Reductions

631−

632−\newcommand{\reduces}{\rhd}

633−\newcommand{\translation}{\Rightarrow}

634−%\newcommand{\reducesn}[1]{\reduces\hspace*{-0.15cm}_{#1}}

635−%\newcommand{\reducesto}{\reduces\hspace*{-0.15cm}^{*}}

636−\newcommand{\reducesn}[1]{\reduces_{#1}}

637−\newcommand{\reducesto}{\reduces^{*}}

638−

639−% Equality

640−

641−\newcommand{\Refl}{\DC{refl}}

642−\newcommand{\leZ}{\DC{O_{\le}}}

643−\newcommand{\leS}{\DC{S_{\le}}}

644−

645−% Random elimination things

646−

647−\newcommand{\lte}{\TC{\leq}}

648−\newcommand{\lten}{\DC{leN}}

649−\newcommand{\lteO}{\DC{leO}}

650−\newcommand{\lteS}{\DC{leS}}

651−

652−\newcommand{\ltelim}{\Elim{\lt}}

653−\newcommand{\leelim}{\Elim{\lte}}

654−

655−\newcommand{\dD}{\TC{D}}

656−\newcommand{\delim}{\Elim{\TC{D}}}

657−\newcommand{\drec}{\Rec{\TC{D}}}

658−\newcommand{\dcase}{\Cases{\TC{D}}}

659−\newcommand{\dview}{\View{\TC{D}}}

660−\newcommand{\dmemo}{\Memo{\TC{D}}}

661−\newcommand{\natrec}{\Rec{\Nat}}

662−\newcommand{\natmemo}{\Memo{\Nat}}

663−\newcommand{\natmemogen}{\Nat\textbf{-MemoGen}}

664−\newcommand{\natelim}{\Elim{\Nat}}

665−\newcommand{\boolcase}{\Cases{\Bool}}

666−\newcommand{\vectrec}{\Rec{\Vect}}

667−\newcommand{\vectelim}{\Elim{\Vect}}

668−\newcommand{\listrec}{\Rec{\List}}

669−\newcommand{\listelim}{\Elim{\List}}

670−\newcommand{\finrec}{\Rec{\Fin}}

671−\newcommand{\finelim}{\Elim{\Fin}}

672−\newcommand{\natcase}{\Cases{\Nat}}

673−\newcommand{\vectcase}{\Cases{\Vect}}

674−\newcommand{\natdoublerec}{\Nat\textbf{-double-elim}}

675−\newcommand{\eqelim}{=\textbf{-elim}}

676−\newcommand{\falsecase}{\Cases{\False}}

677−

678−% Code

679−\newcommand{\Haskell}[1]{\begin{quotation}\begin{verbatim}#1\end{verbatim}\end{quotation}}

