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.hlint.yamldeleted−61

@@ -1,61 +0,0 @@

1−# HLint configuration file

2−# https://github.com/ndmitchell/hlint

3−##########################

4−

5−# This file contains a template configuration file, which is typically

6−# placed as .hlint.yaml in the root of your project

7−

8−

9−# Specify additional command line arguments

10−#

11−# - arguments: [--color, --cpp-simple, -XQuasiQuotes]

12−

13−

14−# Control which extensions/flags/modules/functions can be used

15−#

16−# - extensions:

17−# - default: false # all extension are banned by default

18−# - name: [PatternGuards, ViewPatterns] # only these listed extensions can be used

19−# - {name: CPP, within: CrossPlatform} # CPP can only be used in a given module

20−#

21−# - flags:

22−# - {name: -w, within: []} # -w is allowed nowhere

23−#

24−# - modules:

25−# - {name: [Data.Set, Data.HashSet], as: Set} # if you import Data.Set qualified, it must be as 'Set'

26−# - {name: Control.Arrow, within: []} # Certain modules are banned entirely

27−#

28−# - functions:

29−# - {name: unsafePerformIO, within: []} # unsafePerformIO can only appear in no modules

30−

31−

32−# Add custom hints for this project

33−#

34−# Will suggest replacing "wibbleMany [myvar]" with "wibbleOne myvar"

35−# - error: {lhs: "wibbleMany [x]", rhs: wibbleOne x}

36−

37−

38−# Turn on hints that are off by default

39−#

40−# Ban "module X(module X) where", to require a real export list

41−# - warn: {name: Use explicit module export list}

42−#

43−# Replace a $ b $ c with a . b $ c

44−# - group: {name: dollar, enabled: true}

45−#

46−# Generalise map to fmap, ++ to <>

47−# - group: {name: generalise, enabled: true}

48−

49−

50−# Ignore some builtin hints

51−# - ignore: {name: Use let}

52−# - ignore: {name: Use const, within: SpecialModule} # Only within certain modules

53−- ignore: {name: Use camelCase}

54−- ignore: {name: Reduce duplication}

55−

56−# Define some custom infix operators

57−# - fixity: infixr 3 ~^#^~

58−

59−

60−# To generate a suitable file for HLint do:

61−# $ hlint --default > .hlint.yaml

.travis.yml+30−57

@@ -1,4 +1,5 @@

1−dist: xenial

1+dist: trusty

2+sudo: false

23

34language: c

45

@@ -8,37 +9,26 @@ env:

89

910matrix:

1011 include:

11− - env: CABALVER="2.4" GHCVER="8.6.5" STACKVER="15.4" STYLISH=YES

12− addons: {apt: {packages: [cabal-install-2.4,ghc-8.6.5,hscolour], sources: [hvr-ghc]}}

13− - env: CABALVER="2.4" GHCVER="8.2.2" TESTS="lib_doc doc"

14− compiler: ": #GHC 8.2.2"

15− addons: {apt: {packages: [cabal-install-2.4,ghc-8.2.2,cppcheck,hscolour], sources: [hvr-ghc]}}

16− - env: CABALVER="2.4" GHCVER="8.2.2" TESTS="test_js"

17− compiler: ": #GHC 8.2.2"

18− addons: {apt: {packages: [cabal-install-2.4,ghc-8.2.2,cppcheck,hscolour], sources: [hvr-ghc]}}

19− - env: CABALVER="2.4" GHCVER="8.2.2" TESTS="test_c"

20− compiler: ": #GHC 8.2.2"

21− addons: {apt: {packages: [cabal-install-2.4,ghc-8.2.2,cppcheck,hscolour], sources: [hvr-ghc]}}

22− - env: CABALVER="2.4" GHCVER="8.4.4" TESTS="lib_doc doc"

23− compiler: ": #GHC 8.4.4"

24− addons: {apt: {packages: [cabal-install-2.4,ghc-8.4.4,cppcheck,hscolour], sources: [hvr-ghc]}}

25− - env: CABALVER="2.4" GHCVER="8.4.4" TESTS="test_js"

26− compiler: ": #GHC 8.4.4"

27− addons: {apt: {packages: [cabal-install-2.4,ghc-8.4.4,cppcheck,hscolour], sources: [hvr-ghc]}}

28− - env: CABALVER="2.4" GHCVER="8.4.4" TESTS="test_c"

29− compiler: ": #GHC 8.4.4"

30− addons: {apt: {packages: [cabal-install-2.4,ghc-8.4.4,cppcheck,hscolour], sources: [hvr-ghc]}}

31− - env: CABALVER="3.0" GHCVER="8.8.3" TESTS="lib_doc doc"

32− compiler: ": #GHC 8.8.3"

33− addons: {apt: {packages: [cabal-install-3.0,ghc-8.8.3,cppcheck,hscolour], sources: [hvr-ghc]}}

34− - env: CABALVER="3.0" GHCVER="8.8.3" TESTS="test_js"

35− compiler: ": #GHC 8.8.3"

36− addons: {apt: {packages: [cabal-install-3.0,ghc-8.8.3,cppcheck,hscolour], sources: [hvr-ghc]}}

37− - env: CABALVER="3.0" GHCVER="8.8.3" TESTS="test_c"

38− compiler: ": #GHC 8.8.3"

39− addons: {apt: {packages: [cabal-install-3.0,ghc-8.8.3,cppcheck,hscolour], sources: [hvr-ghc]}}

40− - env: CABALVER="3.0" GHCVER="8.8.3" IDRIS2=YES

41− addons: {apt: {packages: [cabal-install-3.0,ghc-8.8.3], sources: [hvr-ghc]}}

12+ - env: CABALVER="1.24" GHCVER="8.0.1" STACKVER="7.14" STYLISH=YES

13+ addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,hscolour], sources: [hvr-ghc]}}

14+ - env: CABALVER="1.22" GHCVER="7.10.3" TESTS="lib_doc doc"

15+ compiler: ": #GHC 7.10.3"

16+ addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.3,cppcheck,hscolour], sources: [hvr-ghc]}}

17+ - env: CABALVER="1.22" GHCVER="7.10.3" TESTS="test_js"

18+ compiler: ": #GHC 7.10.3"

19+ addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.3,cppcheck,hscolour], sources: [hvr-ghc]}}

20+ - env: CABALVER="1.22" GHCVER="7.10.3" TESTS="test_c"

21+ compiler: ": #GHC 7.10.3"

22+ addons: {apt: {packages: [cabal-install-1.22,ghc-7.10.3,cppcheck,hscolour], sources: [hvr-ghc]}}

23+ - env: CABALVER="1.24" GHCVER="8.0.1" TESTS="lib_doc doc"

24+ compiler: ": #GHC 8.0.1"

25+ addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,cppcheck,hscolour], sources: [hvr-ghc]}}

26+ - env: CABALVER="1.24" GHCVER="8.0.1" TESTS="test_js"

27+ compiler: ": #GHC 8.0.1"

28+ addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,cppcheck,hscolour], sources: [hvr-ghc]}}

29+ - env: CABALVER="1.24" GHCVER="8.0.1" TESTS="test_c"

30+ compiler: ": #GHC 8.0.1"

31+ addons: {apt: {packages: [cabal-install-1.24,ghc-8.0.1,cppcheck,hscolour], sources: [hvr-ghc]}}

4232 fast-finish: true

4333

4434cache:

@@ -57,7 +47,7 @@ before_install:

5747 - unset CC

5848 - if [[ $TRAVIS_OS_NAME == 'linux' ]];

5949 then

60− export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$HOME/.cabal/bin:$HOME/opt/scheme/bin/:$PATH;

50+ export PATH=/opt/ghc/$GHCVER/bin:/opt/cabal/$CABALVER/bin:$HOME/.cabal/bin:$PATH;

6151 export SED=sed;

6252 export ZCAT=zcat;

6353 fi

@@ -72,21 +62,6 @@ before_install:

7262 export PKG_CONFIG_PATH=/usr/local/opt/libffi/lib/pkgconfig:$PKG_CONFIG_PATH;

7363 fi

7464 - if [ -n "$STYLISH" ]; then ./stylize.sh; exit $?; fi

75− - if [ -n "$IDRIS2" ];

76− then

77− git clone https://github.com/edwinb/Idris2 &&

78− wget https://github.com/cisco/ChezScheme/archive/v9.5.2.tar.gz &&

79− tar xvzf v9.5.2.tar.gz &&

80− cd ChezScheme-9.5.2 &&

81− ./configure --threads --installprefix=$HOME/opt/scheme &&

82− make -j install &&

83− cd .. &&

84− cabal v1-update &&

85− travis_wait cabal v1-install &&

86− cd Idris2 &&

87− make idris2 && make base && make contrib;

88− exit $?;

89− fi

9065

9166install:

9267 - which cabal

@@ -104,7 +79,7 @@ install:

10479 # causing cabal's default configuration (jobs: $ncpus)

10580 # to run into the GHC #9221 bug which can result in longer build-times.

10681 - $SED -i -r 's/(^jobs:).*/\1 2/' $HOME/.cabal/config

107− - cabal v1-install -f FFI --only-dependencies --enable-tests --dry -v > installplan.txt

82+ - cabal install -f FFI --only-dependencies --enable-tests --dry -v > installplan.txt

10883 - $SED -i -e '1,/^Resolving /d' installplan.txt; cat installplan.txt

10984 # check whether current requested install-plan matches cached package-db snapshot

11085 - if diff -u installplan.txt $HOME/.cabsnap/installplan.txt;

@@ -117,7 +92,7 @@ install:

11792 echo "cabal build-cache MISS";

11893 rm -rf $HOME/.cabsnap;

11994 mkdir -p $HOME/.ghc $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin;

120− cabal v1-install -f FFI --only-dependencies --enable-tests;

95+ cabal install -f FFI --only-dependencies --enable-tests;

12196 fi

12297 # snapshot package-db on cache miss

12398 - if [ ! -d $HOME/.cabsnap ];

@@ -128,30 +103,28 @@ install:

128103 cp -a $HOME/.cabal/lib $HOME/.cabal/share $HOME/.cabal/bin installplan.txt $HOME/.cabsnap/;

129104 fi

130105

131−

132106before_script:

133107 - ORIGINAL_DIR=$(pwd)

134− - cabal v1-sdist

108+ - cabal sdist

135109 - cd ..

136110 - tar -xf ${ORIGINAL_DIR}/dist/${PKGNAME}*.tar.gz

137111 - cd ${PKGNAME}*

138112script:

139− - export LD_PRELOAD=/opt/ghc/${GHCVER}/lib/ghc-${GHCVER}/rts/libffi.so.7

140113###

141114 - echo 'Configure...' && echo -en 'travis_fold:start:script.configure\\r'

142− - cabal v1-configure -f FFI -f CI --enable-tests

115+ - cabal configure -f FFI -f CI --enable-tests

143116 - echo -en 'travis_fold:end:script.configure\\r'

144117###

145118 - echo 'Build...' && echo -en 'travis_fold:start:script.build\\r'

146− - cabal v1-build

119+ - cabal build

147120 - echo -en 'travis_fold:end:script.build\\r'

148121###

149122 - echo 'Copy...' && echo -en 'travis_fold:start:script.copy\\r'

150− - cabal v1-copy

123+ - cabal copy

151124 - echo -en 'travis_fold:end:script.copy\\r'

152125###

153126 - echo 'Register...' && echo -en 'travis_fold:start:script.register\\r'

154− - cabal v1-register

127+ - cabal register

155128 - echo -en 'travis_fold:end:script.register\\r'

156129###

157130 - echo 'Cppcheck...' && echo -en 'travis_fold:start:script.cppcheck\\r'

CHANGELOG.md+4−143

@@ -1,56 +1,4 @@

1−# New since last release

2−+ Updated to work with GHC 8.8 and cabal 3.0

3−

4−# New in 1.3.2

5−+ Documentation added to proof section

6−

7−## Library updates

8−+ `openFile` opens the file in binary mode on Windows.

9−+ Added library functions `clockTime` and `fRemove`

10−

11−## Tool updates

12−+ Modules no longer require building if imports have changed but all

13− interfaces (i.e. types for names declared `export` and definitions of names

14− declared `public export`) are unchanged.

15−+ The result of calling `:doc` now details the accessbility of items as well as their totality.

16−

17−## Miscellaneous updates

18−+ Compiler flag `--optimise-nat-like-types` enables compilation

19− of `Nat`-like type families to big integers. A type family

20− is `Nat`-like if, after erasure, it has two constructors,

21− one nullary, the other one with exactly one recursive field.

22−

23−# New in 1.3.1

24−

25−## Tool updates

26−+ Fixes for building with GHC 8.6

27−+ Fix for megaparsec update

28−+ Some fixes for memory allocation issues in the C back end

29−

30−# New in 1.3.0

31−

32−## Language updates

33−+ Old 'induction' tactics and eliminator generation functionality ('%elim', '%case', 'elim_for') is no longer supported.

34− Please, rely on the ones provided by Pruviloj and elaborator reflection instead.

35−

36−## Library updates

37−

38−+ Changed rndInt in Effect.Random so that it does not alternate between odd

39− and even.

40−+ Additions to `contrib`:

41− * `Data.SortedBag`: Bag (or Multiset) implemention based on `Data.SortedMap`.

42− * `Data.PosNat`: A `Nat` paired with a proof that it is positive.

43− * `Data.Chain`: A function with an arbitrary number of arguments, plus

44− combinators for working with them.

45−

46−## Tool updates

47−+ Added a switch `--allow-capitalized-pattern-variables` to optionally allow capitalized pattern variables after they were prohibited in 1.2.0.

48−+ REPL now prints an error message if program compiled by `:exec` terminates

49− abnormally.

50−+ Idris now builds with GHC 8.4.

51−+ In the C backend, the representation of Idris values at runtime has been reworked.

52−

53−# New in 1.2.0

1+# New in 1.1.*

542

553## Language updates

564

@@ -66,38 +14,6 @@

6614 other operators, e.g. ``infixr 8 `cons` ``. Backticked operators with

6715 undeclared fixity are treated as non-associative with precedence lower

6816 than all declared operators.

69−+ Allow non-injective implementations if explicitly named, e.g.,

70− ```idris

71− LTB : Nat -> Type

72− LTB b = DPair Nat (\ n => LT n b)

73−

74− implementation [uninhabltb] Uninhabited (LTB Z) where

75− uninhabited (MkDPair n prf) = absurd prf

76− ```

77− It is possible to use `using implementation uninhabltb` to add the

78− implementation to the automated resolution, but if it fails to find the

79− instance due to non-injectivity, one must pass it explicitly to target

80− function, i.e. `absurd @{uninhabltb}`.

81−+ Verbatim strings now support trailing quote characters. All quote characters

82− until the final three are considered part of the string. Now a string such as

83− `""""hello""""` will parse, and is equivalent to `"\"hello\""`.

84−+ C FFI now supports pasting in any expression by prefixing it with '#', e.g.

85− ```idris

86− intMax : IO Int

87− intMax = foreign FFI_C "#INT_MAX" (IO Int)

88− ```

89−+ The deprecated keywords `%assert_total`, `abstract`, and `[static]` have

90− been removed as well as the use of "public" instead of "public export" to

91− expose a symbol.

92−+ The syntax for pattern-match alternatives now works for `let` statements in

93− `do` blocks in addition to `let` expressions and `<-` statements, e.g.

94− ```idris

95− do …

96− let Just x = expr | Nothing => empty

97− …

98− ```

99− This means that a `with`-application (using `|`) cannot be used in that

100− position anymore.

10117

10218## Library Updates

10319

@@ -107,39 +23,10 @@

10723+ Added `discriminate` and `construct` tactics to Pruviloj.

10824+ Added `IsSucc` type to `Prelude`, which proves that a `Nat` is a successor.

10925+ Added `Data.IOArray`, containing primitives for mutable arrays.

110−+ Added `Language.JSON`, for total serialization/deserialization of JSON data.

111−+ Reworked operator fixity for many operators.

112− * Changed `&&` and `||` to be right-associative. Increased precedence of `&&`

113− to be higher than that of `||`.

114− * Removed associativity from Boolean comparison operators `==`, `/=`, `<`, `<=`,

115− `>`, and `>=`. Increased precedence of `/=` and `==` to match the others.

116− * Made `<|>`, `<$>`, and `.` right-associative.

117− * Swapped precedence of `<|>` and `<*>` (and its related operators, `<*` and

118− `*>`). Now `<|>` has a lower precedence.

119− * Lowered the precedence of `>>=` to be below that of `<|>`.

120−+ Added some useful string manipulation functions to `Data.String.Extra`.

121−+ Added `Control.Delayed`, a module for conditionally making a type `Inf` or `Lazy`.

122−+ Added `Data.Fuel`, which implements the `Fuel` data type and the partial `forever` function.

123−+ Added `Data.Bool.Extra`, a module with properties of boolean operations.

124−+ Moved core of `Text.Lexer` to `Text.Lexer.Core`. Added several new combinators

125− and lexers to `Text.Lexer`.

126−+ Moved core of `Text.Parser` to `Text.Parser.Core`. Added several new combinators

127− to `Text.Parser`. Made the following changes.

128− * Flipped argument order of `parse`.

129− * Renamed `optional` to `option` and flip argument order.

130− * Renamed `maybe` to `optional`.

131− * Generalised many combinators to use an unknown `commit` flag where possible.

132−+ `Prelude.Doubles.atan2` is now implemented as a primitive instead of

133− being coded in Idris.

134−+ Added `Test.Unit` to `contrib` for simple unit testing.

135−+ Removed several deprecated items from the libraries shipped with Idris.

136−+ Moved `abs` from the `Neg` interface into its own `Abs` interface. `Nat`

137− implements `Abs` with `abs = id`.

138−+ Added `Control.ST.File`, an ST based implementation of the same behaviour

139− implemented by `Effect.File` in the effects package.

26++ The operator `<|>` is now right-associative (it retains the same precedence).

27++ Reworked operator fixity for `&&` and `||`, as well as the comparison operators: `==`, `/=`, `<`, `<=`, `>`, and `>=`.

14028

14129## Tool Updates

142−

14330+ Private functions are no longer visible in the REPL except for modules

14431 that are explicitly loaded.

14532+ The --interface option now creates CommonJS modules on the node backend.

@@ -147,36 +34,10 @@

14734 as they were given in the source files.

14835+ Backslash, braces and percent symbols are now correctly pretty printed

14936 in LaTeX.

150−+ Errors and warnings now consistently have the following format:

151− ```idris

152− reg068.idr:1:6-8:

153− |

154− 1 | data nat : Type where --error

155− | ~~~

156− Main.nat has a name which may be implicitly bound.

157− This is likely to lead to problems!

158− ```

159− The code is highlighted when highlighting information is available. How

160− much highlighting information is available depends on where the error

161− occurred.

162−+ The parser provider has been switched from Trifecta to Megaparsec. This

163− could possibly cause some subtle deviations in parsing from previous

164− versions of Idris.

165−+ Many more errors now report beginning *and* ending position (which may be

166− on different lines), instead of just a single point. The format is

167− `Foo.idr:9:7-15:` if ending column is on the same line or

168− `Foo.idr:9:7-10:15:` if the ending column is on a different line.

169−+ Error messages were changed so that the last column is inclusive, e.g.

170− `Foo.idr:9:7-15:` includes column 15. Previously the error would have read

171− `Foo.idr:9:7-16:`.

17237

17338## Packaging Updates

174−

17539+ Package names now only accept a restrictive charset of letters, numbers and the `-_` characters.

176− Package names are also case insensitive.

177−+ When building makefiles for the FFI, the environment variables

178− `IDRIS_INCLUDES` and `IDRIS_LDFLAGS` are now set with the correct C

179− flags.

40+ Package names are also case insensitive

18041

18142# New in 1.1.1

18243

CITATION.md+1−1

@@ -17,7 +17,7 @@ If you use `Idris` in your work we would prefer it if you would use the followin

1717 pages = {552--593},

1818 numpages = {42},

1919 doi = {10.1017/S095679681300018X},

20− URL = {https://journals.cambridge.org/article_S095679681300018X},

20+ URL = {http://journals.cambridge.org/article_S095679681300018X},

2121}

2222```

2323

CONTRIBUTING.md+6−6

@@ -6,9 +6,9 @@ Here are a few guidelines that we would like contributors to follow so that we c

66

77## Getting Started

88

9−1. Make sure you are familiar with [Git](https://git-scm.com/book).

9+1. Make sure you are familiar with [Git](http://git-scm.com/book).

10101. Make sure you have a [GitHub account](https://github.com/signup/free).

11−1. Make sure you are familiar with: [Idris](https://eb.host.cs.st-andrews.ac.uk/writings/idris-tutorial.pdf).

11+1. Make sure you are familiar with: [Idris](http://eb.host.cs.st-andrews.ac.uk/writings/idris-tutorial.pdf).

12121. Make sure you can install Idris:

1313 * [Mac OS X](https://github.com/idris-lang/Idris-dev/wiki/Idris-on-OS-X-using-Homebrew)

1414 * [Ubuntu](https://github.com/idris-lang/Idris-dev/wiki/Idris-on-Ubuntu)

@@ -72,7 +72,7 @@ We do not want you wasting your time nor duplicating somebody's work!

7272

7373## Making Changes

7474

75−Idris developers and hackers try to adhere to something similar to the [successful git branching model](https://nvie.com/posts/a-successful-git-branching-model/).

75+Idris developers and hackers try to adhere to something similar to the [successful git branching model](http://nvie.com/posts/a-successful-git-branching-model/).

7676The steps are described below.

7777

7878### New contributors

@@ -83,7 +83,7 @@ For those new to the project:

83832. Clone your fork to your local machine:

8484

8585```

86−$ git clone git@github.com:<your github user name>/Idris-dev.git

86+$ git clone git@github.com/<your github user name>/Idris-dev.git

8787```

8888

89893. Add `idris-lang/Idris-dev` as a remote upstream

@@ -175,8 +175,8 @@ To help increase the chance of your pull request being accepted:

175175* Idris FAQs: [Official](https://idris.readthedocs.io/en/latest/faq/faq.html); [Unofficial](https://github.com/idris-lang/Idris-dev/wiki/Unofficial-FAQ);

176176* [Idris Manual](https://github.com/idris-lang/Idris-dev/wiki/Manual);

177177* [Idris Tutorial](https://idris.readthedocs.io/en/latest/tutorial/index.html);

178−* [Idris News](https://www.idris-lang.org/news/);

179−* [other Idris docs](https://www.idris-lang.org/documentation/).

178+* [Idris News](http://www.idris-lang.org/news/);

179+* [other Idris docs](http://www.idris-lang.org/documentation/).

180180* [Using Pull Requests](https://help.github.com/articles/using-pull-requests)

181181* [General GitHub Documentation](https://help.github.com/).

182182

CONTRIBUTORS−2

@@ -126,7 +126,6 @@ Jonas De Vuyst

126126Jonas Westerlund

127127Jonathan Sterling

128128Joomy Korkut

129−Jorge Acereda

130129Joseph Huang

131130Josh Vera

132131JP Smith

@@ -143,7 +142,6 @@ Luke Palmer

143142Mark Farrell

144143Markus Klink

145144Markus Pfeiffer

146−Martin Baker

147145Mathnerd314

148146Mattias Lundell

149147Matvey B. Aksenov

HLint.hsnew file+34

@@ -0,0 +1,34 @@

1+{-# LANGUAGE TemplateHaskell #-}

2+-- --------------------------------------------------------------- [ HLint.hs ]

3+-- HLint suggestions we like.

4+--

5+-- This is a work in progress and the list of

6+-- suggestions/warnings/errors will vary.

7+--

8+-- -------------------------------------------------------------------- [ EOH ]

9+

10+-- import "hint" HLint.HLint -- In case we want to use all of them.

11+

12+-- ------------------------------------------------------------ [ Suggestions ]

13+-- Styling that are good Suggestions but are okay if found.

14+

15+suggest "Use exitSuccess"

16+suggest "Use concatMap"

17+suggest "Use unwords"

18+suggest "Use null"

19+suggest "Redundant $"

20+suggest "Use list literal pattern"

21+suggest "Use list literal"

22+

23+-- ------------------------------------------------------------------- [ Warn ]

24+-- Styling that we think a programmer should be warned about using.

25+

26+

27+-- ------------------------------------------------------------------ [ Error ]

28+-- Styling that we think a programmer should not use at all.

29+

30+

31+-- ----------------------------------------------------------------- [ Ignore ]

32+-- Suggestions we want to ignore.

33+

34+-- -------------------------------------------------------------------- [ EOF ]

INSTALL.md+3−31

@@ -70,7 +70,7 @@ NixOS unstable.

7070

7171*Important* Stack will not install any external dependencies required

7272to build Idris. Before you try stack please ensure you have the

73−correct dependencies.

73+correct depenencies.

7474

7575To build Idris with stack use the following command:

7676

@@ -81,10 +81,7 @@ To install Idris:

8181* `stack install`

8282

8383Stack will install Idris (and related executables) into `$HOME/.local/bin/`

84−on Unix based systems and an appropriate place on Windows. The libraries that

85−are included with Idris (e.g. Builtins, Prelude) will 'install' into `<source

86−dir>/.stack_work/install/...` so you'll need to keep your source directory

87−around after you've installed Idris using Stack.

84+on Unix based systems and an appropriate place on Windows.

8885

8986Of note: If you haven't used stack before commands will also setup the

9087related infrastructure. For more information about Stack please visit

@@ -125,29 +122,4 @@ encounter this then the fix is to augment the `PKG_CONFIG_PATH` for

125122

126123```

127124PKG_CONFIG_PATH=/usr/local/opt/libffi/lib/pkgconfig stack build

128−```

129−

130−## Issue with GHC on Ubuntu/Fedora

131−

132−There is an upstream issue with GHC on some Ubuntu and Fedora machines.

133−The issue is that for GHC versions greater than 8.4.X linking to libFFI uses the version of libFFI shipped with GHC, instead of the system version.

134−

135−See the following GHC issue page for more information:

136−

137− <https://gitlab.haskell.org/ghc/ghc/issues/15397>

138−

139−This means that an Idris built with `libFFI` support will fail at runtime as the executable would not be able to find the correct `libffi` shared object.

140−This will cause the build to fail.

141−Specifically, one will see an error message along the lines of:

142−

143−> error while loading shared libraries: libffi.so.7: cannot open shared object file: No such file or directory

144−

145−A workround for this bug is to override the used libffi version (this is what we use on CI):

146−

147−```bash

148−export LD_PRELOAD=/opt/ghc/${GHCVER}/lib/ghc-${GHCVER}/rts/libffi.so.7

149−```

150−

151−## GHC 8.6

152−

153−For reasons that haven't been investigated building the Idris compiler with GHC 8.6 leads to a compiler which doesn't pass test.

125+```

Makefile+10−10

@@ -15,14 +15,14 @@ endif

1515endif

1616

1717install:

18− $(CABAL) v1-install $(CABALFLAGS)

18+ $(CABAL) install $(CABALFLAGS)

1919

2020pinstall: CABALFLAGS += --enable-executable-profiling

2121pinstall: dist/setup-config

22− $(CABAL) v1-install $(CABALFLAGS)

22+ $(CABAL) install $(CABALFLAGS)

2323

2424build: dist/setup-config

25− $(CABAL) v1-build $(CABALFLAGS)

25+ $(CABAL) build $(CABALFLAGS)

2626

2727test: doc test_c stylize

2828

@@ -30,15 +30,15 @@ stylize:

3030 ./stylize.sh

3131

3232test_c:

33− $(CABAL) v1-test $(ARGS) --test-options \

33+ $(CABAL) test $(ARGS) --test-options \

3434 "$(TEST-ARGS) --rerun-update +RTS -N$(TEST-JOBS) -RTS"

3535

3636test_js:

37− $(CABAL) v1-test $(ARGS) --test-options \

37+ $(CABAL) test $(ARGS) --test-options \

3838 "$(TEST-ARGS) --node --rerun-update +RTS -N$(TEST-JOBS) -RTS"

3939

4040test_update:

41− $(CABAL) v1-test $(ARGS) --test-options \

41+ $(CABAL) test $(ARGS) --test-options \

4242 "$(TEST-ARGS) --accept +RTS -N$(TEST-JOBS) -RTS"

4343

4444test_clean:

@@ -49,14 +49,14 @@ lib_clean:

4949 $(MAKE) -C libs IDRIS=../../dist/build/idris/idris RTS=../../dist/build/rts/libidris_rts clean

5050

5151relib: lib_clean

52− $(CABAL) v1-install $(CABALFLAGS)

52+ $(CABAL) install $(CABALFLAGS)

5353

5454linecount:

5555 wc -l src/Idris/*.hs src/Idris/Elab/*.hs src/Idris/Core/*.hs src/IRTS/*.hs src/Pkg/*.hs src/Util/*.hs

5656

5757#Note: this doesn't yet link to Hackage properly

5858doc: dist/setup-config

59− $(CABAL) v1-haddock --hyperlink-source --html --hoogle --html-location="https://hackage.haskell.org/packages/archive/\$$pkg/latest/doc/html" --haddock-options="--title Idris"

59+ $(CABAL) haddock --hyperlink-source --html --hoogle --html-location="http://hackage.haskell.org/packages/archive/\$$pkg/latest/doc/html" --haddock-options="--title Idris"

6060

6161lib_doc:

6262 $(MAKE) -C libs IDRIS=../../dist/build/idris/idris doc

@@ -76,7 +76,7 @@ user_doc_pdf:

7676 $(MAKE) -C docs latexpdf

7777

7878fast:

79− $(CABAL) v1-install $(CABALFLAGS) --ghc-option=-O0

79+ $(CABAL) install $(CABALFLAGS) --ghc-option=-O0

8080

8181dist/setup-config:

82− $(CABAL) v1-configure $(CABALFLAGS)

82+ $(CABAL) configure $(CABALFLAGS)

README.md+4−7

@@ -4,11 +4,11 @@

44[](https://ci.appveyor.com/project/idrislang/idris-dev)

55[](https://readthedocs.org/projects/idris/?badge=latest)

66[](https://hackage.haskell.org/package/idris)

7−[](https://stackage.org/lts/package/idris)

8−[](https://stackage.org/nightly/package/idris)

7+[](http://stackage.org/lts/package/idris)

8+[](http://stackage.org/nightly/package/idris)

99[](https://www.irccloud.com/invite?channel=%23idris&hostname=irc.freenode.net&port=6697&ssl=1)

1010

11−Idris (https://idris-lang.org/) is a general-purpose functional programming

11+Idris (http://idris-lang.org/) is a general-purpose functional programming

1212language with dependent types.

1313

1414## Installation Guides.

@@ -28,7 +28,7 @@ Idris has support for external code generators. Supplied with the distribution

2828is a C code generator to compile executables, and a JavaScript code generator

2929with support for node.js and browser JavaScript.

3030

31−More information about [code generators can be found on the wiki](https://idris.readthedocs.io/en/latest/reference/codegen.html).

31+More information about [code generators can be found on the wiki](http://idris.readthedocs.io/en/latest/reference/codegen.html).

3232

3333## More Information

3434

@@ -44,6 +44,3 @@ where some interesting projects are being hosted.

4444

4545For those interested in contributing to Idris directly we kindly ask that

4646prospective developers please consult the [Contributing Guide](CONTRIBUTING.md) first.

47−

48−[Idris 2](https://github.com/edwinb/Idris2) is an early preview of the next generation

49−of Idris, implemented in Idris.

Setup.hs+42−35

@@ -14,11 +14,10 @@ import Distribution.Simple.InstallDirs as I

1414import Distribution.Simple.LocalBuildInfo as L

1515import qualified Distribution.Simple.Setup as S

1616import qualified Distribution.Simple.Program as P

17−import Distribution.Simple.Utils

17+import Distribution.Simple.Utils (createDirectoryIfMissingVerbose, rewriteFile, notice, installOrdinaryFiles)

1818import Distribution.Compiler

1919import Distribution.PackageDescription

2020import Distribution.Text

21−import Distribution.Verbosity

2221

2322import System.Environment

2423import System.Exit

@@ -66,28 +65,28 @@ windres verbosity = P.runProgramInvocation verbosity . P.simpleProgramInvocation

6665

6766usesGMP :: S.ConfigFlags -> Bool

6867usesGMP flags =

69− case lookupFlagAssignment (mkFlagName "gmp") (S.configConfigurationsFlags flags) of

68+ case lookup (mkFlagName "gmp") (S.configConfigurationsFlags flags) of

7069 Just True -> True

7170 Just False -> False

7271 Nothing -> False

7372

7473execOnly :: S.ConfigFlags -> Bool

7574execOnly flags =

76− case lookupFlagAssignment (mkFlagName "execonly") (S.configConfigurationsFlags flags) of

75+ case lookup (mkFlagName "execonly") (S.configConfigurationsFlags flags) of

7776 Just True -> True

7877 Just False -> False

7978 Nothing -> False

8079

8180isRelease :: S.ConfigFlags -> Bool

8281isRelease flags =

83− case lookupFlagAssignment (mkFlagName "release") (S.configConfigurationsFlags flags) of

82+ case lookup (mkFlagName "release") (S.configConfigurationsFlags flags) of

8483 Just True -> True

8584 Just False -> False

8685 Nothing -> False

8786

8887isFreestanding :: S.ConfigFlags -> Bool

8988isFreestanding flags =

90− case lookupFlagAssignment (mkFlagName "freestanding") (S.configConfigurationsFlags flags) of

89+ case lookup (mkFlagName "freestanding") (S.configConfigurationsFlags flags) of

9190 Just True -> True

9291 Just False -> False

9392 Nothing -> False

@@ -97,11 +96,6 @@ mkFlagName :: String -> FlagName

9796mkFlagName = FlagName

9897#endif

9998

100−#if !(MIN_VERSION_Cabal(2,2,0))

101−lookupFlagAssignment :: FlagName -> FlagAssignment -> Maybe Bool

102−lookupFlagAssignment = lookup

103−#endif

104−

10599-- -----------------------------------------------------------------------------

106100-- Clean

107101

@@ -121,18 +115,6 @@ gitHash = do h <- Control.Exception.catch (readProcess "git" ["rev-parse", "--sh

121115 (\e -> let e' = (e :: SomeException) in return "PRE")

122116 return $ takeWhile (/= '\n') h

123117

124−-- Generate a module that contains extra library directories passed

125−-- via command-line to cabal

126−generateBuildFlagsModule :: Verbosity -> FilePath -> [String] -> IO ()

127−generateBuildFlagsModule verbosity dir libdirs = do

128− let buildFlagsModulePath = dir </> "BuildFlags_idris" Px.<.> "hs"

129− putStrLn $ "Generating " ++ buildFlagsModulePath

130− createDirectoryIfMissingVerbose verbosity True dir

131− rewriteFileEx verbosity buildFlagsModulePath contents

132− where contents = "module BuildFlags_idris where \n\n" ++

133− "extraLibDirs :: [String]\n" ++

134− "extraLibDirs = " ++ show libdirs

135−

136118-- Put the Git hash into a module for use in the program

137119-- For release builds, just put the empty string in the module

138120generateVersionModule verbosity dir release = do

@@ -141,7 +123,7 @@ generateVersionModule verbosity dir release = do

141123 putStrLn $ "Generating " ++ versionModulePath ++

142124 if release then " for release" else " for prerelease " ++ hash

143125 createDirectoryIfMissingVerbose verbosity True dir

144− rewriteFileEx verbosity versionModulePath (versionModuleContents hash)

126+ rewriteFile versionModulePath (versionModuleContents hash)

145127

146128 where versionModuleContents h = "module Version_idris where\n\n" ++

147129 "gitHash :: String\n" ++

@@ -155,7 +137,7 @@ generateTargetModule verbosity dir targetDir = do

155137 let targetModulePath = dir </> "Target_idris" Px.<.> "hs"

156138 putStrLn $ "Generating " ++ targetModulePath

157139 createDirectoryIfMissingVerbose verbosity True dir

158− rewriteFileEx verbosity targetModulePath (versionModuleContents absPath targetDir)

140+ rewriteFile targetModulePath (versionModuleContents absPath targetDir)

159141 where versionModuleContents absolute td = "module Target_idris where\n\n" ++

160142 "import System.FilePath\n" ++

161143 "import System.Environment\n" ++

@@ -181,14 +163,12 @@ generateToolchainModule verbosity srcDir toolDir = do

181163 "getToolchainDir = \"\""

182164 let toolPath = srcDir </> "Tools_idris" Px.<.> "hs"

183165 createDirectoryIfMissingVerbose verbosity True srcDir

184− rewriteFileEx verbosity toolPath (commonContent ++ toolContent)

166+ rewriteFile toolPath (commonContent ++ toolContent)

185167

186168idrisConfigure _ flags pkgdesc local = do

187169 configureRTS

188− withLibLBI pkgdesc local $ \lib libcfg -> do

170+ withLibLBI pkgdesc local $ \_ libcfg -> do

189171 let libAutogenDir = autogenComponentModulesDir local libcfg

190− let libDirs = extraLibDirs $ libBuildInfo lib

191− generateBuildFlagsModule verbosity libAutogenDir libDirs

192172 generateVersionModule verbosity libAutogenDir (isRelease (configFlags local))

193173 if isFreestanding $ configFlags local

194174 then do

@@ -215,10 +195,34 @@ idrisConfigure _ flags pkgdesc local = do

215195 autogenComponentModulesDir lbi _ = autogenModulesDir lbi

216196#endif

217197

218−#if !(MIN_VERSION_Cabal(2,0,0))

219−rewriteFileEx :: Verbosity -> FilePath -> String -> IO ()

220−rewriteFileEx _ = rewriteFile

221−#endif

198+idrisPreSDist args flags = do

199+ let dir = S.fromFlag (S.sDistDirectory flags)

200+ let verb = S.fromFlag (S.sDistVerbosity flags)

201+ generateVersionModule verb "src" True

202+ generateTargetModule verb "src" "./libs"

203+ generateToolchainModule verb "src" Nothing

204+ preSDist simpleUserHooks args flags

205+

206+idrisSDist sdist pkgDesc bi hooks flags = do

207+ pkgDesc' <- addGitFiles pkgDesc

208+ sdist pkgDesc' bi hooks flags

209+ where

210+ addGitFiles :: PackageDescription -> IO PackageDescription

211+ addGitFiles pkgDesc = do

212+ files <- gitFiles

213+ return $ pkgDesc { extraSrcFiles = extraSrcFiles pkgDesc ++ files}

214+ gitFiles :: IO [FilePath]

215+ gitFiles = liftM lines (readProcess "git" ["ls-files"] "")

216+

217+idrisPostSDist args flags desc lbi = do

218+ Control.Exception.catch (do let file = "src" </> "Version_idris" Px.<.> "hs"

219+ let targetFile = "src" </> "Target_idris" Px.<.> "hs"

220+ putStrLn $ "Removing generated modules:\n "

221+ ++ file ++ "\n" ++ targetFile

222+ removeFile file

223+ removeFile targetFile)

224+ (\e -> let e' = (e :: SomeException) in return ())

225+ postSDist simpleUserHooks args flags desc lbi

222226

223227-- -----------------------------------------------------------------------------

224228-- Build

@@ -246,7 +250,7 @@ idrisPreBuild args flags = do

246250 return (Nothing, [])

247251#endif

248252

249−idrisBuild _ flags _ local

253+idrisBuild _ flags _ local

250254 = if (execOnly (configFlags local)) then buildRTS

251255 else do buildStdLib

252256 buildRTS

@@ -268,7 +272,7 @@ idrisBuild _ flags _ local

268272-- -----------------------------------------------------------------------------

269273-- Copy/Install

270274

271−idrisInstall verbosity copy pkg local

275+idrisInstall verbosity copy pkg local

272276 = if (execOnly (configFlags local)) then installRTS

273277 else do installStdLib

274278 installRTS

@@ -323,5 +327,8 @@ main = defaultMainWithHooks $ simpleUserHooks

323327 , postInst = \_ flags pkg local ->

324328 idrisInstall (S.fromFlag $ S.installVerbosity flags)

325329 NoCopyDest pkg local

330+ , preSDist = idrisPreSDist

331+ , sDistHook = idrisSDist (sDistHook simpleUserHooks)

332+ , postSDist = idrisPostSDist

326333 , testHook = idrisTestHook

327334 }

appveyor.yml+4−4

@@ -5,15 +5,15 @@ init:

55

66 mkdir C:\ghc

77

8− Invoke-WebRequest "https://downloads.haskell.org/~ghc/8.8.2/ghc-8.8.2-x86_64-unknown-mingw32.tar.xz" -OutFile C:\ghc\ghc.tar.xz -UserAgent "Curl"

8+ Invoke-WebRequest "http://downloads.haskell.org/~ghc/7.10.3/ghc-7.10.3-x86_64-unknown-mingw32.tar.xz" -OutFile C:\ghc\ghc.tar.xz -UserAgent "Curl"

99

1010 7z x C:\ghc\ghc.tar.xz -oC:\ghc

1111

1212 7z x C:\ghc\ghc.tar -oC:\ghc

1313

14− $env:PATH="$env:PATH;c:\ghc\ghc-8.8.2\bin;$HOME\AppData\Roaming\cabal\bin"

14+ $env:PATH="$env:PATH;c:\ghc\ghc-7.10.3\bin;$HOME\AppData\Roaming\cabal\bin"

1515

16− cabal v1-update

16+ cabal update

1717

1818 $env:current_posix=c:\msys64\usr\bin\cygpath -u $(pwd)

1919

@@ -22,6 +22,6 @@ environment:

2222 MSYS2_PATH_TYPE: inherit

2323build_script:

2424- ps: >-

25− c:\msys64\usr\bin\bash -l -c "cd $env:current_posix && cabal v1-install -fffi --enable-tests 2>&1"

25+ c:\msys64\usr\bin\bash -l -c "cd $env:current_posix && cabal install -fffi --enable-tests 2>&1"

2626test_script:

2727- ps: c:\msys64\usr\bin\bash -l -c "cd $env:current_posix && make test_c 2>&1"

azure-pipelines.ymldeleted−143

@@ -1,143 +0,0 @@

1−# Starter pipeline

2−# Start with a minimal pipeline that you can customize to build and deploy your code.

3−# Add steps that build, run tests, deploy, and more:

4−# https://aka.ms/yaml

5−jobs:

6− # Test a configuration with the oldest supported GHC

7− - job: Linux_GHC_710

8− pool:

9− vmImage: 'Ubuntu 16.04'

10− steps:

11− - script: |

12− sudo add-apt-repository ppa:hvr/ghc

13− sudo apt-get update

14− sudo apt-get install ghc-7.10.3 cabal-install-2.2

15− sudo update-alternatives --config opt-ghc

16− sudo update-alternatives --config opt-cabal

17− displayName: 'Prepare system'

18− - script: |

19− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

20− cabal update

21− CABALFLAGS="-fffi -fci" make

22− displayName: 'Build Idris'

23− - script: |

24− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

25− make test_c

26− displayName: 'Run tests'

27− # Test on Linux

28− - job: Linux

29− pool:

30− vmImage: 'Ubuntu 16.04'

31− steps:

32− - script: |

33− sudo add-apt-repository ppa:hvr/ghc

34− sudo apt-get update

35− sudo apt-get install ghc-8.2.2 cabal-install-2.2

36− sudo update-alternatives --config opt-ghc

37− sudo update-alternatives --config opt-cabal

38− displayName: 'Prepare system'

39− - script: |

40− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

41− cabal update

42− CABALFLAGS="-fffi -fci" make

43− displayName: 'Build Idris'

44− - script: |

45− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

46− make test_c

47− displayName: 'Run tests'

48− # Test on MacOS

49− - job: macOS

50− pool:

51− vmImage: 'xcode9-macos10.13'

52− steps:

53− - script: |

54− brew install ghc cabal-install libffi pkgconfig

55− export PKG_CONFIG_PATH=/usr/local/opt/libffi/lib/pkgconfig:$PKG_CONFIG_PATH

56− export PATH=$HOME/.cabal/bin:$PATH

57− cabal update

58− CABALFLAGS="-fffi -fci" make

59− make test_c

60− displayName: 'Build idris and run tests'

61− # Test on Windows

62− - job: Windows

63− pool:

64− vmImage: 'vs2017-win2016'

65− steps:

66− - powershell: |

67− choco install cabal -y --no-progress

68− choco install 7zip.portable -y --no-progress

69− choco install msys2 -y --no-progress --params "/InstallDir=C:/msys64/"

70− mkdir C:\ghc

71− Invoke-WebRequest "https://downloads.haskell.org/~ghc/8.4.3/ghc-8.4.3-x86_64-unknown-mingw32.tar.xz" -OutFile C:\ghc\ghc.tar.xz -UserAgent "Curl"

72− 7z x C:\ghc\ghc.tar.xz -oC:\ghc

73− 7z x C:\ghc\ghc.tar -oC:\ghc

74− displayName: "Setting up environment"

75− - powershell: |

76− cabal update

77− $env:PATH="$env:PATH;$HOME\AppData\Roaming\cabal\bin;c:\ghc\ghc-8.4.3\bin"

78− $env:current_posix=c:\msys64\usr\bin\cygpath -u $(pwd)

79− c:\msys64\usr\bin\bash -l -c "echo `$MSYSTEM && echo `$PATH"

80− c:\msys64\usr\bin\bash -l -c "pacman -S make mingw-w64-x86_64-gcc mingw-w64-x86_64-pkg-config mingw-w64-x86_64-libffi --noconfirm 2>&1"

81− c:\msys64\usr\bin\bash -l -c "cd $env:current_posix && cabal install -fffi --enable-test 2>&1"

82− c:\msys64\usr\bin\bash -l -c "cd $env:current_posix && make test_c 2>&1"

83− env:

84− MSYSTEM: MINGW64

85− MSYS2_PATH_TYPE: inherit

86− displayName: "Build and test Idris"

87− # Check styling

88− - job: Stylize

89− pool:

90− vmImage: 'Ubuntu 16.04'

91− steps:

92− - script: |

93− sudo add-apt-repository ppa:hvr/ghc

94− sudo apt-get update

95− sudo apt-get install ghc-8.2.2 cabal-install-2.2

96− sudo update-alternatives --config opt-ghc

97− sudo update-alternatives --config opt-cabal

98− displayName: 'Prepare system'

99− - script: |

100− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

101− cabal update

102− cabal install stylish-haskell

103− ./stylize.sh

104− displayName: 'Run stylish'

105− # Run tests on the node backend

106− - job: JS

107− pool:

108− vmImage: 'Ubuntu 16.04'

109− steps:

110− - script: |

111− sudo add-apt-repository ppa:hvr/ghc

112− sudo apt-get update

113− sudo apt-get install ghc-8.2.2 cabal-install-2.2

114− sudo update-alternatives --config opt-ghc

115− sudo update-alternatives --config opt-cabal

116− displayName: 'Prepare system'

117− - script: |

118− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

119− cabal update

120− CABALFLAGS="-fffi -fci" make

121− displayName: 'Build Idris'

122− - script: |

123− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

124− make test_js

125− displayName: 'Run tests'

126− # Build docs

127− - job: Docs

128− pool:

129− vmImage: 'Ubuntu 16.04'

130− steps:

131− - script: |

132− sudo add-apt-repository ppa:hvr/ghc

133− sudo apt-get update

134− sudo apt-get install ghc-8.2.2 cabal-install-2.2

135− sudo update-alternatives --config opt-ghc

136− sudo update-alternatives --config opt-cabal

137− displayName: 'Prepare system'

138− - script: |

139− export PATH=/opt/ghc/bin:$HOME/.cabal/bin:$PATH

140− cabal update

141− CABALFLAGS="-fffi -fci" make

142− make lib_doc doc

143− displayName: 'Build Docs'

benchmarks/build.pl+2−3

@@ -2,14 +2,13 @@

22

33$bmarks = `cat ALL`;

44@bm = split(/\n/, $bmarks);

5−$idris = $ENV{'IDRIS'} || "idris";

65

76foreach $b (@bm) {

87 if ($b =~ /([a-zA-Z0-9]+)\/([a-zA-Z0-9]+)\s+(.*)/) {

98 print "Building $1 / $2\n";

109 chdir $1;

11− system("$idris --clean $2.ipkg");

12− system("$idris --build $2.ipkg") == 0 or die "Unable to build $2: $?";

10+ system("idris --clean $2.ipkg");

11+ system("idris --build $2.ipkg");

1312 chdir "..";

1413 }

1514}

benchmarks/fasta/fasta.idr−9

@@ -3,20 +3,11 @@ module Main

33import System

44

55alu : String

6−alu = "GGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGG"

7− ++ "TCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGG"

8− ++ "CGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGC"

9− ++ "GGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAA"

10−

11−{- The following string literal syntax doesn't work anymore. Until fixed we shall concat the strings.

126alu = "GGCCGGGCGCGGTGGCTCACGCCTGTAATCCCAGCACTTTGGGAGGCCGAGGCGGGCGGATCACCTGAGG\

137 \TCAGGAGTTCGAGACCAGCCTGGCCAACATGGTGAAACCCCGTCTCTACTAAAAATACAAAAATTAGCCGGG\

148 \CGTGGTGGCGCGCGCCTGTAATCCCAGCTACTCGGGAGGCTGAGGCAGGAGAATCGCTTGAACCCGGGAGGC\

159 \GGAGGTTGCAGTGAGCCGAGATCGCGCCACTGCACTCCAGCCTGGGCGACAGAGCGAGACTCCGTCTCAAAAA"

1610

17−-}

18−

19−

2011iub : List (Char, Double)

2112iub = [('a',0.27),('c',0.12),('g',0.12),('t',0.27),('B',0.02)

2213 ,('D',0.02),('H',0.02),('K',0.02),('M',0.02),('N',0.02)

benchmarks/pidigits/pidigits.idr+1−1

@@ -3,7 +3,7 @@ import Data.Vect

33

44{- Toy program that outputs the n first digits of Pi.

55

6− Inspired from https://www.haskell.org/haskellwiki/Shootout/Pidigits.

6+ Inspired from http://www.haskell.org/haskellwiki/Shootout/Pidigits.

77 The original ns and str lazy lists have been replaced by strict functions.

88

99 Memory usage seems to be excessive. One of the branches of str is tail recursive, and

config.mk+1−1

@@ -14,7 +14,7 @@ RANLIB ?=ranlib

1414CABAL :=cabal

1515# IDRIS_ENABLE_STATS should not be set in final release

1616# Any flags defined here which alter the RTS API must also be added to src/IRTS/CodegenC.hs

17−CFLAGS :=-O2 -Wall -std=c99 -pipe -fdata-sections -ffunction-sections -D_POSIX_C_SOURCE=200809L -DHAS_PTHREAD -DIDRIS_ENABLE_STATS $(CFLAGS)

17+CFLAGS :=-O2 -Wall -DHAS_PTHREAD -DIDRIS_ENABLE_STATS $(CFLAGS)

1818

1919# CABALFLAGS :=

2020CABALFLAGS += --enable-tests

docs/LICENSE+1−1

@@ -7,4 +7,4 @@ rights to Documentation for Idris.

77

88More information concerning the CC0 can be found online at:

99

10− https://creativecommons.org/publicdomain/zero/1.0/

10+ http://creativecommons.org/publicdomain/zero/1.0/

docs/Makefile+1−1

@@ -9,7 +9,7 @@ BUILDDIR = _build

99

1010# User-friendly check for sphinx-build

1111ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1)

12−$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from https://www.sphinx-doc.org/)

12+$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/)

1313endif

1414

1515# Internal variables.

docs/README.md+3−3

@@ -1,7 +1,7 @@

11# Documentation for the Idris Language.

22

33

4−This manual has been prepared using ReStructured Text and the [Sphinx Documentation Generator](https://www.sphinx-doc.org) for future inclusion on [Read The Docs](https://www.readthedocs.org).

4+This manual has been prepared using ReStructured Text and the [Sphinx Documentation Generator](http://sphinx-doc.org) for future inclusion on [Read The Docs](http://www.readthedocs.org).

55

66## Dependencies

77

@@ -12,7 +12,7 @@ To build the manual the following dependencies must be met. We assume that you h

1212Python should be installed by default on most systems.

1313Sphinx can be installed either through your hosts package manager or using pip/easy_install.

1414

15−*Note* [ReadTheDocs](https://www.readthedocs.org) works with Sphinx

15+*Note* [ReadTheDocs](http://www.readthedocs.org) works with Sphinx

1616 `v1.2.2`. If you install a more recent version of sphinx then

1717 'incorrectly' marked up documentation may get passed the build system

1818 of readthedocs and be ignored. In the past we had several code-blocks

@@ -45,7 +45,7 @@ rights to Documentation for Idris.

4545

4646More information concerning the CC0 can be found online at:

4747

48− https://creativecommons.org/publicdomain/zero/1.0/

48+ http://creativecommons.org/publicdomain/zero/1.0/

4949

5050

5151When contributing material to the manual please bear in mind that the work will be licensed as above.

docs/_static/theme_overrides.cssdeleted−13

@@ -1,13 +0,0 @@

1−/* override table width restrictions */

2−@media screen and (min-width: 767px) {

3−

4− .wy-table-responsive table td {

5− /* !important prevents the common CSS stylesheets from overriding

6− this as on RTD they are loaded after this stylesheet */

7− white-space: normal !important;

8− }

9−

10− .wy-table-responsive {

11− overflow: visible !important;

12− }

13−}

docs/conf.py+5−12

@@ -33,7 +33,7 @@ on_rtd = os.environ.get('READTHEDOCS', None) == 'True'

3333# ones.

3434extensions = [

3535 'sphinx.ext.todo',

36−# 'sphinx.ext.pngmath', # imgmath is not supported on readthedocs.

36+ 'sphinx.ext.pngmath', # imgmath is not supported on readthedocs.

3737 'sphinx.ext.ifconfig',

3838]

3939

@@ -51,7 +51,7 @@ master_doc = 'index'

5151

5252# General information about the project.

5353project = u'Idris'

54−copyright = u'2017-2020, The Idris Community'

54+copyright = u'2017, The Idris Community'

5555author = u'The Idris Community'

5656

5757# The version info for the project you're documenting, acts as replacement for

@@ -59,9 +59,9 @@ author = u'The Idris Community'

5959# built documents.

6060#

6161# The short X.Y version.

62−version = '1.3'

62+version = '1.1'

6363# The full version, including alpha/beta/rc tags.

64−release = '1.3.2'

64+release = '1.1.1'

6565

6666# The language for content autogenerated by Sphinx. Refer to documentation

6767# for a list of supported languages.

@@ -151,12 +151,6 @@ if not on_rtd: # only import and set the theme if we're building docs locally

151151# so a file named "default.css" will overwrite the builtin "default.css".

152152html_static_path = ['_static']

153153

154−html_context = {

155− 'css_files': [

156− '_static/theme_overrides.css', # override wide tables in RTD theme

157− ],

158− }

159−

160154# Add any extra paths that contain custom files (such as robots.txt or

161155# .htaccess) here, relative to this directory. These files are copied

162156# directly to the root of the documentation.

@@ -251,7 +245,6 @@ latex_elements = {

251245# Additional stuff for the LaTeX preamble.

252246'preamble': r'''

253247\usepackage{lmodern}

254−\usepackage{textalpha}

255248\usepackage[T1]{fontenc}

256249\usepackage[utf8x]{inputenc}

257250\usepackage{titlesec}

@@ -301,7 +294,7 @@ latex_elements = {

301294# (source start file, target name, title,

302295# author, documentclass [howto, manual, or own class]).

303296latex_documents = [

304− # (master_doc, 'idris.tex', u'Documentation for the Idris Language', u'The Idris Community', 'report')

297+ ('index', 'idris-documentation-complete.tex', u'Documentation for the Idris Language', u'The Idris Community', 'report'),

305298 ('tutorial/index', 'idris-tutorial.tex', u'The Idris Tutorial', u'The Idris Community', 'howto'),

306299]

307300

docs/effects/conclusions.rst+1−1

@@ -51,7 +51,7 @@ foundations are also well-studied see [5]_, [6]_, [7]_, [8]_.

5151 Programming Languages and Systems (APLAS '09), Zhenjiang Hu

5252 (Ed.). Springer-Verlag, Berlin, Heidelberg,

5353 95-110. DOI=10.1007/978-3-642-10672-9_9

54− https://link.springer.com/chapter/10.1007%2F978-3-642-10672-9_9

54+ http://link.springer.com/chapter/10.1007%2F978-3-642-10672-9_9

5555

5656

5757.. [4] Ohad Kammar, Sam Lindley, and Nicolas Oury. 2013. Handlers in

docs/effects/depeff.rst+9−18

@@ -43,8 +43,8 @@ express this as follows:

4343

4444.. code-block:: idris

4545

46− readInt : Eff () [STATE (Vect n Int), STDIO]

47− [STATE (Vect (S n) Int), STDIO]

46+ readInt : Eff ()[STATE (Vect n Int), STDIO]

47+ [STATE (Vect (S n) Int), STDIO]

4848 readInt = do let x = trim !getStr

4949 putM (cast x :: !get)

5050

@@ -153,21 +153,12 @@ file management follows a resource usage protocol with the following

153153

154154- When a file is closed, its handle should no longer be used

155155

156−These requirements can be expressed formally by creating a

156+These requirements can be expressed formally in , by creating a

157157``FILE_IO`` effect parameterised over a file handle state, which is

158158either empty, open for reading, or open for writing. The ``FILE_IO``

159−effect’s definition is given below.

160−

161−.. note::

162− This effect is mainly for illustrative purposes.

163− Typically we would also like to support random access files and

164− better reporting of error conditions.

165−

166− Moreover, the ``FILE`` effect in the ``Effect.File`` module of

167− the ``effects`` library uses slightly more complicated types to

168− support erroneous behaviour of each function and to support more

169− compilcated modes of opening, like for reading **and** writing,

170− appending or truncating.

159+effect’s definition is given below. Note that this

160+effect is mainly for illustrative purposes—typically we would also like

161+to support random access files and better reporting of error conditions.

171162

172163.. code-block:: idris

173164

@@ -182,7 +173,7 @@ effect’s definition is given below.

182173

183174 open : (fname : String)

184175 -> (m : Mode)

185− -> Eff Bool [FILE_IO ()]

176+ -> Eff Bool [FILE_IO ()]

186177 (\res => [FILE_IO (case res of

187178 True => OpenFile m

188179 False => ())])

@@ -200,7 +191,7 @@ In particular, consider the type of ``open``:

200191

201192 open : (fname : String)

202193 -> (m : Mode)

203− -> Eff Bool [FILE_IO ()]

194+ -> Eff Bool [FILE_IO ()]

204195 (\res => [FILE_IO (case res of

205196 True => OpenFile m

206197 False => ())])

@@ -216,7 +207,7 @@ we continue the protocol accordingly.

