399c102 · laop · git.iko.soy

git.iko.soy/laop

Renamed:

Junc -> Join Split -> Fork kp1 -> fstM kp2 -> sndM identity -> iden fromF' -> fromF fromF -> fromF' (Relation) p1 -> fstR p2 -> fstR fromFRel' -> fromFRel fromFRel -> fromFRel'

commit399c1028b120b05925ce6f73534626f1a6eaed3e authorArmando Santos <armandoifsantos@gmail.com> dateThu 20 Feb 2020, 15:09 (7 years ago) parent63abc15

10 files changed+320−292

compare with master

unifiedsplit

app/Benchmarks.hs+5−5 app/Examples.hs+10−10 app/Quantum.hs+28 app/Spreadsheets.hs+1−1 src/LAoP/Dist/Internal.hs+1−1 src/LAoP/Matrix/Internal.hs+123−123 src/LAoP/Matrix/Nat.hs+34−34 src/LAoP/Matrix/Type.hs+51−51 src/LAoP/Relation.hs+5−5 src/LAoP/Relation/Internal.hs+62−62

app/Benchmarks.hs+5−5

@@ -28,16 +28,16 @@ selectM2 ::

2828 T.FromListsN e b b,

2929 CountableN b

3030 ) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

31−selectM2 m y = junc y identity `comp` m

31+selectM2 m y = join y iden `comp` m

3232

3333selectD2 ::

3434 ( FromListsN b b,

3535 CountableN b

3636 ) => Dist (Either a b) -> Matrix Prob a b -> Dist b

37−selectD2 (D d) m = D (junc m identity `comp` d)

37+selectD2 (D d) m = D (join m iden `comp` d)

3838

39−-- Composition with identity

40−compId m = comp identity m

39+-- Composition with iden

40+compId m = comp iden m

4141

4242randomDist :: forall a . (Countable a, FromListsN () a) => Gen (Dist a)

4343randomDist = do

@@ -162,7 +162,7 @@ benchmark = defaultMain [

162162 , bench "NF - 200x200" $ nf (comp m31) m32

163163 ],

164164 bgroup "200x200 - RULES" [

165− bench "No rules - 200x200" $ nf (comp m21) identity

165+ bench "No rules - 200x200" $ nf (comp m21) iden

166166 , bench "Rules - 200x200" $ nf compId m21

167167 ] ],

168168 env setupEnv2 $ \ ~(m21, m40, dist, dist2, dl1, dl2) -> bgroup "Matrix vs List - `select`" [

app/Examples.hs+10−10

@@ -32,7 +32,7 @@ firstChoice :: Matrix Double () Outcome

3232firstChoice = col [1/3, 2/3]

3333

3434secondChoice :: Matrix Double Outcome Outcome

35−secondChoice = fromF' switch

35+secondChoice = fromF switch

3636

3737-- Dice sum

3838

@@ -41,7 +41,7 @@ type SS = Natural 1 6 -- Sample Space

4141sumSS :: SS -> SS -> Natural 2 12

4242sumSS = coerceNat (+)

4343

44−sumSSM = fromF' (uncurry sumSS)

44+sumSSM = fromF (uncurry sumSS)

4545

4646condition :: (Int, Int) -> Int -> Int

4747condition (fst, snd) thrd = if fst == snd

@@ -51,7 +51,7 @@ condition (fst, snd) thrd = if fst == snd

5151conditionSS :: (SS, SS) -> SS -> Natural 3 18

5252conditionSS = coerceNat2 condition

5353

54−conditionalThrows = fromF' (uncurry conditionSS) . khatri (khatri die die) die

54+conditionalThrows = fromF (uncurry conditionSS) . khatri (khatri die die) die

5555

5656die :: Matrix Double () SS

5757die = col $ map (const (1/6)) [nat @1 @6 1 .. nat 6]

@@ -75,15 +75,15 @@ sprinkler = fromLists [[0.6, 0.99], [0.4, 0.01]]

7575grass :: Matrix Double (S, R) G

7676grass = fromLists [[1, 0.2, 0.1, 0.01], [0, 0.8, 0.9, 0.99]]

7777

78−tag f = khatri f identity

78+tag f = khatri f iden

7979

8080state g s r = tag g `comp` tag s `comp` r

8181

8282grass_wet :: Matrix Double () (G, (S, R)) -> Matrix Double One One

83−grass_wet state = row [0,1] . kp1 . state

83+grass_wet state = row [0,1] . fstM . state

8484

8585rainning :: Matrix Double (G, (S, R)) One

86−rainning = row [0,1] . kp2 . kp2

86+rainning = row [0,1] . sndM . sndM

8787

8888-- Alcuin Puzzle

8989

@@ -106,21 +106,21 @@ cross LeftB = RightB

106106cross RightB = LeftB

107107

108108crossR :: R.Relation Bank Bank

109−crossR = R.fromF' cross

109+crossR = R.fromF cross

110110

111111-- | Initial state, everyone in the left bank

112112locationLeft :: Being -> Bank

113113locationLeft _ = LeftB

114114

115115locationLeftR :: R.Relation Being Bank

116−locationLeftR = R.fromF' locationLeft

116+locationLeftR = R.fromF locationLeft

117117

118118-- | Initial state, everyone in the right bank

119119locationRight :: Being -> Bank

120120locationRight _ = RightB

121121

122122locationRightR :: R.Relation Being Bank

123−locationRightR = R.fromF' locationRight

123+locationRightR = R.fromF locationRight

124124

125125-- Properties

126126

@@ -137,7 +137,7 @@ inv :: R.Relation Being Bank -> Bool

137137inv w = (w `R.comp` canEat w) `R.sse` (w `R.comp` farmer)

138138 where

139139 farmer :: R.Relation Being Being

140− farmer = R.fromF' (const Farmer)

140+ farmer = R.fromF (const Farmer)

141141

142142-- Arbitrary state

143143bankState :: Being -> Bank -> Bool

app/Quantum.hsnew file+28

@@ -0,0 +1,28 @@

1+{-# LANGUAGE StandaloneDeriving #-}

2+module Quantum where

4+import LAoP.Matrix.Type

5+import Data.Complex

7+deriving instance Ord a => Ord (Complex a)

9+xor :: (Bool, Bool) -> Bool

10+xor (False, b) = b

11+xor (True, b) = not b

12+

13+ker :: Num e => Matrix e a b -> Matrix e a a

14+ker m = tr m `comp` m

15+

16+cnot :: Matrix (Complex Double) (Bool, Bool) (Bool, Bool)

17+cnot = khatri fstM (fromF xor)

18+

19+ccnot :: Matrix (Complex Double) ((Bool, Bool), Bool) ((Bool, Bool), Bool)

20+ccnot = khatri fstM (fromF f)

21+ where

22+ f = xor . (tp (uncurry (&&)) id)

23+ tp f g (a,b) = (f a, g b)

24+

25+had :: Matrix (Complex Double) Bool Bool

26+had = fromLists l

27+ where

28+ l = map (map (*(1/sqrt 2))) [[1, 1], [1, -1]]

app/Spreadsheets.hs+1−1

@@ -35,7 +35,7 @@ xls :: Matrix Float Question One

3535 -> Matrix Float Question Student

3636 -> Matrix Float Student One

3737 -> Matrix Float (Either Question Results) (Either One Student)

38−xls w m t = junc (split w m) (split zeros r)

38+xls w m t = join (fork w m) (fork zeros r)

3939 where

4040 rExam = m `comp` tr w

4141 rTest = tr t

src/LAoP/Dist/Internal.hs+1−1

@@ -118,7 +118,7 @@ branchD ::

118118 => Dist (Either a b) -> Matrix Prob a c -> Matrix Prob b c -> Dist c

119119branchD x l r = f x `selectD` g l `selectD` r

120120 where

121− f (D m) = D (split (tr i1) (i1 `comp` tr i2) `comp` m)

121+ f (D m) = D (fork (tr i1) (i1 `comp` tr i2) `comp` m)

122122 g m = i2 `comp` m

123123

124124-- | Branch on a Boolean value, skipping unnecessary computations.

src/LAoP/Matrix/Internal.hs+123−123

@@ -52,8 +52,8 @@ module LAoP.Matrix.Internal

5252 -- * Primitives

5353 empty,

5454 one,

55− junc,

56− split,

55+ join,

56+ fork,

5757

5858 -- * Auxiliary type families

5959 FromNat,

@@ -96,12 +96,12 @@ module LAoP.Matrix.Internal

9696 zipWithM,

9797

9898 -- * Biproduct approach

99− -- ** Split

99+ -- ** Fork

100100 (===),

101101 -- *** Projections

102102 p1,

103103 p2,

104− -- ** Junc

104+ -- ** Join

105105 (|||),

106106 -- *** Injections

107107 i1,

@@ -115,8 +115,8 @@ module LAoP.Matrix.Internal

115115 -- | Note that given the restrictions imposed it is not possible to

116116 -- implement the standard type classes present in standard Haskell.