680−

681−% Quicksort

682−

683−\newcommand{\QSView}{\TC{QuickSort}}

684−\newcommand{\qsempty}{\DC{empty}}

685−\newcommand{\partition}{\DC{partition}}

686−\newcommand{\qsview}{\FN{mkQuickSort}}

687−

688−% More gubbins

689−

690−\newcommand{\converts}{\simeq}

691−\newcommand{\cumul}{\preceq}

692−\newcommand{\whnf}{\Downarrow}

693−\newcommand{\elem}{\in}

694−\newcommand{\proves}{\vdash}

695−\newcommand{\biimplies}{\Longleftrightarrow}

696−

697−\newcommand{\lc}{\lambda_{\mathsf{AC}}}

698−\newcommand{\zed}{\mathbb{Z}}

699−

700−% Haskell keywords

701−

702−\newcommand{\hdata}{\mathtt{data}}

703−\newcommand{\newtype}{\mathtt{newtype}}

704−%\newcommand{\htype}{\mathtt{type}}

705−

706−\newcommand{\HTC}[1]{\mathtt{#1}}

707−\newcommand{\HDC}[1]{\mathtt{#1}}

708−

709−% Nobby

710−

711−\newcommand{\Value}{\HTC{Value}}

712−\newcommand{\VGamma}{\HTC{Env}}

713−\newcommand{\Ctxt}{\HTC{Ctxt}}

714−\newcommand{\Defs}{\HTC{Defs}}

715−\newcommand{\ECtxt}{\HTC{ECtxt}}

716−\newcommand{\TCtxt}{\HTC{TCtxt}}

717−\newcommand{\VG}{\HDC{Env}}

718−\newcommand{\Model}{\HTC{Model}}

719−\newcommand{\Const}{\HTC{Const}}

720−\newcommand{\Normal}{\HTC{Normal}}

721−\newcommand{\Scope}{\HTC{Scope}}

722−\newcommand{\Kripke}{\HTC{Kripke}}

723−\newcommand{\Weakening}{\HTC{Weakening}}

724−\newcommand{\Ready}{\HTC{Ready}}

725−%\newcommand{\Blocked}{\HTC{Blocked}}

726−\newcommand{\Spine}{\HTC{Spine}}

727−

728−\newcommand{\BV}{\HDC{BV}}

729−\newcommand{\BCon}{\HDC{BCon}}

730−\newcommand{\BTyCon}{\HDC{BTyCon}}

731−\newcommand{\RCon}{\HDC{RCon}}

732−\newcommand{\RTyCon}{\HDC{RTyCon}}

733−\newcommand{\BElim}{\HDC{BElim}}

734−\newcommand{\DV}{\HDC{V}}

735−\newcommand{\DP}{\HDC{P}}

736−

737−\newcommand{\MR}{\HDC{R}}

738−\newcommand{\MB}{\HDC{B}}

739−\newcommand{\DSc}{\HDC{Sc}}

740−\newcommand{\DKr}{\HDC{Kr}}

741−\newcommand{\DWk}{\HDC{Wk}}

742−\newcommand{\DSnoc}{\HDC{;}}

743−\newcommand{\DType}{\HDC{Type}}

744−\newcommand{\DName}{\HDC{Name}}

745−\newcommand{\DInt}{\HDC{Int}}

746−\newcommand{\DString}{\HDC{String}}

747−\newcommand{\DElim}{\HDC{Elim}}

748−\newcommand{\Empty}{\HDC{\emptyset}}

749−

750−\newcommand{\ConCode}{\HTC{ConCode}}

751−\newcommand{\ElimRule}{\HTC{ElimRule}}

752−

753−\newcommand{\DConst}{\HDC{Const}}

754−\newcommand{\DCon}{\HDC{Con}}

755−\newcommand{\DTyCon}{\HDC{TyCon}}

756−\newcommand{\RConst}{\HDC{RConst}}

757−\newcommand{\RLam}{\HDC{RLam}}

758−\newcommand{\RPi}{\HDC{RPi}}

759−\newcommand{\DLam}{\HDC{Lam}}

760−\newcommand{\DLet}{\HDC{Let}}

761−\newcommand{\DPi}{\HDC{Pi}}

762−\newcommand{\DApp}{\HDC{App}}

763−

764−\newcommand{\TMaybe}{\HTC{Maybe}}

765−\newcommand{\DNothing}{\HDC{Nothing}}

766−\newcommand{\DJust}{\HDC{Just}}

767−

768−

769−% G-machine and heap

770−

771−\newcommand{\PUSH}{\mathsf{PUSH}}

772−\newcommand{\PUSHNAME}{\mathsf{PUSHNAME}}

773−\newcommand{\POP}{\mathsf{DISCARD}}

774−\newcommand{\PUSHFUN}{\mathsf{PUSHFUN}}

775−\newcommand{\APPLY}{\mathsf{MKAP}}

776−\newcommand{\EVAL}{\mathsf{EVAL}}

777−\newcommand{\GCON}{\mathsf{MKCON}}

778−\newcommand{\GTUP}{\mathsf{MKTUP}}

779−\newcommand{\GTYPE}{\mathsf{MKTYPE}}

780−\newcommand{\UPDATE}{\mathsf{UPDATE}}

781−\newcommand{\RET}{\mathsf{RET}}

782−\newcommand{\UNWIND}{\mathsf{UNWIND}}

783−\newcommand{\CASEJUMP}{\mathsf{CASEJUMP}}

784−\newcommand{\LABEL}{\mathsf{LABEL}}

785−\newcommand{\MOVE}{\mathsf{MOVE}}

786−\newcommand{\JUMP}{\mathsf{JUMP}}

787−\newcommand{\SPLIT}{\mathsf{SPLIT}}

788−\newcommand{\SQUEEZE}{\mathsf{SQUEEZE}}

789−\newcommand{\JFUN}{\mathsf{JFUN}}

790−\newcommand{\PROJ}{\mathsf{PROJ}}

791−\newcommand{\ERROR}{\mathsf{ERROR}}

792−\newcommand{\SLIDE}{\mathsf{SLIDE}}

793−\newcommand{\ALLOC}{\mathsf{ALLOC}}

794−

795−\newcommand{\PUSHBIG}{\mathsf{PUSHBIG}}

796−\newcommand{\PUSHBASIC}{\mathsf{PUSHBASIC}}

797−\newcommand{\PUSHINT}{\mathsf{PUSHINT}}

798−\newcommand{\PUSHBOOL}{\mathsf{PUSHBOOL}}

799−\newcommand{\GET}{\mathsf{GET}}

800−\newcommand{\MKINT}{\mathsf{MKINT}}

801−\newcommand{\MKBOOL}{\mathsf{MKBOOL}}

802−\newcommand{\ADD}{\mathsf{ADD}}

803−\newcommand{\SUB}{\mathsf{SUB}}

804−\newcommand{\MULT}{\mathsf{MULT}}

805−\newcommand{\LT}{\mathsf{LT}}

806−\newcommand{\EQ}{\mathsf{EQ}}

807−\newcommand{\GT}{\mathsf{GT}}

808−\newcommand{\JTRUE}{\mathsf{JTRUE}}

809−

810−\newcommand{\APP}{\mathsf{APP}}

811−\newcommand{\FUN}{\mathsf{FUN}}

812−\newcommand{\CON}{\mathsf{CON}}

813−\newcommand{\TYCON}{\mathsf{TYCON}}

814−\newcommand{\TUP}{\mathsf{TUP}}

815−\newcommand{\TYPE}{\mathsf{TYPE}}

816−\newcommand{\INT}{\mathsf{INT}}

817−\newcommand{\BIGINT}{\mathsf{BIGINT}}

818−\newcommand{\BOOL}{\mathsf{BOOL}}

819−\newcommand{\HOLE}{\mathsf{HOLE}}

820−

821−% G machine translation scheme

822−

823−\newcommand{\sinterp}[1]{\mathcal{S}\interp{#1}}

824−\newcommand{\sinterpm}[1]{\mathcal{S}\AR{\interp{#1}}}

825−\newcommand{\einterp}[3]{\mathcal{E}\interp{#1}\:#2\:#3}

826−\newcommand{\cinterp}[3]{\mathcal{C}\interp{#1}\:#2\:#3}

827−\newcommand{\binterp}[3]{\mathcal{B}\interp{#1}\:#2\:#3}

828−\newcommand{\rinterp}[3]{\mathcal{R}\interp{#1}\:#2\:#3}

829−\newcommand{\iinterp}[3]{\mathcal{I}\interp{#1}\:#2\:#3}

830−\newcommand{\len}[1]{\MO{length}(#1)}

831−

832−\newcommand{\casecomp}[2]{\mathcal{I}(#1,\left\{\ARc{#2}\right\})}

833−\newcommand{\casecompA}[3]{\mathcal{I}(#1,\left\{\ARc{#2}\right\}[#3])}

834−\newcommand{\ischeme}{\mathcal{I}}

835−

836−% tail call markup

837−

838−\newcommand{\tailcall}{\mathsf{tail}}

839−

840−% Trees

841−

842−\newcommand{\Tree}{\TC{Tree}}

843−\newcommand{\Leaf}{\DC{Leaf}}

844−\newcommand{\Node}{\DC{Node}}

845−\newcommand{\treecase}{\Cases{\Tree}}

846−

847−% Languages

848−

849−\newcommand{\Coq}{\textsc{Coq}}

850−\newcommand{\Lego}{\textsc{Lego}}

851−\newcommand{\Oleg}{\textsc{Oleg}}

852−\newcommand{\Alf}{\textsc{Alf}}

853−\newcommand{\Epigram}{\textsc{Epigram}}

854−\newcommand{\SystemF}{System $\mathcal{F}$}

855−\newcommand{\Iswim}{\textsc{Iswim}}

856−\newcommand{\Cynthia}{\textit{C$^Y$\hspace*{-0.1cm}NTHIA}}

857−

858−% Accessibility

859−

860−\newcommand{\Acc}{\TC{Acc}}

861−\newcommand{\acc}{\DC{acc}}

862−\newcommand{\qsAcc}{\TC{qsAcc}}

863−\newcommand{\qsNil}{\DC{qsNil}}

864−\newcommand{\qsCons}{\DC{qsCons}}

865−\newcommand{\allQsAcc}{\FN{allQsAcc}}

866−

867−% Lazy shortcuts

868−

869−\newcommand{\naive}{na\"{\i}ve}

870−\newcommand{\Naive}{Na\"{\i}ve}

871−

872−% Conor's bits

873−

874−\newcommand{\remem}[1]{\left|#1\right|}

875−\newcommand{\idsb}{\MO{id}}

876−\newcommand{\ang}[1]{\langle#1\rangle}

877−

878−\newcommand{\vePm}[1]{\vP #1 \vm_{\Vnil} #1 \vm_{\Vcons}}%

879−\newcommand{\vcrhs}{\vm_{\Vcons}\:\vk\:\va\:\vv\:%

880− (\vectelim\:\vA\:\vk\:\vv\:\vePm{\:})}%

881−

882−\newcommand{\igV}[2]{#1^{\ig{#2}}}

883−\newcommand{\remV}[2]{#1^{\rem{#2}}}

884−

885−% More gubbins

886−

887−\newcommand{\Between}{\TC{between}}

888−\newcommand{\bZ}{\DC{bO}}

889−\newcommand{\bZZS}{\DC{bOOs}}

890−\newcommand{\bZSS}{\DC{b0ss}}

891−\newcommand{\bSSS}{\DC{bsss}}

892−\newcommand{\betelim}{\Elim{\Between}}

893−\newcommand{\betrhs}[1]{\motive#1\meth{\bZ}#1\meth{\bZZS}#1\meth{\bZSS}#1\meth{\bSSS}}