216207

217208 readFile : Eff (List String) [FILE_IO (OpenFile Read)]

218209 readFile = readAcc [] where

219− readAcc : List String -> Eff (List String) [FILE_IO (OpenFile Read)]

210+ readAcc : List String -> Eff (List String) [FILE_IO (OpenFile Read)]

220211 readAcc acc = if (not !eof)

221212 then readAcc (!readLine :: acc)

222213 else pure (reverse acc)

docs/effects/impleff.rst+1−1

@@ -144,7 +144,7 @@ functions in ``Eff``, as follows:

144144

145145**An implementation detail (aside):** The ``call`` function converts

146146an ``Effect`` to a function in ``Eff``, given a proof that the effect

147−is available. This proof can be constructed automatically, since

147+is available. This proof can be constructed automatically by , since

148148it is essentially an index into a statically known list of effects:

149149

150150.. code-block:: idris

docs/effects/index.rst+1−1

@@ -25,7 +25,7 @@ A tutorial on the `Effects` package in `Idris`.

2525 Idris Community* has waived all copyright and related or neighbouring

2626 rights to Documentation for Idris.

2727

28− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

28+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

2929

3030.. toctree::

3131 :maxdepth: 1

docs/effects/introduction.rst+2−3

@@ -3,7 +3,7 @@ Introduction

33************

44

55Pure functional languages with dependent types such as `Idris

6−<https://www.idris-lang.org/>`_ support reasoning about programs directly

6+<http://www.idris-lang.org/>`_ support reasoning about programs directly

77in the type system, promising that we can *know* a program will run

88correctly (i.e. according to the specification in its type) simply

99because it compiles. Realistically, though, things are not so simple:

@@ -17,8 +17,7 @@ exceptions, and verified resource management.

1717This tutorial assumes familiarity with pure programming in Idris,

1818as described in Sections 1–6 of the main tutorial [1]_. The examples

1919presented are tested with Idris and can be found in the

20−examples directory of the Idris repository. The ``-p effects`` flag

21−is needed when starting Idris.

20+examples directory of the Idris repository.

2221

2322Consider, for example, the following introductory function which

2423illustrates the kind of properties which can be expressed in the type

docs/effects/simpleeff.rst+1−2

@@ -212,8 +212,7 @@ from the result of a dynamic check:

212212

213213.. code-block:: idris

214214

215− data So : Bool -> Type where

216− Oh : So True

215+ data So : Bool -> Type = Oh : So True

217216

218217 choose : (b : Bool) -> Either (So b) (So (not b))

219218

docs/effects/summary.rst+23−23

@@ -43,16 +43,16 @@ FILE\_IO

4343 data OpenFile : Mode -> Type

4444

4545 open : (fname : String)

46− -> (m : Mode)

47− -> Eff Bool [FILE_IO ()]

48− (\res => [FILE_IO (case res of

49− True => OpenFile m

50− False => ())])

46+ -> (m : Mode)

47+ -> Eff Bool [FILE_IO ()]

48+ (\res => [FILE_IO (case res of

49+ True => OpenFile m

50+ False => ())])

5151 close : Eff () [FILE_IO (OpenFile m)] [FILE_IO ()]

5252

53− readLine : Eff String [FILE_IO (OpenFile Read)]

53+ readLine : Eff String [FILE_IO (OpenFile Read)]

5454 writeLine : String -> Eff () [FILE_IO (OpenFile Write)]

55− eof : Eff Bool [FILE_IO (OpenFile Read)]

55+ eof : Eff Bool [FILE_IO (OpenFile Read)]

5656

5757 Handler FileIO IO where { ... }

5858

@@ -69,9 +69,9 @@ RND

6969

7070 RND : EFFECT

7171

72− srand : Integer -> Eff () [RND]

73− rndInt : Integer -> Integer -> Eff Integer [RND]

74− rndFin : (k : Nat) -> Eff (Fin (S k)) [RND]

72+ srand : Integer -> Eff m () [RND]

73+ rndInt : Integer -> Integer -> Eff m Integer [RND]

74+ rndFin : (k : Nat) -> Eff m (Fin (S k)) [RND]

7575

7676 Handler Random m where { ... }

7777

@@ -86,7 +86,7 @@ SELECT

8686

8787 SELECT : EFFECT

8888

89− select : List a -> Eff a [SELECT]

89+ select : List a -> Eff m a [SELECT]

9090

9191 Handler Selection Maybe where { ... }

9292 Handler Selection List where { ... }

@@ -102,10 +102,10 @@ STATE

102102

103103 STATE : Type -> EFFECT

104104

105− get : Eff x [STATE x]

106− put : x -> Eff () [STATE x]

107− putM : y -> Eff () [STATE x] [STATE y]

108− update : (x -> x) -> Eff () [STATE x]

105+ get : Eff m x [STATE x]

106+ put : x -> Eff m () [STATE x]

107+ putM : y -> Eff m () [STATE x] [STATE y]

108+ update : (x -> x) -> Eff m () [STATE x]

109109

110110 Handler State m where { ... }

111111

@@ -121,12 +121,12 @@ STDIO

121121

122122 STDIO : EFFECT

123123

124− putChar : Char -> Eff () [STDIO]

125− putStr : String -> Eff () [STDIO]

126− putStrLn : String -> Eff () [STDIO]

124+ putChar : Handler StdIO m => Char -> Eff m () [STDIO]

125+ putStr : Handler StdIO m => String -> Eff m () [STDIO]

126+ putStrLn : Handler StdIO m => String -> Eff m () [STDIO]

127127

128− getStr : Eff String [STDIO]

129− getChar : Eff Char [STDIO]

128+ getStr : Handler StdIO m => Eff m String [STDIO]

129+ getChar : Handler StdIO m => Eff m Char [STDIO]

130130

131131 Handler StdIO IO where { ... }

132132 Handler StdIO (IOExcept a) where { ... }

@@ -144,9 +144,9 @@ SYSTEM

144144

145145 SYSTEM : EFFECT

146146

147− getArgs : Eff (List String) [SYSTEM]

148− time : Eff Int [SYSTEM]

149− getEnv : String -> Eff (Maybe String) [SYSTEM]

147+ getArgs : Handler System e => Eff e (List String) [SYSTEM]

148+ time : Handler System e => Eff e Int [SYSTEM]

149+ getEnv : Handler System e => String -> Eff e (Maybe String) [SYSTEM]

150150

151151 Handler System IO where { ... }

152152 Handler System (IOExcept a) where { ... }

docs/elaboratorReflection/elabReflection.rstdeleted−60

@@ -1,60 +0,0 @@

1−Extending Idris using Elaborator Reflection

2−===========================================

3−

4−Idris provides a mechanism to modify the language without having to recompile Idris itself. We can think of this in terms of metaprogramming or domain specific languages or just building in new capabilities.

5−

6−In order to extend the language we need to know something about how Idris is compiled. This page explains only what is needed to customise the elaboration. For more information about the compiler's implementation see `Edwin Brady's 2013 paper`_ and for customising the elaboration process see `Elaborator reflection: extending Idris in Idris`_ and `David Christiansen's PhD thesis`_.

7−

8−Compilation of Idris proceeds through a number of stages.

9−

10−- First, Idris is desugared by inserting placeholders for terms to be guessed by the compiler and replacing certain syntactic forms, such as do-notation, with the functions that implement them.

11−- Then, this desugared Idris is translated into a much simpler core language, called TT. This translation process is called elaboration.

12−- Finally, TT is type checked a second time to rule out errors, and then compiled into the target language.

13−

14−.. image:: ../image/idrisTopLevel.png

15− :width: 484px

16− :height: 147px

17− :alt: diagram illustrating these stages of Idris compilation

18−

19−TT is a core language which is syntactically very simple. This makes it easy for computers to process but very verbose and hard for humans to read. The Idris elaborator is written in Haskell using an elaboration library that was inspired by the tactics in interactive proof assistants such as Coq.

20−

21−.. list-table::

22−

23− * - There are some similarities with a proof assistant but in Idris the elaborator is an interpreter of Idris source in the elaboration monad, where each syntactic construct of Idris is interpreted as a sequence of tactics.

24− - .. image:: ../image/compareToProofAssist.png

25− :width: 206px

26− :height: 112px

27− :alt: diagram comparing elaboration with proof assistant

28−

29−The primitives in the elaboration library are not just useful for the implementors of Idris itself. They can also be used by authors of extensions to the compiler, using a mechanism known as elaborator reflection.

30−During elaboration TT (Raw) structure contains:

31−

32−- holes - placeholders for terms that have not yet been filled in.

33−- guesses - similar to let bindings, except with no reduction rule, so that elaboration programs can control the precise shape of terms that are under construction.

34−

35−For more information about holes and guesses see `Dependently Typed Functional Programs and their Proofs by McBride 1999`_.

36−

37−The following diagram is intended to illustrate a high level view of the tactics and how this eventually results in the TT language being generated. It is not necessary to understand the details at this stage. The intention is to help build up some intuition so that, when we get into the details, we can recognise how this fits into the big picture.

38−

39−.. image:: ../image/elabOverview.png

40− :width: 410px

41− :height: 282px

42− :alt: diagram illustrating overview of TT language being generated from tactics.

43−

44−As already mentioned the TT core language is kept syntactically very simple, for instance, here are the binders in TT with corresponding code and logic type validity rules:

45−

46−.. list-table::

47−

48− * - This diagram illustrates the basis of the compilation process in logic (in this case for binders). It is not necessary to be an expert logician to understand elaborator reflection. However, when learning about tactics, they may appear arbitrary without knowing some theory. For more information about this see `Edwin Brady's 2013 paper`_.

49− - .. image:: ../image/binders.png

50− :width: 310px

51− :height: 203px

52− :alt: diagram illustrating basis of code in logic

53−

54−.. target-notes::

55−.. _`Edwin Brady's 2013 paper`: https://eb.host.cs.st-andrews.ac.uk/drafts/impldtp.pdf

56−.. _`Elaborator reflection: extending Idris in Idris`: https://dl.acm.org/citation.cfm?doid=2951913.2951932

57−.. _`David Christiansen's PhD thesis`: https://davidchristiansen.dk/david-christiansen-phd.pdf

58−.. _`Dependently Typed Functional Programs and their Proofs by McBride 1999`: https://www.era.lib.ed.ac.uk/handle/1842/374

59−

60−

docs/elaboratorReflection/example1.rstdeleted−192

@@ -1,192 +0,0 @@

1−Elaborator Reflection - Identity Example

2−========================================

3−

4−.. list-table::

5−

6− * - This example of elaborator reflection steps through this metaprogram that generates the identity function:

7− - .. code-block:: idris

8−

9− %language ElabReflection

10−

11− idNat : Nat -> Nat

12− idNat = %runElab (do intro `{{x}}

13− fill (Var `{{x}})

14− solve)

15−

16−.. list-table::

17− :widths: 200 100

18−

19− * - At the beginning of executing the elaboration script, the initial state consists of a single hole of type Nat -> Nat.

20−

21− As a first approximation, the state consists of a term with holes in it, an indicator of which hole is focused, a queue of the next holes to focus on, and miscellaneous information like a source of fresh names. The intro tactic modifies this state, replacing the focused hole with a lambda and focusing on the lambda's body.

22− - .. image:: ../image/tree.png

23− :width: 119px

24− :height: 109px

25−

26−The following is a walkthough looking at the state after each tactic:

27−

28−.. list-table::

29−

30− * - Start with the type signature like this:

31− - .. code-block:: idris

32−

33− %language ElabReflection

34−

35− idNat : Nat -> Nat

36− idNat = %runElab (do

37−

38− * - In order to investigate how the program works this table shows the proof state at each stage as the tactics are applied. So here is the proof state at the start:

39− - .. image:: ../image/elabProofStateEx1_1.png

40− :width: 310px

41− :height: 115px

42−

43− * - This table shows the hole types and what they depend on. The aim is to illustrate the types by analogy with proofs, as a line with the premises above it and the conclusion below it.

44− - .. image:: ../image/elabLogicEx1_1.png

45− :width: 277px

46− :height: 15px

47−

48− * - The term is:

49− - ?{hole_0} ≈ ? {hole_2} . {hole_2} . {hole_0}

50−

51− * - It is possible to read the state from the script by calling getEnv, getGoal and getHoles.

52−

53− - The output of these calls contain structures with TT code. To show the results I hacked this: `my code`_. TT code is not really designed to be readable by humans, all the names are fully expanded, everything has a type down to universes (type of types). This is shown here to illustrate the information available.

54−

55− .. code-block:: idris

56−

57− getEnv=[]

58−

59− getGoal=(hole_2, __pi_arg:(Nat.["Nat", "Prelude"]:{

60− type constructor tag=8 number=0}.Type:U=(20:./Prelude/Nat.idr)->.

61− {name ref{type constructor tag=8 number=0}Nat.["Nat","Prelude"]:

62− Type:U=(20:./Prelude/Nat.idr)

63− })

64− })

65−

66− getHoles=[{hole_2},{hole_0}]

67−

68− * - getGuess

69− - error no guess

70−

71− * - Introduce a lambda binding around the current hole and focus on the body.

72− - intro \`{{x}}

73−

74− * - The state now looks like this:

75− - .. image:: ../image/elabProofStateEx1_2.png

76− :width: 312px

77− :height: 84px

78−

79− * - The hole types now looks like this:

80− - .. image:: ../image/elabLogicEx1_2.png

81− :width: 279px

82− :height: 26px

83−

84− * - The term now looks like this:

85− - ?{hole_0} ≈ λ x . ? {hole_2} . {hole_2} . {hole_0}

86−

87− * - Again we can check the state by calling getEnv, getGoal and getHoles: see `my code`_

88−

89− - .. code-block:: idris

90−

91− getEnv=[(x, {λ (Nat.["Nat", "Prelude"]:{

92− type constructor tag=8 number=0}).

93− Type:U=(20:./Prelude/Nat.idr)

94− })]

95−

96− getGoal=(hole_2, {name ref{type constructor tag=8 number=0}

97− Nat.["Nat","Prelude"]:Type:U=(20:./Prelude/Nat.idr)

98− })

99−

100− getHoles=[{hole_2},{hole_0}]

101−

102− * - getGuess

103− - error no guess

104−

105− * - Place a term into a hole, unifying its type

106− - fill (Var \`{{x}})

107−

108− * - The state still looks like this:

109− - .. image:: ../image/elabProofStateEx1_3.png

110− :width: 312px

111− :height: 57px

112−

113− * - The hole types now looks like this:

114− - .. image:: ../image/elabLogicEx1_3.png

115− :width: 290px

116− :height: 26px

117−

118− * - The term now looks like this:

119− - ?{hole_0} ≈ λ x . ?{hole_2} ≈ x . {hole_2} . {hole_0}

120−

121− * - Again we can check the state by calling getEnv, getGoal and getHoles: see `my code`_

122−

123− - .. code-block:: idris

124−

125− getEnv=[(x, {λ (Nat.["Nat", "Prelude"]:

126− {type constructor tag=8 number=0}).

127− Type:U=(20:./Prelude/Nat.idr)

128− })]

129−

130− getGoal=(hole_2, {name ref{type constructor tag=8 number=0}

131− Nat.["Nat","Prelude"]:Type:U=(20:./Prelude/Nat.idr)

132− })

133−

134− getHoles=[{hole_2}, {hole_0}]

135−

136− * - getGuess

137− - .. code-block:: idris

138−

139− {name ref bound x:

140− {name ref{type constructor tag=8 number=0}

141− Nat.["Nat","Prelude"]:Type:U=(20:./Prelude/Nat.idr)

142− }

143− }

144−

145− * - Substitute a guess into a hole.

146− - solve

147−

148− * - The hole types now looks like this:

149− - .. image:: ../image/elabLogicEx1_4.png

150− :width: 131px

151− :height: 14px

152−

153− * - The term now looks like this:

154− - ?{hole_0} ≈ λ x . x . {hole_0}

155−

156− * - getEnv

157−

158− getGoal

159−

160− getHoles

161−

162− - .. code-block:: idris

163−

164− getEnv=[]

165−

166− getGoal=(hole_0, __pi_arg:(Nat.["Nat", "Prelude"]:{

167− type constructor tag=8 number=0}.

168− Type:U=(20:./Prelude/Nat.idr)

169− ->.{name ref

170− {type constructor tag=8 number=0}

171− Nat.["Nat","Prelude"]:Type:U=(20:./Prelude/Nat.idr)

172− })

173− })

174−

175− getHoles=[{hole_0}]

176−

177− * - getGuess

178− - .. code-block:: idris

179−

180− x:({λ (Nat.["Nat", "Prelude"]:{

181− type constructor tag=8 number=0}).

182− Type:U=(20:./Prelude/Nat.idr)

183− }.{

184− name ref bound

185− x:{name ref {type constructor tag=8 number=0}

186− Nat.["Nat","Prelude"]:Type:U=(20:./Prelude/Nat.idr)

187− }

188− })

189− }

190−

191−.. target-notes::

192−.. _`my code`: https://github.com/martinbaker/Idris-dev/blob/uglyTTPrinter/libs/prelude/Language/Reflection/TTPrinter.idr

docs/elaboratorReflection/generatingData.rstdeleted−385

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1−Generating Datatypes and Functions at Compile Time

2−==================================================

3−

4−Program elements, such as datatypes and functions can be constructed at compile-time in the Elab monad.

5−This can allow proofs to be generated for user defined types or it could allow types to be automatically generated to support user defined types.

6−An example is the code, from `Elaborator reflection: extending Idris in Idris`_, that automatically generates accessibility predicates using the Bove-Capretta method.

7−

8−Generating Datatypes

9−--------------------

10−

11−There are two main 'tactics' associated with generating datatypes:

12−

13−- declareDatatype

14−- defineDatatype

15−

16−Which declare and define the datatype as the names suggest.

17−

18−.. list-table::

19−

20− * - These 'tactics' and the data structures associated with them are listed in the tables later on this page, for now, here is a summary:

21− - .. image:: ../image/generateDatatype.png

22− :width: 332px

23− :height: 246px

24− :alt: diagram illustrating data structures associated with declareDatatype defineDatatype.

25−

26−.. list-table::

27−

28− * - As a first example, the following boolean-like type can be constructed. When the compiler has run it will be available to us as if we had compiled it in the usual way:

29− - .. code-block:: idris

30−

31− λΠ> :printdef Two

32− data Two : Type where

33− F : Two

34− T : Two

35−

36−This was generated by the following code:

37−

38−.. code-block:: idris

39−

40− module TwoDef

41− %language ElabReflection

42−

43− addTwo : Elab ()

44− addTwo = do let twoname : TTName = `{{TwoDef.Two}}

45− let F2 = `{{TwoDef.F}}

46− let T2 = `{{TwoDef.T}}

47− declareDatatype $ Declare twoname [] `(Type)

48− defineDatatype $ DefineDatatype twoname [

49− Constructor `{{F}} [] (Var `{{TwoDef.Two}}),

50− Constructor `{{T}} [] (Var `{{TwoDef.Two}})

51− ]

52−

53− %runElab addTwo

54−

55−.. list-table::

56−

57− * - The constructors T and F can be called as would be expected:

58− - .. code-block:: idris

59−

60− λΠ> F

61− F : Two

62− λΠ> T

63− T : Two

64−

65−Generating Functions

66−--------------------

67−

68−There are two main 'tactics' associated with generating functions:

69−

70−- declareType

71−- defineFunction

72−

73−Which declare and define the function as the names suggest.

74−

75−.. list-table::

76−

77− * - These 'tactics' and the data structures associated with them are listed in the tables later on this page, for now, here is a summary:

78− - .. image:: ../image/generateFunction.png

79− :width: 332px

80− :height: 246px

81− :alt: diagram illustrating data structures associated with function declare and define.

82−

83−Note: The left hand side (lhs) and right hand side (rhs) of FunClause typically is of type 'Raw'.

84−

85−.. list-table::

86−

87− * - Bound pattern variables are represented by 'PVar' binders:

88− This diagram shows an example of a possible Raw structure that might be used in a function definition.

89− - .. image:: ../image/generateFunction2.png

90− :width: 264px

91− :height: 239px

92− :alt: diagram illustrating data structures associated with functions.

93−

94−.. list-table::

95−

96− * - Some function definitions can now be added to the above datatype. This is what they will look like:

97− - .. code-block:: idris

98−

99− λΠ> :printdef perm1

100− perm1 : Two -> Two

101− perm1 F = F

102− perm1 T = T

103− λΠ> :printdef perm2

104− perm2 : Two -> Two

105− perm1 F = T

106− perm1 T = F

107−

108−This was generated with the following code:

109−

110−.. code-block:: idris

111−

112− let perm1 = `{{TwoDef.perm1}}

113− declareType (Declare perm1 [MkFunArg `{{code}} (Var twoname) Explicit NotErased] (Var twoname))

114− defineFunction $ DefineFun perm1 [

115− MkFunClause (RApp (Var perm1) (Var `{{TwoDef.F}})) (Var F2),

116− MkFunClause (RApp (Var perm1) (Var `{{TwoDef.T}})) (Var T2)

117− ]

118−

119− let perm2 = `{{TwoDef.perm2}}

120− declareType (Declare perm2 [MkFunArg `{{code}} (Var twoname) Explicit NotErased] (Var twoname))

121− defineFunction $ DefineFun perm2 [

122− MkFunClause (RApp (Var perm1) (Var `{{TwoDef.F}})) (Var T2),

123− MkFunClause (RApp (Var perm1) (Var `{{TwoDef.T}})) (Var F2)

124− ]

125−

126−.. list-table::

127−

128− * - This is what happens when we call the functions:

129− - .. code-block:: idris

130−

131− λΠ> perm1 F

132− F : Two

133− λΠ> perm1 T

134− T : Two

135− λΠ> perm2 F

136− T : Two

137− λΠ> perm2 T

138− F : Two

139−

140−So far these datatypes and functions could have been written, statically, in the usual way. However, it is possible to imagine situations where we may need a lot of functions to be generated automatically at compile time. For example, if we extend this Boolean datatype to a datatype with more simple constructors (a finite set), we could generate a function for every possible permutation of that datatype back to itself.

141−

142−A Different Example which has Type Parameters

143−---------------------------------------------

144−

145−.. list-table::

146−

147− * - Here is an example of a datatype with type parameters:

148− - .. code-block:: idris

149−

150− data N : Nat -> Type where

151− MkN : N x

152− MkN' : (x : Nat) -> N (S x)

153−

154−This was produced by the following code:

155−

156−.. code-block:: idris

157−

158− module DataDef

159− %language ElabReflection

160−

161− addData : Elab ()

162− addData = do

163− let dataname : TTName = `{{DataDef.N}}

164− declareDatatype $ Declare dataname [MkFunArg `{{n}} `(Nat) Explicit NotErased] `(Type)

165− defineDatatype $ DefineDatatype dataname [

166− Constructor `{{MkN}} [MkFunArg `{{x}} `(Nat) Implicit NotErased]

167− (RApp (Var dataname) (Var `{{x}})),

168− Constructor `{{MkN'}} [MkFunArg `{{x}} `(Nat) Explicit NotErased]

169− (RApp (Var dataname) (RApp (Var `{S}) (Var `{{x}})))

170− ]

171−

172− %runElab addData

173−

174−So this declares and defines the following data structure 'N' with a constructor 'MkN' which can have an implicit or an explicit Nat argument. Which can be used like this:

175−

176−.. code-block:: idris

177−

178− λΠ> :t N

179− N : Nat -> Type

180− λΠ> N 2

181− N 2 : Type

182− λΠ> N 0

183− N 0 : Type

184− λΠ> :t MkN

185− MkN : N x

186−

187−Table of 'tactics' for Generating Data and Functions

188−----------------------------------------------------

189−

190−These are the functions that we can use to create data and functions in the Elab monad:

191−

192−.. list-table::

193− :widths: 10 30

194− :stub-columns: 1

195−

196− * - declareType

197− - Add a type declaration to the global context.

198−

199− Signature:

200−

201− declareType : TyDecl -> Elab ()

202− * - defineFunction

203− - Define a function in the global context. The function must have already been declared, either in ordinary Idris code or using `declareType`.

204−

205− Signature:

206−

207− defineFunction : FunDefn Raw -> Elab ()

208−

209− * - declareDatatype

210− - Declare a datatype in the global context. This step only establishes the type constructor; use `defineDatatype` to give it constructors.

211−

212− Signature:

213−

214− declareDatatype : TyDecl -> Elab ()

215−

216− * - defineDatatype

217− - Signature:

218−

219− defineDatatype : DataDefn -> Elab ()

220−

221− * - addImplementation

222− - Register a new implementation for interface resolution.

223−

224− Arguments:

225−

226− - ifaceName the name of the interface for which an implementation is being registered

227− - implName the name of the definition to use in implementation search

228−

229− Signature:

230−

231− addImplementation : (ifaceName, implName : TTName) -> Elab ()

232−

233− * - isTCName

234− - Determine whether a name denotes an interface.

235−

236− Arguments:

237−

238− - name - a name that might denote an interface.

239−

240− Signature:

241−

242− isTCName : (name : TTName) -> Elab Bool

243−

244−Table of Datatypes Associated with Generating Data and Functions

245−----------------------------------------------------------------

246−

247−The above functions use the following data/records:

248−

249−.. list-table::

250− :widths: 10 30

251− :stub-columns: 1

252−

253− * - Plicity

254− - How an argument is provided in high-level Idris

255−

256− .. code-block:: idris

257−

258− data Plicity=

259− ||| The argument is directly provided at the application site

260− Explicit |

261− ||| The argument is found by Idris at the application site

262− Implicit |

263− ||| The argument is solved using interface resolution

264− Constraint

265−

266− * - FunArg

267− - Function arguments

268−

269− These are the simplest representation of argument lists, and are used for functions. Additionally, because a FunArg provides enough

270− information to build an application, a generic type lookup of a top-level identifier will return its FunArgs, if applicable.

271−

272− .. code-block:: idris

273−

274− record FunArg where

275− constructor MkFunArg

276− name : TTName

277− type : Raw

278− plicity : Plicity

279− erasure : Erasure

280−

281− * - TyConArg

282− - Type constructor arguments

283−

284− Each argument is identified as being either a parameter that is

285−

286− consistent in all constructors, or an index that varies based on

287−

288− which constructor is selected.

289−

290− .. code-block:: idris

291−

292− data TyConArg =

293− ||| Parameters are uniform across the constructors

294− TyConParameter FunArg |

295− ||| Indices are not uniform

296− TyConIndex FunArg

297−

298− * - TyDecl

299− - A type declaration for a function or datatype

300−

301− .. code-block:: idris

302−

303− record TyDecl where

304− constructor Declare

305− ||| The fully-qualified name of the function or datatype being declared.

306− name : TTName

307− ||| Each argument is in the scope of the names of previous arguments.

308− arguments : List FunArg

309− ||| The return type is in the scope of all the argument names.

310− returnType : Raw

311−

312− * - FunClause

313− - A single pattern-matching clause

314−

315− .. code-block:: idris

316−

317− data FunClause : Type -> Type where

318− MkFunClause : (lhs, rhs : a) -> FunClause a

319− MkImpossibleClause : (lhs : a) -> FunClause a

320−

321− * - FunDefn

322− - A reflected function definition.

323−

324− .. code-block:: idris

325−

326− record FunDefn a where

327− constructor DefineFun

328− name : TTName

329− clauses : List (FunClause a)

330−

331− * - ConstructorDefn

332− - A constructor to be associated with a new datatype.

333−

334− .. code-block:: idris

335−

336− record ConstructorDefn where

337− constructor Constructor

338− ||| The name of the constructor. The name must _not_ be qualified -

339− ||| that is, it should begin with the `UN` or `MN` constructors.

340− name : TTName

341− ||| The constructor arguments. Idris will infer which arguments are

342− ||| datatype parameters.

343− arguments : List FunArg

344− ||| The specific type constructed by the constructor.

345− returnType : Raw

346−

347− * - DataDefn

348− - A definition of a datatype to be added during an elaboration script.

349−

350− .. code-block:: idris

351−

352− record DataDefn where

353− constructor DefineDatatype

354− ||| The name of the datatype being defined. It must be

355− ||| fully-qualified, and it must have been previously declared as a

356− ||| datatype.

357− name : TTName

358− ||| A list of constructors for the datatype.

359− constructors : List ConstructorDefn

360−

361− * - CtorArg

362− - CtorParameter

363−

364− .. code-block:: idris

365−

366− data CtorArg = CtorParameter FunArg | CtorField FunArg

367−

368− * - Datatype

369− - A reflected datatype definition

370−

371− .. code-block:: idris

372−

373− record Datatype where

374− constructor MkDatatype

375− ||| The name of the type constructor

376− name : TTName

377− ||| The arguments to the type constructor

378− tyConArgs : List TyConArg

379− ||| The result of the type constructor

380− tyConRes : Raw

381− ||| The constructors for the family

382− constructors : List (TTName, List CtorArg, Raw)</td>

383−

384−.. target-notes::

385−.. _`Elaborator reflection: extending Idris in Idris`: https://dl.acm.org/citation.cfm?doid=2951913.2951932

docs/elaboratorReflection/holes.rstdeleted−196

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1−Elaborator Reflection - Holes

2−=============================

3−

4−The process of doing proofs and elaborator reflection tends to involve stating with a desired conclusion and working back to known premises. This often needs intermediate sub-goals which may only be partially solved, these are encoded using 'holes' and 'guesses'.

5−

6−* A hole is a term (an expression - a chunk of code) which is yet to be determined. We do have information about its type (this process tends to be type driven).

7−* A guess is like a hole that is not yet bound.

8−

9−The theory around this was developed in `Dependently Typed Functional Programs and their Proofs by McBride 1999`_.

10−

11−Notation for Holes and Guesses

12−------------------------------

13−

14−There is a notation used in the McBride 1999 thesis which is adapted for the TT language. When working on elaborator reflection it is useful to know this notation, for instance when reading the output of the 'debug' tactic.

15−

16−* A focused hole is notated like this ?x:t . t

17−* A guess is notated like this ?x ≈ t:t . t

18−

19−The following example shows how this is used:

20−

21−Simple Example

22−--------------

23−

24−Start with a code file that just contains:

25−

26−.. code-block:: idris

27−

28− %language ElabReflection

29−

30− testFn : Nat

31− testFn = %runElab (do debug {a = ()})

32−

33−when this is loaded the following is displayed:

34−

35−.. code-block:: idris

36−

37− Holes:

38− ----------------------------------

39− {hole_2} : Prelude.Nat.Nat

40−

41− ----------------------------------

42− {hole_0} : Prelude.Nat.Nat

43−

44− Term:

45− ?{hole_0} ≈ ? {hole_2} . {hole_2} . {hole_0}

46−

47−This shows information about the state when debug is encountered, during tactic execution, which allows us to investigate what is happening at each stage.

48−

49−* The "Holes" part shows the types of the holes and the local context of each

50−* The "Term" part shows where these holes are in the expression being constructed.

51−

52−So starting with the "Term" part we have.

53−

54−.. code-block:: idris

55−

56− ?{hole_0} ≈ ? {hole_2} . {hole_2} . {hole_0}

57−

58−.. sidebar:: attack tactic

59−

60− This kind of thing tends to arise from "attack", which helps keep binding forms in order.

61−

62−The meaning of this is not immediately apparent so it helps to add some parentheses to make the structure clearer:

63−

64−.. code-block:: idris

65−

66− (?{hole_0} ≈ (? {hole_2} . {hole_2}) . {hole_0})

67−

68−First lets look at the inner part:

69−

70−.. code-block:: idris

71−

72− ? {hole_2} . {hole_2}

73−

74−We can substitute in the type from the "Holes" part:

75−

76−.. code-block:: idris

77−

78− ? {hole_2}:Nat . {hole_2}:Nat

79−

80−So we are looking for a hole of type Nat and all we know is it has type Nat.

81−

82−Going back to the full term, the above is wrapped in a guess, so it means: 'a guess that is itself a hole'.

83−

84−Since the elaborator does not have any further information it has to be given a value:

85−

86−.. code-block:: idris

87−

88− %language ElabReflection

89−

90− testFn : Nat

91− testFn = %runElab (do fill `(Z)

92− debug {a = ()}

93− solve)

94−

95−Now we have a guess for hole_2 which is itself a guess for hole_0:

96−

97−.. code-block:: idris

98−

99− ?{hole_0} ≈ ?{hole_2} ≈ Prelude.Nat.Z . {hole_2} . {hole_0}

100−

101−The guesses can be accepted by calling the 'solve' tactic.

102−

103−Example Showing Patterns

104−------------------------

105−

106−In this next example a parameter 'n' has been added to the function. This allows us to see how patterns are used. Starting with this file:

107−

108−.. code-block:: idris

109−

110− %language ElabReflection

111−

112− testFn : Nat -> Nat

113− testFn n = %runElab (do debug {a = ()})

114−

115−when loaded gives:

116−

117−.. code-block:: idris

118−

119− Holes:

120− n : Prelude.Nat.Nat

121− ----------------------------------

122− {hole_3} : Prelude.Nat.Nat

123−

124− n : Prelude.Nat.Nat

125− ----------------------------------

126− {hole_1} : Prelude.Nat.Nat

127−

128− ----------------------------------

129− {hole_0} : patTy n : Prelude.Nat.Nat . Prelude.Nat.Nat

130−

131− Term:

132− ?{hole_0} ≈ pat n : Prelude.Nat.Nat .

133− ?{hole_1} ≈ ? {hole_3} . {hole_3} . {hole_1} .

134− {hole_0}

135−

136−The ns above the lines show the context of the holes on the right hand side - they include the variable n that is an argument!

137−

138−patTy is a binding form in Idris's core language that introduces a pattern variable. The idea is that the left-hand side and right-hand side of each pattern should have the same type. Because pattern variables may occur multiple times on either side of the equation, we can achieve this by documenting their types with a binding form that wraps each side. This new binding form is why an "attack" was necessary prior to elaborating the RHS.

139−

140−patTy is a type former, and pat is the corresponding introduction form. So you can think of patTy as being a bit like a dependent function type, and pat as being a bit like lambda, except they don't introduce functions (they instead are used for pattern-matching definitions).

141−

142−More Complicated Example

143−------------------------

144−

145−This example does not introduce any new notation but the extra complexity gives a more realistic idea of how it is used. Here we start with this file:

146−

147−.. code-block:: idris

148−

149− %language ElabReflection

150−

151− testFn : (n : Nat) -> (n = plus n Z) -> (S n = S (plus n Z))

152− testFn k ih = %runElab (do debug {a = ()})

153−

154−when loaded gives:

155−

156−.. code-block:: idris

157−

158− Holes:

159− k : Prelude.Nat.Nat

160− ih : = Prelude.Nat.Nat Prelude.Nat.Nat k

161− (Prelude.Nat.plus k Prelude.Nat.Z)

162− ----------------------------------

163− {hole_4} : = Prelude.Nat.Nat Prelude.Nat.Nat (Prelude.Nat.S k)

164− (Prelude.Nat.S (Prelude.Nat.plus k Prelude.Nat.Z))

165−

166− k : Prelude.Nat.Nat

167− ih : = Prelude.Nat.Nat Prelude.Nat.Nat k

168− (Prelude.Nat.plus k Prelude.Nat.Z)

169− ----------------------------------

170− {hole_2} : = Prelude.Nat.Nat Prelude.Nat.Nat (Prelude.Nat.S k)

171− (Prelude.Nat.S (Prelude.Nat.plus k Prelude.Nat.Z))

172−

173− k : Prelude.Nat.Nat

174− ----------------------------------

175− {hole_1} : patTy ih : = Prelude.Nat.Nat Prelude.Nat.Nat k

176− (Prelude.Nat.plus k Prelude.Nat.Z) .

177− = Prelude.Nat.Nat Prelude.Nat.Nat (Prelude.Nat.S k)

178− (Prelude.Nat.S (Prelude.Nat.plus k Prelude.Nat.Z))

179−

180− ----------------------------------

181− {hole_0} : patTy k : Prelude.Nat.Nat .

182− patTy ih : = Prelude.Nat.Nat Prelude.Nat.Nat k

183− (Prelude.Nat.plus k Prelude.Nat.Z) .

184− = Prelude.Nat.Nat Prelude.Nat.Nat (Prelude.Nat.S k)

185− (Prelude.Nat.S (Prelude.Nat.plus k Prelude.Nat.Z))

186−

187− Term:

188− ?{hole_0} ≈ pat k : Prelude.Nat.Nat .

189− ?{hole_1} ≈ pat ih : = Prelude.Nat.Nat Prelude.Nat.Nat k

190− (Prelude.Nat.plus k Prelude.Nat.Z) .

191− ?{hole_2} ≈ ? {hole_4} . {hole_4} . {hole_2} .

192− {hole_1} .

193− {hole_0}

194−

195−.. target-notes::

196−.. _`Dependently Typed Functional Programs and their Proofs by McBride 1999`: https://www.era.lib.ed.ac.uk/handle/1842/374

docs/elaboratorReflection/index.rstdeleted−27

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1−.. _elaborator-index:

2−

3−#####################

4−Elaborator Reflection

5−#####################

6−

7−A tutorial on theorem proving in Idris.

8−

9−.. note::

10−

11− The documentation for Idris has been published under the Creative

12− Commons CC0 License. As such to the extent possible under law, *The

13− Idris Community* has waived all copyright and related or neighboring

14− rights to Documentation for Idris.

15−

16− More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

17−

18−.. toctree::

19− :maxdepth: 1

20−

21− elaborator-reflection

22− elabReflection

23− tactics

24− holes

25− example1

26− primitive

27− generatingData

docs/elaboratorReflection/primitive.rstdeleted−518

@@ -1,518 +0,0 @@

1−Primitive Operators

2−===================

3−

4−.. list-table::

5− :widths: 10 30

6− :stub-columns: 1

7−

8− * - gensym

9− - Generate a unique name based on some hint.

10−

11− Useful when establishing a new binder.

12−

13− **NB**: the generated name is unique **for this run of the elaborator**.

14−

15− Do not assume that they are globally unique.

16−

17− Signature:

18−

19− gensym : (hint : String) -> Elab TTName

20−

21− * - solve

22− - Substitute a guess into a hole.

23−

24−

25− .. image:: ../image/solve.png

26− :width: 141px

27− :height: 74px

28− :alt: diagram illustrating solve tactic

29−

30−

31− Substitute the focused guess throughout its scope, eliminating it and moving focus to the next element of the hole queue. Fail if the focus is not a guess.

32−

33− Signature:

34−

35− solve : Elab ()

36−

37− Example:

38−

39− .. code-block:: idris

40−

41− %language ElabReflection

42−

43− testFn : Nat

44− testFn = %runElab (do fill `(Z)

45− solve)

46−

47− * - fill

48− - Place a term into a hole, unifying its type. Fails if the focus is not a hole.

49−

50−

51− .. image:: ../image/fill.png

52− :width: 140px

53− :height: 74px

54− :alt: diagram illustrating fill tactic

55−

56−

57− Signature:

58−

59− fill : (e : Raw) -> Elab ()

60−

61− Place a term e with type tc into the focused hole:

62−

63− ?h : th.e'

64−

65− and convert it to a guess:

66−

67− ?h ≈ e:t.e'

68−

69− and fail if the current focus is not a hole. The type t of the guess is constructed by unifying tc and th, which may instantiate holes that they refer to. Fail if the current focus is not a hole or if unification fails.

70−

71− This unification can result in the solution of further holes or the establishment of additional unsolved unification constraints.

72−

73− Example:

74−

75− .. code-block:: idris

76−

77− %language ElabReflection

78−

79− testFn : Nat

80− testFn = %runElab (do fill `(Z)

81− solve)

82−

83− * - apply

84− - Attempt to apply an operator to fill the current hole, potentially solving arguments by unification.

85−

86− A hole is established for each argument.

87−

88− The return value is the list of holes established for the arguments to the function.

89−

90− Note that not all of the returned hole names still exist, as they may have been solved.

91−

92− - @ op the term to apply

93− - @ argSpec - A list of booleans, one for each argument that the operator will be applied to. If true then attempt to solve the argument by unification.

94−

95− Signature:

96−

97− apply : (op : Raw) -> (argSpec : List Bool) -> Elab (List TTName)

98−

99− Example: elaborating an application of a function f that takes one implicit and two explicit arguments might invoke:

100−

101− apply \`(f) [False, True, True]

102−

103− Here is an example of an elab script that uses apply to insert the term plus Z (S Z) into a goal of type Nat.

104−

105− .. code-block:: idris

106−

107− do [x,y] <- apply `(plus) [False, False]

108− solve

109− focus x; fill `(Z); solve

110− focus y; fill `(S Z); solve

111−

112− The names of the established holes are returned.

113−

114− Note: This was added to the original tactic language to allow elaborator reflection.

115−

116− * - matchApply

117− - Attempt to apply an operator to fill the current hole, potentially solving arguments by matching.

118−

119− The return value is the list of holes established for the arguments to the function.

120−

121− Note that not all of the returned hole names still exist, as they may have been solved.

122−

123− - @ op the term to apply

124− - @ argSpec instructions for finding the arguments to the term, where the Boolean states whether or not to attempt to solve the argument by matching.

125−

126− Signature:

127−

128− matchApply : (op : Raw) -> (argSpec : List Bool) -> Elab (List TTName)

129−

130− * - focus

131− - Move the focus to the specified hole, bringing it to the front of the hole queue. Fails if the hole does not exist.

132−

133− @ hole the hole to focus on

134−

135− Signature:

136−

137− focus : (hole : TTName) -> Elab ()

138−

139− * - unfocus

140− - Send the currently-focused hole to the end of the hole queue and focus on the next hole.

141−

142− Signature:

143−

144− unfocus : TTName -> Elab ()

145−

146− * - attack

147− - Convert a hole to make it suitable for bindings.

148−

149−

150− .. image:: ../image/attack.png

151− :width: 152px

152− :height: 70px

153− :alt: diagram illustrating attack tactic

154−

155−

156− The binding tactics require that a hole be directly under its binding, or else the scopes of the generated terms won't make sense. This tactic creates a new hole of the proper form, and points the old hole at it.

157−

158− Signature:

159−

160− attack : Elab ()

161−

162− * - claim

163− - Establish a new hole binding named n with type t, surrounding the current focus.

164−

165− Introduce a new hole with a specified name and type.

166−

167− The new hole will be focused, and the previously-focused hole will be immediately after it in the hole queue. Because this tactic introduces a new binding, you may need to 'attack' first.

168−

169− Signature:

170−

171− claim : TTName -> Raw -> Elab ()

172−

173− * - patvar

174− - Convert a hole into a pattern variable.

175−

176− Signature:

177−

178− patvar : TTName -> Elab ()

179−

180− * - compute

181− - Normalise the goal.

182−

183− Often this is not necessary because normanisation is applied during other tactics.

184−

185− Signature:

186−

187− compute : Elab ()

188−

189− * - normalise

190− - Normalise a term in some lexical environment

191−

192− - @ env the environment in which to compute (get one of these from `getEnv`)

193− - @ term the term to normalise

194−

195− Signature:

196−

197− normalise : (env : List (TTName, Binder TT)) -> (term : TT) -> Elab TT

198−

199− * - whnf

200− - Reduce a closed term to weak-head normal form

201−

202− @ term the term to reduce

203−

204− Signature:

205−

206− whnf : (term : TT) -> Elab TT

207−

208− * - convertsInEnv

209− - Check that two terms are convertible in the current context and in some environment.

210−

211− - @ env a lexical environment to compare the terms in (see `getEnv`)

212− - @ term1 the first term to convert

213− - @ term2 the second term to convert

214−

215− Signature:

216−

217− convertsInEnv : (env : List (TTName, Binder TT)) -> (term1, term2 : TT) -> Elab ()

218−

219− * - converts

220− - Check that two terms are convertable in the current context and environment

221−

222− - @ term1 the first term to convert

223− - @ term2 the second term to convertconverts : (term1, term2 : TT) -> Elab ()

224−

225− converts term1 term2 = convertsInEnv !getEnv term1 term2

226−

227− * - getSourceLocation

228− - Find the source context for the elaboration script

229−

230− Signature:

231−

232− getSourceLocation : Elab SourceLocation

233−

234− * - sourceLocation

235− - Attempt to solve the current goal with the source code

236−

237− locationsourceLocation : Elab ()

238−

239− .. code-block:: idris

240−

241− sourceLocation = do loc <- getSourceLocation

242− fill (quote loc)

243− solve

244−

245− * - currentNamespace

246− - Get the current namespace at the point of tactic execution. This allows scripts to define top-level names conveniently.

247−

248− The namespace is represented as a reverse-order list of strings, just as in the representation of names.

249−

250− Signature:

251−

252− currentNamespace : Elab (List String)

253−

254− * - rewriteWith

255− - Attempt to rewrite the goal using an equality.

256−

257− The tactic searches the goal for applicable subterms, and constructs a context for `replace` using them. In some cases, this is not possible, and `replace` must be called manually with an appropriate context.

258−

259− Because this tactic internally introduces a `let` binding, it requires that the hole be immediately under its binder (use 'attack' if it might not be).

260−

261− Signature:

262−

263− rewriteWith : Raw -> Elab ()

264−

265− * - resolveTC

266− - Attempt to solve the current goal with an interface dictionary

267−

268− @ fn the name of the definition being elaborated (to prevent Idris from looping)

269−

270− Signature:

271−

272− resolveTC : (fn : TTName) -> Elab ()

273−

274− * - search

275− - Use Idris's internal proof search.

276−

277− Signature:

278−

279− search : Elab ()

280−

281− * - search'

282− - Use Idris's internal proof search, with more control.

283−

284− - @ depth the search depth

285− - @ hints additional names to try

286−

287− Signature:

288−

289− search' : (depth : Int) -> (hints : List TTName) -> Elab ()

290−

291− * - operatorFixity

292− - Look up the declared fixity for an operator.

293−

294− The lookup fails if the operator does not yet have a fixity or if the string is not a valid operator.

295−

296− @ operator the operator string to look up

297−

298− Signature:

299−

300− operatorFixity : (operator : String) -> Elab Fixity

301−

302− * - debug

303− - Halt elaboration, dumping the internal state for inspection.

304−

305− This is intended for elaboration script developers, not for end-users. Use `fail` for final scripts.

306−

307− Signature:

308−

309− debug : Elab a

310−

311− If 'debug' is not the last tactic then make sure its type is sufficiently constrained. In particular, its type is Elab a, but there's no way for Idris to find out which type was meant for a. This can be fixed by either writing an explicit type (e.g. debug {a = ()}) or by using a helper that constrains the type (such as simple in Pruviloj, e.g. simple debug as a line).

312−

313− .. code-block:: idris

314−

315− %language ElabReflection

316−

317− idNat : Nat -> Nat

318− idNat = %runElab (do intro `{{x}}

319− debug {a = ()}

320− fill (Var `{{x}})

321− solve)

322−

323− * - debugMessage

324− - Halt elaboration, dumping the internal state and displaying a message.

325−

326− This is intended for elaboration script developers, not for end-users. Use `fail` for final scripts.

327−

328− @ msg the message to display

329−

330− Signature:

331−

332− debugMessage : (msg : List ErrorReportPart) -> Elab a

333−

334− If 'debugMessage' is not the last tactic then make sure its type is sufficiently constrained. In particular, its type is Elab a, but there's no way for Idris to find out which type was meant for a. This can be fixed by either writing an explicit type (e.g. debugMessage [TextPart "message"] {a = ()}) or by using a helper that constrains the type (such as simple in Pruviloj, e.g. simple debug as a line).

335−

336− .. code-block:: idris

337−

338− %language ElabReflection

339− idNat : Nat -> Nat

340− idNat = %runElab (do intro `{{x}}

341− debugMessage [TextPart "error message"] {a = ()}

342− fill (Var `{{x}})

343− solve)

344−

345− * - metavar

346− - Create a new top-level metavariable to solve the current hole.

347−

348− @ name the name for the top-level variable

349−

350− Signature:

351−

352− metavar : (name : TTName) -> Elab ()

353−

354− * - runElab

355− - Recursively invoke the reflected elaborator with some goal.

356−

357− The result is the final term and its type.

358−

359− Signature:

360−

361− runElab : Raw -> Elab () -> Elab (TT, TT)

362−

363−

364−Read and Write State

365−--------------------

366−

367−.. list-table::

368− :widths: 10 30

369− :stub-columns: 1

370−

371− * - getEnv

372− - Look up the lexical binding at the focused hole. Fails if no holes are present.

373−

374− Signature:

375−

376− getEnv : Elab (List (TTName, Binder TT))

377−

378− * - getGoal

379− - Get the name and type of the focused hole. Fails if not holes are present.

380−

381− Signature:

382−

383− getGoal : Elab (TTName, TT)

384−

385− * - getHoles

386− - Get the hole queue, in order.

387−

388− Signature:

389−

390− getHoles : Elab (List TTName)

391−

392− * - getGuess

393− - If the current hole contains a guess, return it. Otherwise, fail.

394−

395− Signature:

396−

397− getGuess : Elab TT

398−

399− * - lookupTy

400− - Look up the types of every overloading of a name.

401−

402− Signature:

403−

404− lookupTy : TTName -> Elab (List (TTName, NameType, TT))

405−

406− * - lookupTyExact

407− - Get the type of a fully-qualified name. Fail if it doesn't resolve uniquely.

408−

409− Signature:

410−

411− lookupTyExact : TTName -> Elab (TTName, NameType, TT)

412−

413− * - lookupDatatype

414− - Find the reflected representation of all datatypes whose names are overloadings of some name.

415−

416− Signature:

417−

418− lookupDatatype : TTName -> Elab (List Datatype)

419−

420− * - lookupDatatypeExact

421− - Find the reflected representation of a datatype, given its fully-qualified name. Fail if the name does not uniquely resolve to a datatype.

422−

423− Signature:

424−

425− lookupDatatypeExact : TTName -> Elab Datatype

426−

427− * - lookupFunDefn

428− - Find the reflected function definition of all functions whose names are overloadings of some name.

429−

430− Signature:

431−

432− lookupFunDefn : TTName -> Elab (List (FunDefn TT))

433−

434− * - lookupFunDefnExact

435− - Find the reflected function definition of a function, given its fully-qualified name. Fail if the name does not uniquely resolve to a function.

436−

437− Signature:

438−

439− lookupFunDefnExact : TTName -> Elab (FunDefn TT)

440−

441− * - lookupArgs

442− - Get the argument specification for each overloading of a name.

443−

444− Signature:

445−

446− lookupArgs : TTName -> Elab (List (TTName, List FunArg, Raw))

447−

448− * - lookupArgsExact

449− - Get the argument specification for a name. Fail if the name does not uniquely resolve.

450−

451− Signature:

452−

453− lookupArgsExact : TTName -> Elab (TTName, List FunArg, Raw)

454−

455− * - check

456− - Attempt to type-check a term, getting back itself and its type.

457−

458− - @ env the environment within which to check the type

459− - @ tm the term to check

460−

461− Signature:

462−

463− check : (env : List (TTName, Binder TT)) -> (tm : Raw) -> Elab (TT, TT)

464−

465−Error Handling

466−--------------

467−

468−.. list-table::

469− :widths: 10 30

470− :stub-columns: 1

471−

472− * - tryCatch

473− - `tryCatch t (\err => t')` will run `t`, and if it fails, roll back the elaboration state and run `t'`,

474− but with access to the knowledge of why `t` failed.

475−

476− Signature:

477−

478− tryCatch : Elab a -> (Err -> Elab a) -> Elab a

479−

480− .. code-block:: idris

481−

482− %language ElabReflection

483−

484− f : Err -> Elab ()

485− f (Msg _) = fill `("message error")

486− f (CantUnify _ _ _ _ _ _) = fill `("unification error")

487− f _ = fill `("other")

488−

489− s2 : String

490− s2 = %runElab (do tryCatch (fill `(True)) f ; solve)

491−

492− * - fail

493− - Halt elaboration with an error

494−

495− Signature:

496−

497− fail : List ErrorReportPart -> Elab a

498−

499− Note: we may need to make sure the return type 'a' is sufficiently constrained. If required add an explicit type {a = ()}.

500−

501− Below is some code which includes 'fail'. This will always fail but we could replace 'True' with some more useful condition.

502−

503− .. code-block:: idris

504−

505− %language ElabReflection

506−

507− id1 : Elab ()

508− id1 = do

509− intro `{{x}}

510− fill (Var `{{x}})

511− if True

512− then

513− fail [TextPart "put error message here"]

514− else

515− solve

516−

517− idNat : Nat -> Nat

518− idNat = %runElab id1

docs/elaboratorReflection/tactics.rstdeleted−430

@@ -1,430 +0,0 @@

1−Elaborator Reflection - Tactics

2−===============================

3−

4−The Idris part of the code for elaborator reflection is in

5−Elab.idr `<https://github.com/idris-lang/Idris-dev/blob/master/libs/prelude/Language/Reflection/Elab.idr>`_

6−Before looking at the Elab monad we need to know how to construct terms.

7−

8−

9−Proof State

10−-----------

11−

12−The terminology 'Proof State' is used by analogy to proof assistants but, as used here, it's really more of a metaprogramming state.

13−

14−Tactics operate on the proof state. The proof state contains various pieces of information, at this stage, the important ones for us are:

15−

16−- A hole queue - This contains a list of the names of the holes used in the proof term. The solution to each hole may depend on the other holes. For more information about holes and guesses see `Dependently Typed Functional Programs and their Proofs by McBride 1999`_.

17−- A goal type - The type of the term that is under construction for the current goal.

18−- A possibly incomplete proof term, which is being calculated and should be the goal type at the end of elaboration.

19−- Context - A collection of open unification problems, representing recoverable failures of unification that may yet unify once more variables are solved.

20−

21−There are many other pieces of information in the proof state such as the names used , such as the bodies of case blocks that need to be elaborated.but, for now, we will leave the system to handle these.

22−

23−.. image:: ../image/elabProofState.png

24− :width: 283px

25− :height: 232px

26−

27−Names TTName

28−------------

29−

30−Names in an Idris program are evaluated at runtime but sometimes a 'variable name' is needed, which can be referred to as an unevaluated symbol.

31−The names used in terms have different constructors depending on their type:

32−

33−+---------------------------+-----------------------------------------------+

34−| UN String | A user-provided name |

35−+---------------------------+-----------------------------------------------+

36−| NS (UN "foo") ["B", "A"]) | A name in some namespace |

37−+---------------------------+-----------------------------------------------+

38−| MN Int String | Machine-chosen names |

39−+---------------------------+-----------------------------------------------+

40−| SN SpecialName | Special names, to make conflicts impossible |

41−| | and language features predictable |

42−+---------------------------+-----------------------------------------------+

43−

44−

45−A user defined name can be constructed like this:

46−

47−.. code-block:: idris

48−

49− Idris> UN "x"

50− UN "x" : TTName

51−

52−.. code-block:: idris

53−

54− Idris> NS (UN "x") ["b","a"]

55− NS (UN "x") ["b", "a"] : TTName

56−

57−.. list-table:: machine-chosen names

58−

59− * - A machine-chosen name needs to be generated within an Elab monad (see below for details) and is unique within that monad. This produced: {abc_140}{abc_141} so although gensym "abc" was called twice each one had a different integer:

60− - example of unique names:

61−

62− .. code-block:: idris

63−

64− implementation Show TTName where

65− show (UN s) = "`{{"++s++"}}"

66− show (NS t a) = "{"++(show t)++

67− "."++(show a)++"}"

68− show (MN i s) = "{"++s++"_"++(show i)++"}"

69− show (SN sn) = "TTName special name"

70−

71− showGensym : String

72− showGensym = %runElab (do

73− debugMessage [TextPart (

74− show !(gensym "abc") ++

75− show !(gensym "abc")

76− )]

77− )

78−

79−Quasiquotation

80−--------------

81−

82−Since names are used frequently in elaborator reflection there is a shortcut for constructing them:

83−

84−.. list-table::

85−

86− * - An unresolved variable "x" is wrapped in backtick and double braces:

87− - .. code-block:: idris

88−

89− Idris> `{{x}}

90− UN "x" : TTName

91−

92−

93− * - Single braces are used for existing variables:

94− - .. code-block:: idris

95−

96− Idris> `{x}

97− No such variable x

98− Idris> :let x=2

99− Idris> `{x}

100− UN "x" : TTName

101−

102−

103− * - brackets are used for an expression:

104−

105− here type is inferable

106− - .. code-block:: idris

107−

108− Idris> :let a=2

109− Idris> `(a)

110− P Ref (UN "a") (TConst (AType (ATInt ITBig))) : TT

111−

112−

113− * - Expression with explicit type:

114− - .. code-block:: idris

115−

116− Idris> `(a:Integer)

117− P Ref (UN "a") (TConst (AType (ATInt ITBig))) : TT

118−

119−

120− * - If we want the value we can escape from quasiquotation by using anti-quotation (tilde)

121− - .. code-block:: idris

122−

123− Idris> `(~a)

124− 2 : Integer

125−

126−quasiquotation summary:

127−

128−+------------+-----------+----------------------------------------------------------+

129−| |Reification| |

130−+============+===========+==========================================================+

131−| \`{{n}} | TTName | Use for new names. Unresolved quotation of the name n. |

132−+------------+-----------+----------------------------------------------------------+

133−| \`{n} | TTName | Use for existing names. Resolved quotation of the name |

134−| | | n. n is a reference to a unique name in scope. |

135−+------------+-----------+----------------------------------------------------------+

136−| \`(e) | | expression e for which a type is inferable. |

137−+------------+-----------+----------------------------------------------------------+

138−| \`(e:t) | | expression e with a given type e. |

139−+------------+-----------+----------------------------------------------------------+

140−| ~a | | anti-quotation - sub region which can be evaluated rather|

141−| | | than quoted. |

142−+------------+-----------+----------------------------------------------------------+

143−|(Var\`{{x}})| Raw | |

144−+------------+-----------+----------------------------------------------------------+

145−

146−TT

147−--

148−

149−There is a notation for a term in TT as it is being constructed (based on a BNF-like grammar), this is used for example in the debug output, it is a compact way to see the state of the term so it is used here.

150−So internally the program is stored as a tree structure using the following syntax:

151−

152−+------------+-------+-------------+---------------------------------------------+

153−| | | Syntax | More Information |

154−+============+=======+=============+=============================================+

155−| term | | t | |

156−+------------+-------+-------------+---------------------------------------------+

157−| binding | | b | |

158−+------------+-------+-------------+---------------------------------------------+

159−| constant | t ::= | c | |

160−+------------+-------+-------------+---------------------------------------------+

161−| variable | t ::= | x | |

162−+------------+-------+-------------+---------------------------------------------+

163−| variable | t ::= | b.t | so a dot '.' tells us this is some sort of |

164−| binding | | | binding. |

165−+------------+-------+-------------+---------------------------------------------+

166−| application| t ::= | t t | As with Idris, juxtaposition indicates |

167−| | | | function application. Note: the same symbol |

168−| | | | 't' is used for both terms, this does not |

169−| | | | imply they are the same term. |

170−+------------+-------+-------------+---------------------------------------------+

171−| Type | t ::= | T | |

172−| constructor| | | |

173−+------------+-------+-------------+---------------------------------------------+

174−| Data | t ::= | C | |

175−| constructor| | | |

176−+------------+-------+-------------+---------------------------------------------+

177−| function | b::= | λ c:t | colon ':' separates parameters from body of |

178−| | | | binding. |

179−+------------+-------+-------------+---------------------------------------------+

180−| let binding| b::= | let\|-> t:t | |

181−+------------+-------+-------------+---------------------------------------------+

182−| function | b::= | ∀ x:t | |

183−+------------+-------+-------------+---------------------------------------------+

184−| Type | c::= | \*i | The universe hierarchy is usually handled |

185−| universe | | | automatically so we can just use\* for the |

186−| | | | type of types. |

187−+------------+-------+-------------+---------------------------------------------+

188−| integer | c:== | i | |

189−| literal | | | |

190−+------------+-------+-------------+---------------------------------------------+

191−|integer type| c:== | Integer | |

192−+------------+-------+-------------+---------------------------------------------+

193−| string | c:== | s | |

194−| literal | | | |

195−+------------+-------+-------------+---------------------------------------------+

196−| string type| c:== | String | |

197−+------------+-------+-------------+---------------------------------------------+

198−|focused hole| | ?x : t | Conor McBride 1999 thesis. |

199−+------------+-------+-------------+---------------------------------------------+

200−| guess | | ?x ≈ t : t | Conor McBride 1999 thesis. |

201−+------------+-------+-------------+---------------------------------------------+

202−

203−Sometimes the part of the term in focus is underlined.

