From 43ddff2e7f1e9f4d8855f573384e26b63d34f697 Mon Sep 17 00:00:00 2001 From: Tom Smeding Date: Tue, 14 May 2024 23:30:53 +0200 Subject: WIP GHC nats --- src/Data/Array/Mixed.hs | 93 +++++++--------- src/Data/Array/Nested/Internal.hs | 221 +++++++++++++++++++++++++------------- 2 files changed, 184 insertions(+), 130 deletions(-) (limited to 'src/Data') diff --git a/src/Data/Array/Mixed.hs b/src/Data/Array/Mixed.hs index d782e9f..672b832 100644 --- a/src/Data/Array/Mixed.hs +++ b/src/Data/Array/Mixed.hs @@ -13,6 +13,7 @@ {-# LANGUAGE TypeApplications #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} {-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-} module Data.Array.Mixed where @@ -27,8 +28,10 @@ import Foreign.Storable (Storable) import GHC.TypeLits import Unsafe.Coerce (unsafeCoerce) -import Data.INat +-- | Evidence for the constraint @c a@. +data Dict c a where + Dict :: c a => Dict c a -- | The 'SNat' pattern synonym is complete, but it doesn't have a -- @COMPLETE@ pragma. This copy of it does. @@ -103,11 +106,11 @@ instance KnownShapeX sh => KnownShapeX (Nothing : sh) where knownShapeX = () :!$? knownShapeX type family Rank sh where - Rank '[] = Z - Rank (_ : sh) = S (Rank sh) + Rank '[] = 0 + Rank (_ : sh) = 1 + Rank sh type XArray :: [Maybe Nat] -> Type -> Type -newtype XArray sh a = XArray (S.Array (FromINat (Rank sh)) a) +newtype XArray sh a = XArray (S.Array (Rank sh) a) deriving (Show) zeroIxX :: StaticShX sh -> IIxX sh @@ -217,22 +220,22 @@ staticShapeFrom (n :$@ sh) = n :!$@ staticShapeFrom sh staticShapeFrom (_ :$? sh) = () :!$? staticShapeFrom sh lemRankApp :: StaticShX sh1 -> StaticShX sh2 - -> FromINat (Rank (sh1 ++ sh2)) :~: FromINat (Rank sh1) + FromINat (Rank sh2) + -> Rank (sh1 ++ sh2) :~: Rank sh1 + Rank sh2 lemRankApp _ _ = unsafeCoerce Refl -- TODO improve this lemRankAppComm :: StaticShX sh1 -> StaticShX sh2 - -> FromINat (Rank (sh1 ++ sh2)) :~: FromINat (Rank (sh2 ++ sh1)) + -> Rank (sh1 ++ sh2) :~: Rank (sh2 ++ sh1) lemRankAppComm _ _ = unsafeCoerce Refl -- TODO improve this -lemKnownINatRank :: IShX sh -> Dict KnownINat (Rank sh) -lemKnownINatRank ZSX = Dict -lemKnownINatRank (_ :$@ sh) | Dict <- lemKnownINatRank sh = Dict -lemKnownINatRank (_ :$? sh) | Dict <- lemKnownINatRank sh = Dict +lemKnownNatRank :: IShX sh -> Dict KnownNat (Rank sh) +lemKnownNatRank ZSX = Dict +lemKnownNatRank (_ :$@ sh) | Dict <- lemKnownNatRank sh = Dict +lemKnownNatRank (_ :$? sh) | Dict <- lemKnownNatRank sh = Dict -lemKnownINatRankSSX :: StaticShX sh -> Dict KnownINat (Rank sh) -lemKnownINatRankSSX ZKSX = Dict -lemKnownINatRankSSX (_ :!$@ ssh) | Dict <- lemKnownINatRankSSX ssh = Dict -lemKnownINatRankSSX (_ :!$? ssh) | Dict <- lemKnownINatRankSSX ssh = Dict +lemKnownNatRankSSX :: StaticShX sh -> Dict KnownNat (Rank sh) +lemKnownNatRankSSX ZKSX = Dict +lemKnownNatRankSSX (_ :!$@ ssh) | Dict <- lemKnownNatRankSSX ssh = Dict +lemKnownNatRankSSX (_ :!