894−

895−

896−\newcommand{\valenv}{\TC{ValEnv}}

897−\newcommand{\vempty}{\DC{empty}}

898−\newcommand{\vextend}{\DC{extend}}

899−

900−\newcommand{\EpiVal}{\TC{Epigram}}

901−\newcommand{\unsafeCoerce}{\HF{unsafeCoerce\mbox{\texttt{\#}}}}

902−

903−\newcommand{\qq}{\mbox{\texttt{"}}}

904−\newcommand{\impossible}{\RW{Impossible}}

905−

906−\newcommand{\Real}{\mathbb{R}}

907−

908−\newcommand{\DoubleRec}{\TC{DoubleElim}}

909−\newcommand{\DoubleOn}{\DC{Double_{\Z\vn}}}

910−\newcommand{\DoubleSO}{\DC{Double_{\suc\Z}}}

911−\newcommand{\DoubleSS}{\DC{Double_{\suc\suc}}}

912−

913−\newcommand{\doublerec}{\textbf{double-elim}}

914−

915−\newcommand{\set}{\TC{DList}}

916−\newcommand{\setuser}{\TC{DListTop}}

917−\newcommand{\setempty}{\emptyset}

918−\newcommand{\setinsert}{\DC{insert}}

919−

920−

921−%%%% Type systems

922−

923−\newcommand{\stlc}{\lambda\hspace*{-0.15cm}\to}

924−\newcommand{\plc}{\lambda2}

925−\newcommand{\dlc}{\lambda{}P}

926−

927−\newcommand{\EC}{\mathcal{E}}

928−

929−%%%% reductions

930−

931−\newcommand{\betared}{\iq\hspace*{-0.15cm}_{\beta}}

932−\newcommand{\deltared}{\iq\hspace*{-0.15cm}_{\delta}}

933−\newcommand{\gammared}{\iq\hspace*{-0.15cm}_{\gamma}}

934−\newcommand{\etared}{\iq\hspace*{-0.15cm}_{\eta}}

935−\newcommand{\iotared}{\iq\hspace*{-0.15cm}_{\iota}}

936−\newcommand{\rhored}{\iq\hspace*{-0.15cm}_{\rho}}

937−

938−%%%% ExTT rules

939−

940−\newcommand{\exconverts}{\stackrel{\mathsf{Ex}}{\converts}}

941−\newcommand{\excumul}{\stackrel{\mathsf{Ex}}{\cumul}}

942−\newcommand{\exequiv}{\stackrel{\mathsf{Ex}}{\equiv}}

943−\newcommand{\exreduces}{\stackrel{\mathsf{Ex}}\reduces}

944−\newcommand{\exreducesto}{\stackrel{\mathsf{Ex}}{\reducesto}}

945−\newcommand{\exreducesn}[1]{\exreduces_{#1}}

946−

947−\newcommand{\ttequiv}{\stackrel{\mathsf{TT}}{\equiv}}

948−\newcommand{\ttreduces}{\stackrel{\mathsf{TT}}\reduces}

949−\newcommand{\ttreducesn}[1]{\ttreduces_{#1}}

950−

951−%%% Type synthesis

952−

953−\newcommand{\hastype}{\Longrightarrow}

954−\newcommand{\whnfs}{\twoheadrightarrow}

955−\newcommand{\conv}{\converts}

956−

957−\newcommand{\exhastype}{\stackrel{\mathsf{Ex}}{\hastype}}

958−\newcommand{\exwhnfs}{\stackrel{\mathsf{Ex}}{\whnfs}}

959−\newcommand{\exconv}{\stackrel{\mathsf{Ex}}{\conv}}

960−\newcommand{\exproves}{\stackrel{\mathsf{Ex}}{\proves}}

961−

962−\newcommand{\tthastype}{\stackrel{\mathsf{TT}}{\hastype}}

963−\newcommand{\ttwhnfs}{\stackrel{\mathsf{TT}}{\whnfs}}

964−\newcommand{\ttconv}{\stackrel{\mathsf{TT}}{\conv}}

965−\newcommand{\ttproves}{\stackrel{\mathsf{TT}}{\proves}}

966−

967−%%% Lightning

968−

969−\newcommand{\light}[1]{\lightning^{#1}}

970−\newcommand{\LHab}[1]{\pad{\;}{:^{#1}}}

971−\newcommand{\llam}[3]{\lambda#1\pad{\!}{:}^{#2}#3}

972−\newcommand{\lall}[3]{\forall#1\pad{\!}{:}^{#2}#3}

973−\newcommand{\lapp}[3]{#1(#2)^{#3}}

974−\newcommand{\larg}[2]{(#1)^{#2}}

975−

976−\newcommand{\RName}[1]{\hspace*{0.1in}\mathsf{#1}}

977−

978−%%% LOcal macros

979−

980−\newcommand{\ResState}{\TC{ResourceState}}

981−\newcommand{\Locked}{\DC{Locked}}

982−\newcommand{\ResHandle}{\TC{ResourceHandle}}

983−\newcommand{\Res}{\DC{Resource}}

984−\newcommand{\CLang}{\TC{CLang}}

985−\newcommand{\CFLang}{\TC{CFLang}}

986−\newcommand{\CFType}{\TC{CFType}}

987−\newcommand{\CLType}{\TC{CType}}

988−\newcommand{\RHandle}{\DC{RHandle}}

989−\newcommand{\RType}{\DC{RType}}

990−\newcommand{\RUnit}{\DC{RUnit}}

991−\newcommand{\LOCK}{\DC{LOCK}}

992−\newcommand{\UNLOCK}{\DC{UNLOCK}}

993−\newcommand{\ACTION}{\DC{ACTION}}

994−\newcommand{\FORK}{\DC{FORK}}

995−

996−\newcommand{\FSLang}{\TC{FSLang}}

997−\newcommand{\OPEN}{\DC{OPEN}}

998−\newcommand{\CLOSE}{\DC{CLOSE}}

999−\newcommand{\READ}{\DC{READ}}

1000−\newcommand{\WRITE}{\DC{WRITE}}

1001−\newcommand{\PRINT}{\DC{PRINT}}

1002−\newcommand{\BIND}{\DC{BIND}}

1003−

1004−\newcommand{\FSType}{\TC{FSType}}

1005−\newcommand{\FHandle}{\DC{FHandle}}

1006−\newcommand{\FString}{\DC{FString}}

1007−\newcommand{\FUnit}{\DC{FUnit}}

1008−\newcommand{\ElemIs}{\TC{ElemIs}}

1009−\newcommand{\elemHd}{\TC{atHead}}

1010−\newcommand{\elemTl}{\TC{inTail}}

1011−

1012−\newcommand{\emptyEnv}{\DC{empty}}

1013−\newcommand{\extendEnv}{\DC{extend}}

1014−

1015−\newcommand{\usera}{\FN{Alice}}

1016−\newcommand{\userb}{\FN{Bob}}

1017−\newcommand{\userc}{\FN{Charlie}}

1018−

1019−\newcommand{\FAcc}{\TC{FAcc}}

1020−\newcommand{\UserA}{\DC{UserAcc}}

1021−\newcommand{\GroupA}{\DC{GroupAcc}}

1022−\newcommand{\GlobalA}{\DC{GlobalAcc}}

1023−

1024−\newcommand{\Perm}{\TC{Perm}}

1025−\newcommand{\Username}{\TC{Username}}

1026−\newcommand{\GroupData}{\TC{GroupData}}

1027−\newcommand{\File}{\TC{File}}

1028−\newcommand{\FS}{\DC{file}}

1029−\newcommand{\Filepath}{\TC{Filepath}}

1030−

1031−\newcommand{\Read}{\DC{Read}}

1032−\newcommand{\Write}{\DC{Write}}

1033−\newcommand{\Execute}{\DC{Execute}}

1034−

1035−\newcommand{\Purpose}{\TC{Mode}}

1036−\newcommand{\Reading}{\DC{Reading}}

1037−\newcommand{\Writing}{\DC{Writing}}

1038−

1039−\newcommand{\FileState}{\TC{FileState}}

1040−\newcommand{\FileHandle}{\TC{FileHandle}}

1041−\newcommand{\OpenH}{\DC{OpenH}}

1042−\newcommand{\ClosedH}{\DC{ClosedH}}

1043−\newcommand{\Handle}{\TC{Handle}}

1044−\newcommand{\Open}{\DC{Open}}

1045−\newcommand{\Closed}{\DC{Closed}}

1046−

1047−\newcommand{\UserIO}{\TC{UserIO}}

1048−\newcommand{\uio}{\DC{uio}}

1049−

1050−\newcommand{\CFS}{\TC{C_{fs}}}

1051−\newcommand{\RFS}{\FN{R_{fs}}}

1052−

1053−\newcommand{\String}{\TC{String}}

1054−

1055−% inline idris code

1056−

1057−\newcommand{\Tcon}[1]{\texttt{#1}}

1058−\newcommand{\Dcon}[1]{\texttt{#1}}

1059−\newcommand{\Fname}[1]{\texttt{#1}}

1060−\newcommand{\Vv}[1]{\texttt{#1}}

1061−\newcommand{\TyTy}{\texttt{\#}}

1062−

1063−\newcommand{\direct}[1]{\texttt{\%#1}}

1064−

1065−\newcommand{\Feature}[1]{\textbf{Remark:}}

1066−%\newcommand{\Remark}[1]{\textbf{Remark:}}

papers/impl-paper/overview.texdeleted−35

@@ -1,35 +0,0 @@

1−\subsection{Overview}

2−

3−High level view of steps we've taken to implement this new version:

4−

5−\begin{itemize}

6−\item Syntax tree for raw and well-typed terms

7−\item An evaluator for well-typed terms

8−\item The important bit: a simple type checker. No unification or

9− inference.