204−

205−Reflection of the well typed core language

206−

207−.. code-block:: idris

208−

209− data TT =

210− ||| A reference to some name (P for Parameter)

211− P NameType TTName TT |

212− ||| de Bruijn variables

213− V Int |

214− ||| Bind a variable

215− Bind TTName (Binder TT) TT |

216− ||| Apply one term to another

217− App TT TT |

218− ||| Embed a constant

219− TConst Const |

220− ||| Erased terms

221− Erased |

222− ||| The type of types along (with universe constraints)

223− TType TTUExp |

224− ||| Alternative universes for dealing with uniqueness

225− UType Universe |

226−

227−TT stores local bound variables using De Bruijn index, when working in Idris this does not concern the user because string names are used for variables. Converting bound variables internally to index values means that the same variable name can be used, in different lambda terms, without ambiguity and without the need for α-substitution.

228−De Bruijn index which is a integer where:

229−

230−- 0=inside current (inner) lambda term

231−- 1= next outer lambda term

232−- 2= next outer and so on

233−

234−Raw

235−---

236−

237−Raw is similar to TT except it is used before types are known. The types should be resolved by the type checker.

238−

239−.. code-block:: idris

240−

241− data Raw =

242− ||| Variables, global or local

243− Var TTName |

244− ||| Bind a variable

245− RBind TTName (Binder Raw) Raw |

246− ||| Application

247− RApp Raw Raw |

248− ||| The type of types

249− RType |

250− ||| Alternative universes for dealing with uniqueness

251− RUType Universe |

252− ||| Embed a constant

253− RConstant Const |

254−

255−Expression Syntax

256−-----------------

257−

258−There is a way of notating expressions such as those used in the proof state (example: goal type and proof terms) which is reasonably standard in the papers written about this subject.

259−

260−This notation is not entered directly by metaprogrammers but it is seen, for example in debug output. So this notation is explained here because it is useful to be familiar with it.

261−

262−The notation assumes right-associativity, in the absence of brackets, the term to the right binds more tightly than the one on the left.

263−So, for nested lambda terms:

264−

265−+---------------+--------+-------------------+

266−| λ a . λ b . f | means | λ a .( λ b . f) |

267−+---------------+--------+-------------------+

268−

269−and the same for function application:

270−

271−+---------------+--------+-------------------+

272−| f g x | means | f (g x) |

273−+---------------+--------+-------------------+

274−

275−In contrast, in lambda calculus, function application is usually regarded as left-associative,

276−Here are some typical examples of the notation used for expressions:

277−

278−+-----------------------+

279−| ? {hole_0} . {hole_0} |

280−+-----------------------+

281−

282−The term, to be derived, may start off in this state following something like this:

283−

284−.. code-block:: idris

285−

286− myScript : Elab ()

287− myScript= do

288−

289−The dot '.' tells us this is some sort of binding.

290−

291−+----------------------------------------------+

292−| ?{hole_0} ≈ ? {hole_2} . {hole_2} . {hole_0} |

293−+----------------------------------------------+

294−

295−This is a slightly more complicated example arising from:

296−

297−.. code-block:: idris

298−

299− idNat : Nat -> Nat

300− idNat = %runElab (do

301−

302−This introduces a guess that hole_0 = hole_2 .

303−

304−+----------------------------------------------------+

305−| ?{hole_0} ≈ λ x . ? {hole_2} . {hole_2} . {hole_0} |

306−+----------------------------------------------------+

307−

308−Following on from the previous example a lambda function is introduced like this:

309−

310−.. code-block:: idris

311−

312− intro `{{x}}

313−

314−So now the expression is wrapped in a lambda binding.

315−

316−+-------------------------------------------------------+

317−| ?{hole_0} ≈ λ x . ?{hole_2} ≈ x . {hole_2} . {hole_0} |

318−+-------------------------------------------------------+

319−

320−Following on, we can use the fill tactic like this:

321−

322−.. code-block:: idris

323−

324− fill (Var `{{x}})

325−

326−which introduces another guess.

327−

328−+--------------------------------+

329−| ?{hole_0} ≈ λ x . x . {hole_0} |

330−+--------------------------------+

331−

332−The solve tactic completes the proof

333−

334−Binders

335−-------

336−

337−Here we look at each tactic in turn to see how they affect the proof state.

338−

339−Introduction tactics for binders. The binder types are:

340−

341−- lambda function (intro)

342−- dependent function (forall)

343−- let (letBind)

344−- pattern (patbind)

345−

346−A precondition of these tactics is that the focused hole is of the form:

347−

348−+-----------+

349−| ?h : t.h |

350−+-----------+

351−

352−that is, that the body of its scope consists directly of a reference to the hole-bound variable. If a hole binder were of the form:

353−

354−+--------------------+

355−| ?h : t1 -> t2.f h |

356−+--------------------+

357−

358−and a tactic such as

359−

360−+------------------+

361−| intro \`{{x}} |

362−+------------------+

363−

364−were applied, the result would be the term

365−

366−+---------------------------+

367−| ?h : t2 . λ x:t1. f h |

368−+---------------------------+

369−

370−However this would cause the application of f to be ill-typed, as it expects an argument of type t1->t2, not an argument of type t2. Additionally, some binding tactics require that t, the type of the hole h, have a specific form, because the binder to be established may have a typing rule associated with it.

371−

372−.. list-table:: Binders

373− :widths: 10 30

374− :stub-columns: 1

375−

376− * - intro

377− - Introduce a lambda binding around the current hole and focus on the body.

378−

379− Requires that the hole be in binding form (use 'attack' if it might not be).

380−

381− @ n the name to use for the argument.

382−

383− Signature:

384−

385− intro : (n : TTName) -> Elab ()

386−

387− Result

388−

389− λn:t1.?h:[n/x]t2.h

390−

391− * - intro'

392− - Introduce a lambda binding around the current hole and focus on the body, using the name provided by the type of the hole.

393−

394− Requires that the hole be immediately under its binder (use 'attack' if it might not be).

395−

396− Signature:

397−

398− intro' : Elab ()

399−

400− * - forall

401− - Introduce a dependent function type binding into the current hole, and focus on the body. Requires that the hole be immediately under its binder

402−

403− (use 'attack' if it might not be).

404−

405− Signature:

406−

407− forall : TTName -> Raw -> Elab ()

408−

409− * - patbind

410− - Introduce a new pattern binding. Requires that the hole be immediately under its binder (use 'attack' if it might not be).

411−

412− Signature:

413−

414− patbind : TTName -> Elab ()

415−

416− * - letbind

417− - Introduce a new let binding.

418−

419− Requires that the hole be immediately under its binder (use 'attack' if it might not be).

420−

421− - @ n the name to let bind

422− - @ ty the type of the term to be let-bound

423− - @ tm the term to be bound

424−

425− Signature:

426−

427− letbind : (n : TTName) -> (ty, tm : Raw) -> Elab ()

428−

429−.. target-notes::

430−.. _`Dependently Typed Functional Programs and their Proofs by McBride 1999`: https://www.era.lib.ed.ac.uk/handle/1842/374

docs/faq/faq.rst+12−50

@@ -33,30 +33,6 @@ for use in production would be very welcome - this includes (but is not

3333limited to) extra library support, polishing the run-time system (and ensuring

3434it is robust), providing and maintaining a JVM back end, etc.

3535

36−Is there some documentation for the standard lib? List of functions?

37−=====================================================================

38−

39−API documentation for the shipped packages is listed on `the

40−documentation page <https://www.idris-lang.org/documentation/>`_.

41−

42−Unfortunately, the default prelude and shipped packages for `Idris`

43−are not necessarily complete with regards to documentation. Other

44−ways to find functions include:

45−

46−+ REPL commands:

47−

48− + Use `:apropos` to search for text in documentation and function names.

49− + Use `:search` to search for functions of a given type.

50− + Use `:browse` to list the contents of a given namespace.

51−

52−+ Use the REPL's auto-complete functionality.

53−+ Grep through the source code in `libs/`

54−

55−If you find that the shipped packages are lacking in documentation,

56−please feel free to write some. Or bug someone to do so. `Idris` has

57−syntax for providing rich documentation, which is then viewable using

58−the `:doc` command and listed in generated HTML API documentation.

59−

6036

6137Why does Idris use eager evaluation rather than lazy?

6238=====================================================

@@ -161,7 +137,7 @@ of ``append``, rather than making the type of ``append`` equivalent to...

161137

162138...which is probably not what was intended! The reason for this rule is so

163139that it is clear just from looking at the type of ``append``, and no other

164−context, what the implicitly bound names are.

140+context, what the implicitly bound names are.

165141

166142If you want to use an unapplied name in a type, you have two options. You

167143can either explicitly qualify it, for example, if ``ty`` is defined in the

@@ -173,7 +149,7 @@ namespace ``Main`` you can do the following:

173149

174150Alternatively, you can use a name which does not begin with a lower case

175151letter, which will never be implicitly bound:

176−

152+

177153.. code-block:: idris

178154

179155 Ty : Type

@@ -197,10 +173,8 @@ function back to itself. On such a path, there must be at least one

197173argument which converges to a base case.

198174

199175- Mutually recursive functions are supported

200−

201176- However, all functions on the path must be fully applied. In particular,

202177 higher order applications are not supported

203−

204178- Idris identifies arguments which converge to a base case by looking for

205179 recursive calls to syntactically smaller arguments of inputs. e.g.

206180 ``k`` is syntactically smaller than ``S (S k)`` because ``k`` is a

@@ -215,10 +189,10 @@ function.

215189When will Idris be self-hosting?

216190================================

217191

218−It’s not a priority, though not a bad idea in the long run. It would

219−be a worthwhile effort in the short term to implement libraries in

220−Idris to support self-hosting, such as argument parsing and a

221−POSIX-compliant library for system interaction.

192+It’s not a priority, though not a bad idea in the long run. It would be a

193+worthwhile effort in the short term to implement libraries to support

194+self-hosting, such as a good parsing library.

195+

222196

223197Does Idris have universe polymorphism? What is the type of ``Type``?

224198====================================================================

@@ -259,17 +233,14 @@ where the install directory is unknown at build time. When passing this

259233flag, the IDRIS_LIB_DIR environment variable needs to be set to the path

260234where the Idris libs reside relative to the idris executable. The

261235IDRIS_TOOLCHAIN_DIR environment variable is optional, if that is set,

262−Idris will use that path to find the C compiler. For example:

236+Idris will use that path to find the C compiler.

263237

264−::

238+Example::

265239

266− IDRIS_LIB_DIR="./libs" \

267− IDRIS_TOOLCHAIN_DIR="./mingw/bin" \

268− CABALFLAGS="-fffi -ffreestanding -frelease" \

269− make

240+ IDRIS_LIB_DIR="./libs" IDRIS_TOOLCHAIN_DIR="./mingw/bin" CABALFLAGS="-fffi -ffreestanding -frelease" make

270241

271242

272−What does the name “Idris” mean?

243+What does the name ‘Idris’ mean?

273244================================

274245

275246British people of a certain age may be familiar with this

@@ -285,20 +256,16 @@ There are several reasons why we should not support Unicode operators:

285256- It's hard to type (this is important if you're using someone else's code, for

286257 example). Various editors have their own input methods, but you have to know

287258 what they are.

288−

289259- Not every piece of software easily supports it. Rendering issues have been

290260 noted on some mobile email clients, terminal-based IRC clients, web browsers,

291261 etc. There are ways to resolve these rendering issues but they provide a

292262 barrier to entry to using Idris.

293−

294263- Even if we leave it out of the standard library (which we will in any case!)

295264 as soon as people start using it in their library code, others have to deal

296265 with it.

297−

298266- Too many characters look too similar. We had enough trouble with confusion

299267 between 0 and O without worrying about all the different kinds of colons and

300268 brackets.

301−

302269- There seems to be a tendency to go over the top with use of Unicode. For

303270 example, using sharp and flat for delay and force (or is it the other way

304271 around?) in Agda seems gratuitous. We don't want to encourage this sort of

@@ -310,16 +277,11 @@ better and it will make sense to revisit this. For now, however, Idris will not

310277be offering arbitrary Unicode symbols in operators.

311278

312279This seems like an instance of `Wadler's

313−Law <https://www.haskell.org/haskellwiki/Wadler%27s_Law>`__ in action.

280+Law <http://www.haskell.org/haskellwiki/Wadler%27s_Law>`__ in action.

314281

315282This answer is based on Edwin Brady's response in the following

316−`pull request <https://github.com/idris-lang/Idris-dev/pull/694#issuecomment-29559291>`_.

317−

318−Where can I find the community standards for the Idris community?

319−==================================================================

283+`pull request <https://github.com/idris-lang/Idris-dev/pull/694#issuecomment-29559291>`__.

320284

321−The Idris Community Standards are stated `here

322−<https://www.idris-lang.org/documentation/community-standards/>`_ .

323285

324286Where can I find more answers?

325287==============================

docs/parserLibrary/index.rst → docs/faq/index.rstrenamed+6−11

@@ -1,13 +1,10 @@

1−.. _parserLibrary:

1+.. _faq-index:

22

3−########################

4−Lexer and Parser Library

5−########################

6−

7−A tutorial on the lexer and parser library in Idris.

3+##########################

4+Frequently Asked Questions

5+##########################

86

97.. note::

10−

118 The documentation for Idris has been published under the Creative

129 Commons CC0 License. As such to the extent possible under law, *The

1310 Idris Community* has waived all copyright and related or neighboring

@@ -15,10 +12,8 @@ A tutorial on the lexer and parser library in Idris.

1512

1613 More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1714

15+

1816.. toctree::

1917 :maxdepth: 1

2018

21− introduction

22− lexer

23− parser

24− whitespace

19+ faq

docs/guides/index.rst+1−1

@@ -12,7 +12,7 @@ Tutorials submitted by community members.

1212 Idris Community* has waived all copyright and related or neighboring

1313 rights to Documentation for Idris.

1414

15− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

15+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1616

1717

1818.. toctree::

docs/guides/theorem-prover.rst+1−1

@@ -22,7 +22,7 @@ We will be given the following prompt, in future releases the version string wil

2222 ____ __ _

2323 / _/___/ /____(_)____

2424 / // __ / ___/ / ___/ Version 0.9.18.1

25− _/ // /_/ / / / (__ ) https://www.idris-lang.org/

25+ _/ // /_/ / / / (__ ) http://www.idris-lang.org/

2626 /___/\__,_/_/ /_/____/ Type :? for help

2727

2828 Idris is free software with ABSOLUTELY NO WARRANTY.

docs/guides/type-providers-ffi.rst+2−4

@@ -3,7 +3,7 @@ Type Providers in Idris

33***********************

44

55`Type providers in Idris

6−<https://www.davidchristiansen.dk/pubs/dependent-type-providers.pdf>`__

6+<http://www.itu.dk/people/drc/pubs/dependent-type-providers.pdf>`__

77are simple enough, but there are a few caveats to using them that it

88would be worthwhile to go through the basic steps. We also go over

99foreign functions, because these will often be used with type

@@ -200,7 +200,6 @@ Next, an Idris file to define our providers:

200200 module Providers

201201

202202 %dynamic "./stattypes.so"

203− %access export

204203

205204 sizeOfDevT : IO Int

206205 sizeOfDevT = foreign FFI_C "sizeof_dev_t" (IO Int)

@@ -208,10 +207,9 @@ Next, an Idris file to define our providers:

208207

209208 -- Indicates how many bits are used to represent various system

210209 -- stat types.

211− public export

212210 data BitWidth = B8 | B16 | B32 | B64

213211

214− Show BitWidth where

212+ implementation Show BitWidth where

215213 show B8 = "8 bits"

216214 show B16 = "16 bits"

217215 show B32 = "32 bits"

docs/image/README.mddeleted−16

@@ -1,16 +0,0 @@

1−Many of the images in this directory have two files with the same name but a different extension:

2−

3−* The SVG file, being vector graphics, is best for drawing and modifying.

4−* The PNG file, being raster graphics, gives more consistent rendering.

5−

6−The image has therefore been generated as an SVG file and then exported to the PNG file.

7−

8−So, if you need to modify an image, I suggest the following sequence:

9−

10−* Edit the SVG file using a suitable editor (I use Inkscape).

11−* Export the changes to the PNG file, overwriting the old version.

12−* upload both files.

13−

14−Note, when exporting in Inkscape:

15−* Select everything first, this stops an enormous boundary being exported.

16−* After selecting the file to export to and clicking OK, don't forget to click on export button as well.

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1002− id="tspan968">Representation of expressions ready</tspan><tspan

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1148− sodipodi:role="line">'IDEMode is for</tspan><tspan

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1158− id="tspan984">with external</tspan><tspan

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1162− sodipodi:role="line"

1163− id="tspan987">editors. It uses</tspan><tspan

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1167− sodipodi:role="line"

1168− id="tspan989">SExp structure</tspan><tspan

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1172− sodipodi:role="line"

1173− id="tspan991">which is Lisp-</tspan><tspan

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1177− sodipodi:role="line"

1178− id="tspan993">like.</tspan></text>

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105− id="tspan829"> Lookahead : (positive : Bool) -&gt; Recognise c -&gt; Recognise False</tspan><tspan

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115− id="tspan835"> SeqEat : Recognise True -&gt; Inf (Recognise e) -&gt; Recognise True</tspan><tspan

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135− id="tspan843">||| A token recogniser. Guaranteed to consume at least one character.</tspan><tspan

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186− id="tspan908">(&lt;+&gt;) : Recognise c1 -&gt; inf c1 (Recognise c2) -&gt; </tspan><tspan

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196− id="tspan916">Sequence two recognisers. If either consumes a</tspan><tspan

197− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

198− y="114.1729"

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200− sodipodi:role="line"

201− id="tspan918">character, the sequence is guaranteed to</tspan><tspan

202− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

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206− id="tspan935">consume a character</tspan><tspan

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237− id="tspan973">(&lt;|&gt;) : Recognise c1 -&gt; Recognise c2 -&gt;</tspan><tspan

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242− id="tspan975"> Recognise (c1 &amp;&amp; c2)</tspan><tspan

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247− id="tspan983">Alternative recognisers. If both consume, the</tspan><tspan

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252− id="tspan985">combination is guaranteed to consumer a</tspan><tspan

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257− id="tspan992">character.</tspan><tspan

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297− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

298− id="tspan1087">Recognise no input (doesn't consume any input)</tspan><tspan

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318− y="49.614574"

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320− sodipodi:role="line"

321− id="tspan1025">fail : Recognise c</tspan><tspan

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323− y="54.906242"

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326− id="tspan1089">A recogniser that always fails.</tspan><tspan

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345− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

346− y="61.785423"

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348− sodipodi:role="line"

349− id="tspan1051">expect : Recognise c -&gt; Recognise False</tspan><tspan

350− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

351− y="67.077087"

352− x="128.32292"

353− sodipodi:role="line"

354− id="tspan1059">Positive lookahead. Never consumes input.</tspan><tspan

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377− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332">pred : (Char -&gt; Bool) -&gt; Lexer</tspan><tspan

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381− style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332"

382− id="tspan1085">Recognise a character that matches a predicate</tspan><tspan

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419− id="tspan1073">Negative lookahead. Never consumes input.</tspan><tspan

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docs/index.rst+1−3

@@ -13,7 +13,7 @@ Documentation for the Idris Language

1313 Idris Community* has waived all copyright and related or neighboring

1414 rights to Documentation for Idris.

1515

16− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

16+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1717

1818

1919.. toctree::

@@ -24,7 +24,5 @@ Documentation for the Idris Language

2424 st/index

2525 effects/index

2626 proofs/index

27− elaboratorReflection/index

28− parserLibrary/index

2927 reference/index

3028 guides/index

docs/listing/idris-prompt-helloworld.txt+2−2

@@ -1,8 +1,8 @@

11$ idris hello.idr

22 ____ __ _

33 / _/___/ /____(_)____

4− / // __ / ___/ / ___/ Version 1.3.2

5− _/ // /_/ / / / (__ ) https://www.idris-lang.org/

4+ / // __ / ___/ / ___/ Version 1.0

5+ _/ // /_/ / / / (__ ) http://www.idris-lang.org/

66 /___/\__,_/_/ /_/____/ Type :? for help

77

88Type checking ./hello.idr

docs/listing/idris-prompt-interp.txt+2−2

@@ -1,8 +1,8 @@

11$ idris interp.idr

22 ____ __ _

33 / _/___/ /____(_)____

4− / // __ / ___/ / ___/ Version 1.3.2

5− _/ // /_/ / / / (__ ) https://www.idris-lang.org/

4+ / // __ / ___/ / ___/ Version 1.0

5+ _/ // /_/ / / / (__ ) http://www.idris-lang.org/

66 /___/\__,_/_/ /_/____/ Type :? for help

77

88Type checking ./interp.idr

docs/listing/idris-prompt-start.txt+2−2

@@ -1,8 +1,8 @@

11$ idris

22 ____ __ _

33 / _/___/ /____(_)____

4− / // __ / ___/ / ___/ Version 1.3.2

5− _/ // /_/ / / / (__ ) https://www.idris-lang.org/

4+ / // __ / ___/ / ___/ Version 1.0

5+ _/ // /_/ / / / (__ ) http://www.idris-lang.org/

66/___/\__,_/_/ /_/____/ Type :? for help

77

88Idris>

docs/make.bat+1−1

@@ -65,7 +65,7 @@ if errorlevel 9009 (

6565 echo.may add the Sphinx directory to PATH.

6666 echo.

6767 echo.If you don't have Sphinx installed, grab it from

68− echo.https://www.sphinx-doc.org/

68+ echo.http://sphinx-doc.org/

6969 exit /b 1

7070)

7171

docs/parserLibrary/introduction.rstdeleted−76

@@ -1,76 +0,0 @@

1−.. _parserLibraryIntro:

2−

3−***************************

4−Parser Library Introduction

5−***************************

6−

7−The parser library can be used to build Idris structures from text. It involves a

8−certain amount of complexity and so it would typically be used for big projects.

9−An example might be a compiler for another language, written in Idris.

10−

11−Of course the parser library can also be used to compile to Idris, this is what

12−is done in Idris 2 and that is what the this library appears to have been

13−written for.

14−

15−So a secondary use for this tutorial would be to help understanding the internal

16−workings of Idris 2.

17−

18−The parser library is used in a similar way to Parsec which is a library for

19−writing parsers in Haskell. It is based on higher-order parser combinators, so a

20−complicated parser can be made out of many smaller ones.

21−

22−.. list-table::

23−

24− * - This is a two stage process:

25− - Lexer - This takes the input string and turns it into a list of Tokens.

26− - Parser - This takes the list of tokens and outputs the code.

27−

28− - .. image:: ../image/parserTopLevel.png

29− :width: 307px

30− :height: 76px

31− :alt: diagram illustrating these stages of lexer and parser

32−

33−The advantage of using two stages, like this, is that things like whitespace and

34−comments don't need to be considered in every parser rule.

35−

36−The Idris parser library differs from Parsec in that you need to say, in the

37−Recogniser, whether a rule is guaranteed to consume input. This means that the

38−Idris type system prevents the construction of recognisers/rules that can't

39−consume the input.

40−

41−The Lexer is similar but works at the level of characters rather than tokens, and

42−you need to provide a TokenMap which defines how to build a token from

43−a string when a rule is matched.

44−

45−The following pages contain a tutorial for the :ref:`parserLibraryLexer` and a

46−tutorial for the :ref:`parserLibraryParser`. These tutorials have a running

47−example of a parser for integer expressions. This is a very simple example, there

48−may be easier ways to do something so simple, but it illustrates some of the

49−principles.

50−

51−Parser Library and Idris 2

52−--------------------------

53−

54−The parser library, in Idris 1, is almost the same as the code that the Idris 2

55−parser is built on. Even if you only want to use the Idris 1 parser library it

56−is useful to look at the code in the Idris 2 compilers to see how the library

57−can be used.

58−

59−Idris 2 has at least 3 compilers:

60−

61−- IDEMode - complies to SExp which is a Lisp-like structure used to communicate

62− with external editors like Emacs and Vim.

63−- Idris.Parser - This is the main compiler which compiles from a file to

64− PTerm (and eventually TT structure).

65−- REPL - compiles input from the command line.

66−

67−The following diagram is my first attempt to work out how some of the modules in

68−Idris 2 fit together (with a few of the dependencies between them shown). The

69−Idris 1 library is based on the modules at the bottom of the diagram (shown

70−in red).

71−

72−.. image:: ../image/parserModules.png

73− :width: 460px

74− :height: 496px

75− :alt: diagram illustrating these stages of lexer and parser

76−

docs/parserLibrary/lexer.rstdeleted−288

@@ -1,288 +0,0 @@

1−.. _parserLibraryLexer:

2−

3−Lexer

4−=====

5−

6−The lexer is run by calling the 'lex' function in the Text.Lexer.Core

7−module:

8−

9−.. code-block:: idris

10−

11− lex : TokenMap a -> String -> (List (TokenData a), (Int, Int, String))

12−

13−.. list-table::

14−

15− * - This function takes a String and returns a list of tokens. With the

16− tokens we have indexes back to the original string which can be used

17− in error messages:

18−

19− - .. image:: ../image/tokenise.png

20− :width: 330px

21− :height: 73px

22− :alt: diagram illustrating these stages of lexer

23−

24−TokenMap

25−--------

26−

27−In order to construct this list of tokens we need:

28−

29−- A way to recognise the tokens in the input string.

30−- A way to construct these individual tokens.

31−

32−This is given by the TokenMap which is a list of pairs containing

33−this information:

34−

35−.. code-block:: idris

36−

37− (Lexer, String -> tokenType)

38−

39−So for each Lexer in the list, if a substring in the input matches, run

40−the associated function to produce a token of type ``tokenType``

41−

42−.. list-table::

43−

44− * - from Text.Lexer.Core

45− : https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Lexer/Core.idr

46−

47− - .. code-block:: idris

48−

49− TokenMap : (tokenType : Type) -> Type

50− TokenMap tokenType = List (Lexer, String -> tokenType)

51−

52− * - We can create a tokenMap by using a function like this:

53−

54− - .. code-block:: idris

55−

56− myTokenMap : TokenMap Token

57− myTokenMap = [(is 'a',CharLit)]

58−

59−Once we have a TokenMap we can use it to lex many strings.

60−

61−Recognisers

62−-----------

63−

64−The first part of each entry in the TokenMap is the recogniser.

65−

66−A simple recogniser is 'Pred' which uses a predicate (Char -> Bool) to

67−test whether to accept the character. It can be constructed using the

68−'is' function:

69−

70−.. code-block:: idris

71−

72− *parserEx> is 'a'

73− Pred (\ARG =>

74− intToBool (prim__eqChar ARG 'a'))

75− : Recognise True

76−

77−More complicated structures can be recognised as tokens, this is done using

78−the combinator structure of recognisers. This allows recognisers to be

79−combined, for example,

80−

81−.. list-table::

82−

83− * - ``<+>`` means sequence two recognisers. If either consumes a character,

84− the sequence is guaranteed to consume a character.

85−

86− - .. code-block:: idris

87−

88− *parserEx> is 'a' <+> is 'b'

89− SeqEat (Pred (\ARG => intToBool (prim__eqChar ARG 'a')))

90− (Delay (is 'b')) : Recognise True

91−

92− * - ``<|>`` means if both consume, the combination is guaranteed

93− to consumer a character:

94−

95− - .. code-block:: idris

96−

97− *parserEx> is 'a' <|> is 'b'

98− Alt (Pred (\ARG => intToBool (prim__eqChar ARG 'a')))

99− (Pred (\ARG => intToBool (prim__eqChar ARG 'b')))

100− : Recognise True

101−

102−This diagram shows the recogniser combinator with some of its constructors:

103−

104−.. image:: ../image/recogniser.png

105− :width: 487px

106− :height: 249px

107− :alt: recogniser data structure

108−

109−A recogniser consumes its input, that is it advances the index to its input

110−string, as it generates the token list. In some cases we don't want this to

111−happen, for instance, we may need to lookahead before consuming the input

112−string.

113−

114−If a recogniser does not consume input there is a danger of an infinite loop.

115−To prevent this the recogniser is dependent on a boolean called 'consumes' which

116−is true if the recogniser is guaranteed to consume at least one character.

117−

118−The constructors of Recognise allow us to ensure that, even though parts of

119−the recogniser may not consume, overall the recogniser will consume.

120−

121−Since 'Recognise True' is more common than 'Recognise False' it is convenient to

122−use 'Lexer' as a type synonym for 'Recognise True'.

123−

124−Whitespace and Comments

125−-----------------------

126−

127−An important reason to have a lexer is to simplify the parser when whitespace

128−or comments are required. Without this the parser would require a match for

129−every combination, with and without, whitespace and comments.

130−

131−In some languages the lexer needs to remove whitespace and comments so that

132−they don't appear in the token list. In some cases whitespace is significant

133−but a single whitespace token can stand for any number of spaces, tabs,

134−carriage returns and so on.

135−

136−In some cases, such as when parsing the Idris language itself, whitespace

137−is important to indicate blocks. In this case we might want to output a

138−start-of-block token when the indent increases and an end-of-block token

139−when the indent decreases.

140−

141−This topic will be discussed more fully on this page

142−:ref:`parserLibraryWhitespace`.

143−

144−Simple Expression Example for Lexer

145−-----------------------------------

146−

147−On this page we will implement a lexer to 'lex' a very simple expression as

148−a running example, on the next page, we will go on to implement a parser for it.

149−

150−First import the lexer and parser code:

151−

152−.. code-block:: idris

153−

154− module ParserExample

155−

156− import Text.Lexer

157− import public Text.Parser.Core

158− import public Text.Parser

159−

160−Then decide on the tokens that are needed. For this example the idea is to be

161−able to parse simple arithmetic expressions, like this:

162−

163−.. code-block:: idris

164−

165− 1+(2*3)

166−

167−so we need:

168−

169−- Numbers (for now integer literals are good enough).

170−- Some operators (for now ``+``, ``-`` and ``*`` will do.

171−- Opening and closing Parentheses.

172−

173−We can define these, as tokens, like this:

174−

175−.. code-block:: idris

176−

177− %default total

178−

179− public export

180− data ExpressionToken = Number Integer

181− | Operator String

182− | OParen

183− | CParen

184− | EndInput

185−

186−It may help with debugging and to implement error messages to

187−implement ``show`` for these tokens:

188−

189−.. code-block:: idris

190−

191− export

192− Show ExpressionToken where

193− show (Number x) = "number " ++ show x

194− show (Operator x) = "operator " ++ x

195− show OParen = "("

196− show CParen = ")"

197− show EndInput = "end of input"

198−

199− export

200− Show (TokenData ExpressionToken) where

201− show (MkToken l c t) = "line=" ++ show l ++ " col=" ++ show c ++ "tok=" ++ show t

202−

203−The following defines the 'TokenMap' for this example:

204−

205−.. code-block:: idris

206−

207− ||| integer arithmetic operators plus, minus and multiply.

208− export

209− opChars : String

210− opChars = "+-*"

211−

212− operator : Lexer

213− operator = some (oneOf opChars)

214−

215− toInt' : String -> Integer

216− toInt' = cast

217−

218− expressionTokens : TokenMap ExpressionToken

219− expressionTokens =

220− [(digits, \x => Number (toInt' x)),

221− (operator, \x => Operator x),

222− (is '(' ,\x => OParen),

223− (is ')' ,\x => CParen)]

224−

225−This specifies the lexer. It gives, for each token, a function to recognise

226−the token type and a function to construct the token.

227−

228−The library module 'Text.Lexer' contains useful functions to help with this.

229−For example, the digits function used above, which reads one or more

230−numeric characters.

231−

232−We can now run the code with various strings to see what output the lexer

233−produces. This is done by calling the 'lex' function with the TokenMap and

234−input string as parameters:

235−

236−.. code-block:: idris

237−

238− cd Idris-dev/libs/contrib

239− idris -p contrib parserEx.idr

240− ____ __ _

241− / _/___/ /____(_)____

242− / // __ / ___/ / ___/ Version 1.3.2

243− _/ // /_/ / / / (__ ) http://www.idris-lang.org/

244− /___/\__,_/_/ /_/____/ Type :? for help

245−

246− Idris is free software with ABSOLUTELY NO WARRANTY.

247− For details type :warranty.

248− Type checking ./Text/Token.idr

249− Type checking ./Text/Quantity.idr

250− Type checking ./Control/Delayed.idr

251− Type checking ./Data/Bool/Extra.idr

252− Type checking ./Text/Lexer/Core.idr

253− Type checking ./Text/Lexer.idr

254− Type checking ./parserEx.idr

255−

256− *parserEx> lex expressionTokens "1+2"

257− ([MkToken 0 0 (Number 1),

258− MkToken 0

259− (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "1" of

260− (incol, "") => c + cast (length incol)

261− (incol, b) => cast (length incol))

262− (Operator "+"),

263− MkToken 0

264− (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "+" of

265− (incol, "") => c + cast (length incol)

266− (incol, b) => cast (length incol))

267− (Number 2)],

268− 0,

269− case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "2" of

270− (incol, "") => c + cast (length incol)

271− (incol, b) => cast (length incol),

272− getString (MkStrLen "" 0)) : (List (TokenData ExpressionToken),

273− Int,

274− Int,

275− String)

276−

277−The lexer uses potentially infinite data structures. It has recursive

278−arguments (codata type) so code is lazy. In the output above the indexes

279−have not been computed but we can pick out the tokens:

280−

281−- (Number 1)

282−- (Operator "+")

283−- (Number 2)

284−

285−So the code is working.

286−

287−We can now go ahead and parse this token list. A parser for this example will

288−be constructed on the next page.

docs/parserLibrary/parser.rstdeleted−700

@@ -1,700 +0,0 @@

1−.. _parserLibraryParser:

2−

3−Parser

4−======

5−

6−To run the parser we call ``parse``. This requires a grammar and the output

7−from the lexer (which is a list of tokens).

8−

9−.. code-block:: idris

10−

11− parse : (act : Grammar tok c ty) -> (xs : List tok) ->

12− Either (ParseError tok) (ty, List tok)

13−

14−If successful this returns 'Right' with a pair of

15−

16−- the parse result.

17−- the unparsed tokens (the remaining input).

18−

19−otherwise it returns 'Left' with the error message.

20−

21−So we need to define the grammar for our parser, this is done using the following

22−'Grammar' data structure. This is a combinator structure, similar in principle

23−to the recogniser combinator for the lexer, which was discussed on the

24−previous page.

25−

26−As with the Recogniser the ``Grammar`` type is dependent on a boolean 'consumes'

27−value which allows us to ensure that complicated ``Grammar`` structures will always

28−consume input.

29−

30−.. code-block:: idris

31−

32− ||| Description of a language's grammar. The `tok` parameter is the type

33− ||| of tokens, and the `consumes` flag is True if the language is guaranteed

34− ||| to be non-empty - that is, successfully parsing the language is guaranteed

35− ||| to consume some input.

36− public export

37− data Grammar : (tok : Type) -> (consumes : Bool) -> Type -> Type where

38− Empty : (val : ty) -> Grammar tok False ty

39− Terminal : String -> (tok -> Maybe a) -> Grammar tok True a

40− NextIs : String -> (tok -> Bool) -> Grammar tok False tok

41− EOF : Grammar tok False ()

42−

43− Fail : Bool -> String -> Grammar tok c ty

44− Commit : Grammar tok False ()

45− MustWork : Grammar tok c a -> Grammar tok c a

46−

47− SeqEat : Grammar tok True a -> Inf (a -> Grammar tok c2 b) ->

48− Grammar tok True b

49− SeqEmpty : {c1, c2 : Bool} ->

50− Grammar tok c1 a -> (a -> Grammar tok c2 b) ->

51− Grammar tok (c1 || c2) b

52− Alt : {c1, c2 : Bool} ->

53− Grammar tok c1 ty -> Grammar tok c2 ty ->

54− Grammar tok (c1 && c2) ty

55−

56−So an example of a grammer type may look something like this:

57−``Grammar (TokenData ExpressionToken) True Integer``.

58−This is a complicated type name and a given parser will need to use it a lot.

59−So to reduce the amount of typing we can use the following type synonym (similar

60−to what is done in Idris 2

61−: https://github.com/edwinb/Idris2/blob/master/src/Parser/Support.idr

62−)

63−

64−.. code-block:: idris

65−

66− public export

67− Rule : Type -> Type

68− Rule ty = Grammar (TokenData ExpressionToken) True ty

69−

70−Parser Example

71−--------------

72−

73−On the previous page we implemented a lexer to 'lex' a very simple expression, on

74−this page we will go on to add a parser for this running example.

75−

76−.. list-table::

77−

78− * - The syntax we are aiming at is something

79− like this (expressed in Backus–Naur form (BNF)):

80− - .. code-block:: idris

81−

82− <expr> ::= <integer literal>

83− | <expr>'+'<expr>

84− | <expr>'-'<expr>

85− | <expr>'*'<expr>

86− | '('<expr>')'

87−

88− <integer literal> ::= <digit>|<integer literal><digit>

89−

90−.. list-table::

91−

92− * - To start, here is a grammar to parse an integer literal (that is, a

93− sequence of numeric characters).

94−

95− - .. code-block:: idris

96−

97− export

98− intLiteral : Rule Integer

99− intLiteral

100− = terminal (\x => case tok x of

101− Number i => Just i

102− _ => Nothing)

103−

104−In order to try this out, here is a temporary function, this calls

105−parse which takes two parameters:

106−

107−- The grammar (in this case intLiteral)

108−- The token list from the lexer.

109−

110−.. code-block:: idris

111−

112− test1 : String -> Either (ParseError (TokenData ExpressionToken))

113− (Integer, List (TokenData ExpressionToken))

114− test1 s = parse intLiteral (fst (lex expressionTokens s))

115−

116−As required, if we pass it a string which is a number literal then it will

117−return the number in the 'Right' option.

118−

119−.. code-block:: idris

120−

121− *parserEx> test1 "123"

122− Right (123, []) : Either (ParseError (TokenData ExpressionToken))

123− (Integer, List (TokenData ExpressionToken))

124−

125−If we pass it a string which is not a number literal then it will return an

126−error message.

127−

128−.. code-block:: idris

129−

130− *parserEx> test1 "a"

131− Left (Error "End of input"

132− []) : Either (ParseError (TokenData ExpressionToken))

133− (Integer, List (TokenData ExpressionToken))

134−

135−If we pass it a number followed by something else, then it will still be

136−successful, this is because we are not specifically checking for end-of-file.

137−

138−.. code-block:: idris

139−

140− *parserEx> test1 "123a"

141− Right (123, []) : Either (ParseError (TokenData ExpressionToken))

142− (Integer, List (TokenData ExpressionToken))

143− *parserEx>

144−

145−.. list-table::

146−

147− * - The ``intLiteral`` function above uses the ``terminal`` function to

148− construct the grammar

149− - .. code-block:: idris

150−

151− ||| Succeeds if running the predicate on the

152− ||| next token returns Just x, returning x.

153− ||| Otherwise fails.

154− export

155− terminal : (tok -> Maybe a) -> Grammar tok True a

156− terminal = Terminal

157−

158−This is defined here

159−: https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Parser/Core.idr

160−Idris 2 uses a slightly different version which stores an error message like

161−"Expected integer literal" which can be output if the rule fails

162−: https://github.com/edwinb/Idris2/blob/master/src/Text/Parser/Core.idr

163−

164−.. list-table::

165−

166− * - The 'terminal' function is also used to construct the other

167− elements of the grammar that we require, for instance,

168− opening parenthesis:

169−

170− - .. code-block:: idris

171−

172− openParen : Rule Integer

173− openParen = terminal (\x => case tok x of

174− OParen => Just 0

175− _ => Nothing)

176−

177−Integer value is not really relevant for parenthesis so ``0`` (zero) is used as

178−a default value.

179−

180−As before, this can be tested with a function like this:

181−

182−.. code-block:: idris

183−

184− test2 : String -> Either (ParseError (TokenData ExpressionToken))

185− (Integer, List (TokenData ExpressionToken))

186− test2 s = parse openParen (fst (lex expressionTokens s))

187−

188−We can see below that it correctly parses an open parenthesis and gives an

189−error for anything else:

190−

191−.. code-block:: idris

192−

193− *parserEx> test2 "("

194− Right (0, []) : Either (ParseError (TokenData ExpressionToken))

195− (Integer, List (TokenData ExpressionToken))

196− *parserEx> test2 "123"

197− Left (Error "Unrecognised token"

198− [MkToken 0

199− 0

200− (Number 123)]) : Either (ParseError (TokenData ExpressionToken))

201− (Integer,

202− List (TokenData ExpressionToken))

203−

204−Now we have two Grammars we can try combining them. The following test looks

205−for ``openParen`` followed by ``intLiteral``, the two Grammars are combined using

206−``<*>``. The ``map const`` part uses the integer value from the first.

207−

208−The following test is looking for ``(`` followed by a number:

209−

210−.. code-block:: idris

211−

212− test3 : String -> Either (ParseError (TokenData ExpressionToken))

213− (Integer, List (TokenData ExpressionToken))

214− test3 s = parse (map const openParen <*> intLiteral) (fst (lex expressionTokens s))

215−

216−We can see below that ``(`` followed by a number is successfully parsed but, as

217−required, other token lists are not:

218−

219−.. code-block:: idris

220−

221− *parserEx> test3 "(123"

222− Right (0, []) : Either (ParseError (TokenData ExpressionToken))

223− (Integer, List (TokenData ExpressionToken))

224− *parserEx> test3 "(("

225− Left (Error "Unrecognised token"

226− [MkToken 0

227− (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n')))

228− "(" of

229− (incol, "") => c + cast (length incol)

230− (incol, b) => cast (length incol))

231− OParen]) : Either (ParseError (TokenData ExpressionToken))

232− (Integer, List (TokenData ExpressionToken))

233−

234− *parserEx> test3 "123"

235− Left (Error "Unrecognised token"

236− [MkToken 0

237− 0

238− (Number 123)]) : Either (ParseError (TokenData ExpressionToken))

239− (Integer,

240− List (TokenData ExpressionToken))

241− *parserEx> test3 "123("

242− Left (Error "Unrecognised token"

243− [MkToken 0 0 (Number 123),

244− MkToken 0

245− (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n')))

246− "321" of

247− (incol, "") => c + cast (length incol)

248− (incol, b) => cast (length incol))

249− OParen]) : Either (ParseError (TokenData ExpressionToken))

250− (Integer, List (TokenData ExpressionToken))

251−

252−.. list-table::

253−

254− * - The closing parenthesis is constructed in the same way.

255−

256− - .. code-block:: idris

257−

258− closeParen : Rule Integer

259− closeParen = terminal (\x => case tok x of

260− CParen => Just 0

261− _ => Nothing)

262−

263−.. list-table::

264−

265− * - Now we can generate a Grammar for an expression inside parenthesis

266− like this.

267−

268− - .. code-block:: idris

269−

270− paren : Rule Integer -> Rule Integer

271− paren exp = openParen *> exp <* closeParen

272−

273−The use of ``*>`` and ``<*`` instead of ``<*>`` is an easy way to use the integer

274−value from the inner expression.

275−

276−So lets try to use this to define a grammar which recognises either:

277−

278−- An integer literal

279−- An integer literal inside parenthesis

280−- An integer literal inside parenthesis inside parenthesis

281−- ... and so on.

282−

283−.. list-table::

284−

285− * - This requires a recursively defined structure like this:

286−

287− - .. code-block:: idris

288−

289− partial

290− expr : Rule Integer

291− expr = intLiteral <|> (paren expr)

292−

293−This is a valid grammar because every time it is called it is guaranteed to

294−consume a token. However, as an Idris structure, it is problematic due to

295−the recursion. Defining it as partial allows it to compile but at runtime

296−we are likely to get a crash with an (unhelpful) error message like

297−``killed by signal 11``.

298−

299−So a better method is to use ``do`` notation as described in the following

300−section.

301−

302−Monadic Combinator

303−------------------

304−

305−In addition to ``<|>`` and ``<*>`` there is a ``>>=`` combinator, which is

306−defined like this:

307−

308−.. code-block:: idris

309−

310− ||| Sequence two grammars. If either consumes some input, the sequence is

311− ||| guaranteed to consume some input. If the first one consumes input, the

312− ||| second is allowed to be recursive (because it means some input has been

313− ||| consumed and therefore the input is smaller)

314− export %inline

315− (>>=) : {c1 : Bool} ->

316− Grammar tok c1 a ->

317− inf c1 (a -> Grammar tok c2 b) ->

318− Grammar tok (c1 || c2) b

319− (>>=) {c1 = False} = SeqEmpty

320− (>>=) {c1 = True} = SeqEat

321−

322−.. list-table::

323−

324− * - This allows us to use ``do`` notation for the previous parenthesis example:

325−

326− - .. code-block:: idris

327−

328− expr = intLiteral <|> do

329− openParen

330− r <- expr

331− closeParen

332− pure r

333−

334−This can be more flexible than using the ``<*>`` operator. Also it is defined

335−using ``Inf`` so we can implement recursively defined grammars as above.

336−

337−Implementing the Arithmetic Operators

338−-------------------------------------

339−

340−.. list-table::

341−

342− * - Now for the operations, in this case: ``+``, ``-`` and ``*``.

343− The syntax we require for these infix operators

344− would require recursive grammars like this:

345−

346− - .. code-block:: idris

347−

348− expr = expr (op "+") expr

349−

350−As already explained, ``do`` notation can allow us to use recursive

351−definitions but not necessarily left-recursion like this.

352−

353−In order to work up to this gradually lets start with prefix operators

354−(sometimes known as Polish notation) then modify later for infix operators.

355−

356−.. list-table::

357−

358− * - So prefix operators would have this sort of form:

359−

360− - .. code-block:: idris

361−

362− expr = (add (op "+") expr expr)

363−

364−where ``op`` is defined like this:

365−

366−.. code-block:: idris

367−

368− ||| Matches if this is an operator token and string matches, that is,

369− ||| it is the required type of operator.

370− op : String -> Rule Integer

371− op s = terminal (\x => case tok x of

372− (Operator s1) => if s==s1 then Just 0 else Nothing

373− _ => Nothing)

374−

375−.. list-table::

376−

377− * - and ``add`` is defined like this:

378−

379− Where:

380−

381− - x is the add operator.

382− - y is the first operand.

383− - z is the second operand.

384−

385− - .. code-block:: idris

386−

387− addInt : Integer -> Integer -> Integer

388− addInt a b = a+b

389−

390− export

391− add : Grammar tok c1 Integer ->

392− Grammar tok c2 Integer ->

393− Grammar tok c3 Integer ->

394− Grammar tok ((c1 || c2) || c3) Integer

395− add x y z = map addInt (x *> y) <*> z

396−

397−

398−

399−The resulting integer will be the sum of the two operands.

400−

401−.. list-table::

402−

403− * - The other operators are defined in a similar way:

404−

405− - .. code-block:: idris

406−

407− subInt : Integer -> Integer -> Integer

408− subInt a b = a-b

409−

410− export

411− sub : Grammar tok c1 Integer ->

412− Grammar tok c2 Integer ->

413− Grammar tok c3 Integer ->

414− Grammar tok ((c1 || c2) || c3) Integer

415− sub x y z = map subInt (x *> y) <*> z

416−

417− multInt : Integer -> Integer -> Integer

418− multInt a b = a*b

419−

420− export

421− mult : Grammar tok c1 Integer ->

422− Grammar tok c2 Integer ->

423− Grammar tok c3 Integer ->

424− Grammar tok ((c1 || c2) || c3) Integer

425− mult x y z = map multInt (x *> y) <*> z

426−

427−So the top level ``Grammar`` can now be defined as follows. Note that this is

428−partial as it is a potentially infinite structure and so not total.

429−

430−.. code-block:: idris

431−

432− partial

433− expr : Rule Integer

434− expr = (add (op "+") expr expr)

435− <|> (sub (op "-") expr expr)

436− <|> (mult (op "*") expr expr)

437− <|> intLiteral <|> (paren expr)

438−

439−.. list-table::

440−

441− * - To make the testing easier we can use this function:

442−

443− - .. code-block:: idris

444−

445− partial

446− test : String -> Either (ParseError (TokenData ExpressionToken))

447− (Integer, List (TokenData ExpressionToken))

448− test s = parse expr (fst (lex expressionTokens s))

449−

450−.. list-table::

451−

452− * - First test a valid (prefix) expression:

453−

454− - .. code-block:: idris

455−

456− *parserEx> test "+1*6(4)"

457− Right (25,

458− []) : Either (ParseError (TokenData ExpressionToken))

459− (Integer, List (TokenData ExpressionToken))

460−

461−Then an invalid syntax:

462−

463−.. code-block:: idris

464−

465− *parserEx> test "))"

466− Left (Error "Unrecognised token"

467− [MkToken 0 0 CParen,

468− MkToken 0

469− (case fspan (\ARG =>

470− not (intToBool (prim__eqChar ARG

471− '\n')))

472− ")" of

473− (incol, "") => c + cast (length incol)

474− (incol, b) => cast (length incol))

475− CParen]) : Either (ParseError (TokenData ExpressionToken))

476− (Integer,

477− List (TokenData ExpressionToken))

478−

479−However if we try something that is invalid, but starts with a valid token,

480−then it will return ``Right`` (to indicate success)

481−

482−.. code-block:: idris

483−

484− *parserEx> test "1))"

485− Right (1,

486− [MkToken 0

487− (case fspan (\ARG =>

488− not (intToBool (prim__eqChar ARG '\n')))

489− "1" of

490− (incol, "") => c + cast (length incol)

491− (incol, b) => cast (length incol))

492− CParen,

493− MkToken 0

494− (case fspan (\ARG =>

495− not (intToBool (prim__eqChar ARG '\n')))

496− ")" of

497− (incol, "") => c + cast (length incol)

498− (incol, b) => cast (length incol))

499− CParen]) : Either (ParseError (TokenData ExpressionToken))

500− (Integer,

501− List (TokenData ExpressionToken))

502−

503−Infix Notation

504−--------------

505−

506−So far we have implemented a prefix notation for operators (like this:

507−``+ expr expr``) but the aim is to implemented an infix notation (like this:

508−``expr + expr``). To do this we must be able to deal with potentially

509−infinite data structures (see Codata Types here :ref:`sect-typefuns`).

510−

511−First alter the grammar to have infix operations:

512−

513−.. code-block:: idris

514−

515− addInt : Integer -> Integer -> Integer

516− addInt a b = a+b

517−

518− export

519− add : Grammar tok c1 Integer ->

520− Grammar tok c2 Integer ->

521− Grammar tok c3 Integer ->

522− Grammar tok ((c1 || c2) || c3) Integer

523− add x y z = map addInt (x <* y) <*> z

524−

525− subInt : Integer -> Integer -> Integer

526− subInt a b = a-b

527−

528− export

529− sub : Grammar tok c1 Integer ->

530− Grammar tok c2 Integer ->

531− Grammar tok c3 Integer ->

532− Grammar tok ((c1 || c2) || c3) Integer

533− sub x y z = map subInt (x <* y) <*> z

534−

535−

536− multInt : Integer -> Integer -> Integer

537− multInt a b = a*b

538−

539− export

540− mult : Grammar tok c1 Integer ->

541− Grammar tok c2 Integer ->

542− Grammar tok c3 Integer ->

543− Grammar tok ((c1 || c2) || c3) Integer

544− mult x y z = map multInt (x <* y) <*> z

545−

546− partial

547− expr : Rule Integer

548− expr = (add expr (op "+") expr)

549− <|> (sub expr (op "-") expr)

550− <|> (mult expr (op "*") expr)

551− <|> intLiteral <|> (paren expr)

552−

553−However, if this was run, the code would not terminate.

554−

555−Implement Left Recursion Elimination

556−------------------------------------

557−

558−Left factoring, like this, is a general problem.

559−

560−If we have a rule like this:

561−

562−.. code-block:: idris

563−

564− A -> (x<*>y) <|> (x<*>z)

565−

566−If ``x<*>y`` fails but ``x<*>z`` would succeed a problem is that, ``x<*>y`` has

567−already consumed ``x``, so now ``x<*>z`` will fail.

568−

569−so we could write code to backtrack. That is ``try`` ``x<*>y`` without consuming

570−so that, if the first token succeeds but the following tokens fail, then the

571−first tokens would not be consumed.

572−

573−Another approach is left factoring:

574−

575−Left Factoring

576−--------------

577−

578−Replace the rule with two rules (that is we add a non-terminal symbol) so

579−for example, instead of:

580−

581−.. code-block:: idris

582−

583− A -> (x<*>y) <|> (x<*>z)

584−

585−we add an extra rule to give:

586−

587−.. code-block:: idris

588−

589− A -> x<*>N

590− N -> y <|> z

591−

592−That is we convert a general context-free grammar to a LL(1) grammar. Although

593−not every context-free grammar can be converted to a LL(1) grammar.

594−

595−This still does not solve the infinite recursion issue and there is another

596−problem: the precedence of the operators ``+``, ``-`` and ``*`` is not explicit.

597−

598−.. list-table::

599−

600− * - To resolve this we can alter the example to have a BNF like this:

601− Where braces ``{ ... }`` mean the contents can occur 1 or more times.

602−

603− - .. code-block:: idris

604−

605− 'expression' ::= ('+'|'-') 'term' {('+'|'-') 'term'}

606−

607− 'term' ::= 'factor' {'*' 'factor'}

608−

609− 'factor' ::=

610− number

611− | '(' 'expression' ')'

612−

613−

614−.. code-block:: idris

615−

616− expr : Rule Integer

617−

618− factor : Rule Integer

619− factor = intLiteral <|> do

620− openParen

621− r <- expr

622− closeParen

623− pure r

624−

625− term : Rule Integer

626− term = map multInt factor <*> (

627− (op "*")

628− *> factor)

629− <|> factor

630−

631− expr = map addInt term <*> (

632− (op "+")

633− *> term)

634− <|> map subInt term <*> (

635− (op "-")

636− *> term)

637− <|> term

638−

639− calc : String -> Either (ParseError (TokenData ExpressionToken))

640− (Integer, List (TokenData ExpressionToken))

641− calc s = parse expr (fst (lex expressionTokens s))

642−

643− lft : (ParseError (TokenData ExpressionToken)) -> IO ()

644− lft (Error s lst) = putStrLn ("error:"++s)

645−

646− rht : (Integer, List (TokenData ExpressionToken)) -> IO ()

647− rht i = putStrLn ("right " ++ (show i))

648−

649− main : IO ()

650− main = do

651− putStr "alg>"

652− x <- getLine

653− either lft rht (calc x) -- eliminator for Either

654−

655−As the following tests show, this now handles infix operators and precedence.

656−

657−.. list-table::

658−

659− * - For example '*' is an infix operator:

660−

661− - .. code-block:: idris

662−

663− *algebraREPL> :exec

664− alg>2*3

665− right (6, [])

666−

667− * - Check that atomic number literals work:

668−

669− - .. code-block:: idris

670−

671− *algebraREPL> :exec

672− alg>2

673− right (2, [])

674−

675− * - Check that '*' has a higher precedence than '+'.

676−

677− - .. code-block:: idris

678−

679− *algebraREPL> :exec

680− alg>2+3*4

681− right (14, [])

682−

683− * - Also '*' has a higher precedence than '+' when the order is reversed.

684−

685− - .. code-block:: idris

686−

687− *algebraREPL> :exec

688− alg>3*4+2

689− right (14, [])

690−

691− * - Also precedence can be overridden by parenthesis.

692−

693− - .. code-block:: idris

694−

695− *algebraREPL> :exec

696− alg>(2+3)*4

697− right (20, [])

698−

699−This is still not correct because it does not correctly parse multiple sums or terms

700−like ``1+2+3`` or ``1*2*3``.

docs/parserLibrary/whitespace.rstdeleted−250

@@ -1,250 +0,0 @@

1−.. _parserLibraryWhitespace:

2−

3−Whitespace and Comments

4−=======================

5−

6−The previous two pages introduced the lexer and parser but have not yet

7−discussed how to handle whitespace and comments.

8−

9−In some grammars whitespace and comments would not be considered significant and

10−so we might be tempted not to generate any tokens for them. However, in the

11−running example, we may want to make spaces significant in the future. For

12−example, we might want to implement function application expressed by

13−juxtaposition as in Haskell and Idris like this: ``f x``.

14−

15−So, on this page, we will add a token for whitespace and comments. We will

16−then consider two ways to process this:

17−

18−- Filter all whitespace tokens from the lexer results before passing to

19− the parser.

20−- Process the whitespace tokens in the parser.

21−

22−Whitespace and Comments in Lexer

23−--------------------------------

24−

25−To start with we can use the same token for both whitespace and comments. Here

26−it is called ``Comment`` and added to the ``ExpressionToken`` data structure

27−like this:

28−

29−.. code-block:: idris

30−

31− public export

32− data ExpressionToken = Number Integer

33− | Operator String

34− | OParen

35− | CParen

36− | Comment String

37− | EndInput

38−

39−This is added to the ``TokenMap`` like this:

40−

41−.. code-block:: idris

42−

43− ||| from https://github.com/edwinb/Idris2/blob/master/src/Parser/Lexer.idr

44− comment : Lexer

45− comment = is '-' <+> is '-' <+> many (isNot '\n')

46−

47− expressionTokens : TokenMap ExpressionToken

48− expressionTokens =

49− [(digits, \x => Number (toInt' x)),

50− (operator, \x => Operator x),

51− (is '(' ,\x => OParen),

52− (is ')' ,\x => CParen),

53− (spaces, Comment),

54− (comment, Comment)]

55−

56−As you can see, the comment is defined like a single line Idris comment,

57−it starts with ``--`` and continues for the remainder of the line.