117117 -- *** Matrix pairing projections

118− kp1,

119− kp2,

118+ fstM,

119+ sndM,

120120

121121 -- *** Matrix pairing

122122 khatri,

@@ -127,10 +127,10 @@ module LAoP.Matrix.Internal

127127

128128 -- | Note that given the restrictions imposed it is not possible to

129129 -- implement the standard type classes present in standard Haskell.

130− identity,

130+ iden,

131131 comp,

132− fromF,

133132 fromF',

133+ fromF,

134134

135135 -- * Matrix printing

136136 pretty,

@@ -171,8 +171,8 @@ import Prelude hiding ((.))

171171data Matrix e cols rows where

172172 Empty :: Matrix e Void Void

173173 One :: e -> Matrix e () ()

174− Junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

175− Split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

174+ Join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

175+ Fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

176176

177177deriving instance (Show e) => Show (Matrix e cols rows)

178178

@@ -226,7 +226,7 @@ type Trivial a = FromNat (Count a) ~ a

226226-- implementation is 'undefined'. However 'comp' can be and this partial

227227-- class implementation exists just to make the code more readable.

228228--

229−-- Please use 'identity' instead.

229+-- Please use 'iden' instead.

230230instance (Num e) => Category (Matrix e) where

231231 id = undefined

232232 (.) = comp

@@ -234,16 +234,16 @@ instance (Num e) => Category (Matrix e) where

234234instance NFData e => NFData (Matrix e cols rows) where

235235 rnf Empty = ()

236236 rnf (One e) = rnf e

237− rnf (Junc a b) = rnf a `seq` rnf b

238− rnf (Split a b) = rnf a `seq` rnf b

237+ rnf (Join a b) = rnf a `seq` rnf b

238+ rnf (Fork a b) = rnf a `seq` rnf b

239239

240240instance Eq e => Eq (Matrix e cols rows) where

241241 Empty == Empty = True

242242 (One a) == (One b) = a == b

243− (Junc a b) == (Junc c d) = a == c && b == d

244− (Split a b) == (Split c d) = a == c && b == d

245− x@(Split _ _) == y@(Junc _ _) = x == abideJS y

246− x@(Junc _ _) == y@(Split _ _) = abideJS x == y

243+ (Join a b) == (Join c d) = a == c && b == d

244+ (Fork a b) == (Fork c d) = a == c && b == d

245+ x@(Fork _ _) == y@(Join _ _) = x == abideJS y

246+ x@(Join _ _) == y@(Fork _ _) = abideJS x == y

247247

248248instance Num e => Num (Matrix e cols rows) where

249249

@@ -255,21 +255,21 @@ instance Num e => Num (Matrix e cols rows) where

255255

256256 abs Empty = Empty

257257 abs (One a) = One (abs a)

258− abs (Junc a b) = Junc (abs a) (abs b)

259− abs (Split a b) = Split (abs a) (abs b)

258+ abs (Join a b) = Join (abs a) (abs b)

259+ abs (Fork a b) = Fork (abs a) (abs b)

260260

261261 signum Empty = Empty

262262 signum (One a) = One (signum a)

263− signum (Junc a b) = Junc (signum a) (signum b)

264− signum (Split a b) = Split (signum a) (signum b)

263+ signum (Join a b) = Join (signum a) (signum b)

264+ signum (Fork a b) = Fork (signum a) (signum b)

265265

266266instance Ord e => Ord (Matrix e cols rows) where

267267 Empty <= Empty = True

268268 (One a) <= (One b) = a <= b

269− (Junc a b) <= (Junc c d) = (a <= c) && (b <= d)

270− (Split a b) <= (Split c d) = (a <= c) && (b <= d)

271− x@(Split _ _) <= y@(Junc _ _) = x <= abideJS y

272− x@(Junc _ _) <= y@(Split _ _) = abideJS x <= y

269+ (Join a b) <= (Join c d) = (a <= c) && (b <= d)

270+ (Fork a b) <= (Fork c d) = (a <= c) && (b <= d)

271+ x@(Fork _ _) <= y@(Join _ _) = x <= abideJS y

272+ x@(Join _ _) <= y@(Fork _ _) = abideJS x <= y

273273

274274-- Primitives

275275

@@ -281,25 +281,25 @@ empty = Empty

281281one :: e -> Matrix e () ()

282282one = One

283283

284−-- | Matrix 'Junc' constructor

285−junc :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

286−junc = Junc

284+-- | Matrix 'Join' constructor

285+join :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

286+join = Join

287287

288288infixl 3 |||

289289

290−-- | Matrix 'Junc' constructor

290+-- | Matrix 'Join' constructor

291291(|||) :: Matrix e a rows -> Matrix e b rows -> Matrix e (Either a b) rows

292−(|||) = Junc

292+(|||) = Join

293293

294−-- | Matrix 'Split' constructor

295−split :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

296−split = Split

294+-- | Matrix 'Fork' constructor

295+fork :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

296+fork = Fork

297297

298298infixl 2 ===

299299

300−-- | Matrix 'Split' constructor

300+-- | Matrix 'Fork' constructor

301301(===) :: Matrix e cols a -> Matrix e cols b -> Matrix e cols (Either a b)

302−(===) = Split

302+(===) = Fork

303303

304304-- Construction

305305

@@ -321,23 +321,23 @@ instance {-# OVERLAPPING #-} FromLists e () () where

321321 fromLists _ = error "Wrong dimensions"

322322

323323instance {-# OVERLAPPING #-} (FromLists e cols ()) => FromLists e (Either () cols) () where

324− fromLists [h : t] = Junc (One h) (fromLists [t])

324+ fromLists [h : t] = Join (One h) (fromLists [t])

325325 fromLists _ = error "Wrong dimensions"

326326

327327instance {-# OVERLAPPABLE #-} (FromLists e a (), FromLists e b (), Countable a) => FromLists e (Either a b) () where

328328 fromLists [l] =

329329 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

330− in Junc (fromLists [take rowsA l]) (fromLists [drop rowsA l])

330+ in Join (fromLists [take rowsA l]) (fromLists [drop rowsA l])

331331 fromLists _ = error "Wrong dimensions"

332332

333333instance {-# OVERLAPPING #-} (FromLists e () rows) => FromLists e () (Either () rows) where

334− fromLists ([h] : t) = Split (One h) (fromLists t)

334+ fromLists ([h] : t) = Fork (One h) (fromLists t)

335335 fromLists _ = error "Wrong dimensions"

336336

337337instance {-# OVERLAPPABLE #-} (FromLists e () a, FromLists e () b, Countable a) => FromLists e () (Either a b) where

338338 fromLists l@([_] : _) =

339339 let rowsA = fromInteger (natVal (Proxy :: Proxy (Count a)))

340− in Split (fromLists (take rowsA l)) (fromLists (drop rowsA l))

340+ in Fork (fromLists (take rowsA l)) (fromLists (drop rowsA l))

341341 fromLists _ = error "Wrong dimensions"

342342

343343instance {-# OVERLAPPABLE #-} (FromLists e (Either a b) c, FromLists e (Either a b) d, Countable c) => FromLists e (Either a b) (Either c d) where

@@ -346,7 +346,7 @@ instance {-# OVERLAPPABLE #-} (FromLists e (Either a b) c, FromLists e (Either a

346346 rowsC = fromInteger (natVal (Proxy :: Proxy (Count c)))

347347 condition = all (== lh) (map length t)

348348 in if lh > 0 && condition

349− then Split (fromLists (take rowsC l)) (fromLists (drop rowsC l))

349+ then Fork (fromLists (take rowsC l)) (fromLists (drop rowsC l))

350350 else error "Not all rows have the same length"

351351

352352-- | Matrix builder function. Constructs a matrix provided with

@@ -376,7 +376,7 @@ row = fromLists . (: [])

376376--

377377-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

378378-- types @a@ or @b@ allows.

379−fromF ::

379+fromF' ::

380380 forall a b cols rows e.

381381 ( Liftable e a b,

382382 CountableDimensions cols rows,

@@ -384,7 +384,7 @@ fromF ::

384384 ) =>

385385 (a -> b) ->

386386 Matrix e cols rows

387−fromF f =

387+fromF' f =

388388 let minA = minBound @a

389389 maxA = maxBound @a

390390 minB = minBound @b

@@ -405,7 +405,7 @@ fromF f =

405405

406406-- | Lifts functions to matrices with dimensions matching @a@ and @b@

407407-- cardinality's.

408−fromF' ::

408+fromF ::

409409 forall a b e.