10−\begin{itemize}

11− \item It is extremely tempting to add implicit arguments and unification to the

12− type checker. This is what I did in the first Idris prototype: I learned

13− that it was a bad idea! Scope is a big problem.

14−\end{itemize}

15−\item The proof state and a tactic engine (Oleg style~\cite{McBride1999}).

16−\begin{itemize}

17− \item Dealing with names: typechecking and evaluation in a context, managing de Bruijn

18− indices becomes tricky. Instead: global names, local names during construction,

19− and de Bruijn indices when done.

20−\end{itemize}

21−\item Unification, and incorporation into the tactic engine.

22−\begin{itemize}

23− \item Note that this can introduce constraints on hole ordering. If we can't satisfy them,

24− report an error.

25−\end{itemize}

26−\item An Elaborator, as an EDSL, which is a language for applying primitive tactics and

27− constructing derived tactics, from a high level syntax withe implicit arguments.

28−\item Adding primitive operators and a link to Epic~\cite{brady2011epic}.

29−\item Advanced elaborations: using declarations, where clauses, type classes.

30−\end{itemize}

31−

32−For the high level language: we need nothing more than the core type theory,

33−and a way of putting stuff together. So we typecheck each pattern match clause

34−individually, in an appropriate context. There is no need for the core type

35−theory to have pattern matching.

papers/impl-paper/proofstate.texdeleted−7

@@ -1,7 +0,0 @@

1−\section{Proof State}

2−

3−\subsection{Tactics}

4−

5−\subsection{Unification}

6−

7−\subsection{The Elaboration DSL}

papers/impl-paper/syntax.texdeleted−10

@@ -1,10 +0,0 @@

1−\section{High Level Structures}

2−

3−\subsection{\texttt{where} clauses}

4−

5−\subsection{The \texttt{with} rule}

6−

7−\subsection{Type Classes}

8−

9−\subsection{Syntactic Sugar}

10−

papers/impl-paper/typechecking.texdeleted−718

@@ -1,718 +0,0 @@

1−\section{The Core Type Theory}

2−

3−\label{sect:typechecking}

4−

5−High-level \Idris{} programs, as described in Section \ref{sect:hll}, are

6−\remph{elaborated} to a small core language, \TT{}, then type checked.

7−\TT{} is a dependently-typed $\lambda$-calculus with inductive families

8−and pattern matching definitions similar to UTT~\cite{luo1994}, and building

9−on an earlier implementation, \Ivor{}~\cite{Brady2006b}.

10−The

11−core language is kept as small as is reasonably possible, which has several advantages: it is

12−easy to type check, since type checking dependent type theory is well understood

13−~\cite{loh2010tutorial}; and it is easy to transform, optimise and compile. Keeping

14−the core language small increases confidence that these important components of

15−the language are correct. In this section, we describe \TT{} and

16−its semantics.

17−

18−\subsection{\TT{} syntax}

19−

20−The syntax of \TT{} expressions is given in Figure \ref{ttsyn}. This defines:

21−

22−\begin{itemize}

23−\item \demph{Terms}, $\vt$, which can be variables, bindings, applications or constants.

24−\item \demph{Bindings}, $\vb$, which can be lambda abstractions, let bindings, or function spaces.

25−\item \demph{Constants}, $\vc$, which can be integer or string literals, or $\Type_i$, the

26−type of types, and may be extended with other primitives.

27−\end{itemize}

28−

29−The function space $\all{\vx}{\vS}\SC\vT$ may also be written as $(\vx\Hab\vS)\to\vT$,

30−or $\vS\to\vT$ if $\vx$ is not free in $\vT$, to make the notation more consistent with

31−the high-level language. Universe levels on types ($\Type_i$) may be left implicit and

32−inferred by the machine~\cite{pollack1990implicit}.

33−

34−\FFIG{

35−\begin{array}{rll@{\hg}rll}

36−\mbox{Terms,}\;\vt ::= & \vc & (\mbox{constant}) &

37−\;\mbox{Binders,}\;\vb ::= & \lam{\vx}{\vt} & (\mbox{abstraction}) \\

38−

39− \mid & \vx & (\mbox{variable}) &

40− \mid & \LET\;\vx\defq\vt\Hab\vt & (\mbox{let binding}) \\

41−

42− \mid & \vb\SC\;\vt & (\mbox{binding}) &

43− \mid & \all{\vx}{\vt} & (\mbox{function space}) \\

44−

45− \mid & \vt\;\vt & (\mbox{application}) & \\

46− \mid & \TC{T} & (\mbox{type constructor}) & \\

47− \mid & \TC{D} & (\mbox{data constructor}) &

48−% \mid & \pat{\vx}{\vt} & (\mbox{pattern variable}) \\

49−% & & &

50−% \mid & \pty{\vx}{\vt} & (\mbox{pattern type}) \\

51−\medskip\\

52−\mbox{Constants,}\;\vc ::= & \Type_i & (\mbox{type universes}) \\

53− \mid & \vi & (\mbox{integer literal}) \\

54− \mid & \VV{str} & (\mbox{string literal}) \\

55−\end{array}

56−}

57−{\TT{} expression syntax}

58−{ttsyn}

59−

60−A \TT{} program is a collection of \demph{inductive family} definitions (Section

61−\ref{sect:inductivefams}) and \demph{pattern matching} function definitions (Section

62−\ref{sect:patdefs}), as well as primitive operators on constants.

63−Before defining these, let us define the semantics of \TT{}

64−expressions.

65−

66−\subsection{\TT{} semantics}

67−

68−The static and dynamic semantics of \TT{} are defined mutually, since

69−evaluation relies on a well-typed term, and type checking relies on

70−evaluation. Everything is defined relative

71−to a context, $\Gamma$. The empty context

72−is valid, as is a context extended with a $\lambda$, $\forall$ or

73−$\LET$ binding:

74−

75−\DM{

76−\Axiom{\proves\RW{valid}}

77−\hg

78−\Rule{\Gamma\proves\vS\Hab\Type_i}

79−{\Gamma;\lam{\vx}{\vS}\proves\RW{valid}}

80−\hg

81−\Rule{\Gamma\proves\vS\Hab\Type_i}

82−{\Gamma;\all{\vx}{\vS}\proves\RW{valid}}

83−\hg

84−\Rule{\Gamma\proves\vS\Hab\Type_i\hg\Gamma\proves\vs\Hab\vS}

85−{\Gamma;\LET\;\vx\;\defq\;\vs\Hab\vS\proves\RW{valid}}

86−}

87−

88−\noindent

89−We record the binding form in the context, as well as the type,

90−because type checking relies on evaluation. In particular, $\LET$ bound

91−names may reduce.

92−

93−\subsubsection{Evaluation}

94−

95−\label{sect:evaluation}

96−

97−There are two distinct phases in which \TT{} evaluation occurs, namely

98−\demph{compile-time} and \demph{run-time}. Compile-time evaluation is primarily

99−to support type-checking, in which equivalence of two terms (or types) is

100−determined by comparing their normal forms. It is important that terms are

101−strongly normalising at compile-time, so any pattern matching definition which

102−is not guaranteed to be total does not reduce. In this section we discuss

103−compile-time evaluation; run-time evaluation differs in that there is no

104−reduction under binders, types and duplicated values have been

105−erased~\cite{Brady2003}, and non-normalising definitions may reduce.