58−

59−We don't need to define ``spaces`` because it is already defined in

60−: https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Lexer.idr

61−like this:

62−

63−.. code-block:: idris

64−

65− ||| Recognise a single whitespace character

66− ||| /\\s/

67− space : Lexer

68− space = pred isSpace

69−

70− ||| Recognise one or more whitespace characters

71− ||| /\\s+/

72− spaces : Lexer

73− spaces = some space

74−

75−If these whitespace tokens are not significant, that is, they can appear

76−anywhere and they are optional then we can filter them out before the parser

77−gets them like this:

78−

79−.. code-block:: idris

80−

81− processWhitespace : (List (TokenData ExpressionToken), Int, Int, String)

82− -> (List (TokenData ExpressionToken), Int, Int, String)

83− processWhitespace (x,l,c,s) = ((filter notComment x),l,c,s) where

84− notComment : TokenData ExpressionToken -> Bool

85− notComment t = case tok t of

86− Comment _ => False

87− _ => True

88−

89− calc : String -> Either (ParseError (TokenData ExpressionToken))

90− (Integer, List (TokenData ExpressionToken))

91− calc s = parse expr (fst (processWhitespace (lex expressionTokens s)))

92−

93−

94−Whitespace and Comments in Parser

95−---------------------------------

96−

97−If we sometimes require whitespace to be significant then we can't filter

98−them out as above. In this case the ``Comment`` tokens are sent to the parser

99−which now needs to be able to handle them.

100−

101−.. code-block:: idris

102−

103− commentSpace : Rule Integer

104− commentSpace = terminal (\x => case tok x of

105− Comment s => Just 0

106− _ => Nothing)

107−

108−So far we don't have any syntax that requires spaces to be significant so we

109−need to define the grammar so that it will parse with, or without, spaces.

110−This needs to be done in a systematic way, here I have defined the grammar so

111−that there is an optional space to the right of every atom or operator.

112−First add versions of ``intLiteral`` , ``openParen`` , ``closeParen``

113−and ``op`` that allow optional spaces/comments to the right of them:

114−

115−.. code-block:: idris

116−

117− intLiteralC : Rule Integer

118− intLiteralC = (intLiteral <* commentSpace) <|> intLiteral

119−

120− openParenC : Rule Integer

121− openParenC = (openParen <* commentSpace) <|> openParen

122−

123− closeParenC : Rule Integer

124− closeParenC = (closeParen <* commentSpace) <|> closeParen

125−

126− ||| like op but followed by optional comment or space

127− opC : String -> Rule Integer

128− opC s = ((op s) <* commentSpace) <|> (op s)

129−

130−Then just use these functions instead of the original functions:

131−

132−.. code-block:: idris

133−

134− expr : Rule Integer

135−

136− factor : Rule Integer

137− factor = intLiteralC <|> do

138− openParenC

139− r <- expr

140− closeParenC

141− pure r

142−

143− term : Rule Integer

144− term = map multInt factor <*> (

145− (opC "*")

146− *> factor)

147− <|> factor

148−

149− expr = map addInt term <*> (

150− (opC "+")

151− *> term)

152− <|> map subInt term <*> (

153− (opC "-")

154− *> term)

155− <|> term

156−

157− calc : String -> Either (ParseError (TokenData ExpressionToken))

158− (Integer, List (TokenData ExpressionToken))

159− calc s = parse expr (fst (lex expressionTokens s))

160−

161− lft : (ParseError (TokenData ExpressionToken)) -> IO ()

162− lft (Error s lst) = putStrLn ("error:"++s)

163−

164− rht : (Integer, List (TokenData ExpressionToken)) -> IO ()

165− rht i = putStrLn ("right " ++ (show i))

166−

167− main : IO ()

168− main = do

169− putStr "alg>"

170− x <- getLine

171− either lft rht (calc x) -- eliminator for Either

172−

173−

174−Defining Block Structure using Indents

175−--------------------------------------

176−

177−Many languages such as Python, Haskell and Idris use indents to delimit

178−the block structure of the language.

179−

180−We can see how Idris2 does it here

181−: https://github.com/edwinb/Idris2/blob/master/src/Parser/Support.idr

182−

183−.. code-block:: idris

184−

185− export

186− IndentInfo : Type

187− IndentInfo = Int

188−

189− export

190− init : IndentInfo

191− init = 0

192−

193−EndInput Token

194−--------------

195−

196−So far, the parser will return a successful result even if the full input

197−is not consumed. To ensure that the top level syntax is fully matched we

198−add a ``EndInput`` token to indicate the last token.

199−

200−``EndInput`` is added to the other tokens like this:

201−

202−.. code-block:: idris

203−

204− data ExpressionToken = Number Integer

205− | Operator String

206− | OParen

207− | CParen

208− | Comment String

209− | EndInput

210−

211−A rule to consume this token is added:

212−

213−.. code-block:: idris

214−

215− eoi : Rule Integer

216− eoi = terminal (\x => case tok x of

217− EndInput => Just 0

218− _ => Nothing)

219−

220−Instead of using ``expr`` at the top level of the syntax we can now define

221−``exprFull`` as shown here. This will make sure that only when ``EndInput``

222−is consumed will the parse be successful:

223−

224−.. code-block:: idris

225−

226− exprFull : Rule Integer

227− exprFull = expr <* eoi

228−

229−The following code makes sure ``EndInput`` is added to the end of the token

230−list:

231−

232−.. code-block:: idris

233−

234− processWhitespace : (List (TokenData ExpressionToken), Int, Int, String)

235− -> (List (TokenData ExpressionToken), Int, Int, String)

236− processWhitespace (x,l,c,s) = ((filter notComment x)++

237− [MkToken l c EndInput],l,c,s) where

238− notComment : TokenData ExpressionToken -> Bool

239− notComment t = case tok t of

240− Comment _ => False

241− _ => True

242−

243−All we have to do now is use ``exprFull`` instead of ``expr``:

244−

245−.. code-block:: idris

246−

247− calc : String -> Either (ParseError (TokenData ExpressionToken))

248− (Integer, List (TokenData ExpressionToken))

249− calc s = parse exprFull (fst (processWhitespace (lex expressionTokens s)))

250−

docs/proofs/definitional.rstdeleted−235

@@ -1,235 +0,0 @@

1−*******************

2−Background Material

3−*******************

4−

5−In order to understand how to write proofs in Idris I think its worth clarifying some fundamentals, such as,

6−

7−- Propositions and judgments

8−- Boolean and constructive logic

9−- Curry-Howard correspondence

10−- Definitional and propositional equalities

11−- Axiomatic and constructive approaches

12−

13−Propositions and Judgments

14−==========================

15−

16−Propositions are the subject of our proofs, before the proof then we can't formally say if they are true or not. If the proof is successful then the result is a 'judgment'.

17−For instance, if the ``proposition`` is,

18−

19−+-------+

20−| 1+1=2 |

21−+-------+

22−

23−When we prove it, the ``judgment`` is,

24−

25−+------------+

26−| 1+1=2 true |

27−+------------+

28−

29−Or if the ``proposition`` is,

30−

31−+-------+

32−| 1+1=3 |

33−+-------+

34−

35−Obviously we can't prove it is true, but it is still a valid proposition and perhaps we can prove it is false so the ``judgment`` is,

36−

37−+-------------+

38−| 1+1=3 false |

39−+-------------+

40−

41−This may seem a bit pedantic but it is important to be careful, in mathematics not every proposition is true or false for instance, a proposition may be unproven or even unprovable.

42−

43−So the logic here is different from the logic that comes from boolean algebra. In that case what is not true is false and what is not false is true. The logic we are using here does not have this 'law of excluded middle' so we have to be careful not to use it.

44−

45−A false proposition is taken to be a contradiction and if we have a contradiction then we can prove anything, so we need to avoid this. Some languages, used in proof assistants, prevent contradictions but such languages cannot be Turing complete, so Idris does not prevent contradictions.

46−

47−The logic we are using is called constructive (or sometimes intuitional) because we are constructing a 'database' of judgments.

48−

49−There are also many other types of logic, another important type of logic for Idris programmers is '``linear logic``' but that's not discussed on this page.

50−

51−Curry-Howard correspondence

52−===========================

53−

54−So how to we relate these proofs to Idris programs? It turns out that there is a correspondence between constructive logic and type theory. They are the same structure and we can switch backward and forward between the two notations because they are the same thing.

55−

56−The way that this works is that a proposition is a type so this,

57−

58−.. code-block:: idris

59−

60− Idris> 1+1=2

61− 2 = 2 : Type

62−

63−is a proposition and it is also a type. This is built into Idris so when an '=' equals sign appears in a function type an equality type is generated. The following will also produce an equality type:

64−

65−

66−.. code-block:: idris

67−

68− Idris> 1+1=3

69− 2 = 3 : Type

70−

71−Both of these are valid propositions so both are valid equality types. But how do we represent true judgment, that is, how do we denote 1+1=2 is true but not 1+1=3.

72−A type that is true is inhabited, that is, it can be constructed. An equality type has only one constructor 'Refl' so a proof of 1+1=2 is

73−

74−.. code-block:: idris

75−

76− onePlusOne : 1+1=2

77− onePlusOne = Refl

78−

79−So how can Refl, which is a constructor without any parameters, construct an equality type? If we type it on its own then it can't:

80−

81−.. code-block:: idris

82−

83− Idris> Refl

84− (input):Can't infer argument A to Refl, Can't infer argument x to Refl

85−

86−So it must pattern match on its return type:

87−

88−.. code-block:: idris

89−

90− Idris> the (1=1) Refl

91− Refl : 1 = 1

92−

93−So now that we can represent propositions as types other aspects of propositional logic can also be translated to types as follows:

94−

95−+----------+-------------------+--------------------------+

96−| | propositions | example of possible type |

97−+----------+-------------------+--------------------------+

98−| A | x=y | |

99−+----------+-------------------+--------------------------+

100−| B | y=z | |

101−+----------+-------------------+--------------------------+

102−| and | A /\\ B | ``Pair(x=y,y=z)`` |

103−+----------+-------------------+--------------------------+

104−| or | A \\/ B | ``Either(x=y,y=z)`` |

105−+----------+-------------------+--------------------------+

106−| implies | A -> B | ``(x=y) -> (y=x)`` |

107−+----------+-------------------+--------------------------+

108−| for all | y=z | |

109−+----------+-------------------+--------------------------+

110−| exists | y=z | |

111−+----------+-------------------+--------------------------+

112−

113−

114−And (conjunction)

115−-----------------

116−

117−We can have a type which corresponds to conjunction:

118−

119−.. code-block:: idris

120−

121− AndIntro : a -> b -> A a b

122−

123−There is a built in type called 'Pair'.

124−

125−Or (disjunction)

126−----------------

127−

128−We can have a type which corresponds to disjunction:

129−

130−.. code-block:: idris

131−

132− data Or : Type -> Type -> Type where

133− OrIntroLeft : a -> A a b

134− OrIntroRight : b -> A a b

135−

136−There is a built in type called 'Either'.

137−

138−Definitional and Propositional Equalities

139−=========================================

140−

141−We have seen that we can 'prove' a type by finding a way to construct a term. In the case of equality types there is only one constructor which is 'Refl'.

142−We have also seen that each side of the equation does not have to be identical like '2=2'. It is enough that both sides are ``definitionaly equal`` like this:

143−

144−.. code-block:: idris

145−

146− onePlusOne : 1+1=2

147− onePlusOne = Refl

148−

149−So both sides of this equation nomalise to 2 and so Refl will type match and the proposition is proved.

150−

151−We don't have to stick to terms, can also use symbolic parameters so the following will compile:

152−

153−.. code-block:: idris

154−

155− varIdentity : m = m

156− varIdentity = Refl

157−

158−If a proposition/equality type is not definitionaly equal but is still true then it is ``propositionaly equal``. In this case we may still be able to prove it but some steps in the proof may require us to add something into the terms or at least to take some sideways steps to get to a proof.

159−

160−Especially when working with equalities containing variable terms (inside functions) it can be hard to know which equality types are definitially equal, in this example plusReducesL is '``definitially equal``' but plusReducesR is not (although it is '``propositionaly equal``'). The only difference between them is the order of the operands.

161−

162−.. code-block:: idris

163−

164− plusReducesL : (n:Nat) -> plus Z n = n

165− plusReducesL n = Refl

166−

167− plusReducesR : (n:Nat) -> plus n Z = n

168− plusReducesR n = Refl

169−

170−plusReducesR gives the following error:

171−

172−

173−.. code-block:: idris

174−

175− - + Errors (1)

176− `-- proof.idr line 6 col 17:

177− When checking right hand side of plusReducesR with expected type

178− plus n 0 = n

179−

180− Type mismatch between

181− n = n (Type of Refl)

182− and

183− plus n 0 = n (Expected type)

184−

185− Specifically:

186− Type mismatch between

187− n

188− and

189− plus n 0

190−

191−So why is 'Refl' able to prove some equality types but not others?

192−

193−The first answer is that 'plus' is defined in such a way that it splits on its first argument so it is simple to prove when 0 is the first argument but not the second. So what is the general way to know if Refl will work?

194−

195−If an equality type can be proved/constructed by using Refl alone it is known as a ``definitional equality``. In order to be definitinally equal both sides of the equation must normalise to unique values. That is, each step in the proof must reduce the term so each step is effectively forced.

196−

197−So when we type 1+1 in Idris it is immediately converted to 2 because definitional equality is built in.

198−

199−.. code-block:: idris

200−

201− Idris> 1+1

202− 2 : Integer

203−

204−In the following pages we discuss how to resolve propositionaly equalies.

205−

206−Axiomatic and Constructive Approaches

207−=====================================

208−

209−How should we define types so that we can do proofs on them? In the natural numbers with the plus example we could have started by treating it as a group based on the plus operator. So we have axioms:

210−

211−- for all x,y : ``x+y=y+x``

212−- for all x: ``x + 0 = x = 0 + x``

213−- for all x,y,z: ``(x + y) + z = x + (x + z)``

214−

215−Then we can implement '+' so that it respects these axioms (presumably implemented in hardware).

216−

217−These are axioms, that is a propositions/types that are asserted to be true without proof. In Idris we can use the 'postulate' keyword

218−

219−

220−.. code-block:: idris

221−

222− postulate commutePlus: (x:Nat) -> (y:Nat) -> plus x y = plus y x

223−

224−Alternatively we could define the natural numbers based on Zero and Successor. The axioms above then become derived rules and we also gain the ability to do inductive proofs.

225−

226−As we know, Idris uses both of these approaches with automatic coercion between them which gives the best of both worlds.

227−

228−So what can we learn from this to implement our own types:

229−

230−- Should we try to implement both approaches?

231−- Should we define our types by constructing up from primitive types?

232−

233−Proof theory affects these design decisions.

234−

235−

docs/proofs/index.rst+2−5

@@ -4,7 +4,7 @@

44Theorem Proving

55###############

66

7−A tutorial on theorem proving in Idris.

7+A tutorial on theorem proving in Idris.

88

99.. note::

1010

@@ -13,16 +13,13 @@ A tutorial on theorem proving in Idris.

1313 Idris Community* has waived all copyright and related or neighboring

1414 rights to Documentation for Idris.

1515

16− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

16+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1717

1818.. toctree::

1919 :maxdepth: 1

2020

21− definitional

2221 pluscomm

2322 inductive

2423 patterns

25− propositional

2624 interactive

27− interactiveOld

2825

docs/proofs/inductive.rst−2

@@ -1,5 +1,3 @@

1−.. _sect-inductive:

2−

31****************

42Inductive Proofs

53****************

docs/proofs/interactive.rst+97−224

@@ -1,102 +1,15 @@

1−***************************

2−Interactive Theorem Proving

3−***************************

1+***************************************

2+DEPRECATED: Interactive Theorem Proving

3+***************************************

44

5−Idris supports interactive theorem proving via elaborator reflection.

5+.. warning::

6+ The interactive theorem-proving interface documented here has been

7+ deprecated in favor of :ref:`elaborator-reflection`.

68

7−:ref:`elaborator-reflection` is also used to convert high-level Idris code into

8−the core language and for customising the language. Here we show how to use it

9−to interactively construct proofs.

10−

11−The primary purpose of the elaboration mechanism is to elaborate Idris and so it

12−is not optimised to work as a proof assistant, however it can interactively

13−construct proofs as described on this page.

14−

15−Elab and Pruviloj Libraries

16−===========================

17−

18−Elaborator reflection is defined in ``prelude/Language/Reflection/Elab.idr``

19−and ``pruviloj`` is defined in ``Idris-dev/libs/pruviloj/``.

20−

21−``Elab`` defines the basics such as: ``solve``, ``attack``, ``intro``, ``compute``,

22−``rewriteWith`` and others.

23−``pruviloj`` defines some more advanced derived commands such as:

24−``reflexivity`` and others.

25−

26−To use ``pruviloj`` call Idris with the ``-p pruviloj`` option and add:

27−

28−.. code-block:: idris

29−

30− import Pruviloj

31− import Pruviloj.Induction

32−

33−to the top of your file.

34−

35−It is useful to get the docs at the REPL by using the ``:doc`` command, and

36−search the docstrings using ``:apropos``. So to introduce the functions from

37−``Elab`` and ``Pruviloj``, that we will need for the following example, here are

38−their docstrings:

39−

40−.. code-block:: idris

41−

42− *plusReducesZ> :doc solve

43− Language.Reflection.Elab.Tactics.solve : Elab ()

44− Substitute a guess into a hole.

45−

46−.. code-block:: idris

47−

48− *plusReducesZ> :doc attack

49− Language.Reflection.Elab.Tactics.attack : Elab ()

50− Convert a hole to make it suitable for bindings - that is, transform

51− it such that it has the form ?h : t . h as opposed to ?h : t . f h.

52−

53− The binding tactics require that a hole be directly under its binding,

54− or else the scopes of the generated terms won't make sense. This

55− tactic creates a new hole of the proper form, and points the old hole

56− at it.

57−

58−.. code-block:: idris

59−

60− *plusReducesZ> :doc intro

61− Language.Reflection.Elab.Tactics.intro : (n : TTName) -> Elab ()

62− Introduce a lambda binding around the current hole and focus on the

63− body. Requires that the hole be in binding form (use attack).

64− Arguments:

65− n : TTName -- the name to use for the argument

66−

67−.. code-block:: idris

68−

69− *plusReducesZ> :doc compute

70− Language.Reflection.Elab.Tactics.compute : Elab ()

71− Normalise the goal.

72−

73−.. code-block:: idris

74−

75− *plusReducesZ> :doc rewriteWith

76− Language.Reflection.Elab.Tactics.rewriteWith : Raw -> Elab ()

77− Attempt to rewrite the goal using an equality.

78−

79− The tactic searches the goal for applicable subterms, and constructs a

80− context for replace using them. In some cases, this is not possible,

81− and replace must be called manually with an appropriate context.

82−

83− Because this tactic internally introduces a let binding, it requires

84− that the hole be immediately under its binder (use attack if it might

85− not be).

86−

87−Here is the command from ``pruviloj`` that we will need for the example on

88−this page:

89−

90−.. code-block:: idris

91−

92− *plusReducesZ> :doc reflexivity

93− Pruviloj.Core.reflexivity : Elab ()

94− A special-purpose tactic that attempts to solve a goal using Refl.

95− This is useful for ensuring that goals in fact are trivial when

96− developing or testing other tactics; otherwise, consider using search.

97−

98−Interactive Example: plusReduces

99−================================

9+Idris also supports interactive theorem proving via tactics. This

10+is generally not recommended to be used directly, but rather used as a

11+mechanism for building proof automation which is beyond the scope of this

12+tutorial. In this section, we briefly discus tactics.

10013

10114One way to write proofs interactively is to write the general *structure* of

10215the proof, and use the interactive mode to complete the details.

@@ -112,185 +25,145 @@ hypothesis, and insert *holes* for the rest of the definition:

11225

11326.. code-block:: idris

11427

115− import Pruviloj

116− import Pruviloj.Induction

117−

11828 plusReducesZ' : (n:Nat) -> n = plus n Z

11929 plusReducesZ' Z = ?plusredZ_Z

12030 plusReducesZ' (S k) = let ih = plusReducesZ' k in

12131 ?plusredZ_S

12232

12333On running , two global names are created, ``plusredZ_Z`` and

124−``plusredZ_S``, with no definition.

34+``plusredZ_S``, with no definition. We can use the ``:m`` command at the

35+prompt to find out which holes are still to be solved (or, more

36+precisely, which functions exist but have no definitions), then the

37+``:t`` command to see their types:

12538

12639.. code-block:: idris

12740

128− *theorems> : idris plusReducesZ.idr -p pruviloj

129−

130− . / _/___/ /____(_)____

131− / // __ / ___/ / ___/ Version 1.2.0

132− _/ // /_/ / / / (__ ) https://www.idris-lang.org/

133− /___/\__,_/_/ /_/____/ Type :? for help

134−

135− Idris is free software with ABSOLUTELY NO WARRANTY.

136− For details type :warranty.

137− Holes: Main.plusredZ_S, Main.plusredZ_Z

138−

139−This tells us that we have two holes ``Main.plusredZ_S`` and ``Main.plusredZ_Z``. We can solve

140−these separately, ``plusredZ_Z`` is the simplest so we will do that first.

141−

142−The ``:elab plusredZ_Z`` command enters interactive elaboration mode, which can be used to

143−complete the missing definition for ``plusredZ_Z``.

41+ *theorems> :m

42+ Global holes:

43+ [plusredZ_S,plusredZ_Z]

14444

14545.. code-block:: idris

14646

147− *plusReducesZ> :elab plusredZ_Z

47+ *theorems> :t plusredZ_Z

48+ plusredZ_Z : Z = plus Z Z

14849

149− ---------- Goal: ----------

150− {hole_0} : 0 = 0

50+ *theorems> :t plusredZ_S

51+ plusredZ_S : (k : Nat) -> (k = plus k Z) -> S k = plus (S k) Z

15152

152−This has been normalised to ``0 = 0`` so now we have to prove that ``0`` equals ``0``, which

153−is easy to prove by ``reflexivity`` from the ``pruviloj`` library:

53+The ``:p`` command enters interactive proof mode, which can be used to

54+complete the missing definitions.

15455

15556.. code-block:: idris

15657

157− -Main.plusredZ_Z> reflexivity

158− plusredZ_Z: No more goals.

159−

160−This tells us that the proof is complete. We can now leave the interactive mode which

161−we entered with the ``:elab`` command. We do this with the ``:qed`` command:

162−

163−.. code-block:: idris

164−

165− -Main.plusredZ_Z> :qed

166− Proof completed!

167− Main.plusredZ_Z = %runElab (do reflexivity)

168− Holes: Main.plusredZ_S

169−

170−This gives us a trace of the proof which is ``plusredZ_Z = %runElab (do reflexivity)``. We

171−can cut & paste this into the hole in the original file. This also tells us that we

172−have another hole ``Main.plusredZ_S`` remaining.

58+ *theorems> :p plusredZ_Z

17359

174−This remaining proof is bit more complicated, the following diagram gives an overview:

60+ ---------------------------------- (plusredZ_Z) --------

61+ {hole0} : Z = plus Z Z

17562

176−|image|

177−

178−We approach this remaining proof in the same way by using the ``:elab`` command:

63+This gives us a list of premises (above the line; there are none here)

64+and the current goal (below the line; named ``{hole0}`` here). At the

65+prompt we can enter tactics to direct the construction of the proof. In

66+this case, we can normalise the goal with the ``compute`` tactic:

17967

18068.. code-block:: idris

18169

182− *plusReducesZ> :elab plusredZ_S

70+ -plusredZ_Z> compute

18371

72+ ---------------------------------- (plusredZ_Z) --------

73+ {hole0} : Z = Z

18474

185− ---------- Goal: ----------

186− {hole_0} : (k : Nat) -> (k = plus k 0) -> S k = S (plus k 0)

187−

188−In this case, the goal is a function type, using ``k`` (the argument

189−accessible by pattern matching) and ``ih`` — the local variable

190−containing the result of the recursive call. We can introduce these as

191−assumptions using the ``intro`` tactic twice. The parameter is entered as

192−a constant of type ``TTName`` which is entered as a backtick with double

193−braces ```{{ih}}``. This gives:

75+Now we have to prove that ``Z`` equals ``Z``, which is easy to prove by

76+``Refl``. To apply a function, such as ``Refl``, we use ``refine`` which

77+introduces subgoals for each of the function’s explicit arguments

78+(``Refl`` has none):

19479

19580.. code-block:: idris

19681

197− -Main.plusredZ_S> intro `{{k}}

82+ -plusredZ_Z> refine Refl

83+ plusredZ_Z: no more goals

19884

199− ---------- Assumptions: ----------

200− k : Nat

201− ---------- Goal: ----------

202− {hole_0} : (k = plus k 0) -> S k = S (plus k 0)

203− -Main.plusredZ_S> intro `{{ih}}

85+Here, we could also have used the ``trivial`` tactic, which tries to

86+refine by ``Refl``, and if that fails, tries to refine by each name in

87+the local context. When a proof is complete, we use the ``qed`` tactic

88+to add the proof to the global context, and remove the hole from the

89+unsolved holes list. This also outputs a trace of the proof:

20490

205− ---------- Assumptions: ----------

206− k : Nat

207− ih : k = plus k 0

208− ---------- Goal: ----------

209− {hole_0} : S k = S (plus k 0)

91+.. code-block:: idris

21092

211−We know, from the type of ``ih``, that ``k = plus k 0``, so we would

212−like to use this knowledge to replace ``plus k 0`` in the goal with

213−``k``. We can achieve this with the ``rewriteWith`` tactic:

93+ -plusredZ_Z> qed

94+ plusredZ_Z = proof

95+ compute

96+ refine Refl

21497

21598.. code-block:: idris

21699

217− -Main.plusredZ_S> rewriteWith (Var `{{ih}})

218−

219− ---------- Assumptions: ----------

220− k : Nat

221− ih : k = plus k 0

222− ---------- Goal: ----------

223− {hole_0} : S k = S k

100+ *theorems> :m

101+ Global holes:

102+ [plusredZ_S]

224103

225−The ``rewriteWith`` tactic takes an equality proof as an argument, and tries

226−to rewrite the goal using that proof. The ``ih`` value is entered as a constant

227−of type ``TTName`` which is entered as a backtick with double braces ```{{ih}}`` but

228−``rewriteWith`` requires an expression of type ``Raw``, rather than just a name,

229−so the ``Var`` constructor is used to make a variable. Here, it results in an equality

230−which is trivially provable using ``reflexivity``:

104+The ``:addproof`` command, at the interactive prompt, will add the proof

105+to the source file (effectively in an appendix). Let us now prove the

106+other required lemma, ``plusredZ_S``:

231107

232108.. code-block:: idris

233109

234− -Main.plusredZ_S> reflexivity

235− plusredZ_S: No more goals.

236− -Main.plusredZ_S> :qed

237− Proof completed!

238− Main.plusredZ_S = %runElab (do intro `{{k}}

239− intro `{{ih}}

240− rewriteWith (Var `{{ih}})

241− reflexivity)

110+ *theorems> :p plusredZ_S

242111

243−We can't just cut & paste this into the hole in the original file like this:

112+ ---------------------------------- (plusredZ_S) --------

113+ {hole0} : (k : Nat) -> (k = plus k Z) -> S k = plus (S k) Z

244114

245−.. code-block:: idris

246−

247− import Pruviloj

248− import Pruviloj.Induction

115+In this case, the goal is a function type, using ``k`` (the argument

116+accessible by pattern matching) and ``ih`` — the local variable

117+containing the result of the recursive call. We can introduce these as

118+premises using the ``intro`` tactic twice (or ``intros``, which

119+introduces all arguments as premises). This gives:

249120

250− %language ElabReflection

121+.. code-block:: idris

251122

252− plusReducesZ' : (n:Nat) -> n = plus n Z

253− plusReducesZ' Z = %runElab (do reflexivity)

254− plusReducesZ' (S k) = let ih = plusReducesZ' k in

255− (%runElab (do intro `{{k}}

256− intro `{{ih}}

257− rewriteWith (Var `{{ih}})

258− reflexivity)

259− )

123+ k : Nat

124+ ih : k = plus k Z

125+ ---------------------------------- (plusredZ_S) --------

126+ {hole2} : S k = plus (S k) Z

260127

261−because this gives the following error:

128+Since plus is defined by recursion on its first argument, the term

129+``plus (S k) Z`` in the goal can be simplified, so we use ``compute``.

262130

263131.. code-block:: idris

264132

265− Idris> :load elabInteractiveEx2.idr

266− elabInteractiveEx2.idr:10:32:

267− |

268− 10 | intro `{{ih}}

269− | ^

270− unexpected "in"

271− expecting dependent type signature

133+ k : Nat

134+ ih : k = plus k Z

135+ ---------------------------------- (plusredZ_S) --------

136+ {hole2} : S k = S (plus k Z)

272137

273−However if we put the proof into a separate function like this:

138+We know, from the type of ``ih``, that ``k = plus k Z``, so we would

139+like to use this knowledge to replace ``plus k Z`` in the goal with

140+``k``. We can achieve this with the ``rewrite`` tactic:

274141

275142.. code-block:: idris

276143

277− import Pruviloj

278− import Pruviloj.Induction

144+ -plusredZ_S> rewrite ih

279145

280− %language ElabReflection

146+ k : Nat

147+ ih : k = plus k Z

148+ ---------------------------------- (plusredZ_S) --------

149+ {hole3} : S k = S k

281150

282− plusredZ_S : (k : Nat) -> (ih:(k = plus k Z)) -> (S k = S (plus k Z))

283− plusredZ_S = %runElab (do intro `{{k}}

284− intro `{{ih}}

285− rewriteWith (Var `{{ih}})

286− reflexivity)

151+ -plusredZ_S>

287152

288− plusReducesZ' : (n:Nat) -> n = plus n Z

289− plusReducesZ' Z = %runElab (do reflexivity)

290− plusReducesZ' (S k) = let ih = plusReducesZ' k in plusredZ_S k ih

153+The ``rewrite`` tactic takes an equality proof as an argument, and tries

154+to rewrite the goal using that proof. Here, it results in an equality

155+which is trivially provable:

291156

292−This then loads [#f1]_ .

157+.. code-block:: idris

293158

294−.. [#f1] https://github.com/idris-lang/Idris-dev/issues/4556

159+ -plusredZ_S> trivial

160+ plusredZ_S: no more goals

161+ -plusredZ_S> qed

162+ plusredZ_S = proof {

163+ intros;

164+ rewrite ih;

165+ trivial;

166+ }

295167

296−.. |image| image:: ../image/plusReducesProof.png

168+Again, we can add this proof to the end of our source file using the

169+``:addproof`` command at the interactive prompt.

docs/proofs/interactiveOld.rstdeleted−169

@@ -1,169 +0,0 @@

1−**************************************************************

2−DEPRECATED: Interactive Theorem Proving Using Old Tactics Code

3−**************************************************************

4−

5−.. warning::

6− The interactive theorem-proving interface documented here has been

7− deprecated in favor of :ref:`elaborator-reflection`.

8−

9−Idris also supports interactive theorem proving via tactics. This

10−is generally not recommended to be used directly, but rather used as a

11−mechanism for building proof automation which is beyond the scope of this

12−tutorial. In this section, we briefly discus tactics.

13−

14−One way to write proofs interactively is to write the general *structure* of

15−the proof, and use the interactive mode to complete the details.

16−Consider the following definition, proved in :ref:`sect-theorems`:

17−

18−.. code-block:: idris

19−

20− plusReduces : (n:Nat) -> plus Z n = n

21−

22−We’ll be constructing the proof by *induction*, so we write the cases for ``Z``

23−and ``S``, with a recursive call in the ``S`` case giving the inductive

24−hypothesis, and insert *holes* for the rest of the definition:

25−

26−.. code-block:: idris

27−

28− plusReducesZ' : (n:Nat) -> n = plus n Z

29− plusReducesZ' Z = ?plusredZ_Z

30− plusReducesZ' (S k) = let ih = plusReducesZ' k in

31− ?plusredZ_S

32−

33−On running , two global names are created, ``plusredZ_Z`` and

34−``plusredZ_S``, with no definition. We can use the ``:m`` command at the

35−prompt to find out which holes are still to be solved (or, more

36−precisely, which functions exist but have no definitions), then the

37−``:t`` command to see their types:

38−

39−.. code-block:: idris

40−

41− *theorems> :m

42− Global holes:

43− [plusredZ_S,plusredZ_Z]

44−

45−.. code-block:: idris

46−

47− *theorems> :t plusredZ_Z

48− plusredZ_Z : Z = plus Z Z

49−

50− *theorems> :t plusredZ_S

51− plusredZ_S : (k : Nat) -> (k = plus k Z) -> S k = plus (S k) Z

52−

53−The ``:p`` command enters interactive proof mode, which can be used to

54−complete the missing definitions.

55−

56−.. code-block:: idris

57−

58− *theorems> :p plusredZ_Z

59−

60− ---------------------------------- (plusredZ_Z) --------

61− {hole0} : Z = plus Z Z

62−

63−This gives us a list of premises (above the line; there are none here)

64−and the current goal (below the line; named ``{hole0}`` here). At the

65−prompt we can enter tactics to direct the construction of the proof. In

66−this case, we can normalise the goal with the ``compute`` tactic:

67−

68−.. code-block:: idris

69−

70− -plusredZ_Z> compute

71−

72− ---------------------------------- (plusredZ_Z) --------

73− {hole0} : Z = Z

74−

75−Now we have to prove that ``Z`` equals ``Z``, which is easy to prove by

76−``Refl``. To apply a function, such as ``Refl``, we use ``refine`` which

77−introduces subgoals for each of the function’s explicit arguments

78−(``Refl`` has none):

79−

80−.. code-block:: idris

81−

82− -plusredZ_Z> refine Refl

83− plusredZ_Z: no more goals

84−

85−Here, we could also have used the ``trivial`` tactic, which tries to

86−refine by ``Refl``, and if that fails, tries to refine by each name in

87−the local context. When a proof is complete, we use the ``qed`` tactic

88−to add the proof to the global context, and remove the hole from the

89−unsolved holes list. This also outputs a trace of the proof:

90−

91−.. code-block:: idris

92−

93− -plusredZ_Z> qed

94− plusredZ_Z = proof

95− compute

96− refine Refl

97−

98−.. code-block:: idris

99−

100− *theorems> :m

101− Global holes:

102− [plusredZ_S]

103−

104−The ``:addproof`` command, at the interactive prompt, will add the proof

105−to the source file (effectively in an appendix). Let us now prove the

106−other required lemma, ``plusredZ_S``:

107−

108−.. code-block:: idris

109−

110− *theorems> :p plusredZ_S

111−

112− ---------------------------------- (plusredZ_S) --------

113− {hole0} : (k : Nat) -> (k = plus k Z) -> S k = plus (S k) Z

114−

115−In this case, the goal is a function type, using ``k`` (the argument

116−accessible by pattern matching) and ``ih`` — the local variable

117−containing the result of the recursive call. We can introduce these as

118−premises using the ``intro`` tactic twice (or ``intros``, which

119−introduces all arguments as premises). This gives:

120−

121−.. code-block:: idris

122−

123− k : Nat

124− ih : k = plus k Z

125− ---------------------------------- (plusredZ_S) --------

126− {hole2} : S k = plus (S k) Z

127−

128−Since plus is defined by recursion on its first argument, the term

129−``plus (S k) Z`` in the goal can be simplified, so we use ``compute``.

130−

131−.. code-block:: idris

132−

133− k : Nat

134− ih : k = plus k Z

135− ---------------------------------- (plusredZ_S) --------

136− {hole2} : S k = S (plus k Z)

137−

138−We know, from the type of ``ih``, that ``k = plus k Z``, so we would

139−like to use this knowledge to replace ``plus k Z`` in the goal with

140−``k``. We can achieve this with the ``rewrite`` tactic:

141−

142−.. code-block:: idris

143−

144− -plusredZ_S> rewrite ih

145−

146− k : Nat

147− ih : k = plus k Z

148− ---------------------------------- (plusredZ_S) --------

149− {hole3} : S k = S k

150−

151− -plusredZ_S>

152−

153−The ``rewrite`` tactic takes an equality proof as an argument, and tries

154−to rewrite the goal using that proof. Here, it results in an equality

155−which is trivially provable:

156−

157−.. code-block:: idris

158−

159− -plusredZ_S> trivial

160− plusredZ_S: no more goals

161− -plusredZ_S> qed

162− plusredZ_S = proof {

163− intros;

164− rewrite ih;

165− trivial;

166− }

167−

168−Again, we can add this proof to the end of our source file using the

169−``:addproof`` command at the interactive prompt.

docs/proofs/pluscomm.rst+1−1

@@ -182,7 +182,7 @@ interface rather than using ``plus`` directly. They have the names

182182

183183In the remainder of this tutorial, we will explore several different

184184ways of proving ``plus_commutes`` (or, to put it another way, writing

185−the function). We will also discuss how to use such equality proofs, and

185+the function.) We will also discuss how to use such equality proofs, and

186186see where the need for them arises in practice.

187187

188188.. [1]

docs/proofs/propositional.rstdeleted−133

@@ -1,133 +0,0 @@

1−******************************

2−Proving Propositional Equality

3−******************************

4−

5−This page attempts to explain some of the techniques used in Idris to prove propositional equalities.

6−

7−We have seen that definitional equalities can be proved using ``Refl`` since they always normalise to unique values that can be compared directly.

8−

9−However with propositional equalities we are using symbolic variables they do not always normalise.

10−

11−So to take the previous example:

12−

13−.. code-block:: idris

14−

15− plusReducesR : (n:Nat) -> plus n Z = n

16−

17−In this case ``plus n Z`` does not normalise to ``n``. Even though both sides are equal we cannot pattern match ``Refl``.

18−

19−If the pattern match cannot match for all ``n`` then the way around this is to separately match all possible values of ``n``. In the case of natural numbers we do this by induction.

20−

21−So here:

22−

23−.. code-block:: idris

24−

25− plusReducesR : n = plus n 0

26− plusReducesR {n = Z} = Refl

27− plusReducesR {n = (S k)} = let rec = plus_commutes_Z {n=k} in

28− rewrite rec in Refl

29−

30−we don't call ``Refl`` to match on ``n = plus n 0`` forall ``n`` we call it for every number separately. So, in the second line, the pattern matcher knows to substitute ``Z`` for ``n`` in the type being matched. This uses ``rewrite`` which is explained below.

31−

32−Replace

33−=======

34−

35−This implements the *indiscernability of identicals* principle, if two terms are equal then they have the same properties. In other words, if ``x=y``, then we can substitute ``y`` for ``x`` in any expression. In our proofs we can express this as:

36−

37−.. code-block:: idris

38−

39− if x=y

40− then P x = P y

41−

42−where ``P`` is a pure function representing the property. In the examples below ``P`` is an expression in some variable with a type like this: ``P: n -> Type``.

43−

44−So if ``n`` is a natural number variable then ``P`` could be something like ``2*n + 3``.

45−

46−To use this in our proofs there is the following function in the prelude:

47−

48−.. code-block:: idris

49−

50− ||| Perform substitution in a term according to some equality.

51− replace : {a:_} -> {x:_} -> {y:_} -> {P : a -> Type} -> x = y -> P x -> P y

52− replace Refl prf = prf

53−

54−Removing the implicits, if we supply an equality ``x=y`` and a proof of a property of ``x`` (i.e. ``P x``) then we get a proof of a property of ``y`` (i.e. ``P y``)

55−

56−.. code-block:: idris

57−

58− > :t replace

59− replace : (x = y) -> P x -> P y

60−

61−So, in the following example, if we supply ``p1 x`` which is a proof that ``x=2`` and the equality ``x=y`` then we get a proof that ``y=2``.

62−

63−.. code-block:: idris

64−

65− p1: Nat -> Type

66− p1 n = (n=2)

67−

68− testReplace: (x=y) -> (p1 x) -> (p1 y)

69− testReplace a b = replace a b

70−

71−Rewrite

72−=======

73−

74−Similar to ``replace`` above but Idris provides a nicer syntax which makes ``rewrite`` easier to use in examples like ``plusReducesR`` above.

75−

76−.. code-block:: idris

77−

78− rewrite__impl : (P : a -> Type) -> x = y -> P y -> P x

79− rewrite__impl p Refl prf = prf

80−

81−The difference from ``replace`` above is nicer syntax and the property ``p1`` is explicitly supplied and it goes in the opposite direction (input and output reversed).

82−

83−Example: again we supply ``p1`` which is a proof that ``x=2`` and the equality ``x=y`` then we get a proof that ``y=2``.

84−

85−.. code-block:: idris

86−

87− p1: Nat -> Type

88− p1 x = (x=2)

89−

90− testRewrite2: (x=y) -> (p1 y) -> (p1 x)

91− testRewrite2 a b = rewrite a in b

92−

93−We can think of rewrite doing this:

94−

95− * start with a equation ``x=y`` and a property ``P: x -> Type``;

96− * search ``y`` in ``P``;

97− * replace all occurrences of ``y`` with ``x`` in ``P``.

98−

99−That is, we are doing a substitution.

100−

101−Symmetry and Transitivity

102−=========================

103−

104−In addition to *reflexivity* equality also obeys *symmetry* and *transitivity* and these are also included in the prelude:

105−

106−.. code-block:: idris

107−

108− ||| Symmetry of propositional equality

109− sym : {left:a} -> {right:b} -> left = right -> right = left

110− sym Refl = Refl

111−

112− ||| Transitivity of propositional equality

113− trans : {a:x} -> {b:y} -> {c:z} -> a = b -> b = c -> a = c

114− trans Refl Refl = Refl

115−

116−Heterogeneous Equality

117−======================

118−

119−Also included in the prelude:

120−

121−.. code-block:: idris

122−

123− ||| Explicit heterogeneous ("John Major") equality. Use this when Idris

124− ||| incorrectly chooses homogeneous equality for `(=)`.

125− ||| @ a the type of the left side

126− ||| @ b the type of the right side

127− ||| @ x the left side

128− ||| @ y the right side

129− (~=~) : (x : a) -> (y : b) -> Type

130− (~=~) x y = (x = y)

131−

132−

133−

docs/reference/codegen.rst+4−18

@@ -1,5 +1,3 @@

1−.. _code-generation-targets:

2−

31************************

42Code Generation Targets

53************************

@@ -18,13 +16,6 @@ Official Backends

1816C Language

1917----------

2018

21−The default target of Idris is C. In order to view the generated C code, compile via:

22−

23−::

24−

25− $ idris hello.idr -S -o hello.c

26−

27−

2819Javascript

2920----------

3021

@@ -36,10 +27,10 @@ issue the following command:

3627 $ idris --codegen javascript hello.idr -o hello.js

3728

3829

39−Idris can produce big chunks of JavaScript code (hello world weighs in at about

40−60 lines). However, the generated code can be minified using the

41−`closure-compiler <https://developers.google.com/closure/compiler/>`__ from

42−Google.

30+Idris can produce very big chunks of JavaScript code (hello world

31+weighs in at 1500 lines). However, the generated code can be minified

32+using the `closure-compiler

33+<https://developers.google.com/closure/compiler/>`__ from Google.

4334

4435::

4536

@@ -140,8 +131,3 @@ WS

140131---

141132

142133`Available online <https://github.com/edwinb/WS-idr>`__

143−

144−WebAssembly

145−-----------

146−

147−`Available online <https://github.com/SPY/idris-codegen-wasm>`__

docs/reference/compilation.rst+22−22

@@ -54,7 +54,7 @@ by setting a verbosity level.

5454 Checking, and the individual steps prior to code generation.

5555

5656

57−By default Idris' progress reporting is set to quiet: ``-q``, or ``--quiet``.

57+By default Idris' progress reporting is set to quiet-``-q``, or ``--quiet``.

5858

5959Logging Internal Operation

6060===========================

@@ -63,17 +63,17 @@ For those that develop on the Idris compiler, the internal operation

6363of Idris is captured using a category based logger. Currently, the

6464logging infrastructure has support for the following categories:

6565

66−+ Parser (``parser``)

67−+ Elaborator (``elab``)

68−+ Code generation (``codegen``)

69−+ Erasure (``erasure``)

70−+ Coverage Checking (``coverage``)

71−+ IBC generation (``ibc``)

66++ Parser

67++ Elaborator

68++ Code generation

69++ Erasure

70++ Coverage Checking

71++ IBC generation

7272

7373

7474These categories are specified using the command-line option:

7575``--logging-categories CATS``, where ``CATS`` is a quoted colon

76−separated string of the categories you want to see. By default if this

76+seperated string of the categories you want to see. By default if this

7777option is not specified all categories are allowed. Sub-categories

7878have yet to be defined but will be in the future, especially for the

7979elaborator.

@@ -100,32 +100,32 @@ Environment Variables

100100Several paths set by default within the Idris compiler can be

101101overridden through environment variables. The provided variables are:

102102

103−* ``IDRIS_CC`` Change the *C compiler* used by the *C backend*.

104−* ``IDRIS_CFLAGS`` Change the *C flags* passed to the *C compiler*.

105−* ``TARGET`` Change the target directory i.e. *data dir* where Idris installs files when installing using Cabal/Stack.

106−* ``IDRIS_LIBRARY_PATH`` Change the location of where installed packages are found/installed.

107−* ``IDRIS_DOC_PATH`` Change the location of where generated idrisdoc for packages are installed.

103+* `IDRIS_CC` Change the `C` compiler used by the `C` backend.

104+* `IDRIS_CFLAGS` Change the `C` flags passed to the `C` compiler.

105+* `TARGET` Change the target directory i.e. `data dir` where Idris installs files when installing using Cabal/Stack.

106+* `IDRIS_LIBRARY_PATH` Change the location of where installed packages are found/installed.

107+* `IDRIS_DOC_PATH` Change the location of where generated idrisdoc for packages are installed.

108108

109109.. note::

110110

111111 In versions of Idris prior to 0.12.3 the environment variables

112− ``IDRIS_LIBRARY_PATH`` and ``TARGET`` were both used to affect the

112+ `IDRIS_LIBRARY_PATH` and `TARGET` were both used to affect the

113113 installation of single packages and direct where Idris installed

114114 its data. The meaning of these variables has changed, and command

115115 line options are preferred when changing where individual packages

116116 are installed.

117117

118−The CLI option ``--ibcsubdir`` can be used to direct where generated IBC

118+The CLI option `--ibcsubdir` can be used to direct where generated IBC

119119files are placed. However, this means Idris will install files in a

120120non-standard location separate from the rest of the installed

121−packages. The CLI option ``--idrispath <dir>`` allows you to add a

121+packages. The CLI option `--idrispath <dir>` allows you to add a

122122directory to the library search path; this option can be used multiple

123−times and can be shortened to ``-i <dir>``. Similary, the ``--sourcepath

124−<dir>`` option can be used to add directories to the source search

125−path. There is no shortened version for this option as ``-s`` is a

123+times and can be shortened to `-i <dir>`. Similary, the `--sourcepath

124+<dir>` option can be used to add directories to the source search

125+path. There is no shortened version for this option as `-s` is a

126126reserved flag.

127127

128128Further, Idris also supports options to augment the paths used, and

129−pass options to the code generator backend. The option ``--cg-opt

130−<ARG>`` can be used to pass options to the code generator. The format

131−of ``<ARG>`` is dependent on the selected backend.

129+pass options to the code generator backend. The option `--cg-opt

130+<ARG>` can be used to pass options to the code generator. The format

131+of `<ARG>` is dependent on the selected backend.

docs/elaboratorReflection/elaborator-reflection.rst → docs/reference/elaborator-reflection.rstrenamed+6−13

@@ -1,13 +1,12 @@

11.. _elaborator-reflection:

22

3−**********************************

4−Elaborator Reflection Introduction

5−**********************************

3+*********************

4+Elaborator Reflection

5+*********************

66

77The Idris elaborator is responsible for converting high-level Idris code into the core language.

88It is implemented as a kind of embedded tactic language in Haskell, where tactic scripts are written in an *elaboration monad* that provides error handling and a proof state.

9−For details, see `Edwin Brady's 2013 paper in the Journal of Functional

10−Programming <https://eb.host.cs.st-andrews.ac.uk/drafts/impldtp.pdf>`_.

9+For details, see Edwin Brady's 2013 paper in the Journal of Functional Programming.

1110

1211Elaborator reflection makes the elaboration type as well as a selection of its tactics available to Idris code.

1312This means that metaprograms written in Idris can have complete control over the elaboration process, generating arbitrary code, and they have access to all of the facilities available in the elaborator, such as higher-order unification, type checking, and emitting auxiliary definitions.

@@ -198,12 +197,6 @@ This is primarily useful for code generation, particularly for generating patter

198197

199198Learn More

200199==========

201−

202−Some tactics are introduced in the :ref:`proofs-index` section with further details, of those most relevant to elaborator reflection, on the following pages.

203−

204−The list of built-in tactics can be obtained using the ``:browse`` command in an Idris REPL or the corresponding feature in one of the graphical IDE clients to explore the ``Language.Reflection.Elab.Tactics`` namespace.

200+While this documentation is still incomplete, elaboration reflection works in Idris today.

201+As you wait for the completion of the documentation, the list of built-in tactics can be obtained using the ``:browse`` command in an Idris REPL or the corresponding feature in one of the graphical IDE clients to explore the ``Language.Reflection.Elab.Tactics`` namespace.

205202All of the built-in tactics contain documentation strings.

206−

207−For alternative ways to extend the Idris language see the :ref:`reference-index` section.

208−

209−The following pages explain more about the theory and practice of elaborator reflection.

docs/reference/erasure.rst+5−5

@@ -103,7 +103,7 @@ that's a moot point for two reasons:

103103

104104This ought not to be the case since the ``Nat`` are never used at

105105runtime and they are only there for typechecking purposes. Hence we

106−should get rid of them and get runtime code similar to what an Idris

106+should get rid of them and get runtime code similar to what a idris

107107programmer would write.

108108

109109U-views of lists

@@ -127,7 +127,7 @@ For better intuition, the shape of the U-view of

127127

128128 x0 y0 (two)

129129 x1 y1 (two)

130− x2 y2 (two)

130+ x2 y1 (two)

131131 z (one)

132132

133133When recursing over this structure, the values of ``xs`` range over

@@ -254,7 +254,7 @@ Benchmarks

254254==========

255255

256256- source: https://github.com/ziman/idris-benchmarks

257−- results: https://ziman.functor.sk/erasure-bm/

257+- results: http://ziman.functor.sk/erasure-bm/

258258

259259It can be clearly seen that asymptotics are improved by erasure.

260260

@@ -269,7 +269,7 @@ Usage warnings are quite bad and unhelpful at the moment. We should

269269include more information and at least translate argument numbers to

270270their names.

271271

272−There is no decent documentation yet. This page is the first one.

272+There is no decent documentation yet. This wiki page is the first one.

273273

274274There is no generally accepted terminology. We switch between

275275"dotted", "unused", "erased", "irrelevant", "inaccessible", while each

@@ -499,4 +499,4 @@ References

499499

500500.. [BMM04] Edwin Brady, Conor McBride, James McKinna: `Inductive

501501 families need not store their indices

502− <https://citeseerx.ist.psu.edu/viewdoc/summary;jsessionid=1F796FCF0F2C4C535FC70F62BE2FB821?doi=10.1.1.62.3849>`__

502+ <http://citeseerx.ist.psu.edu/viewdoc/summary;jsessionid=1F796FCF0F2C4C535FC70F62BE2FB821?doi=10.1.1.62.3849>`__

docs/reference/ffi.rst+6−176

@@ -115,26 +115,6 @@ For C, this is:

115115 FFI_C : FFI

116116 FFI_C = MkFFI C_Types String String

117117

118−Linking foreign code

119−====================

120−

121−This is the example of linking C code.

122−

123−.. code-block:: idris

124−

125− %include C "mylib.h"

126− %link C "mylib.o"

127−

128−Example Makefile

129−

130−.. code-block:: shell

131−

132− DEFAULT: mylib.o main.idr

133− idris main.idr -o executableFile

134−

135− clean:

136− rm -f executableFile mylib.o main.ibc

137−

138118Foreign calls

139119=============

140120

@@ -198,16 +178,9 @@ compilation error:

198178 example : (Int -> ()) -> IO ()

199179 example f = foreign FFI_C "callbacker" (CFnPtr (Int -> ()) -> IO ()) f

200180

201−Note that the function that is used as a callback can't be a closure, that is

202−it can't be a partially applied function. This is because the mechanism used is

203−unable to pass the closed-over values through C. If we want to pass Idris values

204−to the callback we have to pass them through C explicitly. Non-primitive Idris

205−values can be passed to C via the ``Raw`` type.

206−

207−The other big limitation is that it doesn't support ``IO`` functions. Use

208−``unsafePerformIO`` to wrap them (i.e. to make an ``IO`` function usable as a

209−callback, change the return type from ``IO r`` to ``r``, and change the ``= do``

210−to ``= unsafePerformIO $ do``).

181+The other big limitation is that it doesn't support IO functions. Use

182+``unsafePerformIO`` to wrap them (i.e. to make an IO function usable as a callback, change the return type

183+from IOr to r, and change the = do to = unsafePerformIO $ do).

211184

212185There are two special function names:

213186``%wrapper`` returns the function pointer that wraps an Idris function. This

@@ -244,157 +217,14 @@ global variable with the following name. The type must be just ``IO Ptr``.

244217 errno : IO Ptr

245218 errno = foreign FFI_C "&errno" (IO Ptr)

246219

247−If the foreign name is prefixed by a ``#``, the name is pasted in literally. This is

248−useful to access constants that are preprocessor definitions (like ``INT_MAX``).

249−

250−.. code-block:: idris

251−

252− %include C "limits.h"

253−

254− -- access the preprocessor definition INT_MAX

255− intMax : IO Int

256− intMax = foreign FFI_C "#INT_MAX" (IO Int)

257−

258− main : IO ()

259− main = print !intMax

260−

261−For more complicated interactions with C (such as reading and setting fields

262−of a C ``struct``), there is a module C FFI available in the contrib package.

263−

264−C heap

265−------

266−

267−Idris has two heaps where objects can be allocated:

268−

269−+--------------------------------------+---------------------------------------+

270−| FP heap | C heap |

271−+======================================+=======================================+

272−| Cheney-collected | Mark-and-sweep-collected |

273−+--------------------------------------+---------------------------------------+

274−| Garbage collections touches only | Garbage collection has to traverse |

275−| live objects. | all registered items. |

276−+--------------------------------------+---------------------------------------+

277−| Ideal for FP-style rapid allocation | Ideal for C-style allocation of a few |

278−| of lots of small short-lived pieces | big buffers. |

279−| of memory, such as data constructors.| |

280−+--------------------------------------+---------------------------------------+

281−| Finalizers are impossible to support | Items have finalizers that are called |

282−| reasonably. | on deallocation. |

283−+--------------------------------------+---------------------------------------+

284−| Data is copied all the time (when | Copying does not happen. |

285−| collecting garbage, modifying data, | |

286−| registering managed pointers, etc.) | |

287−+--------------------------------------+---------------------------------------+

288−| Contains objects of various types. | Contains C heap items: ``(void *)`` |

289−| | pointers with finalizers. A finalizer |

290−| | is a routine that deallocates the |

291−| | resources associated with the item. |

292−+--------------------------------------+---------------------------------------+

293−| Fixed set of object types. | The data pointer may point |

294−| | to anything, as long as the finalizer |

295−| | cleans up correctly. |

296−+--------------------------------------+---------------------------------------+

297−| Not suitable for C resources and | Suitable for C resources and arbitrary|

298−| arbitrary pointers. | pointers. |

299−+--------------------------------------+---------------------------------------+

300−| Values form a compact memory block. | Items are kept in a linked list. |

301−+--------------------------------------+---------------------------------------+

302−| Any Idris value, most notably | Items represented by the |

303−| ``ManagedPtr``. | Idris type ``CData``. |

304−+--------------------------------------+---------------------------------------+

305−| Data of ``ManagedPtr`` allocated | Data allocated in C, pointer copied |

306−| in C, buffer then copied into the FP | into the C heap. |

307−| heap. | |

308−+--------------------------------------+---------------------------------------+

309−| Allocation and reallocation not | Allocated and reallocate freely in C, |

310−| possible from C code (without having | registering the allocated items |

311−| a reference to the VM). Everything | in the FFI. |

312−| is copied instead. | |

313−+--------------------------------------+---------------------------------------+

314−

315−The FP heap is the primary heap. It may contain values of type ``CData``,

316−which are references to items in the C heap. A C heap item contains

317−a ``(void *)`` pointer and the corresponding finalizer. Once a C heap item

318−is no longer referenced from the FP heap, it is marked as unused and

319−the next GC sweep will call its finalizer and deallocate it.

320−

321−There is no Idris interface for ``CData`` other than its type and FFI.

322−

323−Usage from C code

324−~~~~~~~~~~~~~~~~~

325−

326−* Although not enforced in code, ``CData`` is meant to be opaque

327− and non-RTS code (such as libraries or C bindings) should

328− access only its ``(void *)`` field called ``data``.

329−

330−* Feel free to mutate both the pointer ``data`` (eg. after calling ``realloc``)

331− and the memory it points to. However, keep in mind

332− that this must not break Idris's referential transparency.

333−

334−* **WARNING!** If you call ``cdata_allocate`` or ``cdata_manage``,

335− the resulting ``CData`` object *must* be returned from your

336− FFI function so that it is inserted in the C heap by the RTS.

337− Otherwise the memory will be leaked.

338−

339−.. code:: idris

340−

341− some_allocating_fun : Int -> IO CData

342− some_allocating_fun i = foreign FFI_C "some_allocating_fun" (Int -> IO CData) i

343−

344− other_fun : CData -> Int -> IO Int

345− other_fun cd i = foreign FFI_C "other_fun" (CData -> Int -> IO Int) cd i

346−

347−.. code:: cpp

348−

349− #include "idris_rts.h"

350−

351− static void finalizer(void * data)

352− {

353− MyStruct * ptr = (MyStruct *) data;

354− free_something(ptr->something);

355− free(ptr);

356− }

357−

358− CData some_allocating_fun(int arg)

359− {

360− size_t size = sizeof(...);

361− void * data = (void *) malloc(size);

362− // ...

363− return cdata_manage(data, size, finalizer);

364− }

365−

366− int other_fun(CData cd, int arg)

367− {

368− int result = foo(cd->data);

369− return result;

370− }

371−

372−The ``Raw`` type constructor allows you to access or return a runtime

373−representation of the value. For instance, if you want to copy a string

374−generated from C code into an Idris value, you may want to return a

375−``Raw String`` instead of a ``String`` and use ``MKSTR`` or ``MKSTRlen`` to

376−copy it over.

377−

378−.. code-block:: idris

379−

380− getString : () -> IO (Raw String)

381− getString () = foreign FFI_C "get_string" (IO (Raw String))

382−

383−.. code-block:: cpp

384−

385− const VAL get_string ()

386− {

387− char * c_string = get_string_allocated_with_malloc()

388− const VAL idris_string = MKSTR(get_vm(), c_string);

389− free(c_string);

390− return idris_string

391− }

220+For more complicated interactions with C (such as reading and setting fields of a C struct), there is

221+a module CFFI available in the contrib package.

392222

393223FFI implementation

394224------------------

395225

396226In order to write bindings to external libraries, the details of how

397−``foreign`` works are unnecessary: you simply need to know that

227+``foreign`` works are unnecessary --- you simply need to know that

398228``foreign`` takes an FFI descriptor, the function name, and its

399229type. It is instructive to look a little deeper, however:

400230

docs/reference/ide-protocol.rst+1−1

@@ -113,7 +113,7 @@ The available commands include:

113113 Return a highlighted string consisting of the results of making all arguments in serialised term ``TM`` (which would previously have been sent as the ``tt-term`` property of a string) follow their usual implicitness setting.