410410 ( Liftable e a b,

411411 CountableDimensionsN a b,

@@ -413,7 +413,7 @@ fromF' ::

413413 ) =>

414414 (a -> b) ->

415415 Matrix e (Normalize a) (Normalize b)

416−fromF' f =

416+fromF f =

417417 let minA = minBound @a

418418 maxA = maxBound @a

419419 minB = minBound @b

@@ -438,8 +438,8 @@ fromF' f =

438438toLists :: Matrix e cols rows -> [[e]]

439439toLists Empty = []

440440toLists (One e) = [[e]]

441−toLists (Split l r) = toLists l ++ toLists r

442−toLists (Junc l r) = zipWith (++) (toLists l) (toLists r)

441+toLists (Fork l r) = toLists l ++ toLists r

442+toLists (Join l r) = zipWith (++) (toLists l) (toLists r)

443443

444444-- | Converts a matrix to a list of elements.

445445toList :: Matrix e cols rows -> [e]

@@ -474,12 +474,12 @@ bang =

474474 let c = fromInteger $ natVal (Proxy :: Proxy (Count cols))

475475 in fromLists [take c [1, 1 ..]]

476476

477−-- Identity Matrix

477+-- iden Matrix

478478

479−-- | Identity matrix.

480−identity :: (Num e, FromLists e cols cols, Countable cols) => Matrix e cols cols

481−identity = matrixBuilder (bool 0 1 . uncurry (==))

482−{-# NOINLINE identity #-}

479+-- | iden matrix.

480+iden :: (Num e, FromLists e cols cols, Countable cols) => Matrix e cols cols

481+iden = matrixBuilder (bool 0 1 . uncurry (==))

482+{-# NOINLINE iden #-}

483483

484484-- Matrix composition (MMM)

485485

@@ -490,13 +490,13 @@ identity = matrixBuilder (bool 0 1 . uncurry (==))

490490comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

491491comp Empty Empty = Empty

492492comp (One a) (One b) = One (a * b)

493−comp (Junc a b) (Split c d) = comp a c + comp b d -- Divide-and-conquer law

494−comp (Split a b) c = Split (comp a c) (comp b c) -- Split fusion law

495−comp c (Junc a b) = Junc (comp c a) (comp c b) -- Junc fusion law

493+comp (Join a b) (Fork c d) = comp a c + comp b d -- Divide-and-conquer law

494+comp (Fork a b) c = Fork (comp a c) (comp b c) -- Fork fusion law

495+comp c (Join a b) = Join (comp c a) (comp c b) -- Join fusion law

496496{-# NOINLINE comp #-}

497497{-# RULES

498− "comp/identity1" forall m. comp m identity = m ;

499− "comp/identity2" forall m. comp identity m = m

498+ "comp/iden1" forall m. comp m iden = m ;

499+ "comp/iden2" forall m. comp iden m = m

500500#-}

501501

502502-- Projections

@@ -504,16 +504,16 @@ comp c (Junc a b) = Junc (comp c a) (comp c b) -- Junc fusion law

504504-- | Biproduct first component projection

505505p1 :: forall e m n. (Num e, CountableDimensions n m, FromLists e n m, FromLists e m m) => Matrix e (Either m n) m

506506p1 =

507− let iden = identity :: Matrix e m m

507+ let iden = iden :: Matrix e m m

508508 zero = zeros :: Matrix e n m

509− in junc iden zero

509+ in join iden zero

510510

511511-- | Biproduct second component projection

512512p2 :: forall e m n. (Num e, CountableDimensions n m, FromLists e m n, FromLists e n n) => Matrix e (Either m n) n

513513p2 =

514− let iden = identity :: Matrix e n n

514+ let iden = iden :: Matrix e n n

515515 zero = zeros :: Matrix e m n

516− in junc zero iden

516+ in join zero iden

517517

518518-- Injections

519519

@@ -564,19 +564,19 @@ infixl 5 -|-

564564 Matrix e n k ->

565565 Matrix e m j ->

566566 Matrix e (Either n m) (Either k j)

567−(-|-) a b = Junc (i1 . a) (i2 . b)

567+(-|-) a b = Join (i1 . a) (i2 . b)

568568

569569-- Khatri Rao Product and projections

570570

571571-- | Khatri Rao product first component projection matrix.

572−kp1 ::

572+fstM ::

573573 forall e m k .

574574 ( Num e,

575575 CountableDimensions k m,

576576 FromLists e (Normalize (m, k)) m,

577577 CountableN (m, k)

578578 ) => Matrix e (Normalize (m, k)) m

579−kp1 = matrixBuilder f

579+fstM = matrixBuilder f

580580 where

581581 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))

582582 f (x, y)

@@ -584,14 +584,14 @@ kp1 = matrixBuilder f

584584 | otherwise = 0

585585

586586-- | Khatri Rao product second component projection matrix.

587−kp2 ::

587+sndM ::

588588 forall e m k .

589589 ( Num e,

590590 CountableDimensions k m,

591591 FromLists e (Normalize (m, k)) k,

592592 CountableN (m, k)

593593 ) => Matrix e (Normalize (m, k)) k

594−kp2 = matrixBuilder f

594+sndM = matrixBuilder f

595595 where

596596 offset = fromInteger (natVal (Proxy :: Proxy (Count k)))

597597 f (x, y)

@@ -603,9 +603,9 @@ kp2 = matrixBuilder f

603603-- NOTE: That this is not a true categorical product, see for instance:

604604--

605605-- @

606−-- | kp1 . khatri a b == a

606+-- | fstM . khatri a b == a

607607-- khatri a b ==> |

608−-- | kp2 . khatri a b == b

608+-- | sndM . khatri a b == b

609609-- @

610610--

611611-- __Emphasis__ on the implication symbol.

@@ -618,9 +618,9 @@ khatri ::

618618 FromLists e (Normalize (a, b)) b

619619 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (Normalize (a, b))

620620khatri a b =

621− let kp1' = kp1 @e @a @b

622− kp2' = kp2 @e @a @b

623− in (tr kp1') . a * (tr kp2') . b

621+ let fstM' = fstM @e @a @b

622+ sndM' = sndM @e @a @b

623+ in (tr fstM') . a * (tr sndM') . b

624624

625625-- Product Bifunctor (Kronecker)

626626

@@ -640,39 +640,39 @@ infixl 4 ><

640640 )

641641 => Matrix e m p -> Matrix e n q -> Matrix e (Normalize (m, n)) (Normalize (p, q))

642642(><) a b =

643− let kp1' = kp1 @e @m @n

644− kp2' = kp2 @e @m @n

645− in khatri (a . kp1') (b . kp2')

643+ let fstM' = fstM @e @m @n

644+ sndM' = sndM @e @m @n

645+ in khatri (a . fstM') (b . sndM')

646646

647−-- Matrix abide Junc Split

647+-- Matrix abide Join Fork

648648

649−-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.

649+-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

650650--

651651-- Law:

652652--

653653-- @

654−-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

654+-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)

655655-- @

656656abideJS :: Matrix e cols rows -> Matrix e cols rows

657−abideJS (Junc (Split a c) (Split b d)) = Split (Junc (abideJS a) (abideJS b)) (Junc (abideJS c) (abideJS d)) -- Junc-Split abide law

657+abideJS (Join (Fork a c) (Fork b d)) = Fork (Join (abideJS a) (abideJS b)) (Join (abideJS c) (abideJS d)) -- Join-Fork abide law

658658abideJS Empty = Empty

659659abideJS (One e) = One e

660−abideJS (Junc a b) = Junc (abideJS a) (abideJS b)

661−abideJS (Split a b) = Split (abideJS a) (abideJS b)

660+abideJS (Join a b) = Join (abideJS a) (abideJS b)

661+abideJS (Fork a b) = Fork (abideJS a) (abideJS b)

662662

663−-- Matrix abide Split Junc

663+-- Matrix abide Fork Join

664664

665−-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.

665+-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

666666--

667667-- @

668−-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

668+-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)

669669-- @

670670abideSJ :: Matrix e cols rows -> Matrix e cols rows

671−abideSJ (Split (Junc a b) (Junc c d)) = Junc (Split (abideSJ a) (abideSJ c)) (Split (abideSJ b) (abideSJ d)) -- Split-Junc abide law

671+abideSJ (Fork (Join a b) (Join c d)) = Join (Fork (abideSJ a) (abideSJ c)) (Fork (abideSJ b) (abideSJ d)) -- Fork-Join abide law

672672abideSJ Empty = Empty

673673abideSJ (One e) = One e

674−abideSJ (Junc a b) = Junc (abideSJ a) (abideSJ b)

675−abideSJ (Split a b) = Split (abideSJ a) (abideSJ b)

674+abideSJ (Join a b) = Join (abideSJ a) (abideSJ b)

675+abideSJ (Fork a b) = Fork (abideSJ a) (abideSJ b)

676676

677677-- Matrix transposition

678678

@@ -680,17 +680,17 @@ abideSJ (Split a b) = Split (abideSJ a) (abideSJ b)

680680tr :: Matrix e cols rows -> Matrix e rows cols

681681tr Empty = Empty

682682tr (One e) = One e

683−tr (Junc a b) = Split (tr a) (tr b)

684−tr (Split a b) = Junc (tr a) (tr b)

683+tr (Join a b) = Fork (tr a) (tr b)

684+tr (Fork a b) = Join (tr a) (tr b)

685685

686686-- Selective 'select' operator

687687

688688-- | Selective functors 'select' operator equivalent inspired by the

689689-- ArrowMonad solution presented in the paper.