106−

107−Compile-time evaluation of \TT{} is defined by contraction schemes, given in

108−Figure \ref{ttcontract}. \demph{Contraction}, relative to a context $\Gamma$,

109−is given by one of the following schemes:

110−

111−\begin{itemize}

112−\item $\beta$-contraction, which substitutes a value applied to a $\lambda$-binding for

113−the bound variable.

114−%We define $\beta$-contraction simply by replacing the $\lambda$-binding

115−%with a $\LET$ binding.

116−\item $\delta$-contraction, which replaces a $\LET$ bound variable with its value.

117−\end{itemize}

118−

119−\noindent

120−The following contextual closure rule reduces a $\LET$ binding by creating

121−a $\delta$-reducible expression:

122−

123−\DM{

124−\Rule{\Gamma;\LET\;\vx\defq\vs\Hab\vS\proves\vt\leadsto\vu}

125−{\Gamma\proves\LET\;\vx\defq\vs\Hab\vS\SC\vt\leadsto\vu}

126−}

127−

128−\demph{Reduction} ($\reduces$) is the structural closure of contraction, and evaluation

129−is ($\reducesto$) is the transitive closure of reduction. \demph{Conversion} ($\converts$)

130−is the smallest equivalence relation closed under reduction. If $\Gamma\proves\vx\converts\vy$

131−then $\vy$ can be obtained from $\vx$ by a finite, possibly empty, sequence of

132−contractions and reversed contractions. Terms which are convertible are also said to

133−be definitionally equal.

134−The evaluator can also be extended by defining pattern matching functions, which

135−will be described in more detail in Section \ref{sect:patdefs}. In principle, pattern

136−matching functions can be understood as extending the core language with high-level

137−reduction rules.

138−

139−\FFIG{

140−\begin{array}{lc}

141−\beta\mathrm{-contraction} &

142−\Axiom{

143−\Gamma\proves(\lam{\vx}{\vS}\SC\vt)\;\vs\leadsto

144−\vt[\vs/\vx]

145−%\LET\;\vx\defq\vs\Hab\vS\SC\vt

146−} \\

147−\delta\mathrm{-contraction} &

148−\Axiom{

149−\Gamma;\LET\;\vx\defq\vs\Hab\vS;\Gamma'

150−\proves

151−\vx\leadsto\vs

152−}

153−\end{array}

154−}

155−{\TT{} contraction schemes}

156−{ttcontract}

157−

158−

159−

160−\subsubsection{Typing rules}

161−

162−\label{sect:typerules}

163−

164−The type inference rules for \TT{} expressions are given in Figure

165−\ref{typerules}. These rules use the \demph{cumulativity} relation, defined in

166−Figure \ref{cumul}. The type of types, $\Type_i$ is parameterised by a universe

167−level, to prevent Girard's paradox~\cite{coquand1986analysis}. There is an

168−infinite hierarchy of predicative universes. Cumulativity allows programs at

169−lower universe levels to inhabit higher universe levels. In practice, universe levels

170−can be left implicit (and will be left implicit in the rest of this paper) ---

171−the type checker generates a graph of constraints between universe levels (such

172−as that produced by the $\mathsf{Forall}$ typing rule) and checks that there

173−are no cycles. This happens as the last stage of type checking, waiting until

174−we have all uses of a family to establish how many levels are needed in the

175−universe hierarchy.

176−Otherwise, the typing rules are standard and type inference can

177−be implemented in the usual way~\cite{loh2010tutorial}.

178−

179−\FFIG{\begin{array}{c}

180−\mathsf{Type}\;

181−\Rule{\Gamma\proves\RW{valid}}

182−{\Gamma\vdash\Type_n\Hab\Type_{n+1}}

183−\\

184−\mathsf{Const}_1\;

185−\Rule{\Gamma\proves\RW{valid}}

186−{\Gamma\vdash\vi\Hab\TC{Int}}

187−\hg

188−\mathsf{Const}_2\;

189−\Rule{\Gamma\proves\RW{valid}}

190−{\Gamma\vdash\VV{str}\Hab\TC{String}}

191−\\

192−\mathsf{Const}_3\;

193−\Rule{\Gamma\proves\RW{valid}}

194−{\Gamma\vdash\TC{Int}\Hab\Type_0}

195−\hg

196−\mathsf{Const}_4\;

197−\Rule{\Gamma\proves\RW{valid}}

198−{\Gamma\vdash\TC{String}\Hab\Type_0}

199−\\

200−%\mathsf{Pat}_1\;

201−%\Rule{(\pat{\vx}{\vS})\in\Gamma}

202−%{\Gamma\vdash\vx\Hab\vS}

203−%\hg

204−%\mathsf{Pat}_2\;

205−%\Rule{(\pty{\vx}{\vS})\in\Gamma}

206−%{\Gamma\vdash\vx\Hab\vS}

207−\\

208−\mathsf{Var}_1\;

209−\Rule{(\lam{\vx}{\vS})\in\Gamma}

210−{\Gamma\vdash\vx\Hab\vS}

211−\hg

212−\mathsf{Var}_2\;

213−\Rule{(\all{\vx}{\vS})\in\Gamma}

214−{\Gamma\vdash\vx\Hab\vS}

215−\hg

216−\mathsf{Val}\;

217−\Rule{(\LET\;\vx\defq\vs\Hab\vS)\in\Gamma}

218−{\Gamma\vdash\vx\Hab\vS}

219−\\

220−\mathsf{App}\;

221−\Rule{\Gamma\vdash\vf\Hab\fbind{\vx}{\vS}{\vT}\hg\Gamma\vdash\vs\Hab\vS}

222−{\Gamma\vdash\vf\;\vs\Hab\vT[\vs/\vx]} % \LET\;\vx\Hab\vS\;\defq\;\vs\;\IN\;\vT}

223−\\

224−\mathsf{Lam}\;

225−\Rule{\Gamma;\lam{\vx}{\vS}\vdash\ve\Hab\vT\hg\Gamma\proves\fbind{\vx}{\vS}{\vT}\Hab\Type_n}

226−{\Gamma\vdash\lam{\vx}{\vS}.\ve\Hab\fbind{\vx}{\vS}{\vT}}

227−\\

228−\mathsf{Forall}\;

229−\Rule{\Gamma;\all{\vx}{\vS}\vdash\vT\Hab\Type_m\hg\Gamma\vdash\vS\Hab\Type_n}

230−{\Gamma\vdash\fbind{\vx}{\vS}{\vT}\Hab\Type_p}

231−\;(\exists\vp.\vm\le\vp,\;\vn\le\vp)

232−\\

233−\mathsf{Let}\;

234−\Rule{\begin{array}{c}\Gamma\proves\ve_1\Hab\vS\hg

235− \Gamma;\LET\;\vx\defq\ve_1\Hab\vS\proves\ve_2\Hab\vT\\

236− \Gamma\proves\vS\Hab\Type_n\hg

237− \Gamma;\LET\;\vx\defq\ve_1\Hab\vS\proves\vT\Hab\Type_n\end{array}

238− }

239−{\Gamma\vdash\LET\;\vx\defq\ve_1\Hab\vS\SC\;\ve_2\Hab

240− \vT[\ve_1/\vx]}

241−%\Let\;\vx\Hab\vS\defq\ve_1\;\IN\;\vT}

242−\\

243−

244−\mathsf{Conv}\;