114114

115115 ``(:elaborate-term TM)``

116− Return a highlighted string consisting of the core language term corresponding to serialised term ``TM`` (which would previously have been sent as the ``tt-term`` property of a string).

116+ Return a highlighted string consisting of the the core language term corresponding to serialised term ``TM`` (which would previously have been sent as the ``tt-term`` property of a string).

117117

118118 ``(:print-definition NAME)``

119119 Return the definition of ``NAME`` as a highlighted string.

docs/reference/index.rst+2−2

@@ -14,7 +14,7 @@ This will tell you how Idris works, for using it you should read the Idris Tutor

1414 Idris Community* has waived all copyright and related or neighboring

1515 rights to Documentation for Idris.

1616

17− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

17+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1818

1919

2020.. toctree::

@@ -26,7 +26,6 @@ This will tell you how Idris works, for using it you should read the Idris Tutor

2626 uniqueness-types

2727 ffi

2828 syntax-guide

29− syntax-reference

3029 erasure

3130 ide-protocol

3231 semantic-highlighting

@@ -36,6 +35,7 @@ This will tell you how Idris works, for using it you should read the Idris Tutor

3635 internals

3736 language-features

3837 language-extensions

38+ elaborator-reflection

3939 type-directed-search

4040 partial-evaluation

4141 misc

docs/reference/internals.rst+28−31

@@ -10,8 +10,8 @@ free to contribute.

1010This document assumes that you are already familiar with Idris. It is

1111intended for those who want to work on the internals.

1212

13−People looking to develop new back ends may want to look at

14−:ref:`code-generation-targets`

13+People looking to develop new back ends may want to look at [[Idris back

14+end IRs\|Idris-back-end-IRs]]

1515

1616Core/TT.hs

1717==========

@@ -53,7 +53,7 @@ with ``SC`` and ``CaseAlt`` to get GHC to generate a function for

5353mapping over contained terms.

5454

5555Constructor cases (``ConCase`` in ``CaseAlt``) refer to numbered

56−constructors. Every constructor is numbered *0,1,2,…*. At this stage in

56+constructors. Every constructor is numbered 0,1,2,…. At this stage in

5757the compiler, the tags are datatype-local. After defunctionalization,

5858however, they are made globally unique.

5959

@@ -91,12 +91,12 @@ dictionary which makes totality checking easier.

9191The ``normalise*`` functions give different behaviors - but

9292``normalise`` is the most common.

9393

94−- ``normaliseC`` - "resolved" means with names converted to de Bruijn

95− indices as appropriate;

94+``normaliseC`` - "resolved" means with names converted to de Bruijn

95+indices as appropriate.

9696

97−- ``normaliseAll`` - reduce everything, even if it's non-total;

97+``normaliseAll`` - reduce everything, even if it's non-total

9898

99−- ``normaliseTrace`` - special-purpose for debugging.

99+``normaliseTrace`` - special-purpose for debugging

100100

101101``simplify`` - reduce the things that are small - the list argument is

102102the things to not reduce.

@@ -110,8 +110,8 @@ Core/Elaborate.hs

110110=================

111111

112112Idris definitions are elaborated one by one and turned into the

113−corresponding ``TT``. This is done with a tactic language as an EDSL in the

114−``Elab`` monad (or ``Elab'`` when there's a custom state).

113+corresponding TT. This is done with a tactic language as an EDSL in the

114+Elab monad (or Elab' when there's a custom state).

115115

116116Lots of plumbing for errors.

117117

@@ -122,17 +122,17 @@ The string in the pair returned by elaborate is log information.

122122See JFP paper, but the names don't necessarily map to each other. The

123123paper is the "idealized version" without logging, additional state, etc.

124124

125−All the tactics take ``Raw`` s, typechecking happens there.

125+All the tactics take Raws, typechecking happens there.

126126

127−``claim (x : t)`` assumes a new ``x : t``.

127+claim (x : t) assumes a new x : t.

128128

129129PLEASE TIDY THINGS UP!

130130

131−``proofSearch`` flag is to try whether the failure came from a human (so

131+proofSearch flag to try' is whether the failure came from a human (so

132132fail) or from a machine (so continue)

133133

134−Idris-level syntax for providing alternatives explicitly: ``(| x, y, z

135−|)`` try ``x``, ``y``, ``z`` in order, and take the first that succeeds.

134+Idris-level syntax for providing alternatives explicitly: (\| x, y, z

135+\|) try x, y, z in order, and take the first that succeeds.

136136

137137Core/ProofState.hs

138138==================

@@ -140,40 +140,37 @@ Core/ProofState.hs

140140Core/Unify.hs

141141=============

142142

143−Deals with unification. Unification can reply with:

143+Deals with unification. Unification can reply with: - this works - this

144+can never work - this will work if these other unification problems work

145+out (eg unifying f x with 1)

144146

145−- this works

146−- this can never work

147−- this will work if these other unification problems work out (e.g.

148− unifying ``f x`` with ``1``)

149−

150−``match_unify``: same thing as unification except it's just matching name

151−against name, term against term. ``x + y`` matches to ``0 + y`` with

152−``x = 0``. Used for ``<==`` syntax as well as type class resolution.

147+match\_unify: same thing as unification except it's just matching name

148+against name, term against term. x + y matches to 0 + y with x = 0. Used

149+for <== syntax as well as type class resolution.

153150

154151Idris/AbsSyntaxTree.hs

155152======================

156153

157−``PTerm`` is the datatype of Idris syntax. ``P`` is for *Program*.

158−Each ``PTerm`` turns into a TT term by applying a series of tactics.

154+PTerm is the datatype of Idris syntax. P is for Program. Each PTerm

155+turns into a TT term by applying a series of tactics.

159156

160−``IState`` is the major interpreter state. The global context is the

161−``tt_ctxt`` field.

157+IState is the major interpreter state. The global context is the

158+tt\_ctxt field.

162159

163−``Ctxt`` maps possibly ambiguous names to their referents.

160+Ctxt maps possibly ambiguous names to their referents.

164161

165162Idris/ElabDecls.hs

166163==================

167164

168−This is where the actual elaboration from ``PTerm`` to ``TT`` happens.

165+This is where the actual elaboration from PTerm to TT happens.

169166

170167Idris/ElabTerm.hs

171168=================

172169

173−``build`` is the function that creates a ``Raw``. All the "junk" is to deal with

170+build is the function that creates a Raw. All the "junk" is to deal with

174171things like metavars and so forth. It has to remember what names are

175172still to be defined, and it doesn't yet know the type (filled in by

176173unificaiton later). Also case expressions have to turn into top-level

177174functions.

178175

179−``resolveTC`` is type class resolution.

176+resolveTC is type class resolution.

docs/reference/language-extensions.rst+3−8

@@ -3,12 +3,13 @@ Language Extensions

33*******************

44

55

6+

67Type Providers

78===============

89

910Idris type providers are a way to get the type system to reflect

1011observations about the world outside of Idris. Similarly to `F# type

11−providers <https://msdn.microsoft.com/en-us/library/vstudio/hh156509.aspx>`__,

12+providers <http://msdn.microsoft.com/en-us/library/vstudio/hh156509.aspx>`__,

1213they cause effectful computations to run during type checking, returning

1314information that the type checker can use when checking the rest of the

1415program. While F# type providers are based on code generation, Idris

@@ -31,11 +32,5 @@ to the user.

3132Example Idris type providers can be seen at `this

3233repository <https://github.com/david-christiansen/idris-type-providers>`__.

3334More detailed descriptions are available in David Christiansen's `WGP

34−'13 paper <https://dx.doi.org/10.1145/2502488.2502495>`__ and `M.Sc.

35+'13 paper <http://dx.doi.org/10.1145/2502488.2502495>`__ and `M.Sc.

3536thesis <http://itu.dk/people/drc/david-christiansen-thesis.pdf>`__.

36−

37−Elaborator Reflection

38−=====================

39−

40−Another way to extend the language is elaborator reflection which is described

41−in the :ref:`elaborator-index` section.

docs/reference/misc.rst+113−6

@@ -100,6 +100,113 @@ follows:

100100 (x :: qsort (assert_smaller (x :: xs) (filter (>= x) xs))))

101101

102102

103+C heap

104+======

105+

106+Idris has two heaps where objects can be allocated:

107+

108++--------------------------------------+---------------------------------------+

109+| FP heap | C heap |

110++======================================+=======================================+

111+| Cheney-collected | Mark-and-sweep-collected |

112++--------------------------------------+---------------------------------------+

113+| Garbage collections touches only | Garbage collection has to traverse |

114+| live objects. | all registered items. |

115++--------------------------------------+---------------------------------------+

116+| Ideal for FP-style rapid allocation | Ideal for C-style allocation of a few |

117+| of lots of small short-lived pieces | big buffers. |

118+| of memory, such as data constructors.| |

119++--------------------------------------+---------------------------------------+

120+| Finalizers are impossible to support | Items have finalizers that are called |

121+| reasonably. | on deallocation. |

122++--------------------------------------+---------------------------------------+

123+| Data is copied all the time (when | Copying does not happen. |

124+| collecting garbage, modifying data, | |

125+| registering managed pointers, etc.) | |

126++--------------------------------------+---------------------------------------+

127+| Contains objects of various types. | Contains C heap items: ``(void *)`` |

128+| | pointers with finalizers. A finalizer |

129+| | is a routine that deallocates the |

130+| | resources associated with the item. |

131++--------------------------------------+---------------------------------------+

132+| Fixed set of object types. | The data pointer may point |

133+| | to anything, as long as the finalizer |

134+| | cleans up correctly. |

135++--------------------------------------+---------------------------------------+

136+| Not suitable for C resources and | Suitable for C resources and arbitrary|

137+| arbitrary pointers. | pointers. |

138++--------------------------------------+---------------------------------------+

139+| Values form a compact memory block. | Items are kept in a linked list. |

140++--------------------------------------+---------------------------------------+

141+| Any Idris value, most notably | Items represented by the |

142+| ``ManagedPtr``. | Idris type ``CData``. |

143++--------------------------------------+---------------------------------------+

144+| Data of ``ManagedPtr`` allocated | Data allocated in C, pointer copied |

145+| in C, buffer then copied into the FP | into the C heap. |

146+| heap. | |

147++--------------------------------------+---------------------------------------+

148+| Allocation and reallocation not | Allocated and reallocate freely in C, |

149+| possible from C code (without having | registering the allocated items |

150+| a reference to the VM). Everything | in the FFI. |

151+| is copied instead. | |

152++--------------------------------------+---------------------------------------+

153+

154+The FP heap is the primary heap. It may contain values of type ``CData``,

155+which are references to items in the C heap. A C heap item contains

156+a ``(void *)`` pointer and the corresponding finalizer. Once a C heap item

157+is no longer referenced from the FP heap, it is marked as unused and

158+the next GC sweep will call its finalizer and deallocate it.

159+

160+There is no Idris interface for ``CData`` other than its type and FFI.

161+

162+Usage from C code

163+-----------------

164+

165+* Although not enforced in code, ``CData`` is meant to be opaque

166+ and non-RTS code (such as libraries or C bindings) should

167+ access only its ``(void *)`` field called ``data``.

168+

169+* Feel free to mutate both the pointer ``data`` (eg. after calling ``realloc``)

170+ and the memory it points to. However, keep in mind

171+ that this must not break Idris's referential transparency.

172+

173+* **WARNING!** If you call ``cdata_allocate`` or ``cdata_manage``,

174+ the resulting ``CData`` object *must* be returned from your

175+ FFI function so that it is inserted in the C heap by the RTS.

176+ Otherwise the memory will be leaked.

177+

178+.. code:: idris

179+

180+ some_allocating_fun : Int -> IO CData

181+ some_allocating_fun i = foreign FFI_C "some_allocating_fun" (Int -> IO CData) i

182+

183+ other_fun : CData -> Int -> IO Int

184+ other_fun cd i = foreign FFI_C "other_fun" (CData -> Int -> IO Int) cd i

185+

186+.. code:: cpp

187+

188+ #include "idris_rts.h"

189+

190+ static void finalizer(void * data)

191+ {

192+ MyStruct * ptr = (MyStruct *) data;

193+ free_something(ptr->something);

194+ free(ptr);

195+ }

196+

197+ CData some_allocating_fun(int arg)

198+ {

199+ void * data = (void *) malloc(...);

200+ // ...

201+ return cdata_manage(data, finalizer);

202+ }

203+

204+ int other_fun(CData cd, int arg)

205+ {

206+ int result = foo(cd->data);

207+ return result;

208+ }

209+

103210Preorder reasoning

104211==================

105212

@@ -115,11 +222,11 @@ Here is an example:

115222 import Syntax.PreorderReasoning

116223 multThree : (a, b, c : Nat) -> a * b * c = c * a * b

117224 multThree a b c =

118− (a * b * c) ={ sym (multAssociative a b c) }=

119− (a * (b * c)) ={ cong (multCommutative b c) }=

120− (a * (c * b)) ={ multAssociative a c b }=

121− (a * c * b) ={ cong {f = (* b)} (multCommutative a c) }=

122− (c * a * b) QED

225+ (a * b * c) ={ sym (multAssociative a b c) }=

226+ (a * (b * c)) ={ cong (multCommutative b c) }=

227+ (a * (c * b)) ={ multAssociative a c b }=

228+ (a * c * b) ={ cong {f = (* b)} (multCommutative a c) }=

229+ (c * a * b) QED

123230

124231Note that the parentheses are required -- only a simple expression can

125232be on the left of ``={ }=`` or ``QED``. Also, when using preorder

@@ -220,7 +327,7 @@ following command::

220327 source <(idris --bash-completion-script `which idris`)

221328

222329

223−To enable completion permanently you must either:

330+To enable completion permenatly you must either:

224331

225332* Modify your bash init script with the above command.

226333

docs/reference/packages.rst+3−6

@@ -24,7 +24,7 @@ comma separated list of modules. For example, a library test which

2424has two modules ``foo.idr`` and ``bar.idr`` as source files would be

2525written as follows::

2626

27− package test

27+ package foo

2828

2929 modules = foo, bar

3030

@@ -91,10 +91,7 @@ external ``C`` libraries, the following options are available:

9191

9292+ ``makefile = <file>``, which specifies a ``Makefile``, to be built

9393 before the Idris modules, for example to support linking with a

94− ``C`` library. When building, Idris sets the environment variables

95− ``IDRIS_INCLUDES`` (with C include flags) and ``IDRIS_LDFLAGS``

96− (with C linking flags) so they can be used from inside the

97− ``Makefile``.

94+ ``C`` library.

9895

9996+ ``libs = <libs>``, which takes a comma separated list of libraries

10097 which must be present for the package to be usable.

@@ -123,7 +120,7 @@ Package files support comments using the standard Idris singleline ``--`` and mu

123120Using Package files

124121===================

125122

126−Given an Idris package file ``test.ipkg`` it can be used with the Idris compiler as follows:

123+Given an Idris package file ``text.ipkg`` it can be used with the Idris compiler as follows:

127124

128125+ ``idris --build test.ipkg`` will build all modules in the package

129126

docs/reference/partial-evaluation.rst+2−2

@@ -8,7 +8,7 @@ of functions with arguments annotated as ``%static``.

88

99(This is an implementation of the partial evaluator described in `this

1010ICFP 2010

11−paper <https://eb.host.cs.st-andrews.ac.uk/writings/icfp10.pdf>`__.

11+paper <http://eb.host.cs.st-andrews.ac.uk/writings/icfp10.pdf>`__.

1212Please refer to this for more precise definitions of what follows.)

1313

1414Partial evaluation is switched off by default since Idris 1.0. It can

@@ -207,7 +207,7 @@ Specialising Interpreters

207207A particularly useful situation where partial evaluation becomes

208208effective is in defining an interpreter for a well-typed expression

209209language, defined as follows (see the `Idris tutorial, section

210−4 <https://eb.host.cs.st-andrews.ac.uk/writings/idris-tutorial.pdf>`__

210+4 <http://eb.host.cs.st-andrews.ac.uk/writings/idris-tutorial.pdf>`__

211211for more details on how this works):

212212

213213::

docs/reference/syntax-guide.rst+3−8

@@ -168,7 +168,7 @@ The signature of type constructors may use dependent types

168168Records

169169~~~~~~~

170170

171−There is a special syntax for data types with one constructor and

171+There is a special syntax for data types with one constructors and

172172multiple fields.

173173

174174.. code:: idris

@@ -219,7 +219,7 @@ This is syntactic sugar for the following, which is usually preferred:

219219 data Stream : Type -> Type where

220220 (::) a -> Inf (Stream a) -> Stream a

221221

222−Every occurence of the defined type in a constructor argument will be

222+Every occurence of the the defined type in a constructor argument will be

223223wrapped in the ``Inf`` type constructor. This has the effect of delaying the

224224evaluation of the second argument when the data constructor is applied.

225225An ``Inf`` argument is constructed using ``Delay`` (which Idris will insert

@@ -390,12 +390,6 @@ Totality

390390 partial

391391 covering

392392

393−Sets explicitly to which extent pattern matching is terminating and/or

394−exhaustive. A ``partial`` pattern matching makes no assumption. A ``covering``

395−pattern matching ensures that pattern matching is exhaustive on its clauses.

396−Furthermore, a ``total`` pattern matching enforces both exhaustivity and

397−termination of the evaluation of its clauses.

398−

399393Implicit Coercion

400394^^^^^^^^^^^^^^^^^

401395

@@ -413,6 +407,7 @@ Options

413407 %no_implicit

414408 %error_handler

415409 %error_reverse

410+ %assert_total

416411 %reflection

417412 %specialise [<name list>]

418413

docs/reference/syntax-reference.rstdeleted−422

@@ -1,422 +0,0 @@

1−*****************

2−Syntax Reference

3−*****************

4−

5−Here we present a rough description of Idris' surface syntax as an eBNF grammar.

6−This presentend grammar may differ from syntax that Idris' parser can handle due to the parser and grammar description not being in sync.

7−

8−=========

9−Notation

10−=========

11−

12−Grammar shortcut notation::

13−

14− ~CHARSEQ = complement of char sequence (i.e. any character except CHARSEQ)

15− RULE? = optional rule (i.e. RULE or nothing)

16− RULE* = repeated rule (i.e. RULE zero or more times)

17− RULE+ = repeated rule with at least one match (i.e. RULE one or more times)

18− RULE! = invalid rule (i.e. rule that is not valid in context, report meaningful error in case)

19− RULE{n} = rule repeated n times

20−

21−

22−=============

23−Main Grammar

24−=============

25−

26−.. productionlist::

27− ModuleHeader : `DocComment_t`? "module" `Identifier_t` ";"? ;

28− Import : "import" `Identifier_t` ";"? ;

29− Prog : `Decl`* `EOF`;

30− Decl : `DeclP`

31− : | `Using`

32− : | `Params`

33− : | `Mutual`

34− : | `Namespace`

35− : | `Interface`

36− : | `Implementation`

37− : | `DSL`

38− : | `Directive`

39− : | `Provider`

40− : | `Transform`

41− : | `Import`!

42− : | `RunElabDecl` ;

43− DeclP : `Fixity`

44− : | `FunDecl`

45− : | `Data`

46− : | `Record`

47− : | `SyntaxDecl` ;

48−

49−

50−--------------------

51−Syntax Declarations

52−--------------------

53−

54−.. productionlist::

55− SyntaxDecl : `SyntaxRule` ;

56− SyntaxRuleOpts : "term" | "pattern" ;

57− SyntaxRule : `SyntaxRuleOpts`? "syntax" `SyntaxSym`+ "=" `TypeExpr` `Terminator`;

58− SyntaxSym : '[' `Name_t` ']'

59− : | '{' `Name_t` '}'

60− : | `Name_t`

61− : | `StringLiteral_t`;

62− SyntaxSym : '[' `Name_t` ']'

63− : | '{' `Name_t` '}'

64− : | `Name_t`

65− : | `StringLiteral_t`;

66−

67−----------

68−Functions

69−----------

70−

71−.. productionlist::

72− FunDecl : `FunDeclP`;

73− FunDeclP : `DocComment_t`? `FnOpts`* `Accessibility`? `FnOpts`* `FnName` `TypeSig` `Terminator`

74− : | `Postulate`

75− : | `Pattern`

76− : | `CAF` ;

77− FnOpts : `FnOpt`* `Accessibility` `FnOpt`* ;

78− FnOpt : 'total'

79− : | 'partial'

80− : | 'covering'

81− : | 'implicit'

82− : | '%' 'no_implicit'

83− : | '%' 'assert_total'

84− : | '%' 'error_handler'

85− : | '%' 'reflection'

86− : | '%' 'specialise' '[' `NameTimesList`? ']' ;

87− NameTimes : `FnName` `Natural`?;

88− NameTimesList : `NameTimes` | `NameTimes` ',' `NameTimesList` ;

89− Postulate : `DocComment_t`? 'postulate' `FnOpts`* `Accesibility`? `FnOpts`* `FnName` `TypeSig` `Terminator` ;

90−

91−--------------------

92−Blocks & Namespaces

93−--------------------

94−

95−.. productionlist::

96− Using : 'using' '(' `UsingDeclList` ')' `OpenBlock` `Decl`* `CloseBlock` ;

97− UsingDeclList : `UsingDeclListP` | `NameList TypeSig`;

98− UsingDeclListP : `UsingDecl` | `UsingDecl` ',' `UsingDeclListP` ;

99− NameList : `Name` | `Name` ',' `NameList` ;

100− UsingDecl : `FnName` `TypeSig` | `FnName` `FnName`+ ;

101− Params : 'parameters' '(' `TypeDeclList` ')' `OpenBlock` `Decl`* `CloseBlock`;

102− Mutual : 'mutual' `OpenBlock` `Decl`* `CloseBlock` ;

103− Namespace : 'namespace' `identifier` `OpenBlock` `Decl`+ `CloseBlock` ;

104−

105−----------------------------

106−Interfaces & Implementation

107−----------------------------

108−

109−.. productionlist::

110− ImplementationBlock : 'where' `OpenBlock` `FnDecl`* `CloseBlock` ;

111− MethodOrImplementation : `FnDecl` | `Implementation`;

112− InterfaceBlock : 'where' `OpenBlock` `Constructor`? `MethodOrImplementation`* `CloseBlock` ;

113− InterfaceArgument : `Name` | '(' `Name` ':' `Expr` ')';

114− Interface ::= `DocComment_t`? `Accessibility`? 'interface' `ConstraintList`? `Name` `InterfaceArgument`* `InterfaceBlock`?;

115− Implementation : `DocComment_t`? 'implementation' `ImplementationName`? `ConstraintList`? `Name` `SimpleExpr`* `ImplementationBlock`? ;

116− ImplementationName : '[' `Name` ']';

117−

118−

119−-------

120−Bodies

121−-------

122−

123−.. productionlist::

124− Pattern : `Clause`;

125− CAF : 'let' `FnName` '=' `Expr` `Terminator`;

126− ArgExpr : `HSimpleExpr` | "In Pattern External (User-defined) Expression";

127− RHS : '=' `Expr`

128− : | '?=' `RHSName`? `Expr`

129− : | `Impossible` ;

130− RHSName : '{' `FnName` '}' ;

131− RHSOrWithBlock : `RHS` `WhereOrTerminator`

132− : | 'with' `SimpleExpr` `OpenBlock` `FnDecl`+ `CloseBlock`;

133− Clause : `WExpr`+ `RHSOrWithBlock`

134− : | `SimpleExpr` '<==' `FnName` `RHS` `WhereOrTerminator`

135− : | `ArgExpr` `Operator` `ArgExpr` `WExpr`* `RHSOrWithBlock` {- Except "=" and "?=" operators to avoid ambiguity -}

136− : | `FnName` `ConstraintArg`* `ImplicitOrArgExpr`* `WExpr`* `RHSOrWithBlock`;

137− ImplicitOrArgExpr ::= `ImplicitArg` | `ArgExpr`;

138− WhereOrTerminator ::= `WhereBlock` | `Terminator`;

139− WExpr ::= '|' `Expr`';

140− WhereBlock : 'where' `OpenBlock` `Decl`+ `CloseBlock`;

141−

142−----------

143−Directives

144−----------

145−

146−.. productionlist::

147− Codegen: 'C'

148− : | 'Java'

149− : | 'JavaScript'

150− : | 'Node'

151− : | 'LLVM'

152− : | 'Bytecode' ;

153− StringList : `String` | `String` ',' `StringList` ;

154− Directive : '%' `DirectiveP`;

155− DirectiveP : 'lib' `CodeGen` `String_t`

156− : | 'link' `CodeGen` `String_t`

157− : | 'flag' `CodeGen` `String_t`

158− : | 'include' `CodeGen` `String_t`

159− : | 'hide' `Name`

160− : | 'freeze' `Name`

161− : | 'thaw' `Name`

162− : | 'access' `Accessibility`

163− : | 'default' `Totality`

164− : | 'logging' `Natural`

165− : | 'dynamic' `StringList`

166− : | 'name' `Name` `NameList`

167− : | 'error_handlers' `Name` `NameList`

168− : | 'language' 'TypeProviders'

169− : | 'language' 'ErrorReflection'

170− : | 'deprecated' `Name` `String`

171− : | 'fragile' `Name` `Reason` ;

172− LangExt : "TypeProviders"

173− : | "ErrorReflection"

174− : | "UniquenessTypes"

175− : | "LinearTypes"

176− : | "DSLNotation"

177− : | "ElabReflection"

178− : | "FirstClassReflection" ;

179− Totality : 'partial' | 'total' | 'covering'

180− Provider : `DocComment_t`? '%' 'provide' `Provider_What`? '(' `FnName` `TypeSig` ')' 'with' `Expr`;

181− ProviderWhat : 'proof' | 'term' | 'type' | 'postulate'

182− Transform : '%' 'transform' `Expr` '==>' `Expr`;

183− RunElabDecl : '%' 'runElab' `Expr`;

184−

185−

186−===========

187−Expressions

188−===========

189−

190−.. productionlist::

191− FullExpr : `Expr` `EOF_t` ;

192− Expr : `Pi` ;

193− OpExpr : "Expression Parser with Operators based on ExprP" ;

194− ExprP : "External (User-defined) Syntax" | `InternalExpr` ;

195− InternalExpr : `UnifyLog`

196− : | `RecordType`

197− : | `SimpleExpr`

198− : | `Lambda`

199− : | `QuoteGoal`

200− : | `Let`

201− : | `If`

202− : | `RewriteTerm`

203− : | `CaseExpr`

204− : | `DoBlock`

205− : | `App` ;

206−

207−-------

208−Bodies

209−-------

210−

211−.. productionlist::

212− Impossible : `impossible` ;

213− CaseExpr : "case" `Expr` "of" `OpenBlock` `CaseOption`+ `CloseBlock` ;

214− CaseOption : `Expr` (`Impossible` | "=>" `Expr`) `Terminator` ;

215− ProofExpr : "proof" `OpenBlock` `Tactic'`* `CloseBlock` ;

216− TacticsExpr : "tactics" `OpenBlock` `Tactic'`* `CloseBlock` ;

217− SimpleExpr : "External (User-defined) Simple Expression"

218− : | "?" `Name`

219− : | "%" "implementation"

220− : | "Refl" ("{" `Expr` "}")?

221− : | `ProofExpr`

222− : | `TacticsExpr`

223− : | `FnName`

224− : | `Idiom`

225− : | `List`

226− : | `Alt`

227− : | `Bracketed`

228− : | `Constant`

229− : | `Type`

230− : | "Void"

231− : | `Quasiquote`

232− : | `NameQuote`

233− : | `Unquote`

234− : | "_" ;

235− Bracketed : "(" `BracketedP` ;

236− BracketedP : ")"

237− : | `Expr` ")"

238− : | `ExprList` ")"

239− : | `DependentPair` ")"

240− : | `Operator` `Expr` ")"

241− : | `Expr` `Operator` ")" ;

242− Alt : "(|" `Expr_List` "|)" ;

243− Expr_List : `Expr'` | `Expr'` "," `Expr_List` ;

244− HSimpleExpr : "." `SimpleExpr` | `SimpleExpr` ;

245− UnifyLog : "%" "unifyLog" `SimpleExpr` ;

246− RunTactics : "%" "runElab" `SimpleExpr` ;

247− Disamb : "with" `NameList` `Expr` ;

248− NoImplicits : "%" "noImplicits" `SimpleExpr` ;

249− App : "mkForeign" `Arg` `Arg`*

250− : | `MatchApp`

251− : | `SimpleExpr` `Arg`* ;

252− MatchApp : `SimpleExpr` "<==" `FnName` ;

253− Arg :` ImplicitArg` | `ConstraintArg` | `SimpleExpr` ;

254− ImplicitArg : "{" `Name` ("=" `Expr`)? "}" ;

255− ConstraintArg : "@{" `Expr` "}" ;

256− Quasiquote : "`(" `Expr` ")" ;

257− Unquote : "," `Expr` ;

258− RecordType : "record" "{" `FieldTypeList` "}" ;

259− FieldTypeList : `FieldType` | `FieldType` "," `FieldTypeList` ;

260− FieldType : `FnName` "=" `Expr` ;

261− TypeSig : ":" `Expr` ;

262− TypeExpr : `ConstraintList`? `Expr` ;

263− Lambda : "\\" `TypeOptDeclList` `LambdaTail`

264− : | "\\" `SimpleExprList` `LambdaTail` ;

265− SimpleExprList : `SimpleExpr` | `SimpleExpr` "," `SimpleExprList` ;

266− LambdaTail : `Impossible` | "=>" `Expr` ;

267− RewriteTerm : "rewrite" `Expr` ("==>" `Expr`)? "in" `Expr` ;

268− RigCount: "1" : "0" ;

269− Let : "let" `Name` `TypeSig`"? "=" `Expr` "in" `Expr`

270− : | "let" `Expr'` "=" `Expr'` "in" `Expr` ;

271− TypeSig' : ":" `Expr'` ;

272− If : "if" `Expr` "then" `Expr` "else" `Expr` ;

273− QuoteGoal : "quoteGoal" `Name` "by" `Expr` "in" `Expr` ;

274−

275−----

276−Pies

277−----

278−

279−.. productionlist::

280− Pi : `PiOpts` `Static`? `PiP` ;

281− PiP : `OpExpr` ("->" `Pi`)?

282− : | "(" `TypeDeclList` ")" "->" `Pi`

283− : | "{" `TypeDeclList` "}" "->" `Pi`

284− : | "{" "auto" `TypeDeclList` "}" "->" `Pi`

285− : | "{" "default" `SimpleExpr` `TypeDeclList` "}" "->" `Pi` ;

286− PiOpts : "."? ;

287− ConstraintList : "(" `Expr_List` ")" "=>"

288− : | `Expr` "=>" ;

289− TypeDeclList : `FunctionSignatureList`

290− : | `NameList` `TypeSig` ;

291− FunctionSignatureList : `Name` `TypeSig`

292− : | `Name` `TypeSig` "," `FunctionSignatureList` ;

293− TypeOptDeclList : `NameOrPlaceholder` `TypeSig`?

294− : | `NameOrPlaceholder` `TypeSig`? "," `TypeOptDeclList` ;

295− NameOrPlaceHolder : `Name` : "_" ;

296− ListExpr : "[" "]" | "[" `Expr` "|" `DoList` "]" | "[" `ExprList` "]" ;

297− ExprList : `Expr` | `Expr` "," `ExprList` ;

298−

299−

300−-------------------

301−Do Blocks & Idioms

302−-------------------

303−

304−.. productionlist::

305− DoList : `Do` : `Do` "," `DoList` ;

306− Do' : `Do` `KeepTerminator` ;

307− DoBlock : "do" `OpenBlock` `Do'`+ `CloseBlock` ;

308− Do : "let" `Name` `TypeSig`"? "=" `Expr`

309− : | "let" `Expr'` "=" `Expr`

310− : | "rewrite" `Expr`

311− : | `Name` "<-" `Expr`

312− : | `Expr'` "<-" `Expr`

313− : | `Expr` ;

314− Idiom : "[|" `Expr` "|]" ;

315−

316−

317−----------

318−Constants

319−----------

320−

321−.. productionlist::

322− Constant : | "Integer"

323− : | "Int"

324− : | "Char"

325− : | "Double"

326− : | "String"

327− : | "Bits8"

328− : | "Bits16"

329− : | "Bits32"

330− : | "Bits64"

331− : | `Float_t`

332− : | `Natural_t`

333− : | `VerbatimString_t`

334− : | `String_t`

335− : | `Char_t` ;

336− VerbatimString_t : "\"\"\"" ~"\"\"\"" "\""* "\"\"\"" ;

337−

338−-------

339−Tactics

340−-------

341−

342−.. productionlist::

343− Tactic : "intro" `NameList`?

344− : | "intros"

345− : | "refine" `Name` `Imp`+

346− : | "mrefine" `Name`

347− : | "rewrite" `Expr`

348− : | "induction" `Expr`

349− : | "equiv" `Expr`

350− : | "let" `Name` ":" `Expr'` "=" `Expr`

351− : | "let" `Name` "=" `Expr`

352− : | "focus" `Name`

353− : | "exact" `Expr`

354− : | "applyTactic" `Expr`

355− : | "reflect" `Expr`

356− : | "fill" `Expr`

357− : | "try" `Tactic` "|" `Tactic`

358− : | "{" `TacticSeq` "}"

359− : | "compute"

360− : | "trivial"

361− : | "solve"

362− : | "attack"

363− : | "state"

364− : | "term"

365− : | "undo"

366− : | "qed"

367− : | "abandon"

368− : | ":" "q" ;

369− TacticSeq : `Tactic` ";" `Tactic` | `Tactic` ";" `TacticSeq` ;

370−

371−----

372−Misc

373−----

374−

375−.. productionlist::

376− Imp : "?" | "_" ;

377− Static : "%static" ;

378−

379−=====

380−Data

381−=====

382−

383−.. productionlist::

384− Record : `DocComment` `Accessibility`? "record" `FnName` `TypeSig` "where" `OpenBlock` `Constructor` `KeepTerminator` `CloseBlock`;

385− DataI : "data" | "codata";

386− Data : `DocComment`? `Accessibility`? `DataI` `FnName` `TypeSig` `ExplicitTypeDataRest`?

387− : `DocComment`? `Accessibility`? `DataI` `FnName` `Name`* `DataRest`? ;

388− Constructor': `Constructor` `KeepTerminator` ;

389− ExplicitTypeDataRest : "where" `OpenBlock` `Constructor'`* `CloseBlock`;

390− DataRest : "=" `SimpleConstructorList` `Terminator` | "where"!;

391− SimpleConstructorList : `SimpleConstructor` | `SimpleConstructor` "|" `SimpleConstructorList`;

392− Constructor : `DocComment`? `FnName` `TypeSig`;

393− SimpleConstructor : `FnName` `SimpleExpr`* `DocComment`?;

394− DSL : "dsl" `FnName` `OpenBlock` `Overload'`+ `CloseBlock`;

395− OverloadIdentifier : "let" | `Identifier`;

396− Overload : `OverloadIdentifier` "=" `Expr`;

397−

398−

399−=========

400−Operators

401−=========

402−

403−.. productionlist::

404− BacktickOperator: `Name` ;

405− OperatorName: `SymbolicOperator` : `BacktickOperator` ;

406− OperatorFront: "(" "=" ")" | (`Identifier_t` ".")? "(" `Operator_t` ")" ;

407− FnName: `Name` | `OperatorFront`;

408− Fixity: `FixityType` `Natural_t` `OperatorList` `Terminator`;

409− FixityType: "infixl" | "infixr" | "infix" | "prefix";

410−

411−

412−==============

413−Documentation

414−==============

415−

416−.. productionlist::

417− SingleLineComment_t: "--" ~`EOL_t`* `EOL_t` ;

418− MultiLineComment_t: "{" .. "}" | "{ -" `InCommentChars_t` ;

419− InCommentChars_t : "- }" | `MultiLineComment_t` `InCommentChars_t` | ~"- }"+ `InCommentChars_t`;

420− DocComment_t : `DocCommentLine` (`ArgCommentLine` `DocCommentLine`*)* ;

421− DocCommentLine : "|||" ~`EOL_t`* `EOL_t` ;

422− ArgCommentLine : "|||" "@" ~`EOL_t`* `EOL_t` ;

docs/reference/tactics.rst+13

@@ -173,6 +173,19 @@ rewrite

173173 Vect Z a

174174 -lemma>

175175

176+induction

177+---------

178+

179+- ``induction`` - (``Note that this is still experimental`` and you may

180+ get strange results and error messages. We are aware of these and

181+ will finish the implementation eventually!) Prove the goal by

182+ induction. Each constructor of the datatype becomes a goal.

183+ Constructors with recursive arguments become induction steps, while

184+ simple constructors become base cases. Note that this only works for

185+ datatypes that have eliminators: a datatype definition must have the

186+ ``%elim`` modifier.

187+

188+

176189sourceLocation

177190--------------

178191

docs/reference/type-directed-search.rst+1−1

@@ -4,7 +4,7 @@ Type Directed Search ``:search``

44

55Idris' ``:search`` command searches for terms according to their

66approximate type signature (much like

7−`Hoogle <https://www.haskell.org/hoogle/>`__ for Haskell). For

7+`Hoogle <http://www.haskell.org/hoogle/>`__ for Haskell). For

88example::

99

1010 Idris> :search e -> List e -> List e

docs/reference/uniqueness-types.rst+2−2

@@ -13,7 +13,7 @@ ideally while giving up as little high level conveniences as possible.

1313

1414They are inspired by linear types, `Uniqueness Types

1515<https://en.wikipedia.org/wiki/Uniqueness_type>`__ in the `Clean

16−<https://wiki.clean.cs.ru.nl/Clean>`__ programming language, and

16+<http://wiki.clean.cs.ru.nl/Clean>`__ programming language, and

1717ownership types and borrowed pointers in the `Rust

1818<https://www.rust-lang.org/>`__ programming language.

1919

@@ -199,7 +199,7 @@ return it in exactly the condition in which it was received!

199199The restriction is that when a ``Borrowed`` type is matched, any

200200pattern variables under the ``Read`` which have a unique type may not

201201be referred to at all on the right hand side (unless they are

202−themselves lent to another function).

202+themselves ``lent`` to another function).

203203

204204Uniqueness information is stored in the type, and in particular in

205205function types. Once we're in a unique context, any new function which

docs/st/composing.rst+16−16

@@ -1,7 +1,7 @@

11.. _composing:

22

33************************

4−Composing State Machines

4+Composing State Machines

55************************

66

77In the previous section, we defined a ``DataStore`` interface and used it

@@ -28,7 +28,7 @@ there was a login failure in a state.

2828

2929Furthermore, we may have *hierarchies* of state machines, in that one

3030state machine could be implemented by composing several others. For

31−example, we can have a state machine representing the state of a

31+example, we can have a state machine representing the state of a

3232graphics system, and use this to implement a *higher level* graphics API

3333such as turtle graphics, which uses the graphics system plus some additional

3434state for the turtle.

@@ -50,7 +50,7 @@ count to zero, a session might run as follows:

5050 *LoginCount> :exec main

5151 Enter password: Mornington Crescent

5252 Secret is: "Secret Data"

53− Enter password: Dollis Hill

53+ Enter password: Dollis Hill

5454 Failure

5555 Number of failures: 1

5656 Enter password: Mornington Crescent

@@ -63,7 +63,7 @@ count to zero, a session might run as follows:

6363We'll start by adding a state resource to ``getData`` to keep track of the

6464number of failures:

6565

66−.. code-block:: idris

66+.. code-block:: idrs

6767

6868 getData : (ConsoleIO m, DataStore m) =>

6969 (failcount : Var) -> ST m () [failcount ::: State Integer]

@@ -116,7 +116,7 @@ match:

116116 Required result states here are: st2_fn

117117

118118In other words, ``connect`` requires that there are *no* resources on

119−entry, but we have *one*, the failure count!

119+entry, but we have *one*, the failure count!

120120This shouldn't be a problem, though: the required resources are a *subset* of

121121the resources we have, after all, and the additional resources (here, the

122122failure count) are not relevant to ``connect``. What we need, therefore,

@@ -214,7 +214,7 @@ ordering of resources is allowed to change, although resources which

214214appear in ``old`` can't appear in the ``sub`` list more than once (you will

215215get a type error if you try this).

216216

217−The function ``updateWith`` takes the *output* resources of the

217+The function ``updateWith`` takes the *output* resources of the

218218called function, and updates them in the current resource list. It makes

219219an effort to preserve ordering as far as possible, although this isn't

220220always possible if the called function does some complicated resource

@@ -338,7 +338,7 @@ representing a surface on which we'll draw lines and rectangles:

338338

339339.. code-block:: idris

340340

341− interface Draw (m : Type -> Type) where

341+ interface Draw (m : Type -> Type) where

342342 Surface : Type

343343

344344We'll need to be able to create a new ``Surface`` by opening a window:

@@ -369,7 +369,7 @@ succeeds (that is, returns a result of the form ``Just val``.

369369 an operation returns ``Just ty``, there's also ``addIfRight``:

370370

371371 .. code-block:: idris

372−

372+

373373 addIfJust : Type -> Action (Maybe Var)

374374 addIfRight : Type -> Action (Either a Var)

375375

@@ -378,10 +378,10 @@ succeeds (that is, returns a result of the form ``Just val``.

378378 of an operation:

379379

380380 .. code-block:: idris

381−

381+

382382 Add : (ty -> Resources) -> Action ty

383−

384− Using this, you can create your own actions to add resources

383+

384+ Using this, you can create your own actions to add resources

385385 based on the result of an operation, if required. For example,

386386 ``addIfJust`` is implemented as follows:

387387

@@ -479,7 +479,7 @@ For example, assuming we have a surface ``win`` to draw onto, we can write a

479479

480480The ``flip win`` at the end is necessary because the drawing primitives

481481are double buffered, to prevent flicker. We draw onto one buffer, off-screen,

482−and display the other. When we call ``flip``, it displays the off-screen

482+and display the other. When we call ``flip``, it displays the off-screen

483483buffer, and creates a new off-screen buffer for drawing the next frame.

484484

485485To include this in a program, we'll write a main loop which renders our

@@ -496,7 +496,7 @@ application:

496496

497497Finally, we can create a main program which initialises a window, if

498498possible, then runs the main loop:

499−

499+

500500.. code-block:: idris

501501

502502 drawMain : (ConsoleIO m, Draw m) => ST m () []

@@ -593,7 +593,7 @@ is implemented using the following type, defined by ``Control.ST``:

593593

594594.. code-block:: idris

595595

596− data Composite : List Type -> Type

596+ data Composite : List Type -> Type

597597

598598If we have a composite resource, we can split it into its constituent

599599resources, and create new variables for each of those resources, using

@@ -604,7 +604,7 @@ the *split* function. For example:

604604 splitComp : (comp : Var) -> ST m () [comp ::: Composite [State Int, State String]]

605605 splitComp comp = do [int, str] <- split comp

606606 ?whatNow

607−

607+

608608The call ``split comp`` extracts the ``State Int`` and ``State String`` from

609609the composite resource ``comp``, and stores them in the variables ``int``

610610and ``str`` respectively. If we check the type of ``whatNow``, we'll see

@@ -713,7 +713,7 @@ A ``Line`` is defined as a start location, and end location, and a colour:

713713 Line : Type

714714 Line = ((Int, Int), (Int, Int), Col)

715715

716−To implement ``start``, which creates a new ``Turtle`` (or returns ``Nothing``

716+To implement ``start``, which creates a new ``Turtle`` (or returns ``Nothing``

717717if this is impossible), we begin by initialising the drawing surface then

718718all of the components of the state. Finally, we combine all of these

719719into a composite resource for the turtle:

docs/st/examples.rst+1−1

@@ -350,7 +350,7 @@ Implementing ``Sockets``

350350

351351To implement ``Sockets`` in ``IO``, we'll begin by giving a concrete type

352352for ``Sock``. We can use the raw sockets API (implemented in

353−``Network.Socket``) for this, and use a ``Socket`` stored in a ``State``, no

353+``Network.Sockeet``) for this, and use a ``Socket`` stored in a ``State``, no

354354matter what abstract state the socket is in:

355355

356356.. code-block:: idris

docs/st/index.rst+1−1

@@ -14,7 +14,7 @@ the `Control.ST` library in `Idris`.

1414 Idris Community* has waived all copyright and related or neighbouring

1515 rights to Documentation for Idris.

1616

17− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

17+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1818

1919.. toctree::

2020 :maxdepth: 1

docs/st/introduction.rst+2−2

@@ -3,7 +3,7 @@ Overview

33********

44

55Pure functional languages with dependent types such as `Idris

6−<https://www.idris-lang.org/>`_ support reasoning about programs directly

6+<http://www.idris-lang.org/>`_ support reasoning about programs directly

77in the type system, promising that we can *know* a program will run

88correctly (i.e. according to the specification in its type) simply

99because it compiles.

@@ -70,7 +70,7 @@ Outline

7070=======

7171

7272This tutorial starts (:ref:`introst`) by describing how to manipulate

73−individual states, introduces a data type ``STrans`` for describing stateful

73+individual states, introduce a data type ``STrans`` for describing stateful

7474functions, and ``ST`` which describes top level state transitions.

7575Next (:ref:`smstypes`) it describes how to represent state machines in

7676types, and how to define *interfaces* for describing stateful systems.

docs/st/state.rst+20−18

@@ -19,10 +19,10 @@ how those resources change when a function runs:

1919 Type

2020

2121A value of type ``STrans m resultType in_res out_res_fn`` represents a sequence

22−of actions which can manipulate state. The arguments are:

22+of actions which can manipulate state. The arguments are:

2323

2424* ``m``, which is an underlying *computation context* in which the actions will be executed.

25− Usually, this will be a generic type with a ``Monad`` implementation, but

25+ Usually, this will be a generic type with a ``Monad`` implementation, but

2626 it isn't necessarily so. In particular, there is no need to understand monads

2727 to be able to use ``ST`` effectively!

2828* ``resultType``, which is the type of the value the sequence will produce

@@ -76,10 +76,10 @@ resource is still a ``State Integer`` on output:

7676 same. We'll introduce a much more concise way of writing this type at the

7777 end of this section (:ref:`sttype`), when we describe the ``ST`` type

7878 itself.

79−

79+

8080This function reads the value stored at the resource ``x`` with ``read``,

8181increments it then writes the result back into the resource ``x`` with

82−``write``. We'll see the types of ``read`` and ``write`` shortly

82+``write``. We'll see the types of ``read`` and ``write`` shortly

8383(see :ref:`stransprimops`). We can also create and delete resources:

8484

8585.. code-block:: idris

@@ -104,7 +104,7 @@ can run it in *any* context. We can run it in the identity context with

104104``runPure``. For example, try entering the above definitions in a file

105105``Intro.idr`` then running the following at the REPL:

106106

107−.. code::

107+.. code::

108108

109109 *Intro> runPure (makeAndIncrement 93)

110110 94 : Integer

@@ -164,7 +164,7 @@ can define ``ioMakeAndIncrement`` as follows:

164164 lift $ putStrLn ("var = " ++ show !(read var))

165165 delete var

166166

167−The ``lift`` function allows us to use functions from the underlying

167+The ``lift`` function allows us to use funtions from the underlying

168168computation context (``IO`` here) directly. Again, we'll see the exact type

169169of ``lift`` shortly.

170170

@@ -179,7 +179,7 @@ of ``lift`` shortly.

179179 Conceptually, at least, you can think of it as having the following type:

180180

181181 .. code-block:: idris

182−

182+

183183 (!) : STrans m a state_in state_out -> a

184184

185185 It is syntactic sugar for binding a variable immediately before the

@@ -243,7 +243,7 @@ context. Here, we use ``run``, which allows us to execute an ``STrans`` program

243243in any context (as long as it has an implementation of ``Applicative``) and we

244244can execute ``ioMakeAndIncrement`` at the REPL as follows:

245245

246−.. code::

246+.. code::

247247

248248 *Intro> :exec run ioMakeAndIncrement

249249 Enter a number: 93

@@ -269,7 +269,7 @@ its length will change:

269269 addElement vec item = do xs <- read vec

270270 write vec (item :: xs)

271271

272−Note that you'll need to ``import Data.Vect`` to try this example.

272+Note that you'll need to ``import Data.Vect`` to try this example.

273273

274274.. topic:: Updating a state directly with ``update``

275275

@@ -344,7 +344,7 @@ if the input is valid. We can express this in the type as follows:

344344Then, when we implement ``readAndAdd`` we need to return the appropriate

345345value for the output state. If we've added an item to the vector, we need to

346346return ``True``, otherwise we need to return ``False``:

347−

347+

348348.. code-block:: idris

349349

350350 readAndAdd : ConsoleIO io => (vec : Var) ->

@@ -435,7 +435,7 @@ we can do as follows:

435435

436436.. _stransprimops:

437437

438−``STrans`` Primitive operations

438+``STrans`` Primitive operations

439439===============================

440440

441441Now that we've written a few small examples of ``STrans`` functions, it's

@@ -456,7 +456,7 @@ implicit ``prf`` argument, which has the following type:

456456

457457.. code-block:: idris

458458

459− prf : InState lbl (State ty) res

459+ prf : InState lbl (State ty) res}

460460

461461This relies on a predicate ``InState``. A value of type ``InState x ty res``

462462means that the reference ``x`` must have type ``ty`` in the list of

@@ -485,7 +485,7 @@ of type ``State state``:

485485

486486.. code-block:: idris

487487

488− new : (val : state) ->

488+ new : (val : state) ->

489489 STrans m Var res (\lbl => (lbl ::: State state) :: res)

490490

491491It's important that the new resource has type ``State state``, rather than

@@ -526,7 +526,7 @@ the resource list so that it is appropriate for returning that value:

526526

527527.. code-block:: idris

528528

529− returning : (result : ty) ->

529+ returning : (result : ty) ->

530530 STrans m () res (const (out_fn result)) ->

531531 STrans m ty res out_fn

532532

@@ -555,7 +555,7 @@ programming and reasoning in Idris.

555555.. _sttype:

556556

557557`ST`: Representing state transitions directly

558−=============================================

558+============================================

559559

560560We've seen a few examples of small ``STrans`` functions now, and

561561their types can become quite verbose given that we need to provide explicit

@@ -568,7 +568,7 @@ giving input and output resource lists in full. We can do this with

568568.. code-block:: idris

569569

570570 ST : (m : Type -> Type) ->

571− (resultType : Type) ->

571+ (resultType : Type) ->

572572 List (Action resultType) -> Type

573573

574574``ST`` is a type level function which computes an appropriate ``STrans``

@@ -593,8 +593,8 @@ So, we can write some of the function types we've seen so far as follows:

593593That is, ``increment`` begins and ends with ``x`` in state ``State Integer``.

594594

595595.. code-block:: idris

596−

597− makeAndIncrement : Integer -> ST m Integer []

596+

597+ makeAndIncrement : Int -> ST m Int []

598598

599599That is, ``makeAndIncrement`` begins and ends with no resources.

600600

@@ -652,3 +652,5 @@ the rare occasions we need the full precision of ``STrans``. In the next

652652section, we'll see how to use the facilities provided by ``ST`` to write

653653a precise API for a system with security properties: a data store requiring

654654a login.

655+

656+

docs/tutorial/conclusions.rst+6−6

@@ -7,11 +7,11 @@ Further Reading

77Further information about Idris programming, and programming with

88dependent types in general, can be obtained from various sources:

99

10−- The Idris web site (https://www.idris-lang.org/) and by asking

10+- The Idris web site (http://www.idris-lang.org/) and by asking

1111 questions on the mailing list.

1212

1313- The IRC channel ``#idris``, on

14− `webchat.freenode.net <https://webchat.freenode.net/>`__.

14+ `chat.freenode.net <http://chat.freenode.net>`__.

1515

1616- The wiki (https://github.com/idris-lang/Idris-dev/wiki/) has further

1717 user provided information, in particular:

@@ -25,7 +25,7 @@ dependent types in general, can be obtained from various sources:

2525 https://github.com/idris-lang/Idris-dev.

2626

2727- Existing projects on the ``Idris Hackers`` web space:

28− https://idris-hackers.github.io.

28+ http://idris-hackers.github.io.

2929

3030- Various papers (e.g. [1]_, [2]_, and [3]_). Although these mostly

3131 describe older versions of Idris.

@@ -36,14 +36,14 @@ dependent types in general, can be obtained from various sources:

3636 Aspects of Declarative Languages (PADL'12), Claudio Russo and

3737 Neng-Fa Zhou (Eds.). Springer-Verlag, Berlin, Heidelberg,

3838 242-257. DOI=10.1007/978-3-642-27694-1_18

39− https://dx.doi.org/10.1007/978-3-642-27694-1_18

39+ http://dx.doi.org/10.1007/978-3-642-27694-1_18

4040

4141.. [2] Edwin C. Brady. 2011. IDRIS ---: systems programming meets full

4242 dependent types. In Proceedings of the 5th ACM workshop on

4343 Programming languages meets program verification (PLPV

4444 '11). ACM, New York, NY, USA,

4545 43-54. DOI=10.1145/1929529.1929536

46− https://doi.acm.org/10.1145/1929529.1929536

46+ http://doi.acm.org/10.1145/1929529.1929536

4747

4848.. [3] Edwin C. Brady and Kevin Hammond. 2010. Scrapping your

4949 inefficient engine: using partial evaluation to improve

@@ -51,4 +51,4 @@ dependent types in general, can be obtained from various sources:

5151 15th ACM SIGPLAN international conference on Functional

5252 programming (ICFP '10). ACM, New York, NY, USA,

5353 297-308. DOI=10.1145/1863543.1863587

54− https://doi.acm.org/10.1145/1863543.1863587

54+ http://doi.acm.org/10.1145/1863543.1863587

docs/tutorial/index.rst+2−3

@@ -4,7 +4,7 @@

44The Idris Tutorial

55##################

66

7−This is the Idris Tutorial.

7+This is the Idris Tutorial.

88It provides a brief introduction to programming in the Idris Language.

99It covers the core language features, and assumes some familiarity with an

1010existing functional programming language such as Haskell or OCaml.

@@ -15,7 +15,7 @@ existing functional programming language such as Haskell or OCaml.

1515 Idris Community* has waived all copyright and related or neighboring

1616 rights to Documentation for Idris.

1717

18− More information concerning the CC0 can be found online at: https://creativecommons.org/publicdomain/zero/1.0/

18+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/

1919

2020

2121.. toctree::

@@ -30,7 +30,6 @@ existing functional programming language such as Haskell or OCaml.

3030 interp

3131 views

3232 theorems

33− provisional

3433 interactive

3534 syntax

3635 miscellany

docs/tutorial/interactive.rst+6−5

@@ -23,12 +23,13 @@ editor, and specifically how to do so in `Vim

2323for `Emacs <https://github.com/idris-hackers/idris-mode>`_ is also

2424available.

2525

26+

2627Editing at the REPL

2728===================

2829

2930The REPL provides a number of commands, which we will describe

3031shortly, which generate new program fragments based on the currently

31−loaded module. These take the general form:

32+loaded module. These take the general form

3233

3334::

3435

@@ -63,9 +64,9 @@ Editing Commands

6364:addclause

6465----------

6566

66−The ``:addclause n f`` command, abbreviated ``:ac n f``, creates a

67+The ``:addclause n f`` command (abbreviated ``:ac n f``) creates a

6768template definition for the function named ``f`` declared on line

68−``n``. For example, if the code beginning on line 94 contains:

69+``n``. For example, if the code beginning on line 94 contains:

6970

7071.. code-block:: idris

7172

@@ -128,7 +129,7 @@ ys`` would lead to a unification error.

128129

129130The ``:addmissing n f`` command, abbreviated ``:am n f``, adds the

130131clauses which are required to make the function ``f`` on line ``n``

131−cover all inputs. For example, if the code beginning on line 94 is:

132+cover all inputs. For example, if the code beginning on line 94 is

132133

133134.. code-block:: idris

134135

@@ -142,7 +143,7 @@ then ``:am 96 vzipWith`` gives:

142143

143144 vzipWith f (x :: xs) (y :: ys) = ?vzipWith_rhs_2

144145

145−That is, it notices that there are no cases for empty vectors,

146+That is, it notices that there are no cases for non-empty vectors,

146147generates the required clauses, and eliminates the clauses which would

147148lead to unification errors.

148149

docs/tutorial/interfaces.rst+13−12

@@ -11,8 +11,8 @@ data types. For example, we would like arithmetic operators to work on

1111to display different types in a uniform way.

1212

1313To achieve this, we use *interfaces*, which are similar to type classes in

14−Haskell or traits in Rust. To define an interface, we provide a collection of

15−overloadable functions. A simple example is the ``Show``

14+Haskell or traits in Rust. To define an interface, we provide a collection of

15+overloadable functions. A simple example is the ``Show``

1616interface, which is defined in the prelude and provides an interface for

1717converting values to ``String``:

1818

@@ -31,7 +31,8 @@ This generates a function of the following type (which we call a

3131We can read this as: “under the constraint that ``a`` has an implementation

3232of ``Show``, take an input ``a`` and return a ``String``.” An implementation

3333of an interface is defined by giving definitions of the methods of the interface.

34−For example, the ``Show`` implementation for ``Nat`` could be defined as:

34+For example, the

35+``Show`` implementation for ``Nat`` could be defined as:

3536

3637.. code-block:: idris

3738

@@ -47,8 +48,8 @@ For example, the ``Show`` implementation for ``Nat`` could be defined as:

4748Only one implementation of an interface can be given for a type — implementations may

4849not overlap. Implementation declarations can themselves have constraints.

4950To help with resolution, the arguments of an implementation must be

50−constructors (either data or type constructors) or variables

51−(i.e. you cannot give an implementation for a function). For

51+constructors (either data or type constructors) or variables

52+(i.e. you cannot give an implementation for a function). For

5253example, to define a ``Show`` implementation for vectors, we need to know

5354that there is a ``Show`` implementation for the element type, because we are

5455going to use it to convert each element to a ``String``:

@@ -156,7 +157,7 @@ Note: Interfaces and ``mutual`` blocks

156157~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

157158

158159Idris is strictly "define before use", except in ``mutual`` blocks.

159−In a ``mutual`` block, Idris elaborates in two passes: types on the first

160+In a ``mutual`` block, Idris elaborates in two passes: types on the first

160161pass and definitions on the second. When the mutual block contains an

161162interface declaration, it elaborates the interface header but none of the

162163method types on the first pass, and elaborates the method types and any

@@ -258,7 +259,7 @@ are both available, or return ``Nothing`` if one or both are not ("fail fast").

258259 Nothing : Maybe Int

259260

260261Pattern Matching Bind

261−~~~~~~~~~~~~~~~~~~~~~

262+---------------------

262263

263264Sometimes we want to pattern match immediately on the result of a function

264265in ``do`` notation. For example, let's say we have a function ``readNumber``

@@ -322,7 +323,7 @@ of the ``do`` block. The second part gives the alternative bindings, of which

322323there may be more than one.