690690select :: (Num e, FromLists e b b, Countable b) => Matrix e cols (Either a b) -> Matrix e a b -> Matrix e cols b

691−select (Split a b) y = y . a + b -- Divide-and-conquer law

692−select (Junc (Split a c) (Split b d)) y = junc (y . a + c) (y . b + d) -- Pattern matching + DnC law

693−select m y = junc y identity . m

691+select (Fork a b) y = y . a + b -- Divide-and-conquer law

692+select (Join (Fork a c) (Fork b d)) y = join (y . a + c) (y . b + d) -- Pattern matching + DnC law

693+select m y = join y iden . m

694694

695695branch ::

696696 ( Num e,

@@ -711,7 +711,7 @@ branch x l r = f x `select` g l `select` r

711711 where

712712 f :: (Num e, Countable a, CountableDimensions b c, FromLists e a b, FromLists e c b, FromLists e b b, FromLists e b a, FromLists e a a)

713713 => Matrix e cols (Either a b) -> Matrix e cols (Either a (Either b c))

714− f m = split (tr i1) (i1 . tr i2) . m

714+ f m = fork (tr i1) (i1 . tr i2) . m

715715 g :: (Num e, CountableDimensions b c, FromLists e b c, FromLists e c c) => Matrix e a c -> Matrix e a (Either b c)

716716 g m = i2 . m

717717

@@ -731,7 +731,7 @@ cond ::

731731 )

732732 =>

733733 (a -> Bool) -> Matrix e cols rows -> Matrix e cols rows -> Matrix e cols rows

734−cond p f g = junc f g . grd p

734+cond p f g = join f g . grd p

735735

736736grd ::

737737 ( Trivial q,

@@ -746,7 +746,7 @@ grd ::

746746 )

747747 =>

748748 (a -> Bool) -> Matrix e q (Either q q)

749−grd f = split (corr f) (corr (not . f))

749+grd f = fork (corr f) (corr (not . f))

750750

751751corr ::

752752 forall e a q .

@@ -758,8 +758,8 @@ corr ::

758758 Liftable e a Bool

759759 )

760760 => (a -> Bool) -> Matrix e q q

761−corr p = let f = fromF p :: Matrix e q ()

762− in khatri f (identity :: Matrix e q q)

761+corr p = let f = fromF' p :: Matrix e q ()

762+ in khatri f (iden :: Matrix e q q)

763763

764764-- Pretty print

765765

@@ -819,10 +819,10 @@ prettyPrint = putStrLn . pretty

819819zipWithM :: (e -> f -> g) -> Matrix e cols rows -> Matrix f cols rows -> Matrix g cols rows

820820zipWithM f Empty Empty = Empty

821821zipWithM f (One a) (One b) = One (f a b)

822−zipWithM f (Junc a b) (Junc c d) = Junc (zipWithM f a c) (zipWithM f b d)

823−zipWithM f (Split a b) (Split c d) = Split (zipWithM f a c) (zipWithM f b d)

824−zipWithM f x@(Split _ _) y@(Junc _ _) = zipWithM f x (abideJS y)

825−zipWithM f x@(Junc _ _) y@(Split _ _) = zipWithM f (abideJS x) y

822+zipWithM f (Join a b) (Join c d) = Join (zipWithM f a c) (zipWithM f b d)

823+zipWithM f (Fork a b) (Fork c d) = Fork (zipWithM f a c) (zipWithM f b d)

824+zipWithM f x@(Fork _ _) y@(Join _ _) = zipWithM f x (abideJS y)

825+zipWithM f x@(Join _ _) y@(Fork _ _) = zipWithM f (abideJS x) y

826826

827827-- Relational operators functions

828828

@@ -845,51 +845,51 @@ negateM :: Relation cols rows -> Relation cols rows

845845negateM Empty = Empty

846846negateM (One (Nat 0)) = One (Nat 1)

847847negateM (One (Nat 1)) = One (Nat 0)

848−negateM (Junc a b) = Junc (negateM a) (negateM b)

849−negateM (Split a b) = Split (negateM a) (negateM b)

848+negateM (Join a b) = Join (negateM a) (negateM b)

849+negateM (Fork a b) = Fork (negateM a) (negateM b)

850850

851851-- | Relational addition

852852orM :: Relation cols rows -> Relation cols rows -> Relation cols rows

853853orM Empty Empty = Empty

854854orM (One a) (One b) = One (fromBool (toBool a || toBool b))

855−orM (Junc a b) (Junc c d) = Junc (orM a c) (orM b d)

856−orM (Split a b) (Split c d) = Split (orM a c) (orM b d)

857−orM x@(Split _ _) y@(Junc _ _) = orM x (abideJS y)

858−orM x@(Junc _ _) y@(Split _ _) = orM (abideJS x) y

855+orM (Join a b) (Join c d) = Join (orM a c) (orM b d)

856+orM (Fork a b) (Fork c d) = Fork (orM a c) (orM b d)

857+orM x@(Fork _ _) y@(Join _ _) = orM x (abideJS y)

858+orM x@(Join _ _) y@(Fork _ _) = orM (abideJS x) y

859859

860860-- | Relational multiplication

861861andM :: Relation cols rows -> Relation cols rows -> Relation cols rows

862862andM Empty Empty = Empty

863863andM (One a) (One b) = One (fromBool (toBool a && toBool b))

864−andM (Junc a b) (Junc c d) = Junc (andM a c) (andM b d)

865−andM (Split a b) (Split c d) = Split (andM a c) (andM b d)

866−andM x@(Split _ _) y@(Junc _ _) = andM x (abideJS y)

867−andM x@(Junc _ _) y@(Split _ _) = andM (abideJS x) y

864+andM (Join a b) (Join c d) = Join (andM a c) (andM b d)

865+andM (Fork a b) (Fork c d) = Fork (andM a c) (andM b d)

866+andM x@(Fork _ _) y@(Join _ _) = andM x (abideJS y)

867+andM x@(Join _ _) y@(Fork _ _) = andM (abideJS x) y

868868

869869-- | Relational subtraction

870870subM :: Relation cols rows -> Relation cols rows -> Relation cols rows

871871subM Empty Empty = Empty

872872subM (One a) (One b) = if a - b < nat 0 then One (nat 0) else One (a - b)

873−subM (Junc a b) (Junc c d) = Junc (subM a c) (subM b d)

874−subM (Split a b) (Split c d) = Split (subM a c) (subM b d)

875−subM x@(Split _ _) y@(Junc _ _) = subM x (abideJS y)

876−subM x@(Junc _ _) y@(Split _ _) = subM (abideJS x) y

873+subM (Join a b) (Join c d) = Join (subM a c) (subM b d)

874+subM (Fork a b) (Fork c d) = Fork (subM a c) (subM b d)

875+subM x@(Fork _ _) y@(Join _ _) = subM x (abideJS y)

876+subM x@(Join _ _) y@(Fork _ _) = subM (abideJS x) y

877877

878878-- | Matrix relational composition.

879879compRel :: Relation cr rows -> Relation cols cr -> Relation cols rows

880880compRel Empty Empty = Empty

881881compRel (One a) (One b) = One (fromBool (toBool a && toBool b))

882−compRel (Junc a b) (Split c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law

883−compRel (Split a b) c = Split (compRel a c) (compRel b c) -- Split fusion law

884−compRel c (Junc a b) = Junc (compRel c a) (compRel c b) -- Junc fusion law

882+compRel (Join a b) (Fork c d) = orM (compRel a c) (compRel b d) -- Divide-and-conquer law

883+compRel (Fork a b) c = Fork (compRel a c) (compRel b c) -- Fork fusion law

884+compRel c (Join a b) = Join (compRel c a) (compRel c b) -- Join fusion law

885885

886886-- | Matrix relational right division

887887divR :: Relation b c -> Relation b a -> Relation a c

888888divR Empty Empty = Empty

889889divR (One a) (One b) = One (fromBool (not (toBool b) || toBool a)) -- b implies a

890−divR (Junc a b) (Junc c d) = andM (divR a c) (divR b d)

891−divR (Split a b) c = Split (divR a c) (divR b c)

892−divR c (Split a b) = Junc (divR c a) (divR c b)

890+divR (Join a b) (Join c d) = andM (divR a c) (divR b d)

891+divR (Fork a b) c = Fork (divR a c) (divR b c)

892+divR c (Fork a b) = Join (divR c a) (divR c b)

893893

894894-- | Matrix relational left division

895895divL :: Relation c b -> Relation a b -> Relation a c

@@ -905,7 +905,7 @@ divS s r = divL r s `intersection` divR (tr r) (tr s)

905905--

906906-- NOTE: Be careful to not ask for a relation bigger than the cardinality of

907907-- types @a@ or @b@ allows.