245−\Rule{\Gamma\proves\vx\Hab\vA\hg\Gamma\proves\vA'\Hab\Type_n\hg

246− \Gamma\proves\vA\cumul\vA'}

247− {\Gamma\proves\vx\Hab\vA'}

248−\end{array}

249−}

250−{Typing rules for \TT{}}

251−{typerules}

252−

253−\FFIG{

254−\begin{array}{c}

255−\Rule{\Gamma\proves\vS\converts\vT}

256−{\Gamma\proves\vS\cumul\vT}

257−\hg

258−\Axiom{\Gamma\proves\Type_n\cumul\Type_{n+1}}

259−\\

260−\Rule{\Gamma\proves\vR\cumul\vS\hg\Gamma\proves\vS\cumul\vT}

261−{\Gamma\proves\vR\cumul\vT}

262−\\

263−\Rule{\Gamma\proves\vS_1\converts\vS_2\hg\Gamma;\vx\Hab\vS_1\proves\vT_1\cumul\vT_2}

264−{\Gamma\proves\all{\vx}{\vS_1}\SC\vT_1\cumul\all{\vx}{\vS_2}{\vT_2}}

265−\end{array}

266−}

267−{Cumulativity}

268−{cumul}

269−

270−

271−\subsection{Inductive Families}

272−

273−\label{sect:inductivefams}

274−

275−Inductive families \cite{dybjer1994inductive} are a form of simultaneously

276−defined collection of algebraic data types which can be parameterised over

277−\remph{values} as well as types. An inductive family is declared

278−in a similar style to a Haskell GADT declaration~\cite{pj2006gadts}

279−as

280−follows:

281−

282−\DM{

283−\AR{

284−\Data\hg\TC{T}\Hab\vt\hg\Where\hg

285−\DC{D}_1\Hab\vt\;\mid\;\ldots\;\mid\;\DC{D}_n\Hab\vt

286−}

287−}

288−

289−A constructor $\TC{D}$ of a family $\TC{T}$ must return a value in the family

290−$\TC{T}$.

291−It may take recursive arguments in the family $\TC{T}$ which may be

292−higher order.

293−Using vector notation, $\tx$, to indicate a

294−sequence of zero or more $\vx$ (i.e., $\vx_1,\vx_2,\ldots,\vx_n$),

295−recursive arguments have types of the form

296−

297−\DM{

298−\all{\vx_1}{\vS_1}\SC\ldots\all{\vx_n}{\vS_n}\SC\TC{T}\:\ty

299−}

300−

301−where $\TC{T}$ does not occur in any of the $\tS$ or the $\ty$

302−This restriction is known as

303−\demph{strict positivity} and ensures that recursive arguments of the

304−constructor are structurally smaller than the value itself.

305−In

306−practice, this restriction can be relaxed when defining a family, but definitions

307−using families which do not satisfy strict positivity will not pass totality

308−checking.

309−

310−For example, the \Idris{} data type \tTC{Nat} would be declared in \TT{} as follows:

311−

312−\DM{

313−\Data\hg\Nat\Hab\Type\hg\Where\hg\Z\Hab\Nat\;\mid\;\suc\Hab\fbind{\vk}{\Nat}{\Nat}

314−}

315−

316−A data type may have zero or more parameters (which are invariant

317−across a structure) and a number of indices, given by the type. For example,

318−the \TT{} equivalent of \tTC{List} is parameterised over its element type:

319−

320−\DM{

321−\AR{

322−\Data\hg\List\Hab(\va\Hab\Type)\to\Type\hg\Where\\

323−\hg\hg

324−\ARd{

325−& \nil\Hab\List\;\va\\

326−\mid & (\cons)\Hab\fbind{\vx}{\va}{\fbind{\vxs}{\List\;\va}{\List\;\va}}

327−}

328−}

329−}

330−

331−Types can be

332−parameterised or indexed over values. Using this, we can declare the type of

333−vectors (lists with length), where the empty list is statically known

334−to have length zero, and the non empty list is statically known to

335−have a non zero length. The \TT{} equivalent of \tTC{Vect} is parameterised over its element type,

336−like $\List$, but \remph{indexed} over its length. Note also that the length

337−index $\vk$ is given \remph{explicitly}.

338−

339−\DM{

340−\AR{

341−\Data\hg\Vect\Hab\Nat\to(\va\Hab\Type)\to\Type\hg\Where \\

342−\hg\hg\ARd{

343−& \nil\Hab\Vect\;\Z\;\va\\

344−\mid & (\cons)\Hab\fbind{\vk}{\Nat}{

345−\fbind{\vx}{\va}{\fbind{\vxs}{\Vect\;\vk\;\va}{\Vect\;(\suc\;\vk)\;\va}}

346−}

347−}

348−}

349−}

350−

351−\subsection{Pattern matching definitions}

352−

353−\label{sect:patdefs}

354−

355−%\subsubsection{Syntax}

356−

357−

358−A pattern matching definition for a function named $\FN{f}$ takes the following form,

359−consisting of a type declaration followed by one or more pattern clauses:

360−

361−\DM{

362−\AR{

363−\FN{f}\Hab\vt\\

364−\pat{\tx_1}{\ttt_1}\SC\FN{f}\;\ttt_1\;=\;\vt_1\\

365−\ldots\\

366−\pat{\tx_n}{\ttt_n}\SC\FN{f}\;\ttt_n\;=\;\vt_n\\

367−}

368−}

369−

370−A pattern clause consists of a list of pattern variable bindings, introduced by

371−$\RW{var}$,

372−and a left and right hand side, both of which

373−are \TT{} expressions. Each side is type checked relative to the variable bindings,

374−and the types of each side must be convertible. Additionally, the

375−left hand side must take the form of $\FN{f}$ applied to a number of \TT{} expressions,

376−and the number of arguments must be the same in each clause. The right hand

377−sides may include applications of $\FN{f}$, i.e. pattern matching definitions may

378−be recursive. The validity of a pattern

379−clause is defined by the following rule:

380−

381−\DM{

382−\Rule{

383−\Gamma;\lam{\tx}{\tU}\proves\FN{f}\;\tts\Hab\vS\hg

384−\Gamma;\lam{\tx}{\tU}\proves\ve\Hab\vT\hg

385−\Gamma\proves\vS\converts\vT}

386−{

387−\Gamma\proves\pat{\tx}{\tU}\SC\FN{f}\;\tts\;=\;\ve\;\RW{valid}

388−}

389−}

390−

391−Patterns are separated into the accessible patterns (variables and constructor

392−forms which may be inspected) and inaccessible patterns, following

393−Agda~\cite{norell2007thesis} then implemented by compilation into case

394−trees~\cite{Augustsson1985}. Non-terminating definitions are permitted, but do

395−not reduce at compile-time, which means in particular that they cannot be used

396−to construct proofs.

397−Termination analysis is implemented separately.

398−

399−A valid pattern matching definition effectively extends \TT{} with a new

400−constant, with the given type (extending the initial typing rules given in

401−Section \ref{sect:typerules}) and reduction behaviour (extending the initial

402−reduction rules given in Section \ref{sect:evaluation}).

403−

404−

405−% \subsubsection{Semantics}

406−%

407−% Matching on an expression proceeds by comparing the expression to

408−% each match clause in order, resulting in either:

409−%

410−% \begin{itemize}

411−% \item \demph{Success}, with pattern variables mapping to expressions

412−% \item \demph{Failure}, with matching continuing by proceeding to the next match clause

413−% \item Matching being \demph{blocked}, for example by attempting to match a variable

414−% against a constructor pattern. In this case, no reduction occurs, because instantiating

415−% the variable may provide enough information for the clause to match.

416−% \end{itemize}

417−%

418−% % Pat(x args) => x (Pat' args)

419−% % Pat (x) => x

420−% % Pat _ => _

421−%

422−% In order to implement pattern matching, we must separate the \remph{accessible} and

423−% \remph{inaccessible} patterns. A pattern is \demph{accessible} (that is, it is possible

424−% to match against it) if it is constructor headed, or a variable. Inaccessible patterns

425−% are converted to ``match anything'' patterns. Clauses are converted to matchable pattern

426−% clauses with the $\MO{Clause}$ operation, given in Figure \ref{mkclause}.