323324

324325``!``-notation

325−~~~~~~~~~~~~~~

326+--------------

326327

327328In many cases, using ``do``-notation can make programs unnecessarily

328329verbose, particularly in cases such as ``m_add`` above where the value

@@ -366,7 +367,7 @@ is lifted to:

366367 f g'

367368

368369Monad comprehensions

369−~~~~~~~~~~~~~~~~~~~~

370+--------------------

370371

371372The list comprehension notation we saw in Section

372373:ref:`sect-more-expr` is more general, and applies to anything which

@@ -460,7 +461,7 @@ application ``[| f a1 …an |]`` is translated into ``pure f <*> a1 <*>

460461 m_add' x y = [| x + y |]

461462

462463An error-handling interpreter

463−~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

464+-----------------------------

464465

465466Idiom notation is commonly useful when defining evaluators. McBride

466467and Paterson describe such an evaluator [1]_, for a language similar

@@ -533,7 +534,7 @@ Named Implementations

533534

534535It can be desirable to have multiple implementations of an interface for the

535536same type, for example to provide alternative methods for sorting or printing

536−values. To achieve this, implementations can be *named* as follows:

537+values. To achieve this, implementations can be *named* as follows:

537538

538539.. code-block:: idris

539540

@@ -573,7 +574,7 @@ the prelude defines the following ``Semigroup`` interface:

573574 interface Semigroup ty where

574575 (<+>) : ty -> ty -> ty

575576

576−Then it defines ``Monoid``, which extends ``Semigroup`` with a “neutral”

577+Then it defines ``Monoid``, which extends ``Semigroup`` with a "neutral"

577578value:

578579

579580.. code-block:: idris

docs/tutorial/interp.rst+3−3

@@ -30,7 +30,7 @@ calculated just like any other value:

3030 interpTy : Ty -> Type

3131 interpTy TyInt = Integer

3232 interpTy TyBool = Bool

33− interpTy (TyFun a t) = interpTy a -> interpTy t

33+ interpTy (TyFun A T) = interpTy A -> interpTy T

3434

3535We're going to define a representation of our language in such a way

3636that only well-typed programs can be represented. We'll index the

@@ -106,7 +106,7 @@ the ``Var`` constructor:

106106

107107 Var : HasType i G t -> Expr G t

108108

109−So, in an expression ``\x. \y. x y``, the variable ``x`` would have a

109+So, in an expression ``\x,\y. x y``, the variable ``x`` would have a

110110de Bruijn index of 1, represented as ``Pop Stop``, and ``y 0``,

111111represented as ``Stop``. We find these by counting the number of

112112lambdas between the definition and the use.

@@ -194,7 +194,7 @@ each constructor, we translate it into the corresponding Idris value:

194194 interp env (If x t e) = if interp env x then interp env t

195195 else interp env e

196196

197−Let us look at each case in turn. To translate a variable, we simply look it

197+Let us look at each case in turn. To translate a variable, we simply look it

198198up in the environment:

199199

200200.. code-block:: idris

docs/tutorial/introduction.rst+2−2

@@ -6,7 +6,7 @@ Introduction

66

77In conventional programming languages, there is a clear distinction

88between *types* and *values*. For example, in `Haskell

9−<https://www.haskell.org>`_, the following are types, representing

9+<http://www.haskell.org>`_, the following are types, representing

1010integers, characters, lists of characters, and lists of any value

1111respectively:

1212

@@ -49,7 +49,7 @@ Intended Audience

4949

5050This tutorial is intended as a brief introduction to the language, and

5151is aimed at readers already familiar with a functional language such

52−as `Haskell <https://www.haskell.org>`_ or `OCaml <https://ocaml.org>`_.

52+as `Haskell <http://www.haskell.org>`_ or `OCaml <http://ocaml.org>`_.

5353In particular, a certain amount of familiarity with Haskell syntax is

5454assumed, although most concepts will at least be explained

5555briefly. The reader is also assumed to have some interest in using

docs/tutorial/miscellany.rst+20−28

@@ -8,7 +8,7 @@ In this section we discuss a variety of additional features:

88

99+ auto, implicit, and default arguments;

1010+ literate programming;

11−+ interfacing with external libraries through the foreign function;

11++ interfacing with external libraries through the foreign function

1212+ interface;

1313+ type providers;

1414+ code generation; and

@@ -23,7 +23,7 @@ omitted when they can be inferred by the type checker, e.g.

2323.. code-block:: idris

2424

2525 index : {a:Type} -> {n:Nat} -> Fin n -> Vect n a -> a

26−

26+

2727Auto implicit arguments

2828------------------------

2929

@@ -69,17 +69,17 @@ In the case that a proof is not found, it can be provided explicitly as normal:

6969.. code-block:: idris

7070

7171 head xs {p = ?headProof}

72−

72+

7373Default implicit arguments

7474---------------------------

7575

76−Besides having Idris automatically find a value of a given type, sometimes we

76+Besides having Idris automatically find a value of a given type, sometimes we

7777want to have an implicit argument with a specific default value. In Idris, we can

7878do this using the ``default`` annotation. While this is primarily intended to assist

79−in automatically constructing a proof where auto fails, or finds an unhelpful value,

80−it might be easier to first consider a simpler case, not involving proofs.

79+in automatically constructing a proof where auto fails, or finds an unhelpful value,

80+it might be easier to first consider a simpler case, not involving proofs.

8181

82−If we want to compute the n'th fibonacci number (and defining the 0th fibonacci

82+If we want to compute the n'th fibonacci number (and defining the 0th fibonacci

8383number as 0), we could write:

8484

8585.. code-block:: idris

@@ -89,8 +89,8 @@ number as 0), we could write:

8989 fibonacci {lag} {lead} (S n) = fibonacci {lag=lead} {lead=lag+lead} n

9090

9191After this definition, ``fibonacci 5`` is equivalent to ``fibonacci {lag=0} {lead=1} 5``,

92−and will return the 5th fibonacci number. Note that while this works, this is not the

93−intended use of the ``default`` annotation. It is included here for illustrative purposes

92+and will return the 5th fibonacci number. Note that while this works, this is not the

93+intended use of the ``default`` annotation. It is included here for illustrative purposes

9494only. Usually, ``default`` is used to provide things like a custom proof search script.

9595

9696

@@ -131,7 +131,7 @@ an extension of ``.lidr`` then it is assumed to be a literate file. In

131131literate programs, everything is assumed to be a comment unless the line

132132begins with a greater than sign ``>``, for example:

133133

134−.. code-block:: literate-idris

134+.. code-block:: idris

135135

136136 > module literate

137137

@@ -242,7 +242,7 @@ through the following directives:

242242Testing foreign function calls

243243------------------------------

244244

245−Normally, the Idris interpreter (used for typechecking and as the REPL)

245+Normally, the Idris interpreter (used for typechecking and at the REPL)

246246will not perform IO actions. Additionally, as it neither generates C

247247code nor compiles to machine code, the ``%lib``, ``%include`` and

248248``%link`` directives have no effect. IO actions and FFI calls can be

@@ -329,13 +329,13 @@ are available in an external collection [1]_.

329329C Target

330330========

331331

332−The default target of Idris is C. Compiling via:

332+The default target of Idris is C. Compiling via :

333333

334334::

335335

336336 $ idris hello.idr -o hello

337337

338−is equivalent to:

338+is equivalent to :

339339

340340::

341341

@@ -344,14 +344,14 @@ is equivalent to:

344344When the command above is used, a temporary C source is generated, which

345345is then compiled into an executable named ``hello``.

346346

347−In order to view the generated C code, compile via:

347+In order to view the generated C code, compile via :

348348

349349::

350350

351351 $ idris hello.idr -S -o hello.c

352352

353353To turn optimisations on, use the ``%flag C`` pragma within the code, as

354−is shown below:

354+is shown below :

355355

356356.. code-block:: idris

357357

@@ -366,14 +366,6 @@ is shown below:

366366 main = do

367367 putStrLn $ show $ factorial 3

368368

369−To compile the generated C with debugging information e.g. to use

370−``gdb`` to debug segmentation faults in Idris programs, use the

371−``%flag C`` pragma to include debugging symbols, as is shown below:

372−

373−.. code-block:: idris

374−

375− %flag C "-g"

376−

377369JavaScript Target

378370=================

379371

@@ -503,13 +495,13 @@ And for use in the browser:

503495

504496The given files will be added to the top of the generated code.

505497For library packages you can also use the ipkg objs option to include the

506−js file in the installation, and use:

498+js file in the installation, and use

507499

508500.. code-block:: idris

509501

510502 %include Node "package/external.js"

511503

512−The *JavaScript* and *NodeJS* backends of Idris will also lookup for the file

504+This javascript and node backends idris will also lookup for the file on

513505on that location.

514506

515507Including *NodeJS* modules

@@ -552,7 +544,7 @@ types themselves have types. For example:

552544 *universe> :t Vect

553545 Vect : Nat -> Type -> Type

554546

555−But what about the type of ``Type``? If we ask Idris it reports:

547+But what about the type of ``Type``? If we ask Idris it reports

556548

557549::

558550

@@ -560,8 +552,8 @@ But what about the type of ``Type``? If we ask Idris it reports:

560552 Type : Type 1

561553

562554If ``Type`` were its own type, it would lead to an inconsistency due to

563−`Girard’s paradox <https://www.cs.cmu.edu/afs/cs.cmu.edu/user/kw/www/scans/girard72thesis.pdf>`_,

564−so internally there is a *hierarchy* of types (or *universes*):

555+`Girard’s paradox <http://www.cs.cmu.edu/afs/cs.cmu.edu/user/kw/www/scans/girard72thesis.pdf>`_ , so internally there is a

556+*hierarchy* of types (or *universes*):

565557

566558.. code-block:: idris

567559

docs/tutorial/modules.rst+15−8

@@ -53,7 +53,8 @@ Then, this gives a main program (in a file

5353 print (Btree.toList t)

5454

5555The same names can be defined in multiple modules: names are *qualified* with

56−the name of the module. The names defined in the ``Btree`` module are, in full:

56+the name of the module. The names defined in the ``Btree`` module are, in

57+full:

5758

5859+ ``Btree.BTree``

5960+ ``Btree.Leaf``

@@ -73,7 +74,7 @@ directories. For example, ``import foo.bar`` would import the file

7374``foo/bar.idr``, which would conventionally have the module declaration

7475``module foo.bar``. The only requirement for module names is that the

7576main module, with the ``main`` function, must be called

76−``Main`` — although its filename need not be ``Main.idr``.

77+``Main``—although its filename need not be ``Main.idr``.

7778

7879Export Modifiers

7980================

@@ -81,16 +82,18 @@ Export Modifiers

8182Idris allows for fine-grained control over the visibility of a

8283module's contents. By default, all names defined in a module are kept

8384private. This aides in specification of a minimal interface and for

84−internal details to be left hidden. Idris allows for functions,

85+internal details to be left hidden. Idris allows for functions,

8586types, and interfaces to be marked as: ``private``, ``export``, or

86−``public export``. Their general meaning is as follows:

87+``public export``. Their general meaning is as follows:

8788

88−- ``private`` meaning that it's not exported at all. This is the default.

89+- ``private`` meaning that it's not exported at all. This is the

90+ default.

8991

9092- ``export`` meaning that its top level type is exported.

9193

9294- ``public export`` meaning that the entire definition is exported.

9395

96+

9497A further restriction in modifying the visibility is that definitions

9598must not refer to anything within a lower level of visibility. For

9699example, ``public export`` definitions cannot use private names, and

@@ -126,9 +129,10 @@ Meaning for Data Types

126129

127130For data types, the meanings are:

128131

129−- ``export`` the type constructor is exported

132+- ``export`` the type constructor is exported

130133

131−- ``public export`` the type constructor and data constructors are exported

134+- ``public export`` the type constructor and data constructors are

135+ exported

132136

133137

134138Meaning for Interfaces

@@ -137,7 +141,6 @@ Meaning for Interfaces

137141For interfaces, the meanings are:

138142

139143- ``export`` the interface name is exported

140−

141144- ``public export`` the interface name, method names and default

142145 definitions are exported

143146

@@ -186,6 +189,8 @@ the ``public`` modifier on an ``import``. For example:

186189 import B

187190 import public C

188191

192+ public a : AType a = ...

193+

189194The module ``A`` will export the name ``a``, as well as any public or

190195abstract names in module ``C``, but will not re-export anything from

191196module ``B``.

@@ -272,3 +277,5 @@ which can be inferred by the type checker:

272277

273278 *params> show (append _ _ (MkVects _ [1,2,3] [4,5,6]))

274279 "[1, 2, 3, 4, 5, 6]" : String

280+

281+

docs/tutorial/packages.rst+29−41

@@ -1,31 +1,26 @@

1−.. _sect-packages:

2−

31********

42Packages

53********

64

7−Idris includes a simple build system for building packages and executables

8−from a named package description file. These files can be used with the

9−Idris compiler to manage the development process.

5+

6+Idris includes a simple build system for building packages and executables from a named package description file.

7+These files can be used with the Idris compiler to manage the development process .

108

119Package Descriptions

1210====================

1311

1412A package description includes the following:

1513

16−+ A header, consisting of the keyword ``package`` followed by a package

14++ A header, consisting of the keyword package followed by the package

1715 name. Package names can be any valid Idris identifier. The iPKG

1816 format also takes a quoted version that accepts any valid filename.

19−

20−+ Fields describing package contents, ``<field> = <value>``.

17++ Fields describing package contents, ``<field> = <value>``

2118

2219At least one field must be the modules field, where the value is a

23−comma separated list of modules. For example, given an idris package

20+comma separated list of modules. For example, given an idris package

2421``maths`` that has modules ``Maths.idr``, ``Maths.NumOps.idr``,

2522``Maths.BinOps.idr``, and ``Maths.HexOps.idr``, the corresponding

26−package file would be:

27−

28−::

23+package file would be::

2924

3025 package maths

3126

@@ -43,6 +38,7 @@ of the main Idris repository, and in `third-party libraries

4338Using Package files

4439===================

4540

41+

4642Idris itself is aware about packages, and special commands are

4743available to help with, for example, building packages, installing

4844packages, and cleaning packages. For instance, given the ``maths``

@@ -58,9 +54,7 @@ package from earlier we can use Idris as follows:

5854

5955Once the maths package has been installed, the command line option

6056``--package maths`` makes it accessible (abbreviated to ``-p maths``).

61−For example:

62−

63−::

57+For example::

6458

6559 idris -p maths Main.idr

6660

@@ -72,18 +66,20 @@ The integrated build system includes a simple testing framework.

7266This framework collects functions listed in the ``ipkg`` file under ``tests``.

7367All test functions must return ``IO ()``.

7468

69+

7570When you enter ``idris --testpkg yourmodule.ipkg``,

7671the build system creates a temporary file in a fresh environment on your machine

7772by listing the ``tests`` functions under a single ``main`` function.

7873It compiles this temporary file to an executable and then executes it.

7974

75+

8076The tests themselves are responsible for reporting their success or failure.

8177Test functions commonly use ``putStrLn`` to report test results.

8278The test framework does not impose any standards for reporting and consequently

8379does not aggregate test results.

8480

85−For example, lets take the following list of functions that are defined in a

86−module called ``NumOps`` for a sample package ``maths``:

81+

82+For example, lets take the following list of functions that are defined in a module called ``NumOps`` for a sample package ``maths``.

8783

8884.. name: Math/NumOps.idr

8985.. code-block:: idris

@@ -98,8 +94,7 @@ module called ``NumOps`` for a sample package ``maths``:

9894 triple : Num a => a -> a

9995 triple a = a + double a

10096

101−

102−A simple test module, with a qualified name of ``Test.NumOps`` can be declared as:

97+A simple test module, with a qualified name of ``Test.NumOps`` can be declared as

10398

10499.. name: Math/TestOps.idr

105100.. code-block:: idris

@@ -127,11 +122,8 @@ A simple test module, with a qualified name of ``Test.NumOps`` can be declared a

127122 testTriple = assertNotEq (triple 2) 5

128123

129124

130−The functions ``assertEq`` and ``assertNotEq`` are used to run expected passing,

131−and failing, equality tests. The actual tests are ``testDouble`` and ``testTriple``,

132−and are declared in the ``maths.ipkg`` file as follows:

133−

134−::

125+The functions ``assertEq`` and ``assertNotEq`` are used to run expected passing, and failing, equality tests.

126+The actual tests are ``testDouble`` and ``testTriple``, and are declared in the ``maths.ipkg`` file as follows::

135127

136128 package maths

137129

@@ -142,9 +134,7 @@ and are declared in the ``maths.ipkg`` file as follows:

142134 , Test.NumOps.testTriple

143135

144136

145−The testing framework can then be invoked using ``idris --testpkg maths.ipkg``:

146−

147−::

137+The testing framework can then be invoked using ``idris --testpkg maths.ipkg``::

148138

149139 > idris --testpkg maths.ipkg

150140 Type checking ./Maths/NumOps.idr

@@ -156,27 +146,25 @@ The testing framework can then be invoked using ``idris --testpkg maths.ipkg``:

156146Note how both tests have reported success by printing ``Test Passed``

157147as we arranged for with the ``assertEq`` and ``assertNoEq`` functions.

158148

159−Package Dependencies Using Atom

149+Package Dependencies Using Atom

160150===============================

161151

162−If you are using the Atom editor and have a dependency on another package,

163−corresponding to for instance ``import Lightyear`` or ``import Pruviloj``,

164−you need to let Atom know that it should be loaded. The easiest way to

165−accomplish that is with a .ipkg file. The general contents of an ipkg file

166−will be described in the next section of the tutorial, but for now here is

167−a simple recipe for this trivial case:

168−

169−- Create a folder myProject.

152+If you are using the Atom editor and have a dependency on another package,

153+corresponding to for instance ``import Lightyear`` or ``import Pruviloj``,

154+you need to let Atom know that it should be loaded. The easiest way to

155+accomplish that is with a .ipkg file. The general contents of an ipkg file

156+will be described in the next section of the tutorial, but for now here is

157+a simple recipe for this trivial case.

170158

171−- Add a file myProject.ipkg containing just a couple of lines:

159+- Create a folder myProject.

172160

173−.. code-block:: idris

161+- Add a file myProject.ipkg containing just a couple of lines:

174162

175− package myProject

163+``package myProject``

176164

177− pkgs = pruviloj, lightyear

165+``pkgs = pruviloj, lightyear``

178166

179−- In Atom, use the File menu to Open Folder myProject.

167+- In Atom, use the File menu to Open Folder myProject.

180168

181169More information

182170================

docs/tutorial/starting.rst+1−1

@@ -11,7 +11,7 @@ Before installing Idris, you will need to make sure you have all

1111of the necessary libraries and tools. You will need:

1212

1313- A fairly recent version of `GHC <https://www.haskell.org/ghc/>`_. The

14− earliest version we currently test with is 7.10.3.

14+ earliest version we currently test with is 7.6.3.

1515

1616- The *GNU Multiple Precision Arithmetic Library* (GMP) is available from MacPorts/Homebrew and all major Linux distributions.

1717

docs/tutorial/syntax.rst+7−7

@@ -34,7 +34,7 @@ rule, and the right hand side describes its expansion. The syntax rule

3434itself consists of:

3535

3636- **Keywords** — here, ``if``, ``then`` and ``else``, which must be

37− valid identifiers.

37+ valid identifiers

3838

3939- **Non-terminals** — included in square brackets, ``[test]``, ``[t]``

4040 and ``[e]`` here, which stand for arbitrary expressions. To avoid

@@ -44,9 +44,9 @@ itself consists of:

4444- **Names** — included in braces, which stand for names which may be

4545 bound on the right hand side.

4646

47−- **Symbols** — included in quotations marks, e.g. ``":="``. This can

47+- **Symbols** — included in quotations marks, e.g. ``:=``. This can

4848 also be used to include reserved words in syntax rules, such as

49− ``"let"`` or ``"in"``.

49+ ``let`` or ``in``.

5050

5151The limitations on the form of a syntax rule are that it must include

5252at least one symbol or keyword, and there must be no repeated

@@ -63,7 +63,7 @@ recursive. The following syntax extensions would therefore be valid:

6363 syntax select [x] from [t] "where" [w] = SelectWhere x t w;

6464 syntax select [x] from [t] = Select x t;

6565

66−Syntax macros can be further restricted to apply only in patterns (i.e.

66+Syntax macros can be further restricted to apply only in patterns (i.e.,

6767only on the left hand side of a pattern match clause) or only in terms

6868(i.e. everywhere but the left hand side of a pattern match clause) by

6969being marked as ``pattern`` or ``term`` syntax rules. For example, we

@@ -196,16 +196,16 @@ syntax rule, we can even go as far as:

196196 Aspects of Declarative Languages (PADL'12), Claudio Russo and

197197 Neng-Fa Zhou (Eds.). Springer-Verlag, Berlin, Heidelberg,

198198 242-257. DOI=10.1007/978-3-642-27694-1_18

199− https://dx.doi.org/10.1007/978-3-642-27694-1_18

199+ http://dx.doi.org/10.1007/978-3-642-27694-1_18

200200

201201.. [2] Edwin C. Brady. 2011. IDRIS ---: systems programming meets full

202202 dependent types. In Proceedings of the 5th ACM workshop on

203203 Programming languages meets program verification (PLPV

204204 '11). ACM, New York, NY, USA,

205205 43-54. DOI=10.1145/1929529.1929536

206− https://doi.acm.org/10.1145/1929529.1929536

206+ http://doi.acm.org/10.1145/1929529.1929536

207207

208208.. [3] Edwin Brady and Kevin Hammond. 2010. Correct-by-Construction

209209 Concurrency: Using Dependent Types to Verify Implementations of

210210 Effectful Resource Usage Protocols. Fundam. Inf. 102, 2 (April

211− 2010), 145-176. https://dl.acm.org/citation.cfm?id=1883636

211+ 2010), 145-176. http://dl.acm.org/citation.cfm?id=1883636

docs/tutorial/theorems.rst+3−3

@@ -115,8 +115,8 @@ We can do the same for the reduction behaviour of plus on successors:

115115

116116Even for trivial theorems like these, the proofs are a little tricky to

117117construct in one go. When things get even slightly more complicated, it

118−becomes too much to think about to construct proofs in this “batch

119−mode”.

118+becomes too much to think about to construct proofs in this ‘batch

119+mode’.

120120

121121Idris provides interactive editing capabilities, which can help with

122122building proofs. For more details on building proofs interactively in

@@ -383,7 +383,7 @@ will always be smaller than ``(x :: xs)``:

383383 = qsort (filter (< x) xs) ++

384384 (x :: qsort (filter (>= x) xs))

385385

386−The function ``assert_smaller``, defined in the prelude, is intended to

386+The function ``assert_smaller``, defined in the Prelude, is intended to

387387address this problem:

388388

389389.. code-block:: idris

docs/tutorial/typesfuns.rst+31−23

@@ -13,7 +13,8 @@ manipulation, and ``Ptr`` which represents foreign pointers. There are

1313also several data types declared in the library, including ``Bool``,

1414with values ``True`` and ``False``. We can declare some constants with

1515these types. Enter the following into a file ``Prims.idr`` and load it

16−into the Idris interactive environment by typing ``idris Prims.idr``:

16+into the Idris interactive environment by typing ``idris

17+Prims.idr``:

1718

1819.. code-block:: idris

1920

@@ -37,7 +38,7 @@ collection of declarations and definitions. In this example no imports

3738have been specified. However Idris programs can consist of several

3839modules and the definitions in each module each have their own

3940namespace. This is discussed further in Section

40−:ref:`sect-namespaces`. When writing Idris programs both the order in which

41+:ref:`sect-namespaces`). When writing Idris programs both the order in which

4142definitions are given and indentation are significant. Functions and

4243data types must be defined before use, incidentally each definition must

4344have a type declaration, for example see ``x : Int``, ``foo :

@@ -342,7 +343,7 @@ Vectors

342343

343344A standard example of a dependent data type is the type of “lists with

344345length”, conventionally called vectors in the dependent type

345−literature. They are available as part of the Idris library, by

346+literature. They are available as part of the Idris library, by

346347importing ``Data.Vect``, or we can declare them as follows:

347348

348349.. code-block:: idris

@@ -520,8 +521,8 @@ help document a function by making the purpose of an argument more

520521clear.

521522

522523Furthermore, ``{}`` can be used to pattern match on the left hand side, i.e.

523−``{var = pat}`` gets an implicit variable and attempts to pattern match on “pat”;

524−For example:

524+``{var = pat}`` gets an implicit variable and attempts to pattern match on "pat";

525+For example :

525526

526527.. code-block:: idris

527528

@@ -558,6 +559,7 @@ vector. For example:

558559 inVect : IsElem 5 Main.testVec

559560 inVect = There (There Here)

560561

562+

561563.. important:: Implicit Arguments and Scope

562564

563565 Within the type signature the typechecker will treat all variables

@@ -567,6 +569,7 @@ vector. For example:

567569 ``testVec``. In the example above, we have assumed that the code

568570 lives within the ``Main`` module.

569571

572+

570573If the same implicit arguments are being used a lot, it can make a

571574definition difficult to read. To avoid this problem, a ``using`` block

572575gives the types and ordering of any implicit arguments which can

@@ -579,13 +582,15 @@ appear within the block:

579582 Here : IsElem x (x :: xs)

580583 There : IsElem x xs -> IsElem x (y :: xs)

581584

585+

586+

582587Note: Declaration Order and ``mutual`` blocks

583588~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

584589

585590In general, functions and data types must be defined before use, since

586591dependent types allow functions to appear as part of types, and type

587592checking can rely on how particular functions are defined (though this

588−is only true of total functions; see Section :ref:`sect-totality`).

593+is only true of total functions; see Section :ref:`sect-totality`)).

589594However, this restriction can be relaxed by using a ``mutual`` block,

590595which allows data types and functions to be defined simultaneously:

591596

@@ -668,7 +673,7 @@ Note that several of these return ``Either``, since they may fail.

668673I/O programs will typically need to sequence actions, feeding the

669674output of one computation into the input of the next. ``IO`` is an

670675abstract type, however, so we can’t access the result of a computation

671−directly. Instead, we sequence operations with ``do`` notation:

676+directly. Instead, we sequence operations with ``do`` notation:

672677

673678.. code-block:: idris

674679

@@ -708,7 +713,7 @@ not always the best approach. Consider the following function:

708713

709714This function uses one of the ``t`` or ``e`` arguments, but not both

710715(in fact, this is used to implement the ``if...then...else`` construct

711−as we will see later). We would prefer if *only* the argument which was

716+as we will see later. We would prefer if *only* the argument which was

712717used was evaluated. To achieve this, Idris provides a ``Lazy``

713718data type, which allows evaluation to be suspended:

714719

@@ -792,7 +797,7 @@ infinite loop and cause a stack overflow.

792797To fix this we must add explicit ``Inf`` declarations to the constructor

793798parameter types, since codata will not add it to constructor parameters of a

794799**different** type from the one being defined. For example, the following

795−outputs ``1``.

800+outputs "1".

796801

797802.. code-block:: idris

798803

@@ -897,7 +902,7 @@ For more details of the functions available on ``List`` and

897902

898903- ``libs/base/Data/VectType.idr``

899904

900−Functions include filtering, appending, reversing, and so on.

905+Functions include filtering, appending, reversing, and so on.

901906

902907Aside: Anonymous functions and operator sections

903908~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

@@ -994,7 +999,7 @@ Dependent Pairs

994999---------------

9951000

9961001Dependent pairs allow the type of the second element of a pair to depend

997−on the value of the first element:

1002+on the value of the first element.

9981003

9991004.. code-block:: idris

10001005

@@ -1004,7 +1009,7 @@ on the value of the first element:

10041009Again, there is syntactic sugar for this. ``(a : A ** P)`` is the type

10051010of a pair of A and P, where the name ``a`` can occur inside ``P``.

10061011``( a ** p )`` constructs a value of this type. For example, we can

1007−pair a number with a ``Vect`` of a particular length:

1012+pair a number with a ``Vect`` of a particular length.

10081013

10091014.. code-block:: idris

10101015

@@ -1012,7 +1017,7 @@ pair a number with a ``Vect`` of a particular length:

10121017 vec = (2 ** [3, 4])

10131018

10141019If you like, you can write it out the long way, the two are precisely

1015−equivalent:

1020+equivalent.

10161021

10171022.. code-block:: idris

10181023

@@ -1065,7 +1070,7 @@ intermediate values:

10651070

10661071We will see more on ``with`` notation later.

10671072

1068−Dependent pairs are sometimes referred to as “Sigma types”.

1073+Dependent pairs are sometimes referred to as “sigma types”.

10691074

10701075Records

10711076-------

@@ -1075,7 +1080,7 @@ Records

10751080automatically generating field access and update functions. Unlike

10761081the syntax used for data structures, records in Idris follow a

10771082different syntax to that seen with Haskell. For example, we can

1078−represent a person’s name and age in a record:

1083+represent a person's name and age in a record:

10791084

10801085.. code-block:: idris

10811086

@@ -1087,11 +1092,12 @@ represent a person’s name and age in a record:

10871092 fred : Person

10881093 fred = MkPerson "Fred" "Joe" "Bloggs" 30

10891094

1095+

10901096The constructor name is provided using the ``constructor`` keyword,

10911097and the *fields* are then given which are in an indented block

10921098following the `where` keyword (here, ``firstName``, ``middleName``,

10931099``lastName``, and ``age``). You can declare multiple fields on a

1094−single line, provided that they have the same type. The field names

1100+single line, provided that they have the same type. The field names

10951101can be used to access the field values:

10961102

10971103::

@@ -1165,7 +1171,7 @@ syntax:

11651171 record { a->b->c = val } x

11661172

11671173This returns a new record, with the field accessed by the path

1168−``a->b->c`` set to ``val``. The syntax is first class, i.e. ``record {

1174+``a->b->c`` set to ``val``. The syntax is first class, i.e. ``record {

11691175a->b->c = val }`` itself has a function type. Symmetrically, the field

11701176can also be accessed with the following syntax:

11711177

@@ -1190,10 +1196,12 @@ name. For example, a pair type could be defined as follows:

11901196 fst : a

11911197 snd : b

11921198

1193−Using the ``Class`` record from earlier, the size of the class can be

1199+

1200+Using the ``class`` record from earlier, the size of the class can be

11941201restricted using a ``Vect`` and the size included in the type by parameterising

11951202the record with the size. For example:

11961203

1204+

11971205.. code-block:: idris

11981206

11991207 record SizedClass (size : Nat) where

@@ -1206,7 +1214,7 @@ function from earlier, since that would change the size of the class. A

12061214function to add a student must now specify in the type that the

12071215size of the class has been increased by one. As the size is specified

12081216using natural numbers, the new value can be incremented using the

1209−``S`` constructor:

1217+``S`` constructor.

12101218

12111219.. code-block:: idris

12121220

@@ -1319,7 +1327,7 @@ matching ``let`` and lambda bindings. It will *only* work if:

13191327- Each branch *matches* a value of the same type, and *returns* a

13201328 value of the same type.

13211329

1322−- The type of the result is “known”. i.e. the type of the expression

1330+- The type of the result is "known". i.e. the type of the expression

13231331 can be determined *without* type checking the ``case``-expression

13241332 itself.

13251333

@@ -1329,7 +1337,7 @@ Totality

13291337Idris distinguishes between *total* and *partial* functions.

13301338A total function is a function that either:

13311339

1332−+ Terminates for all possible inputs, or

1340++ Terminates for all possible inputs, or

13331341+ Produces a non-empty, finite, prefix of a possibly infinite result

13341342

13351343If a function is total, we can consider its type a precise description of what

@@ -1337,12 +1345,12 @@ that function will do. For example, if we have a function with a return

13371345type of ``String`` we know something different, depending on whether or not

13381346it's total:

13391347

1340−+ If it's total, it will return a value of type ``String`` in finite time;

1348++ If it's total, it will return a value of type ``String`` in finite time

13411349+ If it's partial, then as long as it doesn't crash or enter an infinite loop,

13421350 it will return a ``String``.

13431351

13441352Idris makes this distinction so that it knows which functions are safe to

1345−evaluate while type checking (as we've seen with :ref:`sect-fctypes`). After all,

1353+evaluate while type checking (as we've seen with :ref:`sect-fctypes`). After all,

13461354if it tries to evaluate a function during type checking which doesn't

13471355terminate, then type checking won't terminate!

13481356Therefore, only total functions will be evaluated during type checking.

docs/tutorial/views.rst+17−54

@@ -33,47 +33,24 @@ rule, inspired by views in ``Epigram`` [1]_, which takes account of

3333the fact that matching on a value in a dependently typed language can

3434affect what we know about the forms of other values. In its simplest

3535form, the ``with`` rule adds another argument to the function being

36−defined.

37−

38−We have already seen a vector filter function. This time, we define it

39−using ``with`` as follows:

36+defined, e.g. we have already seen a vector filter function, defined

37+as follows:

4038

4139.. code-block:: idris

4240

4341 filter : (a -> Bool) -> Vect n a -> (p ** Vect p a)

4442 filter p [] = ( _ ** [] )

45− filter p (x :: xs) with (filter p xs)

46− filter p (x :: xs) | ( _ ** xs' ) = if (p x) then ( _ ** x :: xs' ) else ( _ ** xs' )

47−

48−Here, the ``with`` clause allows us to deconstruct the result of

49−``filter p xs``. The view refined argument pattern ``filter p (x ::

50−xs)`` goes beneath the ``with`` clause, followed by a vertical bar

51−``|``, followed by the deconstructed intermediate result ``( _ ** xs'

52−)``. If the view refined argument pattern is unchanged from the

53−original function argument pattern, then the left side of ``|`` is

54−extraneous and may be omitted:

55−

56−.. code-block:: idris

57−

5843 filter p (x :: xs) with (filter p xs)

5944 | ( _ ** xs' ) = if (p x) then ( _ ** x :: xs' ) else ( _ ** xs' )

6045

61−``with`` clauses can also be nested:

62−

63−.. code-block:: idris

64−

65− foo : Int -> Int -> Bool

66− foo n m with (succ n)

67− foo _ m | 2 with (succ m)

68− foo _ _ | 2 | 3 = True

69− foo _ _ | 2 | _ = False

70− foo _ _ | _ = False

46+Here, the ``with`` clause allows us to deconstruct the result of

47+``filter p xs``. Effectively, it adds this value as an extra argument,

48+which we place after the vertical bar.

7149

7250If the intermediate computation itself has a dependent type, then the

7351result can affect the forms of other arguments — we can learn the form

74−of one value by testing another. In these cases, view refined argument

75−patterns must be explicit. For example, a ``Nat`` is either even or

76−odd. If it is even it will be the sum of two equal ``Nat``.

52+of one value by testing another. For example, a ``Nat`` is either even

53+or odd. If it’s even it will be the sum of two equal ``Nat``.

7754Otherwise, it is the sum of two equal ``Nat`` plus one:

7855

7956.. code-block:: idris

@@ -103,29 +80,14 @@ rule:

10380 natToBin (j + j) | Even = False :: natToBin j

10481 natToBin (S (j + j)) | Odd = True :: natToBin j

10582

106−The value of ``parity k`` affects the form of ``k``, because the

107−result of ``parity k`` depends on ``k``. So, as well as the patterns

108−for the result of the intermediate computation (``Even`` and ``Odd``)

109−right of the ``|``, we also write how the results affect the other

110−patterns left of the ``|``. That is:

111−

112−- When ``parity k`` evaluates to ``Even``, we can refine the original

113− argument ``k`` to a refined pattern ``(j + j)`` according to

114− ``Parity (n + n)`` from the ``Even`` constructor definition. So

115− ``(j + j)`` replaces ``k`` on the left side of ``|``, and the

116− ``Even`` constructor appears on the right side. The natural number

117− ``j`` in the refined pattern can be used on the right side of the

118− ``=`` sign.

119−

120−- Otherwise, when ``parity k`` evaluates to ``Odd``, the original

121− argument ``k`` is refined to ``S (j + j)`` according to ``Parity (S

122− (n + n))`` from the ``Odd`` constructor definition, and ``Odd`` now

123− appears on the right side of ``|``, again with the natural number

124− ``j`` used on the right side of the ``=`` sign.

125−

126−Note that there is a function in the patterns (``+``) and repeated

127−occurrences of ``j`` - this is allowed because another argument has

128−determined the form of these patterns.

83+The value of the result of ``parity k`` affects the form of ``k``,

84+because the result of ``parity k`` depends on ``k``. So, as well as

85+the patterns for the result of the intermediate computation (``Even``

86+and ``odd``) right of the ``|``, we also write how the results

87+affect the other patterns left of the ``|``. Note that there is

88+a function in the patterns (``+``) and repeated occurrences of

89+``j``—this is allowed because another argument has determined the form

90+of these patterns.

12991

13092We will return to this function in the next section :ref:`sect-parity` to

13193complete the definition of ``parity``.

@@ -153,4 +115,5 @@ generated by the pattern match will be in scope and named ``p``. For example:

153115

154116.. [1] Conor McBride and James McKinna. 2004. The view from the

155117 left. J. Funct. Program. 14, 1 (January 2004),

156− 69-111. https://doi.org/10.1017/S0956796803004829

118+ 69-111. DOI=10.1017/S0956796803004829

119+ http://dx.doi.org/10.1017/S0956796803004829ñ

idris-tutorial.pdf

Binary file not shown.

idris.cabal+60−120

@@ -1,12 +1,10 @@

1−Cabal-Version: 2.4

21Name: idris

3−Version: 1.3.2

4−License: BSD-3-Clause

2+Version: 1.1.1

3+License: BSD3

54License-file: LICENSE

65Author: Edwin Brady

76Maintainer: Edwin Brady <eb@cs.st-andrews.ac.uk>

8−Homepage: https://www.idris-lang.org/

9−Bug-reports: https://github.com/idris-lang/Idris-dev/issues

7+Homepage: http://www.idris-lang.org/

108

119Stability: Beta

1210Category: Compilers/Interpreters, Dependent Types

@@ -17,7 +15,7 @@ Description: Idris is a general purpose language with full dependent types.

1715 meaning that some aspects of a program's behaviour can be

1816 specified precisely in the type. The language is closely

1917 related to Epigram and Agda. There is a tutorial at

20− <https://www.idris-lang.org/documentation>.

18+ <http://www.idris-lang.org/documentation>.

2119 Features include:

2220 .

2321 * Full, first class, dependent types with dependent pattern matching

@@ -42,25 +40,42 @@ Description: Idris is a general purpose language with full dependent types.

4240 .

4341 * Hugs style interactive environment

4442

43+Cabal-Version: >= 1.18

44+

4545Build-type: Custom

4646

4747Tested-With: GHC == 7.10.3, GHC == 8.0.1

4848

49−-- NOTE: due to https://github.com/haskell/cabal/issues/6125 the use of ** is

50−-- heavily discouraged.

5149Data-files: idrisdoc/styles.css

52− jsrts/jsbn/*.js

53− jsrts/*.js

50+ jsrts/jsbn/jsbn-browser.js

51+ jsrts/jsbn/jsbn-node.js

52+ jsrts/Runtime-common.js

53+ jsrts/Runtime-javascript.js

54+ jsrts/Runtime-node.js

5455 jsrts/jsbn/LICENSE

55− rts/Makefile

56− rts/*.c

57− rts/seL4/*.c

58− rts/arduino/*.c

59− rts/windows/*.c

60− rts/windows/*.h

61− rts/*.h

62− rts/seL4/CMakeLists.txt

63− rts/seL4/README.md

56+ rts/arduino/idris_main.c

57+ rts/idris_bitstring.c

58+ rts/idris_bitstring.h

59+ rts/idris_gc.c

60+ rts/idris_gc.h

61+ rts/idris_gmp.c

62+ rts/idris_gmp.h

63+ rts/idris_heap.c

64+ rts/idris_heap.h

65+ rts/idris_main.c

66+ rts/idris_net.c

67+ rts/idris_net.h

68+ rts/idris_opts.c

69+ rts/idris_opts.h

70+ rts/idris_rts.c

71+ rts/idris_rts.h

72+ rts/idris_stats.c

73+ rts/idris_stats.h

74+ rts/idris_stdfgn.c

75+ rts/idris_stdfgn.h

76+ rts/mini-gmp.c

77+ rts/mini-gmp.h

78+ rts/libtest.c

6479

6580Extra-doc-files:

6681 CHANGELOG.md

@@ -70,75 +85,13 @@ Extra-doc-files:

7085 README.md

7186 RELEASE-CHECKS.md

7287 idris-tutorial.pdf

73− man/idris.1

7488 samples/effects/*.idr

7589 samples/misc/*.idr

76− samples/tutorial/*.idr

77− samples/ST/*.idr

78− samples/ST/Graphics/*.idr

79− samples/ST/Net/*.idr

8090 samples/misc/*.lidr

91+ samples/tutorial/*.idr

8192

8293-- extra-source-files is generated by Setup.hs using `git --ls-files`.

8394Extra-source-files:

84− Makefile

85− config.mk

86− custom.mk-alldeps

87− mkpkg.sh

88− stack-shell.nix

89− stack.yaml

90− stylize.sh

91− win-release.sh

92−

93− benchmarks/*.pl

94− benchmarks/fasta/*.idr

95− benchmarks/fasta/*.ipkg

96− benchmarks/pidigits/*.idr

97− benchmarks/pidigits/*.ipkg

98− benchmarks/quasigroups/*.idr

99− benchmarks/quasigroups/*.ipkg

100− benchmarks/trivial/*.idr

101− benchmarks/trivial/*.ipkg

102− benchmarks/quasigroups/board

103−

104− icons/*.png

105− icons/*.ico

106− icons/*.rc

107− icons/*.svg

108− icons/*.xml

109−

110− libs/**/*.idr

111− libs/**/*.ipkg

112− libs/**/*.txt

113− libs/Makefile

114− libs/base/Makefile

115− libs/contrib/Makefile

116− libs/effects/Makefile

117− libs/prelude/Makefile

118− libs/pruviloj/Makefile

119−

120− scripts/generate-multi-ghc-travis-template

121− scripts/runidris

122− scripts/runidris-node

123−

124− src/.ghci

125−

126− test/*.md

127− test/*.hs

128− test/**/*.idr

129− test/**/*.lidr

130− test/**/*.ipkg

131− test/**/*.out

132− test/**/*.sh

133− test/**/*.c

134− test/**/*.h

135− test/**/*.in

136− test/**/*.txt

137− test/**/*.js

138− test/base001/Makefile

139− test/ffi004/theOtherType

140− test/ffi004/theType

141− test/scripts/timeout

14295

14396source-repository head

14497 type: git

@@ -146,7 +99,7 @@ source-repository head

14699

147100custom-setup

148101 setup-depends:

149− Cabal >= 2.4 && < 3.1,

102+ Cabal >= 1.10 && <2.1,

150103 base >= 4 && <5,

151104 directory,

152105 filepath,

@@ -253,11 +206,10 @@ Library

253206 , Idris.ModeCommon

254207 , Idris.Options

255208 , Idris.Parser

256− , Idris.Parser.Data

257− , Idris.Parser.Expr

258209 , Idris.Parser.Helpers

259210 , Idris.Parser.Ops

260− , Idris.Parser.Stack

211+ , Idris.Parser.Expr

212+ , Idris.Parser.Data

261213 , Idris.PartialEval

262214 , Idris.Primitives

263215 , Idris.ProofSearch

@@ -297,7 +249,6 @@ Library

297249

298250 , Idris.Package

299251 , Idris.Package.Common

300− , Idris.Package.Parser

301252

302253 , Util.DynamicLinker

303254 , Util.ScreenSize

@@ -307,63 +258,56 @@ Library

307258 Util.Pretty

308259 , Util.Net

309260

261+ , Idris.Package.Parser

262+

263+ -- Auto Generated

310264 , Paths_idris

311265 , Version_idris

312266 , Tools_idris

313− , BuildFlags_idris

314−

315− -- Auto Generated

316− Autogen-modules: Paths_idris

317− , Version_idris

318− , Tools_idris

319− , BuildFlags_idris

320267

321268 Build-depends: base >=4 && <5

322− , aeson >= 0.6 && < 1.5

269+ , aeson >= 0.6 && < 1.3

323270 , annotated-wl-pprint >= 0.7 && < 0.8

324− , ansi-terminal < 0.11

271+ , ansi-terminal < 0.7

325272 , ansi-wl-pprint < 0.7

326273 , array >= 0.4.0.1 && < 0.6

327274 , base64-bytestring < 1.1

328275 , binary >= 0.8.4.1 && < 0.9

329276 , blaze-html >= 0.6.1.3 && < 0.10

330− , blaze-markup >= 0.5.2.1 && < 0.10

277+ , blaze-markup >= 0.5.2.1 && < 0.9

331278 , bytestring < 0.11

332− , cheapskate >= 0.1.1.2 && < 0.2

333− , code-page >= 0.1 && < 0.3

334− , containers >= 0.5 && < 0.7

279+ , cheapskate >= 0.1.1 && < 0.2

280+ , code-page >= 0.1 && < 0.2

281+ , containers >= 0.5 && < 0.6

335282 , deepseq < 1.5

336283 , directory >= 1.2.2.0 && < 1.2.3.0 || > 1.2.3.0

337284 , filepath < 1.5

338− , fingertree >= 0.1.4.1 && < 0.2

285+ , fingertree >= 0.1 && < 0.2

339286 , haskeline >= 0.7 && < 0.8

340287 , ieee754 >= 0.7 && < 0.9

341− , megaparsec >= 7.0.4 && < 9

342288 , mtl >= 2.1 && < 2.3

343− , network >= 2.7 && < 3.1.2

344− , optparse-applicative >= 0.13 && < 0.16

345− , parser-combinators >= 1.0.0

289+ , network < 2.7

290+ , optparse-applicative >= 0.13 && < 0.15

291+ , parsers >= 0.9 && < 0.13

346292 , pretty < 1.2

347293 , process < 1.7

348294 , regex-tdfa >= 1.2

349295 , safe >= 0.3.9

350296 , split < 0.3

351297 , terminal-size < 0.4

352− , text >=1.2.1.0 && < 1.4

353− , time >= 1.4 && < 2.0

354− , transformers >= 0.5 && < 0.6

298+ , text >=1.2.1.0 && < 1.3

299+ , time >= 1.4 && < 1.9

300+ , transformers < 0.6

301+ , transformers-compat >= 0.3

302+ , trifecta >= 1.6 && < 1.8

355303 , uniplate >=1.6 && < 1.7

356304 , unordered-containers < 0.3

357305 , utf8-string < 1.1

358306 , vector < 0.13

359307 , vector-binary-instances < 0.3

360− , zip-archive > 0.2.3.5 && < 0.5

361− , fsnotify >= 0.2 && < 0.4

362− , async < 2.3

363−

364− if !impl(ghc >= 8.0)

365− Build-Depends: semigroups == 0.18.*

366− , fail == 4.9.0.*

308+ , zip-archive > 0.2.3.5 && < 0.4

309+ , fsnotify >= 0.2 && < 2.2

310+ , async < 2.2

367311

368312 Default-Language: Haskell2010

369313 ghc-prof-options: -auto-all -caf-all

@@ -382,7 +326,6 @@ Library

382326 cpp-options: -DIDRIS_GMP

383327 if flag(freestanding)

384328 other-modules: Target_idris

385− autogen-modules: Target_idris

386329 cpp-options: -DFREESTANDING

387330 if flag(CI)

388331 ghc-options: -Werror

@@ -416,7 +359,7 @@ Test-suite regression-and-feature-tests

416359 , filepath

417360 , directory

418361 , haskeline >= 0.7

419− , optparse-applicative >= 0.13 && < 0.16

362+ , optparse-applicative >= 0.13 && < 0.15

420363 , tagged

421364 , tasty >= 0.8

422365 , tasty-golden >= 2.0

@@ -431,7 +374,6 @@ Test-suite regression-and-feature-tests

431374

432375Executable idris-codegen-c

433376 Main-is: Main.hs

434− autogen-modules: Paths_idris

435377 other-modules: Paths_idris

436378 hs-source-dirs: codegen/idris-codegen-c

437379

@@ -447,7 +389,6 @@ Executable idris-codegen-c

447389

448390Executable idris-codegen-javascript

449391 Main-is: Main.hs

450− autogen-modules: Paths_idris

451392 other-modules: Paths_idris

452393 hs-source-dirs: codegen/idris-codegen-javascript

453394

@@ -463,7 +404,6 @@ Executable idris-codegen-javascript

463404

464405Executable idris-codegen-node

465406 Main-is: Main.hs

466− autogen-modules: Paths_idris

467407 other-modules: Paths_idris

468408 hs-source-dirs: codegen/idris-codegen-node

469409

jsrts/Runtime-javascript.js+2−6

@@ -7,9 +7,5 @@ $JSRTS.prim_systemInfo = function (index) {

77 }

88 return "";

99};

10−

11−$JSRTS.prim_writeStr = function (x) { return console.log(x) };

12−

13−$JSRTS.prim_readStr = function () { return prompt('Prelude.getLine') };

14−

15−$JSRTS.die = function (message) { throw new Error(message) };

10+$JSRTS.prim_writeStr = function (x) { return console.log(x) }

11+$JSRTS.prim_readStr = function () { return prompt('Prelude.getLine') };

jsrts/Runtime-node.js+4−13

@@ -1,7 +1,5 @@

11$JSRTS.os = require('os');

2−

32$JSRTS.fs = require('fs');

4−

53$JSRTS.prim_systemInfo = function (index) {

64 switch (index) {

75 case 0:

@@ -11,12 +9,10 @@ $JSRTS.prim_systemInfo = function (index) {

119 }

1210 return "";

1311};

14−

15−$JSRTS.prim_writeStr = function (x) { return process.stdout.write(x) };

16−

12+$JSRTS.prim_writeStr = function (x) { return process.stdout.write(x) }

1713$JSRTS.prim_readStr = function () {

1814 var ret = '';

19− var b = Buffer.alloc(1024);

15+ var b = new Buffer(1024);

2016 var i = 0;

2117 while (true) {

2218 $JSRTS.fs.readSync(0, b, i, 1)

@@ -26,15 +22,10 @@ $JSRTS.prim_readStr = function () {

2622 }

2723 i++;

2824 if (i == b.length) {

29− var nb = Buffer.alloc(b.length * 2);

25+ var nb = new Buffer(b.length * 2);

3026 b.copy(nb)

3127 b = nb;

3228 }

3329 }

3430 return ret;

35−};

36−

37−$JSRTS.die = function (message) {

38− console.error(message);

39− process.exit(-1);

40−};

31+};

libs/base/Control/Catchable.idr−1

@@ -7,7 +7,6 @@ import Control.Monad.RWS

77import Control.Monad.Trans

88

99%access public export

10−%default total

1110

1211interface Catchable (m : Type -> Type) t | m where

1312 throw : t -> m a

libs/base/Control/Category.idr+1−1

@@ -4,7 +4,7 @@ import Data.Morphisms

44

55%access public export

66

7−interface Category (cat : k -> k -> Type) where

7+interface Category (cat : Type -> Type -> Type) where

88 id : cat a a

99 (.) : cat b c -> cat a b -> cat a c

1010

libs/base/Control/Isomorphism.idr+29−32

@@ -8,42 +8,35 @@ import Control.Category

88%access public export

99

1010||| An isomorphism between two types

11−record Iso a b where

12− constructor MkIso

13− to : a -> b

14− from : b -> a

15− toFrom : (y : b) -> to (from y) = y

16− fromTo : (x : a) -> from (to x) = x

11+data Iso : Type -> Type -> Type where

12+ MkIso : (to : a -> b) ->

13+ (from : b -> a) ->

14+ (toFrom : (y : b) -> to (from y) = y) ->

15+ (fromTo : (x : a) -> from (to x) = x) ->

16+ Iso a b

1717

1818-- Isomorphism properties

1919

20−||| Isomorphism is reflexive

20+||| Isomorphism is Reflexive

2121isoRefl : Iso a a

22−isoRefl = MkIso id id (\_ => Refl) (\_ => Refl)

22+isoRefl = MkIso id id (\x => Refl) (\x => Refl)

2323

2424||| Isomorphism is transitive

2525isoTrans : Iso a b -> Iso b c -> Iso a c

2626isoTrans (MkIso to from toFrom fromTo) (MkIso to' from' toFrom' fromTo') =

27− MkIso xto xfrom xtoFrom xfromTo where

28− xto : a -> c

29− xto = to' . to

30− xfrom : c -> a

31− xfrom = from . from'

32− xtoFrom : (z : c) -> xto (xfrom z) = z

33− xtoFrom z = rewrite toFrom $ from' z in toFrom' z

34− xfromTo : (x : a) -> xfrom (xto x) = x

35− xfromTo x = rewrite fromTo' (to x) in fromTo x

27+ MkIso (\x => to' (to x))

28+ (\y => from (from' y))

29+ (\y => (to' (to (from (from' y)))) ={ cong (toFrom (from' y)) }=

30+ (to' (from' y)) ={ toFrom' y }=

31+ y QED)

32+ (\x => (from (from' (to' (to x)))) ={ cong (fromTo' (to x)) }=

33+ (from (to x)) ={ fromTo x }=

34+ x QED)

3635

3736Category Iso where

3837 id = isoRefl

3938 (.) = flip isoTrans

4039

41−Semigroup (Iso a a) where

42− (<+>) = isoTrans

43−

44−Monoid (Iso a a) where

45− neutral = isoRefl

46−

4740||| Isomorphism is symmetric

4841isoSym : Iso a b -> Iso b a

4942isoSym (MkIso to from toFrom fromTo) = MkIso from to fromTo toFrom

@@ -100,7 +93,8 @@ eitherBotRight = isoTrans eitherComm eitherBotLeft

10093

10194||| Isomorphism is a congruence with regards to disjunction

10295eitherCong : Iso a a' -> Iso b b' -> Iso (Either a b) (Either a' b')

103−eitherCong (MkIso to from toFrom fromTo)

96+eitherCong {a = a} {a' = a'} {b = b} {b' = b'}

97+ (MkIso to from toFrom fromTo)

10498 (MkIso to' from' toFrom' fromTo') =

10599 MkIso (eitherMap to to') (eitherMap from from') ok1 ok2

106100 where eitherMap : (c -> c') -> (d -> d') -> Either c d -> Either c' d'

@@ -143,7 +137,9 @@ pairAssoc = MkIso to from ok1 ok2

143137

144138||| Conjunction with truth is a no-op

145139pairUnitRight : Iso (a, ()) a

146−pairUnitRight = MkIso fst (\x => (x, ())) (\_ => Refl) (\(_, ()) => Refl)

140+pairUnitRight = MkIso fst (\x => (x, ())) (\x => Refl) ok

141+ where ok : (x : (a, ())) -> (fst x, ()) = x

142+ ok (x, ()) = Refl

147143

148144||| Conjunction with truth is a no-op

149145pairUnitLeft : Iso ((), a) a

@@ -159,7 +155,8 @@ pairBotRight = isoTrans pairComm pairBotLeft

159155

160156||| Isomorphism is a congruence with regards to conjunction

161157pairCong : Iso a a' -> Iso b b' -> Iso (a, b) (a', b')

162−pairCong (MkIso to from toFrom fromTo)

158+pairCong {a = a} {a' = a'} {b = b} {b' = b'}

159+ (MkIso to from toFrom fromTo)

163160 (MkIso to' from' toFrom' fromTo') =

164161 MkIso to'' from'' iso1 iso2

165162 where to'' : (a, b) -> (a', b')

@@ -202,7 +199,7 @@ distribLeft = MkIso to from toFrom fromTo

202199

203200||| Products distribute over sums

204201distribRight : Iso (a, Either b c) (Either (a, b) (a, c))

205−distribRight = (pairComm `isoTrans` distribLeft) `isoTrans` eitherCong pairComm pairComm

202+distribRight {a} {b} {c} = (pairComm `isoTrans` distribLeft) `isoTrans` eitherCong pairComm pairComm

206203

207204

208205-- Enable preorder reasoning syntax over isomorphisms

@@ -219,7 +216,7 @@ step a iso1 iso2 = isoTrans iso1 iso2

219216-- Isomorphisms over Maybe

220217||| Isomorphism is a congruence with respect to Maybe

221218maybeCong : Iso a b -> Iso (Maybe a) (Maybe b)

222−maybeCong (MkIso to from toFrom fromTo) = MkIso (map to) (map from) ok1 ok2

219+maybeCong {a} {b} (MkIso to from toFrom fromTo) = MkIso (map to) (map from) ok1 ok2

223220 where ok1 : (y : Maybe b) -> map to (map from y) = y

224221 ok1 Nothing = Refl

225222 ok1 (Just x) = (Just (to (from x))) ={ cong (toFrom x) }= (Just x) QED

@@ -250,7 +247,7 @@ maybeVoidUnit = (Maybe Void) ={ maybeEither }=

250247 () QED

251248

252249eitherMaybeLeftMaybe : Iso (Either (Maybe a) b) (Maybe (Either a b))

253−eitherMaybeLeftMaybe =

250+eitherMaybeLeftMaybe {a} {b} =

254251 (Either (Maybe a) b) ={ eitherCongLeft maybeEither }=

255252 (Either (Either a ()) b) ={ eitherAssoc }=

256253 (Either a (Either () b)) ={ eitherCongRight eitherComm }=

@@ -260,7 +257,7 @@ eitherMaybeLeftMaybe =

260257

261258

262259eitherMaybeRightMaybe : Iso (Either a (Maybe b)) (Maybe (Either a b))

263−eitherMaybeRightMaybe =

260+eitherMaybeRightMaybe {a} {b} =

264261 (Either a (Maybe b)) ={ eitherComm }=

265262 (Either (Maybe b) a) ={ eitherMaybeLeftMaybe }=

266263 (Maybe (Either b a)) ={ maybeCong eitherComm }=

@@ -285,8 +282,8 @@ maybeIsoS = MkIso forth back fb bf

285282 fb (FS x) = Refl

286283

287284finZeroBot : Iso (Fin 0) Void

288−finZeroBot = MkIso (void . uninhabited)

289− void

285+finZeroBot = MkIso (\x => void (uninhabited x))

286+ (\x => void x)

290287 (\x => void x)

291288 (\x => void (uninhabited x))

292289

libs/base/Control/Monad/Identity.idr+4−23

@@ -6,32 +6,13 @@ public export record Identity (a : Type) where

66 constructor Id

77 runIdentity : a

88

9−Functor Identity where

9+implementation Functor Identity where

1010 map fn (Id a) = Id (fn a)

1111

12−Applicative Identity where

12+implementation Applicative Identity where

1313 pure x = Id x

14+

1415 (Id f) <*> (Id g) = Id (f g)

1516

16−Monad Identity where

17+implementation Monad Identity where

1718 (Id x) >>= k = k x

18−

19−Show a => Show (Identity a) where

20− showPrec d (Id x) = showCon d "Id" $ showArg x

21−

22−Eq a => Eq (Identity a) where

23− (Id x) == (Id y) = x == y

24−

25−Ord a => Ord (Identity a) where

26− compare (Id x) (Id y) = compare x y

27−

28−Enum a => Enum (Identity a) where

29− toNat (Id x) = toNat x

30− fromNat n = Id $ fromNat n

31− pred (Id n) = Id $ pred n

32−

33−(Semigroup a) => Semigroup (Identity a) where

34− (<+>) x y = Id (runIdentity x <+> runIdentity y)

35−

36−(Monoid a) => Monoid (Identity a) where

37− neutral = Id (neutral)

libs/base/Control/Monad/Writer.idr−3

@@ -64,6 +64,3 @@ censor f m = pass $ do a <- m

6464||| The Writer monad itself. See the MonadWriter interface

6565Writer : Type -> Type -> Type

6666Writer w a = WriterT w Identity a

67−

68−runWriter : Writer w a -> (a, w)

69−runWriter = runIdentity . runWriterT

libs/base/Data/Bits.idr−8

@@ -501,13 +501,5 @@ bitsToStr x = pack (helper last x)

501501 helper FZ _ = []

502502 helper (FS x) b = assert_total $ (if getBit x b then '1' else '0') :: helper (weaken x) b

503503

504−bitsToHexStr : %static {n : Nat} -> Bits n -> String

505−bitsToHexStr {n} (MkBits b) with (nextBytes n)

506− | Z = b8ToHexString b

507− | S Z = b16ToHexString b

508− | S (S Z) = b32ToHexString b

509− | S (S (S Z)) = b64ToHexString b

510− | _ = assert_unreachable

511−

512504implementation Show (Bits n) where

513505 show = bitsToStr

libs/base/Data/Buffer.idr+7−58

@@ -2,11 +2,7 @@ module Data.Buffer

22

33%include C "idris_buffer.h"

44

5−||| A buffer is a pointer to a sized, unstructured, mutable chunk of memory.