908−fromFRel ::

908+fromFRel' ::

909909 forall a b cols rows.

910910 ( Liftable Boolean a b,

911911 CountableDimensions cols rows,

@@ -913,7 +913,7 @@ fromFRel ::

913913 ) =>

914914 (a -> b) ->

915915 Relation cols rows

916−fromFRel f =

916+fromFRel' f =

917917 let minA = minBound @a

918918 maxA = maxBound @a

919919 minB = minBound @b

@@ -934,7 +934,7 @@ fromFRel f =

934934

935935-- | Lifts functions to relations with dimensions matching @a@ and @b@

936936-- cardinality's.

937−fromFRel' ::

937+fromFRel ::

938938 forall a b.

939939 ( Liftable Boolean a b,

940940 CountableDimensionsN a b,

@@ -942,7 +942,7 @@ fromFRel' ::

942942 ) =>

943943 (a -> b) ->

944944 Relation (Normalize a) (Normalize b)

945−fromFRel' f =

945+fromFRel f =

946946 let minA = minBound @a

947947 maxA = maxBound @a

948948 minB = minBound @b

src/LAoP/Matrix/Nat.hs+34−34

@@ -69,8 +69,8 @@ module LAoP.Matrix.Nat

6969 -- * Primitives

7070 empty,

7171 one,

72− junc,

73− split,

72+ join,

73+ fork,

7474

7575 -- * Auxiliary type families

7676 I.FromNat,

@@ -112,12 +112,12 @@ module LAoP.Matrix.Nat

112112 zipWithM,

113113

114114 -- * Biproduct approach

115− -- ** Split

115+ -- ** Fork

116116 (===),

117117 -- *** Projections

118118 p1,

119119 p2,

120− -- ** Junc

120+ -- ** Join

121121 (|||),

122122 -- *** Injections

123123 i1,

@@ -131,8 +131,8 @@ module LAoP.Matrix.Nat

131131 -- | Note that given the restrictions imposed it is not possible to

132132 -- implement the standard type classes present in standard Haskell.

133133 -- *** Matrix pairing projections

134− kp1,

135− kp2,

134+ fstM,

135+ sndM,

136136

137137 -- *** Matrix pairing

138138 khatri,

@@ -143,10 +143,10 @@ module LAoP.Matrix.Nat

143143

144144 -- | Note that given the restrictions imposed it is not possible to

145145 -- implement the standard type classes present in standard Haskell.

146− identity,

146+ iden,

147147 comp,

148− fromF,

149148 fromF',

149+ fromF,

150150

151151 -- * Matrix printing

152152 pretty,

@@ -179,7 +179,7 @@ type TrivialP a b = I.FromNat (a * b) ~ I.FromNat (I.Count (I.FromNa

179179-- implementation is 'undefined'. However 'comp' can be and this partial

180180-- class implementation exists just to make the code more readable.

181181--

182−-- Please use 'identity' instead.

182+-- Please use 'iden' instead.

183183instance (Num e) => C.Category (Matrix e) where

184184 id = undefined

185185 (.) = comp

@@ -192,12 +192,12 @@ empty = M I.Empty

192192one :: e -> Matrix e 1 1

193193one = M . I.One

194194

195−junc ::

195+join ::

196196 (TrivialE a b) =>

197197 Matrix e a rows ->

198198 Matrix e b rows ->

199199 Matrix e (a + b) rows

200−junc (M a) (M b) = M (I.Junc a b)

200+join (M a) (M b) = M (I.Join a b)

201201

202202infixl 3 |||

203203(|||) ::

@@ -205,14 +205,14 @@ infixl 3 |||

205205 Matrix e a rows ->

206206 Matrix e b rows ->

207207 Matrix e (a + b) rows

208−(|||) = junc

208+(|||) = join

209209

210−split ::

210+fork ::

211211 (TrivialE a b) =>

212212 Matrix e cols a ->

213213 Matrix e cols b ->

214214 Matrix e cols (a + b)

215−split (M a) (M b) = M (I.Split a b)

215+fork (M a) (M b) = M (I.Fork a b)

216216

217217infixl 2 ===

218218(===) ::

@@ -220,7 +220,7 @@ infixl 2 ===

220220 Matrix e cols a ->

221221 Matrix e cols b ->

222222 Matrix e cols (a + b)

223−(===) = split

223+(===) = fork

224224

225225-- Construction

226226

@@ -238,7 +238,7 @@ col = M . I.col

238238row :: (I.FromLists e (I.FromNat cols) ()) => [e] -> Matrix e cols 1

239239row = M . I.row

240240

241−fromF ::

241+fromF' ::

242242 ( Liftable e a b,

243243 CountableN cols,

244244 CountableN rows,

@@ -246,9 +246,9 @@ fromF ::

246246 ) =>

247247 (a -> b) ->

248248 Matrix e cols rows

249−fromF = M . I.fromF

249+fromF' = M . I.fromF'

250250

251−fromF' ::

251+fromF ::

252252 ( Liftable e a b,

253253 CountableNz a,

254254 CountableNz b,

@@ -256,7 +256,7 @@ fromF' ::

256256 ) =>

257257 (a -> b) ->

258258 Matrix e (I.Count a) (I.Count b)

259−fromF' = undefined -- M . I.fromF'

259+fromF = undefined -- M . I.fromF

260260

261261-- Conversion

262262

@@ -296,12 +296,12 @@ bang ::

296296 Matrix e cols 1

297297bang = M I.bang

298298

299−-- Identity Matrix

299+-- iden Matrix

300300

301−identity ::

301+iden ::

302302 (Num e, FromListsN e cols cols, CountableN cols) =>

303303 Matrix e cols cols

304−identity = M I.identity

304+iden = M I.iden

305305

306306-- Matrix composition (MMM)

307307

@@ -377,7 +377,7 @@ infixl 5 -|-

377377(-|-) (M a) (M b) = M ((I.-|-) a b)

378378

379379-- | Khatri Rao Product and projections

380−kp1 ::

380+fstM ::

381381 forall e m k .

382382 ( Num e,

383383 CountableDimensionsN m k,

@@ -385,9 +385,9 @@ kp1 ::

385385 FromListsN e (m * k) m,

386386 TrivialP m k

387387 ) => Matrix e (m * k) m

388−kp1 = M (I.kp1 @e @(I.FromNat m) @(I.FromNat k))

388+fstM = M (I.fstM @e @(I.FromNat m) @(I.FromNat k))

389389

390−kp2 ::

390+sndM ::

391391 forall e m k.

392392 ( Num e,

393393 CountableDimensionsN k m,

@@ -395,7 +395,7 @@ kp2 ::

395395 CountableN (m * k),

396396 TrivialP m k

397397 ) => Matrix e (m * k) k

398−kp2 = M (I.kp2 @e @(I.FromNat m) @(I.FromNat k))

398+sndM = M (I.sndM @e @(I.FromNat m) @(I.FromNat k))

399399

400400khatri ::

401401 forall e cols a b.

@@ -407,9 +407,9 @@ khatri ::

407407 TrivialP a b

408408 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a * b)

409409khatri a b =

410− let kp1' = kp1 @e @a @b

411− kp2' = kp2 @e @a @b

412− in comp (tr kp1') a * comp (tr kp2') b

410+ let fstM' = fstM @e @a @b

411+ sndM' = sndM @e @a @b

412+ in comp (tr fstM') a * comp (tr sndM') b

413413

414414-- | Product Bifunctor (Kronecker)

415415infixl 4 ><

@@ -428,15 +428,15 @@ infixl 4 ><

428428 TrivialP p q

429429 ) => Matrix e m p -> Matrix e n q -> Matrix e (m * n) (p * q)

430430(><) a b =

431− let kp1' = kp1 @e @m @n

432− kp2' = kp2 @e @m @n

433− in khatri (comp a kp1') (comp b kp2')

431+ let fstM' = fstM @e @m @n

432+ sndM' = sndM @e @m @n

433+ in khatri (comp a fstM') (comp b sndM')

434434

435−-- | Matrix abide Junc Split

435+-- | Matrix abide Join Fork

436436abideJS :: Matrix e cols rows -> Matrix e cols rows

437437abideJS (M m) = M (I.abideJS m)

438438

439−-- | Matrix abide Split Junc

439+-- | Matrix abide Fork Join

440440abideSJ :: Matrix e cols rows -> Matrix e cols rows

441441abideSJ (M m) = M (I.abideSJ m)

442442

src/LAoP/Matrix/Type.hs+51−51

@@ -73,8 +73,8 @@ module LAoP.Matrix.Type

7373 -- * Primitives

7474 empty,

7575 one,

76− junc,

77− split,

76+ join,

77+ fork,

7878

7979 -- * Auxiliary type families

8080 I.FromNat,

@@ -129,12 +129,12 @@ module LAoP.Matrix.Type

129129 zipWithM,

130130

131131 -- * Biproduct approach

132− -- ** Split

132+ -- ** Fork

133133 (===),

134134 -- *** Projections

135135 p1,

136136 p2,

137− -- ** Junc

137+ -- ** Join

138138 (|||),

139139 -- *** Injections

140140 i1,

@@ -148,8 +148,8 @@ module LAoP.Matrix.Type

148148 -- | Note that given the restrictions imposed it is not possible to

149149 -- implement the standard type classes present in standard Haskell.