427−% We extend the vector notation to meta-operations: the notation $\vec{\MO{Pat}}$ lifts the

428−% $\MO{Pat}$ operation across a list of arguments.

429−%

430−% \FFIG{

431−% \AR{

432−% \PA{\A}{

433−% & \MO{Clause} & (\pat{\tx}{\tU}\SC\FN{f}\;\tts\;=\;\ve)

434−% & \MoRet{\FN{f}\;(\vec{\MO{Pat}}\;\tts)\;=\;\ve}

435−% }

436−% \medskip\\

437−% \PA{\A}{

438−% & \MO{Pat} & (\vx\;\tts) & \MoRet{\vx\;(\vec{\MO{Pat}}\;\tts)

439−% \hg\mbox{(if $\MO{Con}\;\vx$ and $\MO{Arity}\;\vx = \MO{Length}\;\tts$)}} \\

440−% & \MO{Pat} & \vx & \MoRet{\vx} \hg\mbox(if $\vx$ is a pattern variable)\\

441−% & \MO{Pat} & \cdot & \MoRet{\_} \hg\mbox(in all other cases)\\

442−% }

443−% }

444−% }

445−% {Building matchable pattern clauses}

446−% {mkclause}

447−%

448−%

449−% % Match (c args, c args') => Match' (args, args')

450−% % Match (c args, x) => Blocked

451−% % Match (x, t) => Success (x => t)

452−% % Match (_, t) => Success ()

453−%

454−% \newcommand{\Blocked}{\mathsf{Blocked}}

455−% \newcommand{\Success}{\mathsf{Success}}

456−% \newcommand{\Failure}{\mathsf{Failure}}

457−%

458−% Pattern matching is invoked by the evaluator on encountering a function with

459−% a pattern matching definition applied to some arguments. If successful, pattern

460−% matching returns a new expression, which can then be reduced further.

461−% Figure \ref{pmatch} gives the semantics of pattern matching a collection of

462−% matchable clauses

463−% $\tc$ against an expression $\ve$. $\MO{Match}$ attempts to match each clause in

464−% turn against $\ve$. If matching a clause returns $\Success$ or $\Blocked$, then

465−% matching terminates. If matching a clause returns $\Failure$, then matching proceeds

466−% with the next clause. The algorithm uses the following meta-operations:

467−%

468−% \begin{itemize}

469−% \item $\MO{Con}\;\vx$, which returns true if $\vx$ is a constructor name

470−% \item $\MO{Arity}\;\vx$, which, if $\vx$ is a constructor name, returns the number of arguments

471−% $\vx$ requires.

472−% \item $\MO{Length}\;\tts$, which returns the length of the vector $\tts$

473−% \end{itemize}

474−%

475−%

476−% \FFIG{

477−% \AR{

478−% \PA{\A\A}{

479−% & \MO{MatchArg} & (\vx\;\tts) & (\vx\;\tts')

480−% & \MoRet{\vec{\MO{MatchArg}}\;\tts\;\tts'\hg\mbox{(if $\MO{Con}\;\vx$)}}\\

481−% & \MO{MatchArg} & (\vx\;\tts) & \vx & \MoRet{\Blocked} \\

482−% & \MO{MatchArg} & \vx & \vt & \MoRet{\Success\;(\vx\mapsto\vt)} \\

483−% & \MO{MatchArg} & \_ & \vt & \MoRet{\Success\;()} \\

484−% & \MO{MatchArg} & \cdot & \cdot & \MoRet{\Failure}

485−% }

486−% \medskip\\

487−% \PA{\A\A}{

488−% & \MO{MatchClause} & (\vf\;\tp = \ve) & (\vf\;\tts) &

489−% \MoRet{

490−% \AR{

491−% \Success\;\ve[\tx/\tv]\hg\mbox{(if $\vec{\MO{MatchArg}}\;\tp\;\tts \mq \Success\;(\tx,\tv)$)}\\

492−% \Blocked\;\;\;\hg\hg\mbox{(if $\vec{\MO{MatchArg}}\;\tp\;\tts \mq \Blocked$)}\\

493−% \Failure\;\;\;\;\;\hg\hg\mbox{(if $\vec{\MO{MatchArg}}\;\tp\;\tts \mq \Failure$)}\\

494−% }

495−% } \\

496−% & \MO{MatchClause} & (\vf\;\tp = \ve) & \cdot & \MoRet{\Failure} \\

497−% }

498−% \medskip\\

499−% \PA{\A\A}{

500−% & \MO{Match} & (\vc ; \tc) & \ve &

501−% \MoRet{

502−% \AR{

503−% \Success\;\vx\;\;\hg\mbox{(if $\MO{MatchClause}\;\vc\;\ve \mq \Success\;\vx)$} \\

504−% \Blocked\hg\;\;\;\;\mbox{(if $\MO{MatchClause}\;\vc\;\ve \mq \Blocked)$} \\

505−% \MO{Match}\;\tc\;\ve\hg\mbox{(otherwise)}

506−% }

507−% } \\

508−% & \MO{Match} & \cdot & \ve & \MoRet{\Failure}

509−% }

510−% }

511−% }

512−% {Pattern matching semantics}

513−% {pmatch}

514−%

515−% By convention, we write the application of a meta-operation $\MO{Op}$

516−% across a vector $\tx$ as $\vec{\MO{Op}}\;\tx$.

517−% In practice, for efficiency, pattern matching is implemented by compiling the match clauses to

518−% a tree of case expressions~\cite{Augustsson1985}.

519−

520−\subsection{Metatheory}

521−

522−\FFIG{

523−\begin{array}{ll}

524−\mbox{\textbf{Church-Rosser}} &

525−\begin{array}{ll}

526−\mbox{If}\hg\Gamma\proves\vs\converts\vt \\

527−\mbox{then there is a common reduct $\vr$ such that}\;\\

528−\Gamma\proves\vs\reducesto\vr\hg\Gamma\proves\vt\reducesto\vr

529−\end{array}

530−\medskip

531−\\

532−\mbox{\textbf{Subject Reduction}} &

533−\begin{array}{ll}

534−\mbox{If} & \Gamma\proves\vs\Hab\vS\hg\Gamma\proves\vs\reduces\vt\\

535−\mbox{then}& \Gamma\proves\vt\Hab\vS

536−\end{array}

537−\medskip

538−\\

539−\mbox{\textbf{Cut}} &

540−\begin{array}{ll}

541−\mbox{If} & \Gamma_0,\LET\;\vx\defq\vs\Hab\vS,\Gamma_1\proves\vt\Hab\vT\\

542−\mbox{then} & \Gamma_0, \Gamma_1[\vs/\vx]\proves\vt[\vs/\vx]\Hab\vT[\vs/\vx]

543−\end{array}

544−\medskip

545−\\

546−\mbox{\textbf{Strengthening}} &

547−\begin{array}{ll}

548−\mbox{If} & \Gamma_0,\mathcal{B}(\vx, \vT),\Gamma_1\proves\vs\Hab\vS

549−\hg\vx\not\in\Gamma_1,\vs,\vS\\

550−\mbox{then} & \Gamma_0,\Gamma_1\proves\vs\Hab\vS\\

551−(\mbox{where} & \mathcal{B}(\vx, \vT) \proves \vx\Hab\vT)

552−\end{array}

553−\medskip

554−\\

555−\mbox{\textbf{Strong normalisation}} &

556−\begin{array}{ll}

557−\mbox{If} & \Gamma\proves\vt\Hab\vT\\

558−\mbox{then} & \vt\:\mbox{is strongly normalising}\\

559−\end{array}

560−\\

561−\end{array}

562−}

563−{Metatheoretic properties of \TT{}}

564−{metatheory}

565−

566−We conjecture that \TT{} respects the usual metatheoretic properties,

567−as shown in

568−Figure \ref{metatheory}. Specifically: the \demph{Church-Rosser} property

569−(i.e. that distinct reduction sequences lead to the same normal form);

570−\demph{subject reduction} (i.e. that computation preserves type); the

571−\demph{cut} property (i.e. that $\RW{let}$-bound terms may be substituted into

572−their scope); and \demph{strengthening} (i.e. that removing unused definitions

573−from scope does not affect type checking).