6−||| There are primitive operations for getting and setting bytes, ints (32 bit)

7−||| and strings at a location in the buffer. These operations silently fail

8−||| if the location is out of bounds, so bounds checking should be done in

9−||| advance.

5+||| A buffer is a pointer to a sized, unstructured, mutable chunk of memory

106export

117record Buffer where

128 constructor MkBuffer

@@ -21,12 +17,11 @@ record Buffer where

2117||| fails

2218export

2319newBuffer : (size : Int) -> IO (Maybe Buffer)

24−newBuffer size = do vm <- getMyVM

25− bptr <- foreign FFI_C "idris_newBuffer" (Ptr -> Int -> IO ManagedPtr)

26− vm size

27− bad <- nullManagedPtr bptr

20+newBuffer size = do bptr <- foreign FFI_C "idris_newBuffer" (Int -> IO Ptr)

21+ size

22+ bad <- nullPtr bptr

2823 if bad then pure Nothing

29− else pure (Just (MkBuffer bptr size 0))

24+ else pure (Just (MkBuffer (prim__registerPtr bptr (size + 8)) size 0))

3025

3126||| Reset the 'next location' pointer of the buffer to 0.

3227||| The 'next location' pointer gives the location for the next file read/write

@@ -52,24 +47,6 @@ setByte b loc val

5247 = foreign FFI_C "idris_setBufferByte" (ManagedPtr -> Int -> Bits8 -> IO ())

5348 (rawdata b) loc val

5449

55−||| Set the int at position 'loc' to 'val'.

56−||| Uses 4 bytes (assumes up to 32 bit Int).

57−||| Does nothing if the location is outside the bounds of the buffer

58−export

59−setInt : Buffer -> (loc : Int) -> (val : Int) -> IO ()

60−setInt b loc val

61− = foreign FFI_C "idris_setBufferInt" (ManagedPtr -> Int -> Int -> IO ())

62− (rawdata b) loc val

63−

64−||| Set the double at position 'loc' to 'val'.

65−||| Uses 8 bytes (assumes 64 bit double).

66−||| Does nothing if the location is outside the bounds of the buffer

67−export

68−setDouble : Buffer -> (loc : Int) -> (val : Double) -> IO ()

69−setDouble b loc val

70− = foreign FFI_C "idris_setBufferDouble" (ManagedPtr -> Int -> Double -> IO ())

71− (rawdata b) loc val

72−

7350||| Set the byte at position 'loc' to 'val'.

7451||| Does nothing if the location is out of bounds of the buffer, or the string

7552||| is too long for the location

@@ -89,41 +66,13 @@ copyData src start len dest loc

8966 = foreign FFI_C "idris_copyBuffer" (ManagedPtr -> Int -> Int -> ManagedPtr -> Int -> IO ())

9067 (rawdata src) start len (rawdata dest) loc

9168

92−||| Return the value at the given location in the buffer.

93−||| Returns 0 if out of bounds.

69+||| Return the value at the given location in the buffer

9470export

9571getByte : Buffer -> (loc : Int) -> IO Bits8

9672getByte b loc

9773 = foreign FFI_C "idris_getBufferByte" (ManagedPtr -> Int -> IO Bits8)

9874 (rawdata b) loc

9975

100−||| Return the value at the given location in the buffer, assuming 4

101−||| bytes to store the Int.

102−||| Returns 0 if out of bounds.

103−export

104−getInt : Buffer -> (loc : Int) -> IO Int

105−getInt b loc

106− = foreign FFI_C "idris_getBufferInt" (ManagedPtr -> Int -> IO Int)

107− (rawdata b) loc

108−

109−||| Return the value at the given location in the buffer, assuming 8

110−||| bytes to store the Double.

111−||| Returns 0 if out of bounds.

112−export

113−getDouble : Buffer -> (loc : Int) -> IO Double

114−getDouble b loc

115− = foreign FFI_C "idris_getBufferDouble" (ManagedPtr -> Int -> IO Double)

116− (rawdata b) loc

117−

118−||| Return the string at the given location in the buffer, with the given

119−||| length. Returns "" if out of bounds.

120−export

121−getString : Buffer -> (loc : Int) -> (len : Int) -> IO String

122−getString b loc len

123− = do MkRaw str <- foreign FFI_C "idris_getBufferString" (ManagedPtr -> Int -> Int -> IO (Raw String))

124− (rawdata b) loc len

125− pure str

126−

12776||| Read 'maxbytes' into the buffer from a file, returning a new

12877||| buffer with the 'locaton' pointer moved along

12978export

@@ -134,7 +83,7 @@ readBufferFromFile (FHandle h) buf max

13483 pure (record { location $= (+numread) } buf)

13584

13685||| Write 'maxbytes' from the buffer from a file, returning a new

137−||| buffer with the 'location' pointer moved along

86+||| buffer with the 'locaton' pointer moved along

13887export

13988writeBufferToFile : File -> Buffer -> (maxbytes : Int) -> IO Buffer

14089writeBufferToFile (FHandle h) buf max

libs/base/Data/Complex.idr+21−11

@@ -27,6 +27,18 @@ implementation Show a => Show (Complex a) where

2727 plus_i = User 6

2828

2929

30+-- when we have an interface 'Fractional' (which contains Double),

31+-- we can do:

32+{-

33+implementation Fractional a => Fractional (Complex a) where

34+ (/) (a:+b) (c:+d) = let

35+ real = (a*c+b*d)/(c*c+d*d)

36+ imag = (b*c-a*d)/(c*c+d*d)

37+ in

38+ (real:+imag)

39+-}

40+

41+

3042

3143------------------------------ Polarform

3244

@@ -58,18 +70,16 @@ implementation Neg a => Num (Complex a) where

5870 (*) (a:+b) (c:+d) = ((a*c-b*d):+(b*c+a*d))

5971 fromInteger x = (fromInteger x:+0)

6072

61−implementation Neg a => Neg (Complex a) where

73+-- We can't do "implementation Neg a => Neg (Complex a)" because

74+-- we need "abs" which needs "magnitude" which needs "sqrt" which needs Double

75+implementation Neg (Complex Double) where

6276 negate = map negate

6377 (-) (a:+b) (c:+d) = ((a-c):+(b-d))

64−

65−-- Specific to Double because `abs` needs `magnitude` which needs `sqrt` which

66−-- operates on Double.

67−implementation Abs (Complex Double) where

6878 abs (a:+b) = (magnitude (a:+b):+0)

6979

70−implementation (Neg a, Fractional a) => Fractional (Complex a) where

71− (/) (a:+b) (c:+d) = let

72− real = (a*c+b*d)/(c*c+d*d)

73− imag = (b*c-a*d)/(c*c+d*d)

74− in

75− (real:+imag)

80+-- As soon as abs moves out of Neg (issue #3500), the following would become a

81+-- valid instance:

82+

83+-- implementation Neg a => Neg (Complex a) where

84+-- negate = map negate

85+-- (-) (a:+b) (c:+d) = ((a-c):+(b-d))

libs/base/Data/Fin.idr+1−10

@@ -65,11 +65,6 @@ weakenN : (n : Nat) -> Fin m -> Fin (m + n)

6565weakenN n FZ = FZ

6666weakenN n (FS f) = FS (weakenN n f)

6767

68−||| Weaken the bound on a Fin using an inequality proof

69−weakenLTE : LTE n m -> Fin n -> Fin m

70−weakenLTE (LTESucc p) FZ = FZ

71−weakenLTE (LTESucc p) (FS f) = FS $ weakenLTE p f

72−

7368||| Attempt to tighten the bound on a Fin.

7469||| Return `Left` if the bound could not be tightened, or `Right` if it could.

7570strengthen : Fin (S n) -> Either (Fin (S n)) (Fin n)

@@ -106,10 +101,6 @@ implementation MinBound (Fin (S n)) where

106101implementation MaxBound (Fin (S n)) where

107102 maxBound = last

108103

109−||| Add two Fins

110−addFin : (x : Fin n) -> (y : Fin m) -> Fin (finToNat x + m)

111−addFin FZ y = y

112−addFin (FS x) y = FS $ addFin x y

113104

114105-- Construct a Fin from an integer literal which must fit in the given Fin

115106

@@ -144,7 +135,7 @@ restrict n val = let val' = assert_total (abs (mod val (cast (S n)))) in

144135 -- reasoning about primitives, so we need the

145136 -- 'believe_me'. It's fine because val' must be

146137 -- in the right range

147− fromInteger {n = S n} val'

138+ fromInteger val'

148139 {prf = believe_me {a=IsJust (Just val')} ItIsJust}

149140

150141%language ErrorReflection

libs/base/Data/IORef.idr−7

@@ -1,8 +1,5 @@

11module Data.IORef

22

3−%default total

4−

5−||| A mutable variable in the IO monad.

63export

74data IORef a = MkIORef a

85

@@ -40,22 +37,18 @@ implementation HasReference FFI_JS where

4037 writeIORef' (MkIORef ref) val =

4138 foreign FFI_JS "%0.val = %1" (Ptr -> Ptr -> JS_IO ()) (believe_me ref) (believe_me val)

4239

43−||| Build a new IORef

4440export

4541newIORef : a -> IO (IORef a)

4642newIORef = newIORef'

4743

48−||| read the value of an IORef

4944export

5045readIORef : IORef a -> IO a

5146readIORef = readIORef'

5247

53−||| write the value of an IORef

5448export

5549writeIORef : IORef a -> a -> IO ()

5650writeIORef = writeIORef'

5751

58−||| mutate the contents of an IORef

5952export

6053modifyIORef : IORef a -> (a -> a) -> IO ()

6154modifyIORef = modifyIORef'

libs/base/Data/List.idr+9−24

@@ -15,31 +15,10 @@ data Elem : a -> List a -> Type where

1515 ||| Example: `the (Elem "b" ["a", "b"]) (There Here)`

1616 There : (later : Elem x xs) -> Elem x (y :: xs)

1717

18−||| `Here` will never equal `There`.

19−hereIsNotThere : Not (Here = There _)

20−hereIsNotThere Refl impossible

21−

22−||| If the tails don't match, neither will references to them.

23−tailMismatch : Not (this = that) -> Not (There this = There that)

24−tailMismatch f Refl = f Refl

25−

26−implementation DecEq (Elem x xs) where

27− decEq Here Here = Yes Refl

28− decEq Here (There later) = No hereIsNotThere

29− decEq (There later) Here = No (hereIsNotThere . sym)

30− decEq (There this) (There that) with (decEq this that)

31− decEq (There this) (There this) | Yes Refl = Yes Refl

32− decEq (There this) (There that) | No contra = No (tailMismatch contra)

33−

3418implementation Uninhabited (Elem {a} x []) where

3519 uninhabited Here impossible

3620 uninhabited (There p) impossible

3721

38−||| An item not in the head and not in the tail is not in the List at all

39−neitherHereNorThere : {x, y : a} -> {xs : List a} -> Not (x = y) -> Not (Elem x xs) -> Not (Elem x (y :: xs))

40−neitherHereNorThere xneqy xninxs Here = xneqy Refl

41−neitherHereNorThere xneqy xninxs (There xinxs) = xninxs xinxs

42−

4322||| Is the given element a member of the given list.

4423|||

4524||| @x The element to be tested.

@@ -48,9 +27,15 @@ isElem : DecEq a => (x : a) -> (xs : List a) -> Dec (Elem x xs)

4827isElem x [] = No absurd

4928isElem x (y :: xs) with (decEq x y)

5029 isElem x (x :: xs) | (Yes Refl) = Yes Here

51− isElem x (y :: xs) | (No xneqy) with (isElem x xs)

52− isElem x (y :: xs) | (No xneqy) | (Yes xinxs) = Yes (There xinxs)

53− isElem x (y :: xs) | (No xneqy) | (No xninxs) = No (neitherHereNorThere xneqy xninxs)

30+ isElem x (y :: xs) | (No contra) with (isElem x xs)

31+ isElem x (y :: xs) | (No contra) | (Yes prf) = Yes (There prf)

32+ isElem x (y :: xs) | (No contra) | (No f) = No (mkNo contra f)

33+ where

34+ mkNo : {xs' : List a} ->

35+ ((x' = y') -> Void) -> (Elem x' xs' -> Void) ->

36+ Elem x' (y' :: xs') -> Void

37+ mkNo f g Here = f Refl

38+ mkNo f g (There x) = g x

5439

5540||| Remove the element at the given position.

5641|||

libs/base/Data/List/Quantifiers.idr−5

@@ -75,8 +75,3 @@ all d (x::xs) with (d x)

7575 case all d xs of

7676 Yes prf' => Yes (prf :: prf')

7777 No prf' => No (notAllThere prf')

78−

79−||| Given a proof of membership for some element, extract the property proof for it

80−indexAll : Elem x xs -> All p xs -> p x

81−indexAll Here (p::_ ) = p

82−indexAll (There e) ( _::ps) = indexAll e ps

libs/base/Data/Morphisms.idr+27−43

@@ -1,61 +1,45 @@

11module Data.Morphisms

22

3−%default total

43%access public export

54

6−record Morphism a b where

7− constructor Mor

8− applyMor : a -> b

9−infixr 1 ~>

10−(~>) : Type -> Type -> Type

11−(~>) = Morphism

5+data Morphism : Type -> Type -> Type where

6+ Mor : (a -> b) -> Morphism a b

127

13−record Endomorphism a where

14− constructor Endo

15− applyEndo : a -> a

8+data Endomorphism : Type -> Type where

9+ Endo : (a -> a) -> Endomorphism a

1610

17−record Kleislimorphism (f : Type -> Type) a b where

18− constructor Kleisli

19− applyKleisli : a -> f b

11+data Kleislimorphism : (Type -> Type) -> Type -> Type -> Type where

12+ Kleisli : Monad m => (a -> m b) -> Kleislimorphism m a b

2013

21−Functor (Morphism r) where

22− map f (Mor a) = Mor $ f . a

14+applyKleisli : Monad m => (Kleislimorphism m a b) -> a -> m b

15+applyKleisli (Kleisli f) a = f a

2316

24−Applicative (Morphism r) where

25− pure a = Mor $ const a

26− (Mor f) <*> (Mor a) = Mor $ \r => f r $ a r

17+applyMor : Morphism a b -> a -> b

18+applyMor (Mor f) a = f a

2719

28−Monad (Morphism r) where

29− (Mor h) >>= f = Mor $ \r => applyMor (f $ h r) r

20+applyEndo : Endomorphism a -> a -> a

21+applyEndo (Endo f) a = f a

22+

23+implementation Functor (Morphism r) where

24+ map f (Mor a) = Mor (f . a)

3025

31−Semigroup a => Semigroup (Morphism r a) where

32− f <+> g = [| f <+> g |]

26+implementation Applicative (Morphism r) where

27+ pure a = Mor $ const a

28+ (Mor f) <*> (Mor a) = Mor $ \r => f r $ a r

3329

34−Monoid a => Monoid (Morphism r a) where

35− neutral = [| neutral |]

30+implementation Monad (Morphism r) where

31+ (Mor h) >>= f = Mor $ \r => applyMor (f $ h r) r

3632

37−Semigroup (Endomorphism a) where

33+implementation Semigroup (Endomorphism a) where

3834 (Endo f) <+> (Endo g) = Endo $ g . f

3935

40−Monoid (Endomorphism a) where

36+implementation Monoid (Endomorphism a) where

4137 neutral = Endo id

4238

43−Functor f => Functor (Kleislimorphism f a) where

44− map f (Kleisli g) = Kleisli (map f . g)

45−

46−Applicative f => Applicative (Kleislimorphism f a) where

47− pure a = Kleisli $ const $ pure a

48− (Kleisli f) <*> (Kleisli a) = Kleisli $ \r => f r <*> a r

49−

50−Monad f => Monad (Kleislimorphism f a) where

51− (Kleisli f) >>= g = Kleisli $ \r => applyKleisli (g !(f r)) r

52−

53−-- Applicative is a bit too strong, but there is no suitable superclass

54−(Semigroup a, Applicative f) => Semigroup (Kleislimorphism f r a) where

55− f <+> g = [| f <+> g |]

39+infixr 1 ~>

5640

57−(Monoid a, Applicative f) => Monoid (Kleislimorphism f r a) where

58− neutral = [| neutral |]

41+(~>) : Type -> Type -> Type

42+a ~> b = Morphism a b

5943

6044Cast (Endomorphism a) (Morphism a a) where

6145 cast (Endo f) = Mor f

@@ -63,8 +47,8 @@ Cast (Endomorphism a) (Morphism a a) where

6347Cast (Morphism a a) (Endomorphism a) where

6448 cast (Mor f) = Endo f

6549

66−Cast (Morphism a (f b)) (Kleislimorphism f a b) where

50+Monad m => Cast (Morphism a (m b)) (Kleislimorphism m a b) where

6751 cast (Mor f) = Kleisli f

6852

69−Cast (Kleislimorphism f a b) (Morphism a (f b)) where

53+Cast (Kleislimorphism m a b) (Morphism a (m b)) where

7054 cast (Kleisli f) = Mor f

libs/base/Data/Nat/Views.idr+1−1

@@ -14,7 +14,7 @@ data HalfRec : Nat -> Type where

1414 HalfRecOdd : {n : Nat} -> (rec : Lazy (HalfRec n)) -> HalfRec (S (n + n))

1515

1616||| Covering function for the `Half` view

17−public export

17+export

1818half : (n : Nat) -> Half n

1919half Z = HalfEven {n=0}

2020half (S k) with (half k)

libs/base/Data/So.idr+1−11

@@ -12,7 +12,7 @@ module Data.So

1212||| If you find yourself using `So` for something other than primitive types,

1313||| it may be appropriate to define a type of evidence for the property that you

1414||| care about instead.

15−data So : Bool -> Type where

15+data So : Bool -> Type where

1616 Oh : So True

1717

1818implementation Uninhabited (So False) where

@@ -23,14 +23,4 @@ choose : (b : Bool) -> Either (So b) (So (not b))

2323choose True = Left Oh

2424choose False = Right Oh

2525

26−||| Absurd when you have proof that both `b` and `not b` is true.

27−export

28−soAbsurd : So b -> So (not b) -> Void

29−soAbsurd sb snb with (sb)

30− | Oh = uninhabited snb

31−

32−||| Transmission between usage of value-level `not` and type-level `Not`.

33−export

34−soNotToNotSo : So (not b) -> Not (So b)

35−soNotToNotSo = flip soAbsurd

3626

libs/base/Data/Vect.idr+22−408

@@ -11,6 +11,7 @@ infixr 7 ::

1111||| Vectors: Generic lists with explicit length in the type

1212||| @ len the length of the list

1313||| @ elem the type of elements

14+%elim

1415data Vect : (len : Nat) -> (elem : Type) -> Type where

1516 ||| Empty vector

1617 Nil : Vect Z elem

@@ -45,64 +46,36 @@ lengthCorrect (S n) (x :: xs) = rewrite lengthCorrect n xs in Refl

4546--------------------------------------------------------------------------------

4647

4748||| All but the first element of the vector

48−|||

49−||| ```idris example

50−||| tail [1,2,3,4]

51−||| ```

5249tail : Vect (S len) elem -> Vect len elem

5350tail (x::xs) = xs

5451

5552||| Only the first element of the vector

56−|||

57−||| ```idris example

58−||| head [1,2,3,4]

59−||| ```

6053head : Vect (S len) elem -> elem

6154head (x::xs) = x

6255

6356||| The last element of the vector

64−|||

65−||| ```idris example

66−||| last [1,2,3,4]

67−||| ```

6857last : Vect (S len) elem -> elem

6958last (x::[]) = x

7059last (x::y::ys) = last $ y::ys

7160

7261||| All but the last element of the vector

73−|||

74−||| ```idris example

75−||| init [1,2,3,4]

76−||| ```

7762init : Vect (S len) elem -> Vect len elem

7863init (x::[]) = []

7964init (x::y::ys) = x :: init (y::ys)

8065

8166||| Extract a particular element from a vector

82−|||

83−||| ```idris example

84−||| index 1 [1,2,3,4]

85−||| ```

8667index : Fin len -> Vect len elem -> elem

8768index FZ (x::xs) = x

8869index (FS k) (x::xs) = index k xs

8970

9071

9172||| Insert an element at a particular index

92−|||

93−||| ```idris example

94−||| insertAt 1 8 [1,2,3,4]

95−||| ```

9673insertAt : Fin (S len) -> elem -> Vect len elem -> Vect (S len) elem

9774insertAt FZ y xs = y :: xs

9875insertAt (FS k) y (x::xs) = x :: insertAt k y xs

9976insertAt (FS k) y [] = absurd k

10077

10178||| Construct a new vector consisting of all but the indicated element

102−|||

103−||| ```idris example

104−||| deleteAt 1 [1,2,3,4]

105−||| ```

10679deleteAt : Fin (S len) -> Vect (S len) elem -> Vect len elem

10780deleteAt FZ (x::xs) = xs

10881deleteAt {len = S m} (FS k) (x::xs) = x :: deleteAt k xs

@@ -110,10 +83,6 @@ deleteAt {len = Z} (FS k) (x::xs) = absurd k

11083deleteAt _ [] impossible

11184

11285||| Replace an element at a particlar index with another

113−|||

114−||| ```idris example

115−||| replaceAt 1 8 [1,2,3,4]

116−||| ```

11786replaceAt : Fin len -> elem -> Vect len elem -> Vect len elem

11887replaceAt FZ y (x::xs) = y :: xs

11988replaceAt (FS k) y (x::xs) = x :: replaceAt k y xs

@@ -122,10 +91,6 @@ replaceAt (FS k) y (x::xs) = x :: replaceAt k y xs

12291||| @ i the index to replace at

12392||| @ f the update function

12493||| @ xs the vector to replace in

125−|||

126−||| ```idris example

127−||| updateAt 1 (+10) [1,2,3,4]

128−||| ```

12994updateAt : (i : Fin len) -> (f : elem -> elem) -> (xs : Vect len elem) -> Vect len elem

13095updateAt FZ f (x::xs) = f x :: xs

13196updateAt (FS k) f (x::xs) = x :: updateAt k f xs

@@ -136,54 +101,20 @@ updateAt (FS k) f (x::xs) = x :: updateAt k f xs

136101

137102||| Get the first n elements of a Vect

138103||| @ n the number of elements to take

139−|||

140−||| ```idris example

141−||| take 2 [1,2,3,4]

142−||| ```

143104take : (n : Nat) -> Vect (n + m) elem -> Vect n elem

144105take Z xs = []

145106take (S k) (x :: xs) = x :: take k xs

146107

147108||| Remove the first n elements of a Vect

148109||| @ n the number of elements to remove

149−|||

150−||| ```idris example

151−||| drop 2 [1,2,3,4]

152−||| ```

153110drop : (n : Nat) -> Vect (n + m) elem -> Vect m elem

154111drop Z xs = xs

155112drop (S k) (x :: xs) = drop k xs

156113

157−||| Take up to the first n elements of a Vect if they exist.

158−||| @ n the maximum number of elements to take

159−|||

160−||| ```idris example

161−||| takeUpto 10 [1,2,3,4]

162−||| ```

163−takeUpto : (x : Nat) -> Vect n elem -> Vect (minimum x n) elem

164−takeUpto Z ys = []

165−takeUpto x [] = rewrite minimumZeroZeroLeft x in []

166−takeUpto (S x) (y::ys) = y :: takeUpto x ys

167−

168−||| Drop up to the first n elements of a Vect if they exist.

169−||| @ n the maximum number of elements to remove.

170−|||

171−||| ```idris example

172−||| dropUpto 10 [1,2,3,4]

173−||| ```

174−dropUpto : (x : Nat) -> Vect n elem -> Vect (n `minus` minimum x n) elem

175−dropUpto Z ys {n} = rewrite minusZeroRight n in ys

176−dropUpto x [] = []

177−dropUpto (S x) (y :: ys) = dropUpto x ys

178−

179114||| Take the longest prefix of a Vect such that all elements satisfy some

180115||| Boolean predicate.

181116|||

182117||| @ p the predicate

183−|||

184−||| ```idris example

185−||| takeWhile (<3) [1,2,3,4]

186−||| ```

187118takeWhile : (p : elem -> Bool) -> Vect len elem -> (q ** Vect q elem)

188119takeWhile p [] = (_ ** [])

189120takeWhile p (x::xs) =

@@ -197,10 +128,6 @@ takeWhile p (x::xs) =

197128||| Boolean predicate.

198129|||

199130||| @ p the predicate

200−|||

201−||| ```idris example

202−||| dropWhile (<3) [1,2,3,4]

203−||| ```

204131dropWhile : (p : elem -> Bool) -> Vect len elem -> (q ** Vect q elem)

205132dropWhile p [] = (_ ** [])

206133dropWhile p (x::xs) =

@@ -214,10 +141,6 @@ dropWhile p (x::xs) =

214141--------------------------------------------------------------------------------

215142

216143||| Reverse the order of the elements of a vector

217−|||

218−||| ```idris example

219−||| reverse [1,2,3,4]

220−||| ```

221144reverse : Vect len elem -> Vect len elem

222145reverse xs = go [] xs

223146 where go : Vect n elem -> Vect m elem -> Vect (n+m) elem

@@ -228,10 +151,6 @@ reverse xs = go [] xs

228151||| Alternate an element between the other elements of a vector

229152||| @ sep the element to intersperse

230153||| @ xs the vector to separate with `sep`

231−|||

232−||| ```idris example

233−||| intersperse 0 [1,2,3,4]

234−||| ```

235154intersperse : (sep : elem) -> (xs : Vect len elem) -> Vect (len + pred len) elem

236155intersperse sep [] = []

237156intersperse sep (x::xs) = x :: intersperse' sep xs

@@ -256,10 +175,6 @@ fromList' {len} ys (x::xs) =

256175||| Convert a list to a vector.

257176|||

258177||| The length of the list should be statically known.

259−|||

260−||| ```idris example

261−||| fromList [1,2,3,4]

262−||| ```

263178fromList : (l : List elem) -> Vect (length l) elem

264179fromList l =

265180 rewrite (sym $ plusZeroRightNeutral (length l)) in

@@ -270,31 +185,19 @@ fromList l =

270185--------------------------------------------------------------------------------

271186

272187||| Append two vectors

273−|||

274−||| ```idris example

275−||| [1,2,3,4] ++ [5,6]

276−||| ```

277188(++) : (xs : Vect m elem) -> (ys : Vect n elem) -> Vect (m + n) elem

278189(++) [] ys = ys

279190(++) (x::xs) ys = x :: xs ++ ys

280191

281−||| Repeat some value some number of times.

192+||| Repeate some value some number of times.

282193|||

283194||| @ len the number of times to repeat it

284195||| @ x the value to repeat

285−|||

286−||| ```idris example

287−||| replicate 4 1

288−||| ```

289196replicate : (len : Nat) -> (x : elem) -> Vect len elem

290197replicate Z x = []

291198replicate (S k) x = x :: replicate k x

292199

293200||| Merge two ordered vectors

294−|||

295−||| ```idris example

296−||| mergeBy compare (fromList [1,3,5]) (fromList [2,3,4,5,6])

297−||| ```

298201mergeBy : (elem -> elem -> Ordering) -> (xs : Vect n elem) -> (ys : Vect m elem) -> Vect (n + m) elem

299202mergeBy order [] [] = []

300203mergeBy order [] (x :: xs) = x :: xs

@@ -318,54 +221,30 @@ merge = mergeBy compare

318221||| @ f the function to combine elements with

319222||| @ xs the first vector of elements

320223||| @ ys the second vector of elements

321−|||

322−||| ```idris example

323−||| zipWith (+) (fromList [1,2,3,4]) (fromList [5,6,7,8])

324−||| ```

325224zipWith : (f : a -> b -> c) -> (xs : Vect n a) -> (ys : Vect n b) -> Vect n c

326225zipWith f [] [] = []

327226zipWith f (x::xs) (y::ys) = f x y :: zipWith f xs ys

328227

329228||| Combine three equal-length vectors into a vector with some function

330−|||

331−||| ```idris example

332−||| zipWith3 (\x,y,z => x+y+z) (fromList [1,2,3,4]) (fromList [5,6,7,8]) (fromList [1,1,1,1])

333−||| ```

334229zipWith3 : (a -> b -> c -> d) -> (xs : Vect n a) -> (ys : Vect n b) -> (zs : Vect n c) -> Vect n d

335230zipWith3 f [] [] [] = []

336231zipWith3 f (x::xs) (y::ys) (z::zs) = f x y z :: zipWith3 f xs ys zs

337232

338233||| Combine two equal-length vectors pairwise

339−|||

340−||| ```idris example

341−||| zip (fromList [1,2,3,4]) (fromList [1,2,3,4])

342−||| ```

343234zip : (xs : Vect n a) -> (ys : Vect n b) -> Vect n (a, b)

344235zip = zipWith (\x,y => (x,y))

345236

346237||| Combine three equal-length vectors elementwise into a vector of tuples

347−|||

348−||| ```idris example

349−||| zip3 (fromList [1,2,3,4]) (fromList [1,2,3,4]) (fromList [1,2,3,4])

350−||| ```

351238zip3 : (xs : Vect n a) -> (ys : Vect n b) -> (zs : Vect n c) -> Vect n (a, b, c)

352239zip3 = zipWith3 (\x,y,z => (x,y,z))

353240

354241||| Convert a vector of pairs to a pair of vectors

355−|||

356−||| ```idris example

357−||| unzip (fromList [(1,2), (1,2)])

358−||| ```

359242unzip : (xs : Vect n (a, b)) -> (Vect n a, Vect n b)

360243unzip [] = ([], [])

361244unzip ((l, r)::xs) with (unzip xs)

362245 | (lefts, rights) = (l::lefts, r::rights)

363246

364247||| Convert a vector of three-tuples to a triplet of vectors

365−|||

366−||| ```idris example

367−||| unzip3 (fromList [(1,2,3), (1,2,3)])

368−||| ```

369248unzip3 : (xs : Vect n (a, b, c)) -> (Vect n a, Vect n b, Vect n c)

370249unzip3 [] = ([], [], [])

371250unzip3 ((l,c,r)::xs) with (unzip3 xs)

@@ -407,10 +286,6 @@ implementation Functor (Vect n) where

407286|||

408287||| @ f the partial function (expressed by returning `Maybe`)

409288||| @ xs the vector to check for results

410−|||

411−||| ```idris example

412−||| mapMaybe ((find (=='a')) . unpack) (fromList ["abc","ade","bgh","xyz"])

413−||| ```

414289mapMaybe : (f : a -> Maybe b) -> (xs : Vect len a) -> (m : Nat ** Vect m b)

415290mapMaybe f [] = (_ ** [])

416291mapMaybe f (x::xs) =

@@ -419,6 +294,7 @@ mapMaybe f (x::xs) =

419294 Just y => (S len ** y :: ys)

420295 Nothing => ( len ** ys)

421296

297+

422298--------------------------------------------------------------------------------

423299-- Folds

424300--------------------------------------------------------------------------------

@@ -435,57 +311,25 @@ implementation Foldable (Vect n) where

435311--------------------------------------------------------------------------------

436312

437313||| Flatten a vector of equal-length vectors

438−|||

439−||| ```idris example

440−||| concat [[1,2,3], [4,5,6]]

441−||| ```

442314concat : (xss : Vect m (Vect n elem)) -> Vect (m * n) elem

443315concat [] = []

444316concat (v::vs) = v ++ concat vs

445317

446318||| Foldr without seeding the accumulator

447−|||

448−||| ```idris example

449−||| foldr1 (-) (fromList [1,2,3])

450−||| ```

451319foldr1 : (t -> t -> t) -> Vect (S n) t -> t

452−foldr1 f [x] = x

453−foldr1 f (x::y::xs) = f x (foldr1 f (y::xs))

320+foldr1 f (x::xs) = foldr f x xs

454321

455322||| Foldl without seeding the accumulator

456−|||

457−||| ```idris example

458−||| foldl1 (-) (fromList [1,2,3])

459−||| ```

460323foldl1 : (t -> t -> t) -> Vect (S n) t -> t

461324foldl1 f (x::xs) = foldl f x xs

462−

463325--------------------------------------------------------------------------------

464326-- Scans

465327--------------------------------------------------------------------------------

466328

467−||| The scanl function is similar to foldl, but returns all the intermediate

468−||| accumulator states in the form of a vector.

469−|||

470−||| ```idris example

471−||| scanl (-) 0 (fromList [1,2,3])

472−||| ```

473329scanl : (res -> elem -> res) -> res -> Vect len elem -> Vect (S len) res

474330scanl f q [] = [q]

475331scanl f q (x::xs) = q :: scanl f (f q x) xs

476332

477−||| The scanl1 function is a variant of scanl that doesn't require an explicit

478−||| starting value.

479−||| It assumes the first element of the vector to be the starting value and then

480−||| starts the fold with the element following it.

481−|||

482−||| ```idris example

483−||| scanl1 (-) (fromList [1,2,3])

484−||| ```

485−scanl1 : (elem -> elem -> elem) -> Vect len elem -> Vect len elem

486−scanl1 f [] = []

487−scanl1 f (x::xs) = scanl f x xs

488−

489333--------------------------------------------------------------------------------

490334-- Membership tests

491335--------------------------------------------------------------------------------

@@ -494,10 +338,6 @@ scanl1 f (x::xs) = scanl f x xs

494338||| @ p the equality test

495339||| @ e the item to search for

496340||| @ xs the vector to search in

497−|||

498−||| ```idris example

499−||| elemBy (==) 2 [1,2,3,4]

500−||| ```

501341elemBy : (p : elem -> elem -> Bool) -> (e : elem) -> (xs : Vect len elem) -> Bool

502342elemBy p e [] = False

503343elemBy p e (x::xs) = p e x || elemBy p e xs

@@ -505,29 +345,17 @@ elemBy p e (x::xs) = p e x || elemBy p e xs

505345||| Use the default Boolean equality on elements to search for an item

506346||| @ x what to search for

507347||| @ xs where to search

508−|||

509−||| ```idris example

510−||| elem 3 [1,2,3,4]

511−||| ```

512348elem : Eq elem => (x : elem) -> (xs : Vect len elem) -> Bool

513349elem = elemBy (==)

514350

515351||| Find the association of some key with a user-provided comparison

516352||| @ p the comparison operator for keys (True if they match)

517353||| @ e the key to look for

518−|||

519−||| ```idris example

520−||| lookupBy (==) 2 [(1, 'a'), (2, 'b'), (3, 'c')]

521−||| ```

522354lookupBy : (p : key -> key -> Bool) -> (e : key) -> (xs : Vect n (key, val)) -> Maybe val

523355lookupBy p e [] = Nothing

524356lookupBy p e ((l, r)::xs) = if p e l then Just r else lookupBy p e xs

525357

526358||| Find the assocation of some key using the default Boolean equality test

527−|||

528−||| ```idris example

529−||| lookup 3 [(1, 'a'), (2, 'b'), (3, 'c')]

530−||| ```

531359lookup : Eq key => key -> Vect n (key, val) -> Maybe val

532360lookup = lookupBy (==)

533361

@@ -535,19 +363,11 @@ lookup = lookupBy (==)

535363||| @ p the comparison operator

536364||| @ elems the vector to search

537365||| @ xs what to search for

538−|||

539−||| ```idris example

540−||| hasAnyBy (==) [2,5] [1,2,3,4]

541−||| ```

542366hasAnyBy : (p : elem -> elem -> Bool) -> (elems : Vect m elem) -> (xs : Vect len elem) -> Bool

543367hasAnyBy p elems [] = False

544368hasAnyBy p elems (x::xs) = elemBy p x elems || hasAnyBy p elems xs

545369

546370||| Check if any element of xs is found in elems using the default Boolean equality test

547−|||

548−||| ```idris example

549−||| hasAny [2,5] [1,2,3,4]

550−||| ```

551371hasAny : Eq elem => Vect m elem -> Vect len elem -> Bool

552372hasAny = hasAnyBy (==)

553373

@@ -557,62 +377,30 @@ hasAny = hasAnyBy (==)

557377

558378||| Find the first element of the vector that satisfies some test

559379||| @ p the test to satisfy

560−|||

561−||| ```idris example

562−||| find (== 3) [1,2,3,4]

563−||| ```

564380find : (p : elem -> Bool) -> (xs : Vect len elem) -> Maybe elem

565381find p [] = Nothing

566382find p (x::xs) = if p x then Just x else find p xs

567383

568384||| Find the index of the first element of the vector that satisfies some test

569−|||

570−||| ```idris example

571−||| findIndex (== 3) [1,2,3,4]

572−||| ```

573385findIndex : (elem -> Bool) -> Vect len elem -> Maybe (Fin len)

574386findIndex p [] = Nothing

575387findIndex p (x :: xs) = if p x then Just 0 else map FS (findIndex p xs)

576388

577389||| Find the indices of all elements that satisfy some test

578−|||

579−||| ```idris example

580−||| findIndices (< 3) [1,2,3,4]

581−||| ```

582390findIndices : (elem -> Bool) -> Vect m elem -> List (Fin m)

583391findIndices p [] = []

584392findIndices p (x :: xs) = let is = map FS $ findIndices p xs

585393 in if p x then 0 :: is else is

586394

587−||| Find the index of the first element of the vector that satisfies some test

588−|||

589−||| ```idris example

590−||| elemIndexBy (==) 3 [1,2,3,4]

591−||| ```

592395elemIndexBy : (elem -> elem -> Bool) -> elem -> Vect m elem -> Maybe (Fin m)

593396elemIndexBy p e = findIndex $ p e

594397

595−||| Find the index of the first element of the vector equal to the given one.

596−|||

597−||| ```idris example

598−||| elemIndex 3 [1,2,3,4]

599−||| ```

600398elemIndex : Eq elem => elem -> Vect m elem -> Maybe (Fin m)

601399elemIndex = elemIndexBy (==)

602400

603−||| Find the indices of all elements that satisfy some test

604−|||

605−||| ```idris example

606−||| elemIndicesBy (<=) 3 [1,2,3,4]

607−||| ```

608401elemIndicesBy : (elem -> elem -> Bool) -> elem -> Vect m elem -> List (Fin m)

609402elemIndicesBy p e = findIndices $ p e

610403

611−||| Find the indices of all elements uquals to the given one

612−|||

613−||| ```idris example

614−||| elemIndices 3 [1,2,3,4,3]

615−||| ```

616404elemIndices : Eq elem => elem -> Vect m elem -> List (Fin m)

617405elemIndices = elemIndicesBy (==)

618406

@@ -621,10 +409,6 @@ elemIndices = elemIndicesBy (==)

621409--------------------------------------------------------------------------------

622410

623411||| Find all elements of a vector that satisfy some test

624−|||

625−||| ```idris example

626−||| filter (< 3) (fromList [1,2,3,4])

627−||| ```

628412filter : (elem -> Bool) -> Vect len elem -> (p ** Vect p elem)

629413filter p [] = ( _ ** [] )

630414filter p (x::xs) =

@@ -635,10 +419,6 @@ filter p (x::xs) =

635419 (_ ** tail)

636420

637421||| Make the elements of some vector unique by some test

638−|||

639−||| ```idris example

640−||| nubBy (==) (fromList [1,2,2,3,4,4])

641−||| ```

642422nubBy : (elem -> elem -> Bool) -> Vect len elem -> (p ** Vect p elem)

643423nubBy = nubBy' []

644424 where

@@ -650,29 +430,15 @@ nubBy = nubBy' []

650430 | (_ ** tail) = (_ ** x::tail)

651431

652432||| Make the elements of some vector unique by the default Boolean equality

653−|||

654−||| ```idris example

655−||| nub (fromList [1,2,2,3,4,4])

656−||| ```

657433nub : Eq elem => Vect len elem -> (p ** Vect p elem)

658434nub = nubBy (==)

659435

660−||| Delete first element from list according to some test

661−|||

662−||| ```idris example

663−||| deleteBy (<) 3 (fromList [1,2,2,3,4,4])

664−||| ```

665436deleteBy : (elem -> elem -> Bool) -> elem -> Vect len elem -> (p ** Vect p elem)

666437deleteBy _ _ [] = (_ ** [])

667438deleteBy eq x (y::ys) =

668439 let (len ** zs) = deleteBy eq x ys

669440 in if x `eq` y then (_ ** ys) else (S len ** y ::zs)

670441

671−||| Delete first element from list equal to the given one

672−|||

673−||| ```idris example

674−||| delete 2 (fromList [1,2,2,3,4,4])

675−||| ```

676442delete : (Eq elem) => elem -> Vect len elem -> (p ** Vect p elem)

677443delete = deleteBy (==)

678444

@@ -680,28 +446,14 @@ delete = deleteBy (==)

680446-- Splitting and breaking lists

681447--------------------------------------------------------------------------------

682448

683−||| A tuple where the first element is a `Vect` of the `n` first elements and

684−||| the second element is a `Vect` of the remaining elements of the original.

685−||| It is equivalent to `(take n xs, drop n xs)` (`splitAtTakeDrop`),

686−||| but is more efficient.

687−|||

449+||| A tuple where the first element is a Vect of the n first elements and

450+||| the second element is a Vect of the remaining elements of the original Vect

451+||| It is equivalent to (take n xs, drop n xs)

688452||| @ n the index to split at

689−||| @ xs the `Vect` to split in two

690−|||

691−||| ```idris example

692−||| splitAt 2 (fromList [1,2,3,4])

693−||| ```

453+||| @ xs the Vect to split in two

694454splitAt : (n : Nat) -> (xs : Vect (n + m) elem) -> (Vect n elem, Vect m elem)

695−splitAt Z xs = ([], xs)

696−splitAt (S k) (x :: xs) with (splitAt k xs)

697− | (tk, dr) = (x :: tk, dr)

455+splitAt n xs = (take n xs, drop n xs)

698456

699−||| A tuple where the first element is a `Vect` of the `n` elements passing given test

700−||| and the second element is a `Vect` of the remaining elements of the original.

701−|||

702−||| ```idris example

703−||| partition (== 2) (fromList [1,2,3,2,4])

704−||| ```

705457partition : (elem -> Bool) -> Vect len elem -> ((p ** Vect p elem), (q ** Vect q elem))

706458partition p [] = ((_ ** []), (_ ** []))

707459partition p (x::xs) =

@@ -715,37 +467,17 @@ partition p (x::xs) =

715467-- Predicates

716468--------------------------------------------------------------------------------

717469

718−||| Verify vector prefix

719−|||

720−||| ```idris example

721−||| isPrefixOfBy (==) (fromList [1,2]) (fromList [1,2,3,4])

722−||| ```

723470isPrefixOfBy : (elem -> elem -> Bool) -> Vect m elem -> Vect len elem -> Bool

724471isPrefixOfBy p [] right = True

725472isPrefixOfBy p left [] = False

726473isPrefixOfBy p (x::xs) (y::ys) = p x y && isPrefixOfBy p xs ys

727474

728−||| Verify vector prefix

729−|||

730−||| ```idris example

731−||| isPrefixOf (fromList [1,2]) (fromList [1,2,3,4])

732−||| ```

733475isPrefixOf : Eq elem => Vect m elem -> Vect len elem -> Bool

734476isPrefixOf = isPrefixOfBy (==)

735477

736−||| Verify vector suffix

737−|||

738−||| ```idris example

739−||| isSuffixOfBy (==) (fromList [3,4]) (fromList [1,2,3,4])

740−||| ```

741478isSuffixOfBy : (elem -> elem -> Bool) -> Vect m elem -> Vect len elem -> Bool

742479isSuffixOfBy p left right = isPrefixOfBy p (reverse left) (reverse right)

743480

744−||| Verify vector suffix

745−|||

746−||| ```idris example

747−||| isSuffixOf (fromList [3,4]) (fromList [1,2,3,4])

748−||| ```

749481isSuffixOf : Eq elem => Vect m elem -> Vect len elem -> Bool

750482isSuffixOf = isSuffixOfBy (==)

751483

@@ -753,20 +485,10 @@ isSuffixOf = isSuffixOfBy (==)

753485-- Conversions

754486--------------------------------------------------------------------------------

755487

756−||| Convert Maybe type into Vect

757−|||

758−||| ```idris example

759−||| maybeToVect (Just 2)

760−||| ```

761488maybeToVect : Maybe elem -> (p ** Vect p elem)

762489maybeToVect Nothing = (_ ** [])

763490maybeToVect (Just j) = (_ ** [j])

764491

765−||| Convert first element of Vect (if exists) into Maybe.

766−|||

767−||| ```idris example

768−||| vectToMaybe [2]

769−||| ```

770492vectToMaybe : Vect len elem -> Maybe elem

771493vectToMaybe [] = Nothing

772494vectToMaybe (x::xs) = Just x

@@ -775,11 +497,6 @@ vectToMaybe (x::xs) = Just x

775497-- Misc

776498--------------------------------------------------------------------------------

777499

778−||| Filter out Nothings from Vect

779−|||

780−||| ```idris example

781−||| catMaybes [Just 1, Just 2, Nothing, Nothing, Just 5]

782−||| ```

783500catMaybes : Vect n (Maybe elem) -> (p ** Vect p elem)

784501catMaybes [] = (_ ** [])

785502catMaybes (Nothing::xs) = catMaybes xs

@@ -787,11 +504,6 @@ catMaybes ((Just j)::xs) =

787504 let (_ ** tail) = catMaybes xs

788505 in (_ ** j::tail)

789506

790−||| Get diagonal elements

791−|||

792−||| ```idris example

793−||| diag [[1,2,3], [4,5,6], [7,8,9]]

794−||| ```

795507diag : Vect len (Vect len elem) -> Vect len elem

796508diag [] = []

797509diag ((x::xs)::xss) = x :: diag (map tail xss)

@@ -800,18 +512,12 @@ range : {len : Nat} -> Vect len (Fin len)

800512range {len=Z} = []

801513range {len=S _} = FZ :: map FS range

802514

803−||| Transpose a `Vect` of `Vect`s, turning rows into columns and vice versa.

804−|||

805−||| This is like zipping all the inner `Vect`s together and is equivalent to `traverse id` (`transposeTraverse`).

515+||| Transpose a Vect of Vects, turning rows into columns and vice versa.

806516|||

807517||| As the types ensure rectangularity, this is an involution, unlike `Prelude.List.transpose`.

808−|||

809−||| ```idris example

810−||| transpose [[1,2], [3,4], [5,6], [7,8]]

811−||| ```

812−transpose : Vect m (Vect n elem) -> Vect n (Vect m elem)

813−transpose [] = replicate _ [] -- = [| [] |]

814−transpose (x :: xs) = zipWith (::) x (transpose xs) -- = [| x :: xs |]

518+transpose : {n : Nat} -> Vect m (Vect n elem) -> Vect n (Vect m elem)

519+transpose [] = replicate _ []

520+transpose (x :: xs) = zipWith (::) x (transpose xs)

815521

816522--------------------------------------------------------------------------------

817523-- Applicative/Monad/Traversable

@@ -819,6 +525,7 @@ transpose (x :: xs) = zipWith (::) x (transpose xs) -- = [| x :: xs |]

819525

820526implementation Applicative (Vect k) where

821527 pure = replicate _

528+

822529 fs <*> vs = zipWith apply fs vs

823530

824531||| This monad is different from the List monad, (>>=)

@@ -827,8 +534,8 @@ implementation Monad (Vect len) where

827534 m >>= f = diag (map f m)

828535

829536implementation Traversable (Vect n) where

830− traverse f [] = [| [] |]

831− traverse f (x :: xs) = [| f x :: traverse f xs |]

537+ traverse f [] = pure Vect.Nil

538+ traverse f (x::xs) = [| Vect.(::) (f x) (traverse f xs) |]

832539

833540--------------------------------------------------------------------------------

834541-- Show

@@ -837,29 +544,13 @@ implementation Traversable (Vect n) where

837544implementation Show elem => Show (Vect len elem) where

838545 show = show . toList

839546

840−--------------------------------------------------------------------------------

841−-- Uninhabited

842−--------------------------------------------------------------------------------

843−

844−Uninhabited a => Uninhabited (Vect (S n) a) where

845− uninhabited (x :: _) = uninhabited x

846−

847547--------------------------------------------------------------------------------

848548-- Properties

849549--------------------------------------------------------------------------------

850550

851−vectMustBeNil : (xs : Vect Z a) -> xs = []

852−vectMustBeNil [] = Refl

853−

854551vectConsCong : (x : elem) -> (xs : Vect len elem) -> (ys : Vect m elem) -> (xs = ys) -> (x :: xs = x :: ys)

855552vectConsCong x xs xs Refl = Refl

856553

857−vectInjective1 : {xs : Vect n a} -> {ys : Vect m b} -> x :: xs ~=~ y :: ys -> x ~=~ y

858−vectInjective1 Refl = Refl

859−

860−vectInjective2 : {xs : Vect n a} -> {ys : Vect m b} -> x :: xs ~=~ y :: ys -> xs ~=~ ys

861−vectInjective2 Refl = Refl

862−

863554vectNilRightNeutral : (xs : Vect n a) -> xs ++ [] = xs

864555vectNilRightNeutral [] = Refl

865556vectNilRightNeutral (x :: xs) =

@@ -873,93 +564,16 @@ vectAppendAssociative [] y z = Refl

873564vectAppendAssociative (x :: xs) ys zs =

874565 vectConsCong _ _ _ (vectAppendAssociative xs ys zs)

875566

876−||| Adding a prefix and then taking the prefix gets the prefix. Or,

877−||| adding a suffix and then dropping the suffix does nothing.

878−takePrefix : (ns : Vect n a) -> (ms : Vect m a) -> take n (ns ++ ms) = ns

879−takePrefix [] _ = Refl

880−takePrefix (n :: ns) ms = cong $ takePrefix ns ms

881−

882−||| Adding a prefix and then dropping the prefix does nothing. Or,

883−||| adding a suffix and then taking the suffix gets the suffix.

884−dropPrefix : (ns : Vect n a) -> (ms : Vect m a) -> drop n (ns ++ ms) = ms

885−dropPrefix [] ms = Refl

886−dropPrefix (_ :: ns) ms = dropPrefix ns ms

887−

888−||| `take n . take (n + m) = take n`

889−takeTake : (n : Nat) -> (m : Nat) ->

890− (xs : Vect ((n + m) + l) a) -> (ys : Vect (n + (m + l)) a) ->

891− xs ~=~ ys ->

892− take n (take (n + m) xs) = take n ys

893−takeTake Z m _ _ _ = Refl

894−takeTake (S n) m (x :: xs) (y :: ys) prf = rewrite vectInjective1 prf in cong (takeTake n m xs ys (vectInjective2 prf))

895−

896−||| `drop (n + m) = drop m . drop n`

897−dropDrop : (n : Nat) -> (m : Nat) ->

898− (xs : Vect ((n + m) + l) a) -> (ys : Vect (n + (m + l)) a) ->

899− xs ~=~ ys ->

900− drop (n + m) xs = drop m (drop n ys)

901−dropDrop Z m xs xs Refl = Refl

902−dropDrop (S n) m (_ :: xs) (_ :: ys) prf = dropDrop n m xs ys (vectInjective2 prf)

903−

904−||| A `Vect` may be restored from its components.

905−takeDropConcat : (n : Nat) -> (xs : Vect (n + m) a) -> take n xs ++ drop n xs = xs

906−takeDropConcat Z xs = Refl

907−takeDropConcat (S n) (x :: xs) = cong $ takeDropConcat n xs

908−

909−||| `drop n . take (n + m) = take m . drop n`.

910−|||

911−||| Or: there are two ways to extract a subsequence.

912−dropTakeTakeDrop : (n : Nat) -> (m : Nat) ->

913− (xs : Vect ((n + m) + l) a) -> (ys : Vect (n + (m + l)) a) ->

914− xs ~=~ ys ->

915− drop n (take (n + m) xs) = take m (drop n ys)

916−dropTakeTakeDrop Z m xs xs Refl = Refl

917−dropTakeTakeDrop (S n) m (_ :: xs) (_ :: ys) prf = dropTakeTakeDrop n m xs ys (vectInjective2 prf)

918−

919−splitAtTakeDrop : (n : Nat) -> (xs : Vect (n + m) a) -> splitAt n xs = (take n xs, drop n xs)

920−splitAtTakeDrop Z xs = Refl

921−splitAtTakeDrop (S k) (x :: xs) with (splitAt k xs) proof p

922− | (tk, dr) = let prf = trans p (splitAtTakeDrop k xs)

923− in aux (cong {f=(x ::) . fst} prf) (cong {f=snd} prf)

924− where aux : {a, b : Type} -> {w, x : a} -> {y, z : b} -> w = x -> y = z -> (w, y) = (x, z)

925− aux Refl Refl = Refl

926−

927−zipWithIsLiftA2 : (f : a -> b -> c) -> (as : Vect n a) -> (bs : Vect n b) -> zipWith f as bs = [| f as bs |]

928−zipWithIsLiftA2 _ [] [] = Refl

929−zipWithIsLiftA2 f (a :: as) (b :: bs) = rewrite zipWithIsLiftA2 f as bs in Refl

930−zipWithIsLiftA3 : (f : a -> b -> c -> d) -> (as : Vect n a) -> (bs : Vect n b) -> (cs : Vect n c) -> zipWith3 f as bs cs = [| f as bs cs |]

931−zipWithIsLiftA3 _ [] [] [] = Refl

932−zipWithIsLiftA3 f (a :: as) (b :: bs) (c :: cs) = rewrite zipWithIsLiftA3 f as bs cs in Refl

933−

934−-- Note relationship to Applicative (Morphism (Fin n))

935−indexReplicate : (x : a) -> (n : Nat) -> (i : Fin n) -> index i (replicate n x) = x

936−indexReplicate x (S n) FZ = Refl

937−indexReplicate x (S n) (FS i) = indexReplicate x n i

938−indexZipWith : (f : a -> b -> c) -> (as : Vect n a) -> (bs : Vect n b) -> (i : Fin n) -> index i (zipWith f as bs) = f (index i as) (index i bs)

939−indexZipWith f (a :: _) (b :: _) FZ = Refl

940−indexZipWith f (_ :: as) (_ :: bs) (FS i) = indexZipWith f as bs i

941−indexTranspose : (x : Fin o) -> (y : Fin i) -> (xss : Vect o (Vect i a)) -> index y (index x xss) = index x (index y (transpose xss))

942−indexTranspose x y (xs :: xss) = rewrite prf in

943− rewrite sym $ indexZipWith Vect.(::) xs (transpose xss) y in Refl

944− where prf : index y (index x (xs :: xss)) = index x (index y xs :: index y (transpose xss))

945− prf = case x of

946− FZ => Refl

947− FS k => indexTranspose k y xss

948−

949−transposeTraverse : (xss : Vect o (Vect i a)) -> transpose xss = traverse Basics.id xss

950−transposeTraverse [] = Refl

951−transposeTraverse (xs :: xss) = rewrite zipWithIsLiftA2 Vect.(::) xs (transpose xss) in cong (transposeTraverse xss)

952−

953−traverseIdCons : (xs : Vect o a) -> (xss : Vect o (Vect i a)) -> traverse Basics.id [| xs :: xss |] = xs :: traverse Basics.id xss

954−traverseIdCons [] [] = Refl

955−traverseIdCons (x :: xs) (ys :: xss) = rewrite traverseIdCons xs xss in Refl

956−transposeCons : (xs : Vect o a) -> (xss : Vect o (Vect i a)) -> transpose (zipWith (::) xs xss) = xs :: transpose xss

957−transposeCons xs xss = rewrite zipWithIsLiftA2 Vect.(::) xs xss in rewrite transposeTraverse (pure (::) <*> xs <*> xss) in rewrite transposeTraverse xss in traverseIdCons xs xss

958−

959567--------------------------------------------------------------------------------

960568-- DecEq

961569--------------------------------------------------------------------------------

962570

571+vectInjective1 : {xs, ys : Vect n a} -> {x, y : a} -> x :: xs = y :: ys -> x = y

572+vectInjective1 {x=x} {y=x} {xs=xs} {ys=xs} Refl = Refl

573+

574+vectInjective2 : {xs, ys : Vect n a} -> {x, y : a} -> x :: xs = y :: ys -> xs = ys

575+vectInjective2 {x=x} {y=x} {xs=xs} {ys=xs} Refl = Refl

576+

963577implementation DecEq a => DecEq (Vect n a) where

964578 decEq [] [] = Yes Refl

965579 decEq (x :: xs) (y :: ys) with (decEq x y)

libs/base/Language/Reflection/Utils.idr+4−8

@@ -91,6 +91,7 @@ mutual

9191 showPrec d (ParentN n s) = showCon d "ParentN" $ showArg n ++ showArg s

9292 showPrec d (MethodN n) = showCon d "MethodN" $ showArg n

9393 showPrec d (CaseN fc n) = showCon d "CaseN" $ showArg fc ++ showArg n

94+ showPrec d (ElimN n) = showCon d "ElimN" $ showArg n

9495 showPrec d (ImplementationCtorN n) = showCon d "ImplementationCtorN" $ showArg n

9596 showPrec d (MetaN parent meta) = showCon d "MetaN" $ showArg parent ++ showArg meta

9697

@@ -115,6 +116,7 @@ mutual

115116 (ParentN n s) == (ParentN n' s') = n == n' && s == s'

116117 (MethodN n) == (MethodN n') = n == n'

117118 (CaseN fc n) == (CaseN fc' n') = fc == fc' && n == n'

119+ (ElimN n) == (ElimN n') = n == n'

118120 (ImplementationCtorN n) == (ImplementationCtorN n') = n == n'

119121 (MetaN parent meta) == (MetaN parent' meta') = parent == parent' && meta == meta'

120122 _ == _ = False

@@ -306,7 +308,7 @@ implementation Show Raw where

306308 my_show d (RApp tm tm') = assert_total $ showCon d "RApp" $ " " ++ my_show App tm ++ " " ++ my_show App tm'

307309 my_show d RType = "RType"

308310 my_show d (RConstant c) = assert_total $ showCon d "RConstant" $ showArg c

309− my_show d (RUType u) = "RUType"

311+ my_show d (RUType u) = "RUType"

310312

311313

312314implementation Show Err where

@@ -334,6 +336,7 @@ implementation Show Err where

334336 showPrec d (CantResolveAlts xs) = showCon d "CantResolveAlts" $ showArg xs

335337 showPrec d (NoValidAlts xs) = showCon d "NoValidAlts" $ showArg xs

336338 showPrec d (IncompleteTerm tm) = showCon d "IncompleteTerm" $ showArg tm

339+ showPrec d (NoEliminator s tm) = showCon d "NoEliminator" $ showArg s ++ showArg tm

337340 showPrec d UniverseError = "UniverseError"

338341 showPrec d ProgramLineComment = "ProgramLineComment"

339342 showPrec d (Inaccessible n) = showCon d "Inaccessible" $ showArg n

@@ -384,10 +387,3 @@ implementation Show tm => Show (FunClause tm) where

384387 showCon d "MkFunClause" $ showArg lhs ++ showArg rhs

385388 showPrec d (MkImpossibleClause lhs) =

386389 showCon d "MkImpossibleClause" $ showArg lhs

387−

388−implementation Functor FunClause where

389− map f (MkFunClause lhs rhs) = MkFunClause (f lhs) (f rhs)

390− map f (MkImpossibleClause lhs) = MkImpossibleClause (f lhs)

391−

392−implementation Functor FunDefn where

393− map f (DefineFun n clauses) = DefineFun n (map (map f) clauses)

libs/base/Makefile+1−1

@@ -1,4 +1,4 @@

1−IDRIS ?= idris

1+IDRIS := idris

22PKG := base

33

44build:

libs/base/System.idr+3−16

@@ -93,22 +93,9 @@ time : IO Integer

9393time = do MkRaw t <- foreign FFI_C "idris_time" (IO (Raw Integer))

9494 pure t

9595

96−||| Wall clock time

97−record Clock where

98− constructor MkClock

99− seconds : Integer

100− nanoseconds : Integer

101−

102−||| Get the system's wall clock time.