150150 -- *** Matrix pairing projections

151− kp1,

152− kp2,

151+ fstM,

152+ sndM,

153153

154154 -- *** Matrix pairing

155155 khatri,

@@ -160,10 +160,10 @@ module LAoP.Matrix.Type

160160

161161 -- | Note that given the restrictions imposed it is not possible to

162162 -- implement the standard type classes present in standard Haskell.

163− identity,

163+ iden,

164164 comp,

165− fromF,

166165 fromF',

166+ fromF,

167167

168168 -- * Relation

169169 toRel,

@@ -202,7 +202,7 @@ type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a,

202202-- implementation is 'undefined'. However 'comp' can be and this partial

203203-- class implementation exists just to make the code more readable.

204204--

205−-- Please use 'identity' instead.

205+-- Please use 'iden' instead.

206206instance (Num e) => C.Category (Matrix e) where

207207 id = undefined

208208 (.) = comp

@@ -216,7 +216,7 @@ bimapM ::

216216 FromListsN e d c,

217217 FromListsN e b a

218218 ) => (a -> b) -> (c -> d) -> Matrix e a c -> Matrix e b d

219−bimapM f g m = fromF' g `comp` m `comp` tr (fromF' f)

219+bimapM f g m = fromF g `comp` m `comp` tr (fromF f)

220220

221221-- | Zero type alias

222222type Zero = Void

@@ -234,35 +234,35 @@ empty = M I.Empty

234234one :: e -> Matrix e One One

235235one = M . I.One

236236

237−-- | Matrix 'Junc' constructor

238−junc ::

237+-- | Matrix 'Join' constructor

238+join ::

239239 Matrix e a rows ->

240240 Matrix e b rows ->

241241 Matrix e (Either a b) rows

242−junc (M a) (M b) = M (I.Junc a b)

242+join (M a) (M b) = M (I.Join a b)

243243

244244infixl 3 |||

245−-- | Matrix 'Junc' constructor

245+-- | Matrix 'Join' constructor

246246(|||) ::

247247 Matrix e a rows ->

248248 Matrix e b rows ->

249249 Matrix e (Either a b) rows

250−(|||) = junc

250+(|||) = join

251251

252−-- | Matrix 'Split' constructor

253−split ::

252+-- | Matrix 'Fork' constructor

253+fork ::

254254 Matrix e cols a ->

255255 Matrix e cols b ->

256256 Matrix e cols (Either a b)

257−split (M a) (M b) = M (I.Split a b)

257+fork (M a) (M b) = M (I.Fork a b)

258258

259259infixl 2 ===

260−-- | Matrix 'Split' constructor

260+-- | Matrix 'Fork' constructor

261261(===) ::

262262 Matrix e cols a ->

263263 Matrix e cols b ->

264264 Matrix e cols (Either a b)

265−(===) = split

265+(===) = fork

266266

267267-- Functor hierarchy

268268

@@ -274,7 +274,7 @@ fmapM ::

274274 )

275275 =>

276276 (a -> b) -> Matrix e c a -> Matrix e c b

277−fmapM f m = fromF' f `comp` m

277+fmapM f m = fromF f `comp` m

278278

279279-- | Applicative instance equivalent 'unit' function,

280280unitM :: (Num e) => Matrix e () ()

@@ -336,23 +336,23 @@ row = M . I.row

336336--

337337-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

338338-- types @a@ or @b@ allows.

339−fromF ::

339+fromF' ::

340340 ( Liftable e a b,

341341 CountableDimensionsN cols rows,

342342 FromListsN e rows cols

343343 ) =>

344344 (a -> b) -> Matrix e cols rows

345−fromF = M . I.fromF

345+fromF' = M . I.fromF'

346346

347347-- | Lifts functions to matrices with dimensions matching @a@ and @b@

348348-- cardinality's.

349−fromF' ::

349+fromF ::

350350 ( Liftable e a b,

351351 CountableDimensionsN a b,

352352 FromListsN e b a

353353 ) =>

354354 (a -> b) -> Matrix e a b

355−fromF' = M . I.fromF'

355+fromF = M . I.fromF

356356

357357-- | Lifts relation functions to Boolean Matrix

358358toRel ::

@@ -418,16 +418,16 @@ point ::

418418 CountableN a,

419419 FromListsN e a One

420420 ) => a -> Matrix e One a

421−point = fromF' . const

421+point = fromF . const

422422

423−-- Identity Matrix

423+-- iden Matrix

424424

425−-- | Identity matrix

426−identity ::

425+-- | iden matrix

426+iden ::

427427 (Num e, FromListsN e a a, CountableN a) =>

428428 Matrix e a a

429−identity = M I.identity

430−{-# NOINLINE identity #-}

429+iden = M I.iden

430+{-# NOINLINE iden #-}

431431

432432-- Matrix composition (MMM)

433433

@@ -439,8 +439,8 @@ comp :: (Num e) => Matrix e cr rows -> Matrix e cols cr -> Matrix e cols rows

439439comp (M a) (M b) = M (I.comp a b)

440440{-# NOINLINE comp #-}

441441{-# RULES

442− "comp/identity1" forall m. comp m identity = m ;

443− "comp/identity2" forall m. comp identity m = m

442+ "comp/iden1" forall m. comp m iden = m ;

443+ "comp/iden2" forall m. comp iden m = m

444444#-}

445445

446446-- | Biproduct first component projection

@@ -528,7 +528,7 @@ infixl 5 -|-

528528-- Khatri Rao Product and projections

529529

530530-- | Khatri Rao product first component projection matrix.

531−kp1 ::

531+fstM ::

532532 forall e m k .

533533 ( Num e,

534534 CountableDimensionsN m k,

@@ -536,10 +536,10 @@ kp1 ::

536536 FromListsN e (m, k) m,

537537 TrivialP m k

538538 ) => Matrix e (m, k) m

539−kp1 = M (I.kp1 @e @(I.Normalize m) @(I.Normalize k))

539+fstM = M (I.fstM @e @(I.Normalize m) @(I.Normalize k))

540540

541541-- | Khatri Rao product second component projection matrix.

542−kp2 ::

542+sndM ::

543543 forall e m k.

544544 ( Num e,

545545 CountableDimensionsN k m,

@@ -547,16 +547,16 @@ kp2 ::

547547 FromListsN e (m, k) k,

548548 TrivialP m k

549549 ) => Matrix e (m, k) k

550−kp2 = M (I.kp2 @e @(I.Normalize m) @(I.Normalize k))

550+sndM = M (I.sndM @e @(I.Normalize m) @(I.Normalize k))

551551

552552-- | Khatri Rao Matrix product also known as matrix pairing.

553553--

554554-- NOTE: That this is not a true categorical product, see for instance:

555555--

556556-- @

557−-- | kp1 `comp` khatri a b == a

557+-- | fstM `comp` khatri a b == a

558558-- khatri a b ==> |

559−-- | kp2 `comp` khatri a b == b

559+-- | sndM `comp` khatri a b == b

560560-- @

561561--

562562-- __Emphasis__ on the implication symbol.

@@ -570,9 +570,9 @@ khatri ::

570570 TrivialP a b

571571 ) => Matrix e cols a -> Matrix e cols b -> Matrix e cols (a, b)

572572khatri a b =

573− let kp1' = kp1 @e @a @b

574− kp2' = kp2 @e @a @b

575− in comp (tr kp1') a * comp (tr kp2') b

573+ let fstM' = fstM @e @a @b

574+ sndM' = sndM @e @a @b

575+ in comp (tr fstM') a * comp (tr sndM') b

576576

577577-- Product Bifunctor (Kronecker)

578578

@@ -593,30 +593,30 @@ infixl 4 ><

593593 TrivialP p q

594594 ) => Matrix e m p -> Matrix e n q -> Matrix e (m, n) (p, q)

595595(><) a b =

596− let kp1' = kp1 @e @m @n

597− kp2' = kp2 @e @m @n

598− in khatri (comp a kp1') (comp b kp2')

596+ let fstM' = fstM @e @m @n

597+ sndM' = sndM @e @m @n

598+ in khatri (comp a fstM') (comp b sndM')

599599

600−-- Matrix abide Junc Split

600+-- Matrix abide Join Fork

601601

602−-- | Matrix "abiding" followin the 'Junc'-'Split' abide law.