574−\demph{Strong normalisation} holds at compile-time because pattern matching

575−definitions which cannot be shown to be terminating do not have compile-time

576−reduction behaviour.

577−

578−%One property which is noticeably absent is \demph{strong normalisation}.

579−%Although desirable to preserve termination and decidability of type checking,

580−%we allow diverging terms for pragmatic reasons as \Idris{} is primarily a

581−%programming language rather than a theorem prover. Nevertheless, we do

582−%\emph{check} for totality in order to be sure which terms are safe to

583−%evaluate at compile time.

584−

585−\subsection{Totality checking}

586−

587−In order to ensure termination of type checking we must distinguish terms for

588−which evaluation definitely terminates, and those which may diverge. \TT{}

589−takes a simple but pragmatic and effective approach to termination checking:

590−any functions which do not satisfy a syntactic constraint on recursive calls

591−are marked as \emph{partial}. Additionally, any function which calls a partial

592−function or uses a data type which is not strictly positive is also marked as

593−partial. We use the size change principle~\cite{Lee2001} to determine whether

594−(possibly mutually defined) recursive functions are guaranteed to

595−terminate. Higher order function arguments are assumed to be total, though

596−if a higher order function is called with a partial function as an argument,

597−the calling function will be marked partial.

598−\TT{} also marks functions which do not cover

599−all possible inputs as partial. This totality checking is independent of the

600−rest of the type theory, and can be extended.

601−

602−This approach, separating the termination requirement from the type theory,

603−means that an \Idris{} programmer makes the decision about the importance of

604−totality for each function rather than having the totality requirement imposed

605−by the type theory.

606−

607−\subsection{From \Idris{} to \TT{}}

608−

609−\TT{} is a very small language, consisting only of data declarations and pattern matching

610−function definitions. There is no significant innovation in the design of \TT{}, and this

611−is a deliberate choice --- it is a combination of small, well-understood components.

612−The kernel of the \TT{} implementation, consisting of a type checker, evaluator and

613−pattern match compiler, is less than 1000 lines of Haskell code. If we are confident

614−in the correctness of the kernel of \TT{}, and any higher level language feature

615−can be translated into \TT{}, we can be more confident of the correctness of

616−the high-level language implementation than if it were implemented directly.

617−

618−The process of elaborating a high-level language into a core type theory like \TT{} is,

619−however, less well understood, and presents several challenges depending on the

620−features of the high-level language.

621−%Elaboration has been implemented in various different ways,

622−%for example in Agda~\cite{norell2007thesis} and Epigram~\cite{McBride2004a}.

623−

624−\subsubsection{Example Elaboration}

625−

626−Recall the following \Idris{} function:

627−

628−\useverb{vadd}

629−

630−\noindent

631−In order to elaborate

632−this to \TT{}, we must resolve the implicit arguments, and make the type class explicit.

633−The first step is to make the implicit arguments explicit, using a placeholder

634−to stand for the arguments we have not yet resolved. The type class argument is

635−also treated as an implicit argument, to which we give the name \texttt{c}:

636−

637−\begin{SaveVerbatim}{vAddImp}

638−

639−vAdd : (a : _) -> (n : _) ->

640− Num a -> Vect n a -> Vect n a -> Vect n a

641−vAdd _ _ c (Nil _) (Nil _) = (Nil _)

642−vAdd _ _ c ((::) _ _ x xs) ((::) _ _ y ys)

643− = (::) _ _ ((+) _ x y) (vAdd _ _ _ xs ys)

644−

645−\end{SaveVerbatim}

646−\useverb{vAddImp}

647−

648−Next, we resolve the implicit arguments. Each implicit argument can only take

649−one value for this program to be type correct --- these are solved by a unification

650−algorithm:

651−

652−\begin{SaveVerbatim}{vAddImpSolve}

653−

654−vAdd : (a : Type) -> (n : Nat) ->

655− Num a -> Vect n a -> Vect n a -> Vect n a

656−vAdd a O c (Nil a) (Nil a) = Nil a

657−vAdd a (S k) c ((::) a k x xs) ((::) a k y ys)

658− = (::) a k ((+) c x y) (vAdd a k c xs ys)

659−

660−\end{SaveVerbatim}

661−\useverb{vAddImpSolve}

662−

663−Finally, to build the \TT{} definition, we need to find the type of each

664−pattern variable and state it explicitly. This leads to the following

665−\TT{} definition, switching to \TT{} notation from the ASCII \Idris{}

666−syntax:

667−

668−\DM{

669−\AR{

670−\FN{vAdd} \Hab(\va\Hab\Type)\to(\vn\Hab\Nat)\to\TC{Num}\;\va\to

671− \Vect\;\vn\;\va\to\Vect\;\vn\;\va\to\Vect\;\vn\;\va\\

672−\RW{var}\;\va\Hab\Type,\;\vc\Hab\TC{Num}\;\va\SC\\

673−\hg\FN{vAdd} \; \va \; \Z \; \vc \; (\DC{Nil}\;\va) \; (\DC{Nil}\;\va) \;

674−\cq\;\DC{Nil}\;\va \\

675−\RW{var}\;\AR{

676−\va\Hab\Type,\;\vk\Hab\Nat,\;\vc\Hab\TC{Num}\;\va,\\

677−\vx\Hab\va,\;\vxs\Hab\Vect\;\vk\;\va,\;

678−\vy\Hab\va,\;\vys\Hab\Vect\;\vk\;\va

679−\SC

680−\\

681−\FN{vAdd} \; \va \; (\suc\;\vk) \; \vc

682− \; ((\DC{::})\;\va\;\vk\;\vx\;\vxs)

683− \; ((\DC{::})\;\va\;\vk\;\vy\;\vys)

684− \\

685− \hg\hg\cq\:((\DC{::})\;\va\;\vk\;((+)\;\vc\;\vx\;\vy)\; (\FN{vAdd}\;\va\;\vk\;\vc\;\vxs\;\vys))

686−}

687−}

688−}

689−

690−\subsubsection{An Observation: Programming vs Theorem Proving}

691−

692−\Idris{} programs may contain several high-level constructs not present in \TT{}, such

693−as implicit arguments, type classes, \texttt{where} clauses, pattern matching \texttt{let}

694−and \texttt{case} constructs. We would like the high-level language to be as expressive

695−as possible, while remaining possible to translate to \TT{}.

696−

697−Before considering how to achieve this, we make an observation about the distinction between

698−programming and theorem proving with dependent types, and appropriate mechanisms for

699−constructing programs and theorems:

700−

701−\begin{itemize}

702−\item \remph{Pattern matching} is a convenient abstraction for humans to write

703−programs, in that it allows a programmer to express exactly the computational

704−behaviour of a function.

705−\item \remph{Tactics}, such as those used in the Coq theorem

706−prover~\cite{Bertot2004}, are a convenient abstraction for building proofs and

707−programs by \remph{refinement}.

708−\end{itemize}

709−

710−The idea behind the \Idris{} elaborator, therefore, is to use the high-level

711−program to direct \demph{tactics} to build \TT{} programs by refinement. The

712−elaborator is implemented as a Haskell monad capturing proof state, with a

713−collection of tactics for updating and refining the proof state. The remainder

714−of this paper describes this elaborator and demonstrates how it is used to

715−implement the high-level features of \Idris{}.

716−

717−

718−