103−clockTime : IO Clock

104−clockTime

105− = do vm <- getMyVM

106− MkRaw c <- foreign FFI_C "idris_clock" (Ptr -> IO (Raw Clock)) vm

107− pure c

108−

109−||| Specify interval to sleep for in microseconds, must be nonnegative

110−usleep : (i : Int) -> { auto prf : So (i >= 0) } -> IO ()

111−usleep i = foreign FFI_C "idris_usleep" (Int -> IO ()) i

96+||| Specify interval to sleep for, must be in range [0, 1000000]

97+usleep : (i : Int) -> { auto prf : So (i >= 0 && i <= 1000000) } -> IO ()

98+usleep i = foreign FFI_C "usleep" (Int -> IO ()) i

11299

113100||| Execute a program and returns its exit status code.

114101system : String -> IO Int

libs/base/System/Concurrency/Raw.idr+10−9

@@ -8,7 +8,7 @@ import System

88

99||| Send a message of any type to the thread with the given thread id

1010||| Returns channel ID if the message was sent successfully, 0 otherwise

11−|||

11+|||

1212||| @channel an ID of a specific channel to send the message on. If 0,

1313||| the receiver will create a new channel ID

1414sendToThread : (thread_id : Ptr) -> (channel : Int) -> a -> IO Int

@@ -29,7 +29,7 @@ checkMsgs = do me <- getMyVM

2929checkMsgsTimeout : Int -> IO Bool

3030checkMsgsTimeout timeout

3131 = do me <- getMyVM

32− msgs <- foreign FFI_C "idris_checkMessagesTimeout"

32+ msgs <- foreign FFI_C "idris_checkMessagesTimeout"

3333 (Ptr -> Int -> IO Ptr) me timeout

3434 null <- nullPtr msgs

3535 pure (not null)

@@ -43,7 +43,7 @@ channel_id : Ptr -> IO Int

4343channel_id msg = foreign FFI_C "idris_getChannel" (Ptr -> IO Int) msg

4444

4545||| Check for messages initiating a conversation in the process inbox.

46−||| Returns either 'Nothing', if none, or 'Just (pid, channel)' as pid

46+||| Returns either 'Nothing', if none, or 'Just (pid, channel)' as pid

4747||| of sender and new channel id.

4848listenMsgs : IO (Maybe (Ptr, Int))

4949listenMsgs = do me <- getMyVM

@@ -58,7 +58,7 @@ listenMsgs = do me <- getMyVM

5858||| Check for messages from a specific sender/channel in the process inbox

5959||| If channel is '0', accept on any channel.

6060checkMsgsFrom : Ptr -> (channel : Int) -> IO Bool

61−checkMsgsFrom sender channel

61+checkMsgsFrom sender channel

6262 = do me <- getMyVM

6363 msgs <- foreign FFI_C "idris_checkMessagesFrom" (Ptr -> Int -> Ptr -> IO Ptr)

6464 me channel sender

@@ -73,7 +73,6 @@ getMsg : IO a

7373getMsg {a} = do me <- getMyVM

7474 m <- foreign FFI_C "idris_recvMessage" (Ptr -> IO Ptr) me

7575 MkRaw x <- foreign FFI_C "idris_getMsg" (Ptr -> IO (Raw a)) m

76− foreign FFI_C "idris_freeMsg" (Ptr -> IO ()) m

7776 pure x

7877

7978||| Check inbox for messages. If there are none, blocks until a message

@@ -81,9 +80,9 @@ getMsg {a} = do me <- getMyVM

8180||| Note that this is not at all type safe! It is intended to be used in

8281||| a type safe wrapper.

8382getMsgWithSender : IO (Ptr, Int, a)

84−getMsgWithSender {a}

83+getMsgWithSender {a}

8584 = do me <- getMyVM

86− m <- foreign FFI_C "idris_recvMessage"

85+ m <- foreign FFI_C "idris_recvMessage"

8786 (Ptr -> IO Ptr) me

8887 MkRaw x <- foreign FFI_C "idris_getMsg" (Ptr -> IO (Raw a)) m

8988 vm <- sender m

@@ -95,12 +94,12 @@ getMsgWithSender {a}

9594||| blocks until a message arrives. Returns `Nothing` if the sender isn't

9695||| alive

9796getMsgFrom : Ptr -> (channel : Int) -> IO (Maybe a)

98−getMsgFrom {a} sender channel

97+getMsgFrom {a} sender channel

9998 = do me <- getMyVM

10099 m <- foreign FFI_C "idris_recvMessageFrom"

101100 (Ptr -> Int -> Ptr -> IO Ptr) me channel sender

102101 null <- nullPtr m

103− if null

102+ if null

104103 then pure Nothing

105104 else do

106105 MkRaw x <- foreign FFI_C "idris_getMsg" (Ptr -> IO (Raw a)) m

@@ -111,3 +110,5 @@ stopThread : IO a

111110stopThread = do vm <- getMyVM

112111 MkRaw res <- foreign FFI_C "idris_stopThread" (Ptr -> IO (Raw a)) vm

113112 pure res

113+

114+

libs/base/base.ipkg+1−11

@@ -1,20 +1,18 @@

11package base

22

3−opts = "--nobasepkgs --total --partial-eval -i ../prelude"

3+opts = "--nobasepkgs --total --no-elim-deprecation-warnings --partial-eval -i ../prelude"

44

55modules = Control.Arrow

66 , Control.Catchable

77 , Control.Category

88 , Control.IOExcept

99 , Control.Isomorphism

10−

1110 , Control.Monad.Identity

1211 , Control.Monad.Reader

1312 , Control.Monad.RWS

1413 , Control.Monad.State

1514 , Control.Monad.Trans

1615 , Control.Monad.Writer

17−

1816 , Data.Bits

1917 , Data.Buffer

2018 , Data.Complex

@@ -22,31 +20,23 @@ modules = Control.Arrow

2220 , Data.Fin

2321 , Data.HVect

2422 , Data.IORef

25−

2623 , Data.List

2724 , Data.List.Quantifiers

2825 , Data.List.Views

29−

3026 , Data.Mod2

3127 , Data.Morphisms

3228 , Data.Nat.Views

3329 , Data.Primitives.Views

3430 , Data.So

35−

3631 , Data.String

3732 , Data.String.Views

38−

3933 , Data.Vect

4034 , Data.Vect.Quantifiers

4135 , Data.Vect.Views

42−

4336 , Debug.Error

4437 , Debug.Trace

45−

4638 , Language.Reflection.Utils

47−

4839 , Syntax.PreorderReasoning

49−

5040 , System

5141 , System.Concurrency.Channels

5242 , System.Concurrency.Raw

libs/contrib/CFFI/Types.idr+2−2

@@ -70,9 +70,9 @@ mutual

7070 alignOfCT I8 = 1

7171 alignOfCT I16 = 2

7272 alignOfCT I32 = 4

73− alignOfCT I64 = min prim__sizeofPtr 8

73+ alignOfCT I64 = 8

7474 alignOfCT FLOAT = 4

75− alignOfCT DOUBLE = min prim__sizeofPtr 8

75+ alignOfCT DOUBLE = 8

7676 alignOfCT PTR = prim__sizeofPtr

7777

7878 ||| Alignment requirement of the type

libs/contrib/Control/Algebra.idr−14

@@ -126,20 +126,6 @@ pow' : RingWithUnity a => a -> Nat -> a

126126pow' _ Z = unity

127127pow' x (S n) = x <.> pow' x n

128128

129−-- TODO: This can be more efficient:

130−-- stimes 5 x = x <+> (x <+> (x <+> (x <+> x)))

131−-- = x <+> ((x <+> x) <+> (x <+> x))

132−-- = let y = x <+> x in x <+> (y <+> y)

133−-- 4 <+>s into 3 <+>

134−||| Combine `n` copies of a value with `<+>`

135−stimes : Semigroup a => (n : Nat) -> {auto prf : IsSucc n} -> a -> a

136−stimes (S Z) x = x

137−stimes (S (S k)) x = x <+> stimes (S k) x

138−

139−||| Like `stimes`, but accepting `Z` as argument.

140−mtimes : Monoid a => (n : Nat) -> a -> a

141−mtimes Z x = neutral

142−mtimes (S k) x = stimes (S k) x

143129

144130-- XXX todo:

145131-- Structures where "abs" make sense.

libs/contrib/Control/Algebra/Lattice.idr−16

@@ -25,9 +25,6 @@ implementation JoinSemilattice Nat where

2525implementation Ord a => JoinSemilattice (MaxiphobicHeap a) where

2626 join = merge

2727

28−JoinSemilattice Bool where

29− join a b = a || b

30−

3128||| Sets equipped with a binary operation that is commutative, associative and

3229||| idempotent. Must satisfy the following laws:

3330|||

@@ -45,9 +42,6 @@ interface MeetSemilattice a where

4542implementation MeetSemilattice Nat where

4643 meet = minimum

4744

48−MeetSemilattice Bool where

49− meet a b = a && b

50−

5145||| Sets equipped with a binary operation that is commutative, associative and

5246||| idempotent and supplied with a unitary element. Must satisfy the following

5347||| laws:

@@ -69,9 +63,6 @@ interface JoinSemilattice a => BoundedJoinSemilattice a where

6963implementation BoundedJoinSemilattice Nat where

7064 bottom = Z

7165

72−BoundedJoinSemilattice Bool where

73− bottom = False

74−

7566||| Sets equipped with a binary operation that is commutative, associative and

7667||| idempotent and supplied with a unitary element. Must satisfy the following

7768||| laws:

@@ -90,9 +81,6 @@ BoundedJoinSemilattice Bool where

9081interface MeetSemilattice a => BoundedMeetSemilattice a where

9182 top : a

9283

93−BoundedMeetSemilattice Bool where

94− top = True

95−

9684||| Sets equipped with two binary operations that are both commutative,

9785||| associative and idempotent, along with absorbtion laws for relating the two

9886||| binary operations. Must satisfy the following:

@@ -113,8 +101,6 @@ interface (JoinSemilattice a, MeetSemilattice a) => Lattice a where { }

113101

114102implementation Lattice Nat where { }

115103

116−Lattice Bool where { }

117−

118104||| Sets equipped with two binary operations that are both commutative,

119105||| associative and idempotent and supplied with neutral elements, along with

120106||| absorbtion laws for relating the two binary operations. Must satisfy the

@@ -136,5 +122,3 @@ Lattice Bool where { }

136122||| forall a, meet a top == top

137123||| forall a, join a bottom == bottom

138124interface (BoundedJoinSemilattice a, BoundedMeetSemilattice a) => BoundedLattice a where { }

139−

140−BoundedLattice Bool where { }

libs/contrib/Control/Algebra/Laws.idrdeleted−153

@@ -1,153 +0,0 @@

1−module Control.Algebra.Laws

2−

3−import Prelude.Algebra as A

4−import Control.Algebra

5−import Interfaces.Verified

6−

7−%access export

8−

9−||| -(-x) = x in any verified group.

10−inverseSquaredIsIdentity : VerifiedGroup t => (x : t) ->

11− inverse (inverse x) = x

12−inverseSquaredIsIdentity x =

13− let

14− ix = inverse x

15− iix = inverse ix

16− in

17− rewrite sym $ monoidNeutralIsNeutralR iix in

18− rewrite sym $ groupInverseIsInverseL x in

19− rewrite sym $ semigroupOpIsAssociative x ix iix in

20− rewrite groupInverseIsInverseL ix in

21− monoidNeutralIsNeutralL x

22−

23−||| -0 = 0 in any verified group.

24−inverseNeutralIsNeutral : VerifiedGroup t =>

25− inverse (the t A.neutral) = A.neutral

26−inverseNeutralIsNeutral {t} =

27− let e = the t neutral in

28− rewrite sym $ cong {f = inverse} (groupInverseIsInverseL e) in

29− rewrite monoidNeutralIsNeutralR $ inverse e in

30− inverseSquaredIsIdentity e

31−

32−||| -(x + y) = -y + -x in any verified group.

33−inverseOfSum : VerifiedGroup t => (l, r : t) ->

34− inverse (l <+> r) = inverse r <+> inverse l

35−inverseOfSum {t} l r =

36− let

37− e = the t neutral

38− il = inverse l

39− ir = inverse r

40− sum = l <+> r

41− ilr = inverse sum

42− iril = ir <+> il

43− ile = il <+> e

44− in

45− -- expand

46− rewrite sym $ monoidNeutralIsNeutralR ilr in

47− rewrite sym $ groupInverseIsInverseR r in

48− rewrite sym $ monoidNeutralIsNeutralL ir in

49− rewrite sym $ groupInverseIsInverseR l in

50− -- shuffle

51− rewrite semigroupOpIsAssociative ir il l in

52− rewrite sym $ semigroupOpIsAssociative iril l r in

53− rewrite sym $ semigroupOpIsAssociative iril sum ilr in

54− -- contract

55− rewrite sym $ monoidNeutralIsNeutralL il in

56− rewrite groupInverseIsInverseL sum in

57− rewrite sym $ semigroupOpIsAssociative (ir <+> ile) l ile in

58− rewrite semigroupOpIsAssociative l il e in

59− rewrite groupInverseIsInverseL l in

60− rewrite monoidNeutralIsNeutralL e in

61− Refl

62−

63−||| -(x + y) = -x + -y in any verified abelian group.

64−inverseDistributesOverGroupOp : VerifiedAbelianGroup t => (l, r : t) ->

65− inverse (l <+> r) = inverse l <+> inverse r

66−inverseDistributesOverGroupOp l r =

67− rewrite abelianGroupOpIsCommutative (inverse l) (inverse r) in

68− inverseOfSum l r

69−

70−||| Anything multiplied by zero yields zero back in a verified ring.

71−multNeutralAbsorbingL : VerifiedRing t => (r : t) ->

72− A.neutral <.> r = A.neutral

73−multNeutralAbsorbingL {t} r =

74− let

75− e = the t neutral

76− ir = inverse r

77− exr = e <.> r

78− iexr = inverse exr

79− in

80− rewrite sym $ monoidNeutralIsNeutralR exr in

81− rewrite sym $ groupInverseIsInverseR exr in

82− rewrite sym $ semigroupOpIsAssociative iexr exr ((iexr <+> exr) <.> r) in

83− rewrite groupInverseIsInverseR exr in

84− rewrite sym $ ringOpIsDistributiveR e e r in

85− rewrite monoidNeutralIsNeutralR e in

86− groupInverseIsInverseR exr

87−

88−||| Anything multiplied by zero yields zero back in a verified ring.

89−multNeutralAbsorbingR : VerifiedRing t => (l : t) ->

90− l <.> A.neutral = A.neutral

91−multNeutralAbsorbingR {t} l =

92− let

93− e = the t neutral

94− il = inverse l

95− lxe = l <.> e

96− ilxe = inverse lxe

97− in

98− rewrite sym $ monoidNeutralIsNeutralL lxe in

99− rewrite sym $ groupInverseIsInverseL lxe in

100− rewrite semigroupOpIsAssociative (l <.> (lxe <+> ilxe)) lxe ilxe in

101− rewrite groupInverseIsInverseL lxe in

102− rewrite sym $ ringOpIsDistributiveL l e e in

103− rewrite monoidNeutralIsNeutralL e in

104− groupInverseIsInverseL lxe

105−

106−||| Inverse operator can be extracted before multiplication.

107−||| (-x)y = -(xy)

108−multInverseInversesL : VerifiedRing t => (l, r : t) ->

109− inverse l <.> r = inverse (l <.> r)

110−multInverseInversesL l r =

111− let

112− il = inverse l

113− lxr = l <.> r

114− ilxr = il <.> r

115− i_lxr = inverse lxr

116− in

117− rewrite sym $ monoidNeutralIsNeutralR ilxr in

118− rewrite sym $ groupInverseIsInverseR lxr in

119− rewrite sym $ semigroupOpIsAssociative i_lxr lxr ilxr in

120− rewrite sym $ ringOpIsDistributiveR l il r in

121− rewrite groupInverseIsInverseL l in

122− rewrite multNeutralAbsorbingL r in

123− monoidNeutralIsNeutralL i_lxr

124−

125−||| Inverse operator can be extracted before multiplication.

126−||| x(-y) = -(xy)

127−multInverseInversesR : VerifiedRing t => (l, r : t) ->

128− l <.> inverse r = inverse (l <.> r)

129−multInverseInversesR l r =

130− let

131− ir = inverse r

132− lxr = l <.> r

133− lxir = l <.> ir

134− ilxr = inverse lxr

135− in

136− rewrite sym $ monoidNeutralIsNeutralL lxir in

137− rewrite sym $ groupInverseIsInverseL lxr in

138− rewrite semigroupOpIsAssociative lxir lxr ilxr in

139− rewrite sym $ ringOpIsDistributiveL l ir r in

140− rewrite groupInverseIsInverseR r in

141− rewrite multNeutralAbsorbingR l in

142− monoidNeutralIsNeutralR ilxr

143−

144−||| Multiplication of inverses is the same as multiplication of

145−||| original elements.

146−||| (-x)(-y) = xy

147−multNegativeByNegativeIsPositive : VerifiedRing t => (l, r : t) ->

148− inverse l <.> inverse r = l <.> r

149−multNegativeByNegativeIsPositive l r =

150− rewrite multInverseInversesR (inverse l) r in

151− rewrite sym $ multInverseInversesL (inverse l) r in

152− rewrite inverseSquaredIsIdentity l in

153− Refl

libs/contrib/Control/Delayed.idrdeleted−26

@@ -1,26 +0,0 @@

1−||| Utilities functions for contitionally delaying values.

2−module Control.Delayed

3−

4−%default total

5−

6−||| Type-level function for a conditionally delayed type (`Lazy` or `Inf`).

7−public export

8−delayed : DelayReason -> Bool -> Type -> Type

9−delayed r False a = a

10−delayed r True a = Delayed r a

11−

12−||| Type-level function for a conditionally infinite type.

13−public export

14−inf : Bool -> Type -> Type

15−inf = delayed Infinite

16−

17−||| Type-level function for a conditionally lazy type.

18−public export

19−lazy : Bool -> Type -> Type

20−lazy = delayed LazyValue

21−

22−||| Conditionally delay a value.

23−export

24−delay : (d : Bool) -> a -> delayed r d a

25−delay False x = x

26−delay True x = Delay x

libs/contrib/Control/Isomorphism/Extra.idrdeleted−42

@@ -1,42 +0,0 @@

1−module Control.Isomorphism.Extra

2−

3−import Control.Isomorphism

4−import Interfaces.Verified

5−

6−%default total

7−%access public export

8−

9−||| Form an `Iso` that is the identity for almost all inputs, except it will swap either of the arguments for the other.

10−||| It is the same function in both directions.

11−|||

12−||| @ l the value that will be turned into `r`

13−||| @ r the value that will be turned into `l`

14−swapped : DecEq a => (l : a) -> (r : a) -> Iso a a

15−swapped {a} l r = MkIso swap swap prf prf

16− where swap : a -> a

17− swap x = case decEq l x of { Yes _ => r; No _ => case decEq r x of { Yes _ => l; No _ => x } }

18− prf : (x : a) -> swap (swap x) = x

19− prf x with (decEq l x)

20− | (Yes lex) with (decEq r x)

21− | (Yes rex) with (decEq l r)

22− | (Yes ler) = rex

23− | (No lnr) = absurd $ lnr $ trans lex $ sym rex

24− | (No rnx) with (decEq l r)

25− | (Yes ler) = absurd $ rnx $ trans (sym ler) lex

26− | (No lnr) with (decEq r r)

27− | (Yes Refl) = lex

28− | (No rnr) = absurd $ rnr Refl

29− | (No lnx) with (decEq r x)

30− | (Yes rex) with (decEq l l)

31− | (Yes Refl) = rex

32− | (No lnl) = absurd $ lnl Refl

33− | (No rnx) with (decEq l x)

34− | (Yes lex) = absurd $ lnx lex

35− | (No lnx') with (decEq r x)

36− | (Yes rex) = absurd $ rnx rex

37− | (No rnx') = Refl

38−

39−mapIso : VerifiedFunctor f => Iso a b -> Iso (f a) (f b)

40−mapIso {f} (MkIso to from toFrom fromTo) = MkIso (map to) (map from) (prf to from toFrom) (prf from to fromTo)

41− where prf : {a : Type} -> {b : Type} -> (to : a -> b) -> (from : b -> a) -> (toFrom : (x : b) -> to (from x) = x) -> (x : f b) -> map to (map from x) = x

42− prf to' from' toFrom' x = rewrite sym $ functorComposition x from' to' in functorIdentity (to' . from') toFrom' x

libs/contrib/Control/Isomorphism/Fin.idrdeleted−54

@@ -1,54 +0,0 @@

1−module Control.Isomorphism.Fin

2−

3−import Control.Isomorphism

4−import Data.Fin

5−

6−%default total

7−%access public export

8−

9−strengthenLeft : (i : Fin (S n)) -> (prf : strengthen i = Left x) -> i = Fin.last

10−strengthenLeft {n = Z} FZ Refl = Refl

11−strengthenLeft {n = S _} FZ Refl impossible

12−strengthenLeft {n = S k} (FS x) prf with (strengthen x) proof p

13− | (Left l) = rewrite strengthenLeft x (sym p) in Refl

14− | (Right r) = absurd $ leftNotRight $ sym prf

15−strengthenRight : (i : Fin (S n)) -> (prf : strengthen i = Right x) -> weaken x = i

16−strengthenRight {n = Z} FZ Refl impossible

17−strengthenRight {n = S _} FZ Refl = Refl

18−strengthenRight {n = S k} (FS x) prf with (strengthen x) proof p

19− | (Left l) = absurd $ leftNotRight prf

20− | (Right r) = rewrite rightInjective $ sym prf in rewrite strengthenRight x $ sym p in Refl

21−strengthenLast : (n : Nat) -> strengthen (last {n=n}) = Left last

22−strengthenLast Z = Refl

23−strengthenLast (S k) with (strengthen (last {n=k})) proof p

24− | (Left l) = cong {f = Left . FS} $ leftInjective $ trans p $ strengthenLast k

25− | (Right _) with (trans p (strengthenLast k))

26− | Refl impossible

27−strengthenWeaken : (n : Fin k) -> strengthen (weaken n) = Right n

28−strengthenWeaken FZ = Refl

29−strengthenWeaken (FS n) with (strengthen (weaken n)) proof p

30− | (Left _) with (trans p (strengthenWeaken n))

31− | Refl impossible

32− | (Right r) = cong {f = Right . FS} $ rightInjective $ trans p $ strengthenWeaken n

33−

34−||| Sends `FZ` to `last`, and `FS x` to `x`.

35−rotatedDown : Iso (Fin n) (Fin n)

36−rotatedDown = MkIso to from toFrom fromTo

37− where to : Fin k -> Fin k

38− to FZ = last

39− to (FS x) = weaken x

40− from : Fin k -> Fin k

41− from {k = Z} _ impossible

42− from {k = S k} j = either (const FZ) FS $ strengthen j

43− toFrom : (j : Fin k) -> to (from j) = j

44− toFrom {k = S Z} FZ = Refl

45− toFrom {k = S (S k)} FZ = Refl

46− toFrom {k = S (S k)} (FS i) with (strengthen i) proof p

47− toFrom {k = S (S k)} (FS i) | (Left l) = rewrite strengthenLeft i (sym p) in Refl

48− toFrom {k = S (S k)} (FS i) | (Right r) = rewrite strengthenRight i (sym p) in Refl

49− fromTo : (j : Fin k) -> from (to j) = j

50− fromTo {k = S k} FZ = rewrite strengthenLast k in Refl

51− fromTo (FS x) = rewrite strengthenWeaken x in Refl

52−||| Sends `last` to `FZ` and every other `x` to `FS x`.

53−rotatedUp : Iso (Fin n) (Fin n)

54−rotatedUp = isoSym rotatedDown

libs/contrib/Control/Isomorphism/Vect.idrdeleted−155

@@ -1,155 +0,0 @@

1−module Control.Isomorphism.Vect

2−

3−import Control.Isomorphism

4−import Data.Vect

5−import Interfaces.Verified

6−

7−%default total

8−%access public export

9−

10−||| `Vect Z a` has only one value: `[]`.

11−nilUnit : Iso (Vect Z a) ()

12−nilUnit = MkIso (const ()) (const []) (\() => Refl) (\[] => Refl)

13−

14−||| A `Vect (S Z) a` is just an `a`.

15−oneIdentity : Iso (Vect (S Z) a) a

16−oneIdentity = MkIso to (\x => [x]) (\x => Refl) (\[x] => Refl)

17− where to : Vect 1 a -> a

18− to [x] = x

19−

20−||| Moves between `x :: xs` and `(x, xs)`.

21−consPair : Iso (Vect (S n) a) (a, Vect n a)

22−consPair = MkIso to (uncurry (::)) (\(x, xs) => Refl) (\(x :: xs) => Refl)

23− where to : Vect (S n) a -> (a, Vect n a)

24− to (x :: xs) = (x, xs)

25−

26−||| An `Iso` based on `splitAt` and `(++)`.

27−splitPair : Iso (Vect (n + m) a) (Vect n a, Vect m a)

28−splitPair {n} {m} = MkIso (splitAt n) (uncurry (++)) toFrom fromTo

29− where pairify : q = w -> e = r -> (q, e) = (w, r)

30− pairify Refl Refl = Refl

31− toFrom (ns, ms) = trans (splitAtTakeDrop n (ns ++ ms)) $ pairify (takePrefix ns ms) (dropPrefix ns ms)

32− fromTo xs = rewrite splitAtTakeDrop {m} n xs in takeDropConcat n xs

33−

34−||| An `Iso` based on `zip` and `unzip`.

35−zipped : Iso (Vect n a, Vect n b) (Vect n (a, b))

36−zipped = MkIso (uncurry zip) unzip toFrom (\(as, bs) => fromTo as bs)

37− where toFrom : {n : Nat} -> (xs : Vect n (a, b)) -> uncurry Vect.zip (unzip xs) = xs

38− toFrom [] = Refl

39− toFrom ((a, b) :: xs) with (unzip xs) proof p

40− | (as, bs) = cong $ trans (cong p) (toFrom xs)

41− fromTo : {n : Nat} -> (as : Vect n a) -> (bs : Vect n b) -> unzip (zip as bs) = (as, bs)

42− fromTo [] [] = Refl

43− fromTo (a :: as) (b :: bs) = rewrite fromTo as bs in Refl

44−

45−||| An `Iso` based on `zip3` and `unzip3`.

46−zipped3 : Iso (Vect n a, Vect n b, Vect n c) (Vect n (a, b, c))

47−zipped3 = MkIso (uncurrry zip3) unzip3 toFrom (\(as, bs, cs) => fromTo as bs cs)

48− where uncurrry : (w -> x -> y -> z) -> ((w, x, y) -> z)

49− uncurrry w (x, y, z) = w x y z

50− toFrom : {n : Nat} -> (xs : Vect n (a, b, c)) -> uncurrry Vect.zip3 (unzip3 xs) = xs

51− toFrom [] = Refl

52− toFrom ((a, b, c) :: xs) with (unzip3 xs) proof p

53− | (as, bs, cs) = cong $ trans (cong p) (toFrom xs)

54− fromTo : {n : Nat} -> (as : Vect n a) -> (bs : Vect n b) -> (cs : Vect n c) -> unzip3 (zip3 as bs cs) = (as, bs, cs)

55− fromTo [] [] [] = Refl

56− fromTo (a :: as) (b :: bs) (c :: cs) = rewrite fromTo as bs cs in Refl

57−

58−||| An `Iso` based on `transpose`.

59−transposition : Iso (Vect o (Vect i a)) (Vect i (Vect o a))

60−transposition {a} = MkIso transpose transpose prf prf

61− where prf : {i : Nat} -> {o : Nat} -> (xss : Vect o (Vect i a)) -> transpose (transpose xss) = xss

62− prf [] = vectMustBeNil $ transpose [| [] |]

63− prf (xs :: xss) = rewrite transposeCons xs (transpose xss) in cong (prf xss)

64−

65−||| Split the `Vect` every `m` elements, making `n` `Vect m a`s.

66−||| The result is rectangular and has the same order as the original.

67−|||

68−||| This is the inverse of `concat`.

69−unconcat : Vect (n * m) a -> Vect n (Vect m a)

70−unconcat {n = Z} [] = []

71−unconcat {n = S k} {m} xs with (splitAt m xs)

72− | (xs', xss) = xs' :: unconcat xss

73−||| An `Iso` based on `unconcat` and `concat`.

74−|||

75−||| ```idris example

76−||| from rectangular [[1,2,3],[4,5,6]]

77−||| ```

78−rectangular : Iso (Vect (n * m) a) (Vect n (Vect m a))

79−rectangular = MkIso unconcat concat toFrom fromTo

80− where toFrom : (xss : Vect i (Vect o a)) -> unconcat (concat xss) = xss

81− toFrom {i = Z} [] = Refl

82− toFrom {i = S i} {o} (xs :: xss) = rewrite splitAtTakeDrop o {m = i * o} (xs ++ concat xss) in

83− rewrite takePrefix xs (concat xss) in

84− rewrite dropPrefix xs (concat xss) in

85− cong (toFrom xss)

86− fromTo : (xs : Vect (i * o) a) -> concat (unconcat xs) = xs

87− fromTo {i = Z} [] = Refl

88− fromTo {i = S i} {o} xs = rewrite splitAtTakeDrop o {m = i * o} xs in

89− rewrite fromTo {i} {o} (drop o xs) in

90− takeDropConcat o xs

91−

92−-- Not an Iso because (=) is not extensional, but it works in spirit

93−||| Go through all possible inputs and tabulate the outputs in a `Vect`.

94−|||

95−||| Or: turn a function from indices to values into a `Vect`.

96−||| Or: the inverse of `index`.

97−unindex : (Fin n -> a) -> Vect n a

98−unindex {n = Z} _ = []

99−unindex {n = S k} f = f FZ :: unindex (f . FS)

100−

101−||| Indexing into the table of outputs of `f` is like calling `f` itself.

102−indexUnindex : (i : Fin n) -> (f : Fin n -> a) -> index i (unindex f) = f i

103−indexUnindex FZ _ = Refl

104−indexUnindex (FS k) f = rewrite indexUnindex k (f . FS) in Refl

105−||| Given a function `f`, a `Vect` `xs`, and a proof that calling `f` gives the same result as indexing into `xs`,

106−||| prove that `xs` is the table of outputs of `f`.

107−unindexIndex' : (xs : Vect n a) -> (f : Fin n -> a) -> ((i : Fin n) -> f i = index i xs) -> unindex f = xs

108−unindexIndex' [] _ _ = Refl

109−unindexIndex' (x :: xs) f prf = rewrite prf FZ in rewrite unindexIndex' xs (f . FS) (\i => rewrite prf $ FS i in Refl) in Refl

110−||| If `f` and `g` are extensionally equal (equal outputs for all inputs), then `unindex f = unindex g`.

111−congExtUnindex : (f : Fin n -> a) -> (g : Fin n -> a) -> ((i : Fin n) -> f i = g i) -> unindex f = unindex g

112−congExtUnindex f g p = unindexIndex' (unindex g) f $ \i => trans (p i) $ sym $ indexUnindex i g

113−||| Functions with the same tables are the same themselves.

114−injExtUnindex : (f : Fin n -> a) -> (g : Fin n -> a) -> unindex f = unindex g -> ((i : Fin n) -> f i = g i)

115−injExtUnindex f g p i = rewrite sym $ indexUnindex i f in rewrite sym $ indexUnindex i g in cong p

116−||| A simpler version of `unindexIndex'` which only proves that `unindex` is the inverse of `index`.

117−unindexIndex : (xs : Vect n a) -> unindex (\i => index i xs) = xs

118−unindexIndex xs = unindexIndex' xs (\i => index i xs) (\i => Refl)

119−

120−||| Given a function that computes an index in the input from the index in the output, produce a `Vect o` of elements from the input.

121−|||

122−||| This is the map function of the functor `\i => Vect i a` from `\i, o => Fin o -> Fin i` to `\i, o => Vect i a -> Vect o a`.

123−fromIndices : (Fin o -> Fin i) -> Vect i a -> Vect o a

124−fromIndices f xs = unindex (flip index xs . f)

125−indexFromIndices : (f : Fin o -> Fin i) -> (xs : Vect i a) -> (n : Fin o) -> index n (fromIndices f xs) = index (f n) xs

126−indexFromIndices f xs n = indexUnindex n (\i => index (f i) xs)

127−fromIndicesFromIndices : (to : Fin n -> Fin n) -> (from : Fin n -> Fin n) -> (fromTo : (i : Fin n) -> from (to i) = i) -> (xs : Vect n a) -> fromIndices to (fromIndices from xs) = xs

128−fromIndicesFromIndices to from fromTo xs = unindexIndex' xs (\x => index (to x) (unindex (\x' => index (from x') xs))) $ \i =>

129− rewrite indexUnindex (to i) (\x' => index (from x') xs) in rewrite fromTo i in Refl

130−

131−||| Given a permutation of the indices, provide an `Iso` that can permute a `Vect n` the "same" way. More precisely,

132−||| if the index `i` is sent to `j`, then the element at index `i` ends up at index `j` (`indexPermuted`). An

133−||| `Iso (Fin n) (Fin n)` represents a permutation of the integers `[0, n)` because it ensures that no elements

134−||| are "lost" or "duplicated".

135−|||

136−||| Note this has the *opposite* behavior to `fromIndices`. This function is more "visceral"; it can be imagined

137−||| as shuffling a `Vect` in the same way `map (to permutation)` shuffles `range`. Or, in more categorical terms,

138−||| `fromIndices` represents a contravariant functor from the category `\i, o => Fin i -> Fin o` to `\i, o => Vect i a -> Vect o a`,

139−||| and `permuted` represents that functor restricted to isomorphisms and made covariant with `isoSym`.

140−|||

141−||| ```idris example

142−||| to (permuted (stimes 2 rotatedDown)) [1, 2, 3, 4, 5] == [3, 4, 5, 1, 2]

143−||| to (permuted (swapped 3 0)) [1, 2, 3, 4, 5] == [4, 2, 3, 1, 5]

144−||| ```

145−|||

146−||| @ permutation an `Iso` representing the transformation on the indices

147−permuted : (permutation : Iso (Fin n) (Fin n)) -> Iso (Vect n a) (Vect n a)

148−-- [to, from => f from, f to] is not a typo

149−-- fromIndices needs a function outputIdx => inputIdx, so to "align" the "motion" of the Fins with the elements, to uses from and from uses to.

150−permuted (MkIso toI fromI toFromI fromToI) = MkIso (fromIndices fromI) (fromIndices toI) (fromIndicesFromIndices fromI toI toFromI) (fromIndicesFromIndices toI fromI fromToI)

151−permutedSym : (permutation : Iso (Fin n) (Fin n)) -> permuted (isoSym permutation) = isoSym (permuted permutation)

152−permutedSym (MkIso to from toFrom fromTo) = Refl

153−indexPermuted : (permutation : Iso (Fin n) (Fin n)) -> (i : Fin n) -> (xs : Vect n a) -> index i xs = index (to permutation i) (to (permuted permutation) xs)

154−indexPermuted (MkIso to from toFrom fromTo) i xs = replace {P = \xs' => index i xs' = index (to i) (fromIndices from xs) } (fromIndicesFromIndices to from fromTo xs) $

155− rewrite indexFromIndices to (fromIndices from xs) i in Refl

libs/contrib/Control/Monad/Syntax.idrdeleted−18

@@ -1,18 +0,0 @@

1−module Control.Monad.Syntax

2−

3−%default total

4−%access public export

5−

6−infixr 1 =<<, <=<, >=>

7−

8−||| Left-to-right Kleisli composition of monads.

9−(>=>) : Monad m => (a -> m b) -> (b -> m c) -> (a -> m c)

10−(>=>) f g = \x => f x >>= g

11−

12−||| Right-to-left Kleisli composition of monads, flipped version of `>=>`.

13−(<=<) : Monad m => (b -> m c) -> (a -> m b) -> (a -> m c)

14−(<=<) = flip (>=>)

15−

16−||| Right-to-left monadic bind, flipped version of `>>=`.

17−(=<<) : Monad m => (a -> m b) -> m a -> m b

18−(=<<) = flip (>>=)

libs/contrib/Control/ST.idr+12−7

@@ -1,9 +1,7 @@

11module Control.ST

22

3−import Control.IOExcept

43import Language.Reflection.Utils

5−

6−import public Data.Fuel

4+import Control.IOExcept

75

86%default total

97

@@ -396,10 +394,17 @@ runST env (Call prog res_prf) k

396394runST env (Read lbl prf) k = k (lookupEnv prf env) env

397395runST env (Write lbl prf val) k = k () (updateEnv prf env val)

398396

397+export

398+data Fuel = Empty | More (Lazy Fuel)

399+

400+export partial

401+forever : Fuel

402+forever = More forever

403+

399404runSTLoop : Fuel -> Env invars -> STransLoop m a invars outfn ->

400405 (k : (x : a) -> Env (outfn x) -> m b) ->

401406 (onDry : m b) -> m b

402−runSTLoop Dry _ _ _ onDry = onDry

407+runSTLoop Empty _ _ _ onDry = onDry

403408runSTLoop (More x) env (Bind prog next) k onDry

404409 = runST env prog (\prog', env' => runSTLoop x env' (next prog') k onDry)

405410runSTLoop (More x) env (Pure result) k onDry = k result env

@@ -584,10 +589,10 @@ run prog = runST [] prog (\res, env' => pure res)

584589

585590export

586591runLoop : Applicative m => Fuel -> STLoop m a [] ->

587− (onDry : m a) ->

592+ (onEmpty : m a) ->

588593 m a

589−runLoop fuel prog onDry

590− = runSTLoop fuel [] prog (\res, env' => pure res) onDry

594+runLoop fuel prog onEmpty

595+ = runSTLoop fuel [] prog (\res, env' => pure res) onEmpty

591596

592597||| runWith allows running an STrans program with an initial environment,

593598||| which must be consumed.

libs/contrib/Control/ST/File.idrdeleted−247

@@ -1,247 +0,0 @@

1−module Control.ST.File

2−

3−import Control.ST

4−import Control.IOExcept

5−

6−%default total

7−

8−||| A record of the file modes that can read from a file.

9−public export

10−data ValidModeRead : Mode -> Type where

11− VMRRead : ValidModeRead Read

12− VMRReadW : ValidModeRead ReadWrite

13− VMRReadWT : ValidModeRead ReadWriteTruncate

14− VMRReadA : ValidModeRead ReadAppend

15−

16−||| A record of the file modes that can write from a file.

17−public export

18−data ValidModeWrite : Mode -> Type where

19− VMWWrite : ValidModeWrite WriteTruncate

20− VMWAppend : ValidModeWrite Append

21− VMWReadW : ValidModeWrite ReadWrite

22− VMWReadWT : ValidModeWrite ReadWriteTruncate

23−

24−||| The file handle which will be used as a State Transition

25−||| resource in the `IO` and `IOExcept` implementations of `File`.

26−|||

27−||| @mode The `Mode` that the handle was generated under.

28−|||

29−public export

30−data FileHandle : (mode : Mode) -> Type where

31− FH : File -> FileHandle mode

32−

33−||| Description of state transition operations on a file.

34−|||

35−||| +------------+-------------+----------------+----------------+----------------+

36−||| | Operation | State in | Mode in | State out | Mode out |

37−||| +------------+-------------+----------------+----------------+----------------+

38−||| | open | - | - | file handle | input paramater|

39−||| | close | file handle | any | - | - |

40−||| | eof | file handle | ValidModeRead | file handle | ValidModeRead |

41−||| | flush | file handle | any | file handle | unchanged |

42−||| | readLine | file handle | ValidModeRead | file handle | ValidModeRead |

43−||| | readChar | file handle | ValidModeRead | file handle | ValidModeRead |

44−||| | readFile | - | - | - | - |

45−||| | writeString| file handle | ValidModeWrite | file handle | ValidModeWrite |

46−||| | writeLine | file handle | ValidModeWrite | file handle | ValidModeWrite |

47−||| | writeFile | - | - | - | - |

48−||| +------------+-------------+----------------+----------------+----------------+

49−|||

50−public export

51−interface File (m : Type -> Type) where

52− FileHandleI : Mode -> Type

53−

54− ||| Open a file.

55− |||

56− ||| @fname the filename.

57− ||| @mode the mode; either Read, WriteTruncate, Append, ReadWrite,

58− ||| ReadWriteTruncate, or ReadAppend

59− |||

60− open : (fname : String)

61− -> (mode : Mode)

62− -> ST m (Either FileError Var) [ addIfRight (FileHandleI mode) ]

63−

64− ||| Close a file.

65− close : (fileHandle : Var)

66− -> ST m () [ remove fileHandle (FileHandleI mode) ]

67−

68− ||| Have we reached the end of the file.

69− eof : (fileHandle : Var)

70− -> {auto prf : ValidModeRead mode}

71− -> ST m Bool [ fileHandle ::: (FileHandleI mode) ]

72−

73− ||| Flush

74− flush : (fileHandle : Var)

75− -> ST m () [ fileHandle ::: (FileHandleI mode) ]

76−

77− ||| Read a complete line.

78− readLine : (fileHandle : Var)

79− -> {auto prf : ValidModeRead mode}

80− -> ST m (Either FileError String) [ fileHandle ::: (FileHandleI mode) ]

81−

82− ||| Read a `Char`.

83− readChar : (fileHandle : Var)

84− -> {auto prf : ValidModeRead mode}

85− -> ST m (Either FileError Char) [ fileHandle ::: (FileHandleI mode) ]

86−

87− ||| Read the contents of a file into a string.

88− |||

89− ||| This checks the size of

90− ||| the file before beginning to read, and only reads that many bytes,

91− ||| to ensure that it remains a total function if the file is appended

92− ||| to while being read.

93− |||

94− ||| Returns an error if fname is not a normal file.

95− |||

96− readFile : (fileName : String)

97− -> ST m (Either FileError String) []

98−

99− ||| Write a complete line to the file.

100− |||

101− ||| @string The string to be written to file.

102− |||

103− writeString : (fileHandle : Var)

104− -> (string : String)

105− -> {auto prf : ValidModeWrite mode}

106− -> ST m (Either FileError ()) [ fileHandle ::: (FileHandleI mode) ]

107−

108− ||| Write a complete line to the file.

109− |||

110− ||| @string The text to be written to file.

111− |||

112− writeLine : (fileHandle : Var)

113− -> (string : String)

114− -> {auto prf : ValidModeWrite mode}

115− -> ST m (Either FileError ()) [ fileHandle ::: (FileHandleI mode) ]

116−

117− ||| Create a file and write contents to the file.

118− |||

119− ||| @fname The fileName of the file.

120− ||| @string The text to be written to file.

121− |||

122− writeFile : (fname : String)

123− -> (string : String)

124− -> ST m (Either FileError ()) []

125−

126−public export

127−File IO where

128− FileHandleI mode = State (FileHandle mode)

129−

130− open fname mode = do

131− (Right file) <- lift ( openFile fname mode )

132− | (Left error ) => pure (Left error)

133− let fh = FH file

134− var <- new fh

135− pure (Right var)

136−

137− close fh = do

138− (FH file) <- read fh

139− lift (closeFile file)

140− delete fh

141− pure ()

142−

143− eof fh = do

144− (FH file) <- read fh

145− isEof <- lift (fEOF file)

146− pure (isEof)

147−

148− flush fh = do

149− (FH file) <- read fh

150− lift (fEOF file)

151− pure ()

152−

153− readLine fh = do

154− (FH file) <- read fh

155− (Right string) <- lift (fGetLine file)

156− | (Left error ) => pure (Left error)

157− pure (Right string)

158−

159− readChar fh = do

160− (FH file) <- read fh

161− (Right chr) <- lift (fgetc file)

162− | (Left error ) => pure (Left error)

163− pure (Right chr)

164−

165− readFile fname = do

166− (Right content) <- lift ( readFile fname )

167− | (Left error ) => pure (Left error)

168− pure (Right content)

169−

170− writeString fh str = do

171− (FH file) <- read fh

172− Right x <- lift (fPutStr file str)

173− | (Left error ) => pure (Left error)

174− pure (Right x)

175−

176− writeLine fh str = do

177− (FH file) <- read fh

178− Right x <- lift (fPutStrLn file str)

179− | (Left error ) => pure (Left error)

180− pure (Right x)

181−

182− writeFile fname str = do

183− Right x <- lift (writeFile fname str)

184− | (Left error ) => pure (Left error)

185− pure (Right x)

186−

187−public export

188−File (IOExcept a) where

189− FileHandleI mode = State (FileHandle mode)

190−

191− open fname mode = do

192− (Right file) <- lift (ioe_lift (openFile fname mode))

193− | (Left error ) => pure (Left error)

194− let fh = FH file

195− var <- new fh

196− pure (Right var)

197−

198− close fh = do

199− (FH file) <- read fh

200− lift (ioe_lift (closeFile file))

201− delete fh

202− pure ()

203−

204− eof fh = do

205− (FH file) <- read fh

206− isEof <- lift (ioe_lift (fEOF file))

207− pure (isEof)

208−

209− flush fh = do

210− (FH file) <- read fh

211− lift (ioe_lift (fEOF file))

212− pure ()

213−

214− readLine fh = do

215− (FH file) <- read fh

216− (Right string) <- lift (ioe_lift (fGetLine file))

217− | (Left error ) => pure (Left error)

218− pure (Right string)

219−

220− readChar fh = do

221− (FH file) <- read fh

222− (Right chr) <- lift (ioe_lift (fgetc file))

223− | (Left error ) => pure (Left error)

224− pure (Right chr)

225−

226− readFile fname = do

227− (Right content) <- lift (ioe_lift (readFile fname))

228− | (Left error ) => pure (Left error)

229− pure (Right content)

230−

231− writeString fh str = do

232− (FH file) <- read fh

233− Right x <- lift (ioe_lift (fPutStr file str))

234− | (Left error ) => pure (Left error)

235− pure (Right x)

236−

237− writeLine fh str = do

238− (FH file) <- read fh

239− Right x <- lift (ioe_lift (fPutStrLn file str))

240− | (Left error ) => pure (Left error)

241− pure (Right x)

242−

243− writeFile fname str = do

244− Right x <- lift (ioe_lift (writeFile fname str))

245− | (Left error ) => pure (Left error)

246− pure (Right x)

247−--- EOF -------------------------------------------------------------------------

libs/contrib/Control/ST/Random.idr+2−28

@@ -1,13 +1,12 @@

11module Control.ST.Random

22

33import Control.ST

4−import Data.Vect

5−

6−%access public export

74

5+public export

86Random : Type

97Random = State Integer

108

9+export

1110getRandom : (rnd : Var) -> ST m Integer [rnd ::: Random]

1211getRandom rnd =

1312 do

@@ -15,28 +14,3 @@ getRandom rnd =

1514 let st' = assert_total ((1664525 * st + 1013904223) `prim__sremBigInt` (pow 2 32))

1615 write rnd st'

1716 pure st'

18−

19−||| Generates a random Integer in a given range

20−rndInt : (rnd : Var) -> Integer -> Integer -> ST m Integer [rnd ::: Random]

21−rndInt rnd lower upper = do v <- getRandom rnd

22− pure $ assert_total ((v `prim__sremBigInt` (upper - lower)) + lower)

23−

24−||| Generate a random number in `Fin (S k)`

25−|||

26−||| Note that rndFin k takes values 0, 1, ..., k.

27−rndFin : (rnd : Var) -> (k : Nat) -> ST m (Fin (S k)) [rnd ::: Random]

28−rndFin rnd k = do let v = assert_total $ !(getRandom rnd) `prim__sremBigInt` (cast (S k))

29− pure (toFin v)

30− where toFin : Integer -> Fin (S k)

31− toFin x = case integerToFin x (S k) of

32− Just v => v

33− Nothing => toFin (assert_smaller x (x - cast (S k)))

34−

35−||| Select a random element from a vector

36−rndSelect' : (rnd : Var) -> Vect (S k) a -> ST m a [rnd ::: Random]

37−rndSelect' {k} rnd xs = pure (Vect.index !(rndFin rnd k) xs)

38−

39−||| Select a random element from a non-empty list

40−rndSelect : (rnd : Var) -> (xs : List a) -> {auto ok : NonEmpty xs} -> ST m a [rnd ::: Random]

41−rndSelect rnd (x::xs) {ok=NonEmpty} = pure ( !(rndSelect' rnd (x::(fromList xs))))

42−rndSelect rnd [] {ok=NonEmpty} impossible

libs/contrib/Data/Bool/Extra.idrdeleted−82

@@ -1,82 +0,0 @@

1−module Data.Bool.Extra

2−

3−%access public export

4−%default total

5−

6−notInvolutive : (x : Bool) -> not (not x) = x

7−notInvolutive True = Refl

8−notInvolutive False = Refl

9−

10−-- AND

11−

12−andSameNeutral : (x : Bool) -> x && x = x

13−andSameNeutral False = Refl

14−andSameNeutral True = Refl

15−

16−andFalseFalse : (x : Bool) -> x && False = False

17−andFalseFalse False = Refl

18−andFalseFalse True = Refl

19−

20−andTrueNeutral : (x : Bool) -> x && True = x

21−andTrueNeutral False = Refl

22−andTrueNeutral True = Refl

23−

24−andAssociative : (x, y, z : Bool) -> x && (y && z) = (x && y) && z

25−andAssociative True _ _ = Refl

26−andAssociative False _ _ = Refl

27−

28−andCommutative : (x, y : Bool) -> x && y = y && x

29−andCommutative x True = andTrueNeutral x

30−andCommutative x False = andFalseFalse x

31−

32−andNotFalse : (x : Bool) -> x && not x = False

33−andNotFalse False = Refl

34−andNotFalse True = Refl

35−

36−-- OR

37−

38−orSameNeutral : (x : Bool) -> x || x = x

39−orSameNeutral False = Refl

40−orSameNeutral True = Refl

41−

42−orFalseNeutral : (x : Bool) -> x || False = x

43−orFalseNeutral False = Refl

44−orFalseNeutral True = Refl

45−

46−orTrueTrue : (x : Bool) -> x || True = True

47−orTrueTrue False = Refl

48−orTrueTrue True = Refl

49−

50−orAssociative : (x, y, z : Bool) -> x || (y || z) = (x || y) || z

51−orAssociative True _ _ = Refl

52−orAssociative False _ _ = Refl

53−

54−orCommutative : (x, y : Bool) -> x || y = y || x

55−orCommutative x True = orTrueTrue x

56−orCommutative x False = orFalseNeutral x

57−

58−orNotTrue : (x : Bool) -> x || not x = True

59−orNotTrue False = Refl

60−orNotTrue True = Refl

61−

62−-- interaction & De Morgan's laws

63−

64−orSameAndRightNeutral : (x, y : Bool) -> x || (x && y) = x

65−orSameAndRightNeutral False _ = Refl

66−orSameAndRightNeutral True _ = Refl

67−

68−andDistribOrR : (x, y, z : Bool) -> x && (y || z) = (x && y) || (x && z)

69−andDistribOrR False _ _ = Refl

70−andDistribOrR True _ _ = Refl

71−

72−orDistribAndR : (x, y, z : Bool) -> x || (y && z) = (x || y) && (x || z)

73−orDistribAndR False _ _ = Refl

74−orDistribAndR True _ _ = Refl

75−

76−notAndIsOr : (x, y : Bool) -> not (x && y) = not x || not y

77−notAndIsOr False _ = Refl

78−notAndIsOr True _ = Refl

79−

80−notOrIsAnd : (x, y : Bool) -> not (x || y) = not x && not y

81−notOrIsAnd False _ = Refl

82−notOrIsAnd True _ = Refl

libs/contrib/Data/BoundedList.idr−29

@@ -1,7 +1,6 @@

11module Data.BoundedList

22

33import Data.Fin

4−import Data.Vect

54

65%access public export

76%default total

@@ -51,20 +50,6 @@ fromList : (xs : List a) -> BoundedList (length xs) a

5150fromList [] = []

5251fromList (x :: xs) = x :: fromList xs

5352

54−--------------------------------------------------------------------------------

55−-- Conversions to and from vector

56−--------------------------------------------------------------------------------

57−

58−||| Convert bounded list to vector.

59−toVect : (xs : BoundedList n a) -> Vect (finToNat (length xs)) a

60−toVect [] = []

61−toVect (x :: xs) = x :: toVect xs

62−

63−||| Convert vector to bounded list.

64−fromVect : (xs : Vect n a) -> BoundedList n a

65−fromVect [] = []

66−fromVect (x :: xs) = x :: fromVect xs

67−

6853--------------------------------------------------------------------------------

6954-- Building (bigger) bounded lists

7055--------------------------------------------------------------------------------

@@ -91,20 +76,6 @@ implementation Functor (BoundedList n) where

9176 map f [] = []

9277 map f (x :: xs) = f x :: map f xs

9378

94−--------------------------------------------------------------------------------

95−-- Monoid

96−--------------------------------------------------------------------------------

97−

98−implementation Semigroup a => Semigroup (BoundedList n a) where

99− (x :: xs) <+> (y :: ys) = (x <+> y) :: (xs <+> ys)

100− xs <+> [] = xs

101− [] <+> ys = ys

102−

103−-- The Semigroup constraint is only needed because that's how we make a

104−-- semigroup from BoundedList, not used in this implementation.

105−implementation Semigroup a => Monoid (BoundedList n a) where

106− neutral = []

107−

10879--------------------------------------------------------------------------------

10980-- Misc

11081--------------------------------------------------------------------------------

libs/contrib/Data/Chain.idrdeleted−46

@@ -1,46 +0,0 @@

1−module Data.Chain

2−

3−import Data.Vect

4−import Control.Isomorphism

5−

6−%default total

7−%access public export

8−

9−||| Repeated function application

10−Chain : Nat -> (i, o : Type) -> Type

11−Chain Z _ o = o

12−Chain (S k) i o = i -> Chain k i o

13−

14−||| Repeated endofunction application

15−EndoChain : Nat -> Type -> Type

16−EndoChain n t = Chain n t t

17−

18−||| (.) generalized to any number of arguments.

19−after : (o -> o') -> (Chain n i o) -> (Chain n i o')

20−after {n=Z} f x = f x

21−after {n=S k} f fs = after f . fs

22−

23−||| `on` generalized to any number of arguments

24−before : (i -> i') -> (Chain n i' o) -> (Chain n i o)

25−before {n=Z} _ x = x

26−before {n=S k} f fs = (f `before`) . (fs . f)

27−

28−||| Fill in the same argument for all items (available for a single argument as

29−||| Data.Combinators.reflex)

30−reflexes : (Chain n i o) -> (i -> o)

31−reflexes {n=Z} x _ = x

32−reflexes {n=S k} fs y = reflexes (fs y) y

33−

34−||| Create a vect of a given length from the arguments given.

35−packVect : Chain n i (Vect n i)

36−packVect {n=Z} = []

37−packVect {n=S k} = (`after` packVect) . Data.Vect.(::)

38−-- For some reason we get a can't disambiguate name: Prelude.List.::,

39−-- Prelude.Stream.::, Data.Vect.:: if we leave out the Data.Vect specification

40−

41−||| Apply a function over a vector to our new type

42−fromVectFunc : (Vect n i -> o) -> (Chain n i o)

43−fromVectFunc f = (f `after` packVect)

44−

45−withIso : Iso t t' -> EndoChain n t -> EndoChain n t'

46−withIso (MkIso to from _ _) = (from `before`) . (to `after`)

libs/contrib/Data/Combinators.idr+4−3

@@ -5,7 +5,8 @@

55||| hasn't actually read). See

66||| http://www.angelfire.com/tx4/cus/combinator/birds.html and

77||| https://hackage.haskell.org/package/data-aviary-0.4.0/docs/Data-Aviary-Birds.html

8−||| an (incomplete?) list of birds introduced.

8+||| an (incomplete?) list of birds introduced. Also includes some operations defined

9+||| over Arrows.

910

1011module Data.Combinators

1112

@@ -26,13 +27,13 @@ infixl 9 ...

2627(...) = (.) . (.)

2728

2829||| Warbler, as named in "To Mock a Mockingbird".

29−||| See https://code.jsoftware.com/wiki/Vocabulary/tilde

30+||| See http://code.jsoftware.com/wiki/Vocabulary/tilde

3031||| Equivalent to `join` on the Reader monad (`(->) e` in Haskell)

3132reflex : (a -> a -> b) -> (a -> b)

3233reflex f x = f x x

3334

3435||| Phoenix, according to Data.Aviary.

35−||| See https://code.jsoftware.com/wiki/Vocabulary/fork.

36+||| See http://code.jsoftware.com/wiki/Vocabulary/fork.

3637||| Equivalent to `liftA2` on the Reader monad (`(->) e` in Haskell)

3738fork2 : (b -> c -> d) -> (a -> b) -> (a -> c) -> (a -> d)

3839fork2 f g h x = f (g x) (h x)

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