602+-- | Matrix "abiding" followin the 'Join'-'Fork' abide law.

603603--

604604-- Law:

605605--

606606-- @

607−-- 'Junc' ('Split' a c) ('Split' b d) == 'Split' ('Junc' a b) ('Junc' c d)

607+-- 'Join' ('Fork' a c) ('Fork' b d) == 'Fork' ('Join' a b) ('Join' c d)

608608-- @

609609abideJS :: Matrix e cols rows -> Matrix e cols rows

610610abideJS (M m) = M (I.abideJS m)

611611

612−-- Matrix abide Split Junc

612+-- Matrix abide Fork Join

613613

614−-- | Matrix "abiding" followin the 'Split'-'Junc' abide law.

614+-- | Matrix "abiding" followin the 'Fork'-'Join' abide law.

615615--

616616-- Law:

617617--

618618-- @

619−-- 'Split' ('Junc' a b) ('Junc' c d) == 'Junc' ('Split' a c) ('Split' b d)

619+-- 'Fork' ('Join' a b) ('Join' c d) == 'Join' ('Fork' a c) ('Fork' b d)

620620-- @

621621abideSJ :: Matrix e cols rows -> Matrix e cols rows

622622abideSJ (M m) = M (I.abideSJ m)

src/LAoP/Relation.hs+5−5

@@ -43,9 +43,9 @@ module LAoP.Relation

4343 -- * Primitives

4444 empty,

4545 one,

46− junc,

46+ join,

4747 (|||),

48− split,

48+ fork,

4949 (===),

5050

5151 -- * Auxiliary type families

@@ -108,8 +108,8 @@ module LAoP.Relation

108108 splitR,

109109

110110 -- ** Projections

111− p1,

112− p2,

111+ fstR,

112+ sndR,

113113 -- ** Bifunctor

114114 (><),

115115 -- * Relational coproduct

@@ -148,7 +148,7 @@ module LAoP.Relation

148148 cond,

149149

150150 -- * Relational composition and lifting

151− identity,

151+ iden,

152152 comp,

153153 fromF,

154154 fromF',

src/LAoP/Relation/Internal.hs+62−62

@@ -53,9 +53,9 @@ module LAoP.Relation.Internal

5353 -- * Primitives

5454 empty,

5555 one,

56− junc,

56+ join,

5757 (|||),

58− split,

58+ fork,

5959 (===),

6060

6161 -- * Auxiliary type families

@@ -66,8 +66,8 @@ module LAoP.Relation.Internal

6666 -- * Matrix construction and conversion

6767 I.FromLists,

6868 fromLists,

69− fromF,

7069 fromF',

70+ fromF,

7171 toRel,

7272 toLists,

7373 toList,

@@ -118,8 +118,8 @@ module LAoP.Relation.Internal

118118 splitR,

119119

120120 -- ** Projections

121− p1,

122− p2,

121+ fstR,

122+ sndR,

123123 -- ** Bifunctor

124124 (><),

125125 -- * Relational coproduct

@@ -158,10 +158,10 @@ module LAoP.Relation.Internal

158158 cond,

159159

160160 -- * Relational composition and lifting

161− identity,

161+ iden,

162162 comp,

163− fromF,

164163 fromF',

164+ fromF,

165165

166166 -- ** Relational application

167167 pointAp,

@@ -205,19 +205,19 @@ type TrivialP a b = I.Normalize (a, b) ~ I.Normalize (I.Normalize a,

205205-- implementation is 'undefined'. However 'comp' can be and this partial

206206-- class implementation exists just to make the code more readable.

207207--

208−-- Please use 'identity' instead.

208+-- Please use 'iden' instead.

209209instance C.Category Relation where

210210 id = undefined

211211 (.) = comp

212212

213213instance Num (Relation a b) where

214− -- | Matrix addition becomes Boolean matrix disjunction

214+ -- | Matrix addition becomes Boolean matrix disjointion

215215 (R a) + (R b) = R (I.orM a b)

216216

217217 -- | Matrix subtraction becomes Relational subtraction

218218 (R a) - (R b) = R (I.subM a b)

219219

220− -- | Matrix multiplication becomes Boolean matrix conjunction

220+ -- | Matrix multiplication becomes Boolean matrix conjointion

221221 (R a) * (R b) = R (I.andM a b)

222222

223223 -- | Matrix negation becomes Boolean matrix negation

@@ -237,33 +237,33 @@ empty = R I.Empty

237237one :: Boolean -> Relation One One

238238one = R . I.One

239239

240−-- | Boolean Matrix 'Junc' constructor, also known as relational coproduct.

240+-- | Boolean Matrix 'Join' constructor, also known as relational coproduct.

241241--

242242-- See 'eitherR'.

243−junc :: Relation a c -> Relation b c -> Relation (Either a b) c

244−junc (R a) (R b) = R (I.Junc a b)

243+join :: Relation a c -> Relation b c -> Relation (Either a b) c

244+join (R a) (R b) = R (I.Join a b)

245245

246246infixl 3 |||

247−-- | Boolean Matrix 'Junc' constructor

247+-- | Boolean Matrix 'Join' constructor

248248--

249249-- See 'eitherR'.

250250(|||) ::

251251 Relation a c ->

252252 Relation b c ->

253253 Relation (Either a b) c

254−(|||) = junc

254+(|||) = join

255255

256−-- | Boolean Matrix 'Split' constructor, also known as relational product.

257−split :: Relation c a -> Relation c b -> Relation c (Either a b)

258−split (R a) (R b) = R (I.Split a b)

256+-- | Boolean Matrix 'Fork' constructor, also known as relational product.

257+fork :: Relation c a -> Relation c b -> Relation c (Either a b)

258+fork (R a) (R b) = R (I.Fork a b)

259259

260260infixl 2 ===

261−-- | Boolean Matrix 'Split' constructor

261+-- | Boolean Matrix 'Fork' constructor

262262(===) ::

263263 Relation c a ->

264264 Relation c b ->

265265 Relation c (Either a b)

266−(===) = split

266+(===) = fork

267267

268268-- Construction

269269

@@ -283,23 +283,23 @@ relationBuilder = R . I.matrixBuilder

283283--

284284-- NOTE: Be careful to not ask for a matrix bigger than the cardinality of

285285-- types @a@ or @b@ allows.

286−fromF ::

286+fromF' ::

287287 ( Liftable a b,

288288 CountableDimensionsN c d,

289289 FromListsN d c

290290 )

291291 => (a -> b) -> Relation c d

292−fromF f = R (I.fromFRel f)

292+fromF' f = R (I.fromFRel' f)

293293

294294-- | Lifts functions to matrices with dimensions matching @a@ and @b@

295295-- cardinality's.

296−fromF' ::

296+fromF ::

297297 ( Liftable a b,

298298 CountableDimensionsN a b,

299299 FromListsN b a

300300 )

301301 => (a -> b) -> Relation a b

302−fromF' f = R (I.fromFRel' f)

302+fromF f = R (I.fromFRel f)

303303

304304-- | Lifts relation functions to 'Relation'

305305toRel ::

@@ -412,18 +412,18 @@ point ::

412412 CountableN a,

413413 FromListsN a One

414414 ) => a -> Relation One a

415−point = fromF' . const

415+point = fromF . const

416416

417−-- Identity Matrix

417+-- iden Matrix

418418

419−-- | Identity matrix

419+-- | iden matrix

420420--

421421-- @

422−-- 'identity' ``comp`` r == r == r ``comp`` 'identity'

422+-- 'iden' ``comp`` r == r == r ``comp`` 'iden'

423423-- @

424−identity ::

424+iden ::

425425 (FromListsN a a, CountableN a) => Relation a a

426−identity = relationBuilder (bool (nat 0) (nat 1) . uncurry (==))

426+iden = relationBuilder (bool (nat 0) (nat 1) . uncurry (==))

427427

428428-- | Relational composition

429429--

@@ -530,7 +530,7 @@ iff r s = r == s

530530

531531-- | Relational intersection

532532--

533−-- Lifts pointwise conjunction.

533+-- Lifts pointwise conjointion.

534534--

535535-- @

536536-- (r ``intersection`` s) ``intersection`` t == r ``intersection`` (s ``intersection`` t)

@@ -541,7 +541,7 @@ intersection a b = a * b

541541

542542-- | Relational union

543543--

544−-- Lifts pointwise disjunction.

544+-- Lifts pointwise disjointion.

545545--

546546-- @

547547-- (r ``union`` s) ``union`` t == r `'union' (s ``union`` t)

@@ -658,13 +658,13 @@ bijection r = injection r && surjection r

658658

659659-- Properties of relations

660660

661−-- | A 'Relation' @r@ is 'reflexive' 'iff' @'identity' ``sse`` r@

661+-- | A 'Relation' @r@ is 'reflexive' 'iff' @'iden' ``sse`` r@

662662reflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

663−reflexive r = identity <= r

663+reflexive r = iden <= r

664664

665−-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'identity'@

665+-- | A 'Relation' @r@ is 'coreflexive' 'iff' @r ``sse`` 'iden'@

666666coreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

667−coreflexive r = r <= identity

667+coreflexive r = r <= iden

668668

669669-- | A 'Relation' @r@ is 'transitive' 'iff' @(r ``comp`` r) ``sse`` r@

670670transitive :: Relation a a -> Bool

@@ -674,13 +674,13 @@ transitive r = (r `comp` r) `sse` r

674674symmetric :: Relation a a -> Bool

675675symmetric r = r == conv r

676676

677−-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'identity'@

677+-- | A 'Relation' @r@ is anti-symmetric 'iff' @(r ``intersection`` 'conv' r) ``sse`` 'iden'@

678678antiSymmetric :: (CountableN a, FromListsN a a) => Relation a a -> Bool

679−antiSymmetric r = (r `intersection` conv r) `sse` identity

679+antiSymmetric r = (r `intersection` conv r) `sse` iden

680680

681−-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'identity') == 'zeros'@

681+-- | A 'Relation' @r@ is 'irreflexive' 'iff' @(r ``intersection`` 'iden') == 'zeros'@

682682irreflexive :: (CountableN a, FromListsN a a) => Relation a a -> Bool

683−irreflexive r = (r `intersection` identity) == zeros

683+irreflexive r = (r `intersection` iden) == zeros

684684

685685-- | A 'Relation' @r@ is 'connected' 'iff' @(r ``union`` 'conv' r) == 'ones'@

686686connected :: (CountableN a, FromListsN a a) => Relation a a -> Bool

@@ -718,9 +718,9 @@ difunctional r = r `comp` conv r `comp` r == r

718718-- NOTE: That this is not a true categorical product, see for instance:

719719--

720720-- @

721−-- | 'p1' ``comp`` 'splitR' a b ``sse`` a

721+-- | 'fstR' ``comp`` 'splitR' a b ``sse`` a

722722-- 'splitR' a b <=> |

723−-- | 'p2' ``comp`` 'splitR' a b ``sse`` b

723+-- | 'sndR' ``comp`` 'splitR' a b ``sse`` b

724724-- @

725725--

726726-- __Emphasis__ on the 'sse'.

@@ -747,9 +747,9 @@ splitR (R f) (R g) = R (I.khatri f g)

747747-- | Relational pairing first component projection

748748--

749749-- @

750−-- 'p1' ``comp`` 'splitR' r s ``sse`` r

750+-- 'fstR' ``comp`` 'splitR' r s ``sse`` r

751751-- @

752−p1 ::

752+fstR ::

753753 forall a b .

754754 ( CountableDimensionsN a b,

755755 CountableN (a, b),

@@ -757,14 +757,14 @@ p1 ::

757757 TrivialP a b

758758 )

759759 => Relation (a, b) a

760−p1 = R (I.kp1 @Boolean @(I.Normalize a) @(I.Normalize b))

760+fstR = R (I.fstM @Boolean @(I.Normalize a) @(I.Normalize b))

761761

762762-- | Relational pairing second component projection

763763--

764764-- @

765−-- 'p2' ``comp`` 'splitR' r s ``sse`` s

765+-- 'sndR' ``comp`` 'splitR' r s ``sse`` s

766766-- @

767−p2 ::

767+sndR ::

768768 forall a b .

769769 ( CountableDimensionsN a b,

770770 CountableN (a, b),

@@ -772,7 +772,7 @@ p2 ::

772772 TrivialP a b

773773 )

774774 => Relation (a, b) b

775−p2 = R (I.kp2 @Boolean @(I.Normalize a) @(I.Normalize b))

775+sndR = R (I.sndM @Boolean @(I.Normalize a) @(I.Normalize b))

776776

777777-- Relational pairing functor

778778

@@ -780,7 +780,7 @@ infixl 4 ><

780780-- | Relational pairing functor

781781--

782782-- @

783−-- r '><' s == 'splitR' (r ``comp`` p1) (s ``comp`` p2)

783+-- r '><' s == 'splitR' (r ``comp`` fstR) (s ``comp`` sndR)

784784-- (r '><' s) ``comp`` (p '><' q) == (r ``comp`` p) '><' (s ``comp`` q)

785785-- @

786786(><) ::

@@ -815,12 +815,12 @@ infixl 4 ><

815815-- 'eitherR' ('splitR' r s) ('splitR' t v) == 'splitR' ('eitherR' r t) ('eitherR' s v)

816816-- @

817817eitherR :: Relation a c -> Relation b c -> Relation (Either a b) c

818−eitherR = junc

818+eitherR = join

819819

820820-- | Relational coproduct first component injection

821821--

822822-- @

823−-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'

823+-- 'img' 'i1' ``union`` 'img' 'i2' == 'iden'

824824-- 'i1' ``comp`` 'i2' = 'zeros'

825825-- @

826826i1 ::

@@ -834,7 +834,7 @@ i1 = R I.i1

834834-- | Relational coproduct second component injection

835835--

836836-- @

837−-- 'img' 'i1' ``union`` 'img' 'i2' == 'identity'

837+-- 'img' 'i1' ``union`` 'img' 'i2' == 'iden'

838838-- 'i1' ``comp`` 'i2' = 'zeros'

839839-- @

840840i2 ::

@@ -883,7 +883,7 @@ trans ::

883883 TrivialP c b

884884 )

885885 => Relation (a, b) c -> Relation a (c, b)

886−trans r = splitR r p2 `comp` conv p1

886+trans r = splitR r sndR `comp` conv fstR

887887

888888-- | Relational 'untrans'

889889--

@@ -904,12 +904,12 @@ untrans ::

904904 TrivialP c b

905905 )

906906 => Relation a (c, b) -> Relation (a, b) c

907−untrans s = p1 `comp` conv (splitR (conv s) p2)

907+untrans s = fstR `comp` conv (splitR (conv s) sndR)

908908

909909-- | Transforms predicate @p@ into a correflexive relation.

910910--

911911-- @

912−-- 'predR' ('const' True) == 'identity'

912+-- 'predR' ('const' True) == 'iden'

913913-- 'predR' ('const' False) == 'zeros'

914914-- @

915915--

@@ -924,14 +924,14 @@ predR ::

924924 FromListsN Bool a

925925 )

926926 => Relation a Bool -> Relation a a

927−predR p = identity `intersection` divisionF (fromF' (const True)) p

927+predR p = iden `intersection` divisionF (fromF (const True)) p

928928

929929-- | Equalizes functions @f@ and @g@.

930930-- That is, @'equalizer' f g@ is the largest coreflexive

931931-- that restricts @g@ so that @f@ and @g@ yield the same outputs.

932932--

933933-- @

934−-- 'equalizer' r r == 'identity'

934+-- 'equalizer' r r == 'iden'

935935-- 'equalizer' ('point' True) ('point' False) == 'zeros'

936936-- @

937937equalizer ::

@@ -939,7 +939,7 @@ equalizer ::

939939 FromListsN a a

940940 )

941941 => Relation a b -> Relation a b -> Relation a a

942−equalizer f g = identity `intersection` divisionF f g

942+equalizer f g = iden `intersection` divisionF f g

943943

944944-- | Relational conditional guard.

945945--

@@ -969,22 +969,22 @@ cond p r s = eitherR r s `comp` guard p

969969-- | Relational domain.

970970--

971971-- For injective relations, 'domain' and 'ker'nel coincide,

972−-- since @'ker' r ``sse`` 'identity'@ in such situations.

972+-- since @'ker' r ``sse`` 'iden'@ in such situations.

973973domain ::

974974 ( CountableN a,

975975 FromListsN a a

976976 ) => Relation a b -> Relation a a

977−domain r = ker r `intersection` identity

977+domain r = ker r `intersection` iden

978978

979979-- | Relational range.

980980--

981981-- For functions, 'range' and 'img' (image) coincide,

982−-- since @'img' f ``sse`` 'identity'@ for any @f@.

982+-- since @'img' f ``sse`` 'iden'@ for any @f@.

983983range ::

984984 ( CountableN b,

985985 FromListsN b b

986986 ) => Relation a b -> Relation b b

987−range r = img r `intersection` identity

987+range r = img r `intersection` iden

988988

989989-- Relation pretty print

990990