$? ssh) | Dict <- lemKnownNatRankSSX ssh = Dict lemKnownShapeX :: StaticShX sh -> Dict KnownShapeX sh lemKnownShapeX ZKSX = Dict @@ -259,8 +262,7 @@ shape (XArray arr) = go (knownShapeX @sh) (S.shapeL arr) fromVector :: forall sh a. Storable a => IShX sh -> VS.Vector a -> XArray sh a fromVector sh v - | Dict <- lemKnownINatRank sh - , Dict <- knownNatFromINat (Proxy @(Rank sh)) + | Dict <- lemKnownNatRank sh = XArray (S.fromVector (shapeLshape sh) v) toVector :: Storable a => XArray sh a -> VS.Vector a @@ -274,15 +276,14 @@ unScalar (XArray a) = S.unScalar a constant :: forall sh a. Storable a => IShX sh -> a -> XArray sh a constant sh x - | Dict <- lemKnownINatRank sh - , Dict <- knownNatFromINat (Proxy @(Rank sh)) + | Dict <- lemKnownNatRank sh = XArray (S.constant (shapeLshape sh) x) generate :: Storable a => IShX sh -> (IIxX sh -> a) -> XArray sh a generate sh f = fromVector sh $ VS.generate (shapeSize sh) (f . fromLinearIdx sh) -- generateM :: (Monad m, Storable a) => IShX sh -> (IIxX sh -> m a) -> m (XArray sh a) --- generateM sh f | Dict <- lemKnownINatRank sh = +-- generateM sh f | Dict <- lemKnownNatRank sh = -- XArray . S.fromVector (shapeLshape sh) -- <$> VS.generateM (shapeSize sh) (f . fromLinearIdx sh) @@ -305,8 +306,7 @@ type family AddMaybe n m where append :: forall n m sh a. (KnownShapeX sh, Storable a) => XArray (n : sh) a -> XArray (m : sh) a -> XArray (AddMaybe n m : sh) a append (XArray a) (XArray b) - | Dict <- lemKnownINatRankSSX (knownShapeX @sh) - , Dict <- knownNatFromINat (Proxy @(Rank sh)) + | Dict <- lemKnownNatRankSSX (knownShapeX @sh) = XArray (S.append a b) rerank :: forall sh sh1 sh2 a b. @@ -315,15 +315,12 @@ rerank :: forall sh sh1 sh2 a b. -> (XArray sh1 a -> XArray sh2 b) -> XArray (sh ++ sh1) a -> XArray (sh ++ sh2) b rerank ssh ssh1 ssh2 f (XArray arr) - | Dict <- lemKnownINatRankSSX ssh - , Dict <- knownNatFromINat (Proxy @(Rank sh)) - , Dict <- lemKnownINatRankSSX ssh2 - , Dict <- knownNatFromINat (Proxy @(Rank sh2)) + | Dict <- lemKnownNatRankSSX ssh + , Dict <- lemKnownNatRankSSX ssh2 , Refl <- lemRankApp ssh ssh1 , Refl <- lemRankApp ssh ssh2 - , Dict <- lemKnownINatRankSSX (ssxAppend ssh ssh2) -- these two should be redundant but the - , Dict <- knownNatFromINat (Proxy @(Rank (sh ++ sh2))) -- solver is not clever enough - = XArray (S.rerank @(FromINat (Rank sh)) @(FromINat (Rank sh1)) @(FromINat (Rank sh2)) + , Dict <- lemKnownNatRankSSX (ssxAppend ssh ssh2) -- should be redundant but the solver is not clever enough + = XArray (S.rerank @(Rank sh) @(Rank sh1) @(Rank sh2) (\a -> unXArray (f (XArray a))) arr) where @@ -342,15 +339,12 @@ rerank2 :: forall sh sh1 sh2 a b c. -> (XArray sh1 a -> XArray sh1 b -> XArray sh2 c) -> XArray (sh ++ sh1) a -> XArray (sh ++ sh1) b -> XArray (sh ++ sh2) c rerank2 ssh ssh1 ssh2 f (XArray arr1) (XArray arr2) - | Dict <- lemKnownINatRankSSX ssh - , Dict <- knownNatFromINat (Proxy @(Rank sh)) - , Dict <- lemKnownINatRankSSX ssh2 - , Dict <- knownNatFromINat (Proxy @(Rank sh2)) + | Dict <- lemKnownNatRankSSX ssh + , Dict <- lemKnownNatRankSSX ssh2 , Refl <- lemRankApp ssh ssh1 , Refl <- lemRankApp ssh ssh2 - , Dict <- lemKnownINatRankSSX (ssxAppend ssh ssh2) -- these two should be redundant but the - , Dict <- knownNatFromINat (Proxy @(Rank (sh ++ sh2))) -- solver is not clever enough - = XArray (S.rerank2 @(FromINat (Rank sh)) @(FromINat (Rank sh1)) @(FromINat (Rank sh2)) + , Dict <- lemKnownNatRankSSX (ssxAppend ssh ssh2) -- these two should be redundant but the + = XArray (S.rerank2 @(Rank sh) @(Rank sh1) @(Rank sh2) (\a b -> unXArray (f (XArray a) (XArray b))) arr1 arr2) where @@ -359,8 +353,7 @@ rerank2 ssh ssh1 ssh2 f (XArray arr1) (XArray arr2) -- | The list argument gives indices into the original dimension list. transpose :: forall sh a. KnownShapeX sh => [Int] -> XArray sh a -> XArray sh a transpose perm (XArray arr) - | Dict <- lemKnownINatRankSSX (knownShapeX @sh) - , Dict <- knownNatFromINat (Proxy @(Rank sh)) + | Dict <- lemKnownNatRankSSX (knownShapeX @sh) = XArray (S.transpose perm arr) transpose2 :: forall sh1 sh2 a. @@ -369,10 +362,8 @@ transpose2 :: forall sh1 sh2 a. transpose2 ssh1 ssh2 (XArray arr) | Refl <- lemRankApp ssh1 ssh2 , Refl <- lemRankApp ssh2 ssh1 - , Dict <- lemKnownINatRankSSX (ssxAppend ssh1 ssh2) - , Dict <- knownNatFromINat (Proxy @(Rank (sh1 ++ sh2))) - , Dict <- lemKnownINatRankSSX (ssxAppend ssh2 ssh1) - , Dict <- knownNatFromINat (Proxy @(Rank (sh2 ++ sh1))) + , Dict <- lemKnownNatRankSSX (ssxAppend ssh1 ssh2) + , Dict <- lemKnownNatRankSSX (ssxAppend ssh2 ssh1) , Refl <- lemRankAppComm ssh1 ssh2 , let n1 = ssxLength ssh1 = XArray (S.transpose (ssxIotaFrom n1 ssh2 ++ ssxIotaFrom 0 ssh1) arr) @@ -395,13 +386,12 @@ sumOuter ssh ssh' fromList1 :: forall n sh a. Storable a => StaticShX (n : sh) -> [XArray sh a] -> XArray (n : sh) a fromList1 ssh l - | Dict <- lemKnownINatRankSSX ssh - , Dict <- knownNatFromINat (Proxy @(Rank (n : sh))) + | Dict <- lemKnownNatRankSSX ssh = case ssh of m@GHC_SNat :!$@ _ | natVal m /= fromIntegral (length l) -> error $ "Data.Array.Mixed.fromList: length of list (" ++ show (length l) ++ ")" ++ "does not match the type (" ++ show (natVal m) ++ ")" - _ -> XArray (S.ravel (ORB.fromList [length l] (coerce @[XArray sh a] @[S.Array (FromINat (Rank sh)) a] l))) + _ -> XArray (S.ravel (ORB.fromList [length l] (coerce @[XArray sh a] @[S.Array (Rank sh) a] l))) toList1 :: Storable a => XArray (n : sh) a -> [XArray sh a] toList1 (XArray arr) = coerce (ORB.toList (S.unravel arr)) @@ -409,8 +399,7 @@ toList1 (XArray arr) = coerce (ORB.toList (S.unravel arr)) -- | Throws if the given shape is not, in fact, empty. empty :: forall sh a. Storable a => IShX sh -> XArray sh a empty sh - | Dict <- lemKnownINatRank sh - , Dict <- knownNatFromINat (Proxy @(Rank sh)) + | Dict <- lemKnownNatRank sh = XArray (S.constant (shapeLshape sh) (error "Data.Array.Mixed.empty: shape was not empty")) @@ -423,17 +412,13 @@ rev1 (XArray arr) = XArray (S.rev [0] arr) -- | Throws if the given array and the target shape do not have the same number of elements. reshape :: forall sh1 sh2 a. Storable a => StaticShX sh1 -> IShX sh2 -> XArray sh1 a -> XArray sh2 a reshape ssh1 sh2 (XArray arr) - | Dict <- lemKnownINatRankSSX ssh1 - , Dict <- knownNatFromINat (Proxy @(Rank sh1)) - , Dict <- lemKnownINatRank sh2 - , Dict <- knownNatFromINat (Proxy @(Rank sh2)) + | Dict <- lemKnownNatRankSSX ssh1 + , Dict <- lemKnownNatRank sh2 = XArray (S.reshape (shapeLshape sh2) arr) -- | Throws if the given array and the target shape do not have the same number of elements. reshapePartial :: forall sh1 sh2 sh' a. Storable a => StaticShX sh1 -> StaticShX sh' -> IShX sh2 -> XArray (sh1 ++ sh') a -> XArray (sh2 ++ sh') a reshapePartial ssh1 ssh' sh2 (XArray arr) - | Dict <- lemKnownINatRankSSX (ssxAppend ssh1 ssh') - , Dict <- knownNatFromINat (Proxy @(Rank (sh1 ++ sh'))) - , Dict <- lemKnownINatRankSSX (ssxAppend (staticShapeFrom sh2) ssh') - , Dict <- knownNatFromINat (Proxy @(Rank (sh2 ++ sh'))) + | Dict <- lemKnownNatRankSSX (ssxAppend ssh1 ssh') + , Dict <- lemKnownNatRankSSX (ssxAppend (staticShapeFrom sh2) ssh') = XArray (S.reshape (shapeLshape sh2 ++ drop (length sh2) (S.shapeL arr)) arr) diff --git a/src/Data/Array/Nested/Internal.hs b/src/Data/Array/Nested/Internal.hs index d041aff..54b567a 100644 --- a/src/Data/Array/Nested/Internal.hs +++ b/src/Data/Array/Nested/Internal.hs @@ -20,16 +20,51 @@ {-# LANGUAGE TypeOperators #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE ViewPatterns #-} +{-# OPTIONS_GHC -fplugin GHC.TypeLits.Normalise #-} {-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-} +{-# OPTIONS_GHC -Wno-unused-imports #-} {-| TODO: * We should be more consistent in whether functions take a 'StaticShX' argument or a 'KnownShapeX' constraint. -* Document the choice of using 'INat' for ranks and 'Nat' for shapes. Point - being that we need to do induction over the former, but the latter need to be - able to get large. +* Mikolaj wants these: + + About your wishlist of operations: these are already there + + OR.index + OR.append + OR.transpose + + These can be easily lifted from the definition for XArray (5min work): + + OR.scalar + OR.unScalar + OR.constant + + These should not be hard: + + OR.fromList + ORB.toList . OR.unravel + OR.ravel . ORB.fromList + OR.slice + OR.rev + OR.reshape + + though it's a bit unfortunate that we end up needing toList. Looking in + horde-ad I see that you seem to need them to do certain operations in Haskell + that orthotope doesn't support? + + For this one we'll need to see to what extent you really need it, and what API + you'd need precisely: + + OR.rerank + + and for these we have an API design question: + + OR.toVector + OR.fromVector -} @@ -51,10 +86,10 @@ import qualified Data.Vector.Storable as VS import qualified Data.Vector.Storable.Mutable as VSM import Foreign.Storable (Storable) import GHC.TypeLits +import Unsafe.Coerce (unsafeCoerce) -import Data.Array.Mixed (XArray, IxX(..), IIxX, ShX(..), IShX, KnownShapeX(..), StaticShX(..), type (++), pattern GHC_SNat) +import Data.Array.Mixed (XArray, IxX(..), IIxX, ShX(..), IShX, KnownShapeX(..), StaticShX(..), type (++), pattern GHC_SNat, Dict(..)) import qualified Data.Array.Mixed as X -import Data.INat -- Invariant in the API @@ -91,34 +126,71 @@ import Data.INat type family Replicate n a where - Replicate Z a = '[] - Replicate (S n) a = a : Replicate n a + Replicate 0 a = '[] + Replicate n a = a : Replicate (n - 1) a type family MapJust l where MapJust '[] = '[] MapJust (x : xs) = Just x : MapJust xs -lemKnownReplicate :: forall n. KnownINat n => Proxy n -> Dict KnownShapeX (Replicate n Nothing) -lemKnownReplicate _ = X.lemKnownShapeX (go (inatSing @n)) +pattern SZ :: () => (n ~ 0) => SNat n +pattern SZ <- ((\sn -> testEquality sn (SNat @0)) -> Just Refl) + where SZ = SNat + +pattern SS :: forall np1. () => forall n. (n + 1 ~ np1) => SNat n -> SNat np1 +pattern SS sn <- (snatPred -> Just (SNatPredResult sn Refl)) + where SS = snatSucc + +{-# COMPLETE SZ, SS #-} + +snatSucc :: SNat n -> SNat (n + 1) +snatSucc SNat = SNat + +data SNatPredResult np1 = forall n. SNatPredResult (SNat n) (n + 1 :~: np1) +snatPred :: forall np1. SNat np1 -> Maybe (SNatPredResult np1) +snatPred snp1 = + withKnownNat snp1 $ + case cmpNat (Proxy @1) (Proxy @np1) of + LTI -> Just (SNatPredResult (SNat @(np1 - 1)) Refl) + EQI -> Just (SNatPredResult (SNat @(np1 - 1)) Refl) + GTI -> Nothing + +subst1 :: forall f a b. a :~: b -> f a :~: f b +subst1 Refl = Refl + +subst2 :: forall f c a b. a :~: b -> f a c :~: f b c +subst2 Refl = Refl + +lemReplicateSucc :: (a : Replicate n a) :~: Replicate (n + 1) a +lemReplicateSucc = unsafeCoerce Refl + +lemKnownReplicate :: forall n. KnownNat n => Proxy n -> Dict KnownShapeX (Replicate n Nothing) +lemKnownReplicate _ = X.lemKnownShapeX (go (natSing @n)) where - go :: SINat m -> StaticShX (Replicate m Nothing) + go :: SNat m -> StaticShX (Replicate m Nothing) go SZ = ZKSX - go (SS n) = () :!$? go n + go (SS (n :: SNat nm1)) | Refl <- lemReplicateSucc @(Nothing @Nat) @nm1 = () :!$? go n -lemRankReplicate :: forall n. KnownINat n => Proxy n -> X.Rank (Replicate n (Nothing @Nat)) :~: n -lemRankReplicate _ = go (inatSing @n) +lemRankReplicate :: forall n. KnownNat n => Proxy n -> X.Rank (Replicate n (Nothing @Nat)) :~: n +lemRankReplicate _ = go (natSing @n) where - go :: SINat m -> X.Rank (Replicate m (Nothing @Nat)) :~: m + go :: forall m. SNat m -> X.Rank (Replicate m (Nothing @Nat)) :~: m go SZ = Refl - go (SS n) | Refl <- go n = Refl - -lemReplicatePlusApp :: forall n m a. KnownINat n => Proxy n -> Proxy m -> Proxy a - -> Replicate (n +! m) a :~: Replicate n a ++ Replicate m a -lemReplicatePlusApp _ _ _ = go (inatSing @n) + go (SS (n :: SNat nm1)) + | Refl <- lemReplicateSucc @(Nothing @Nat) @nm1 + , Refl <- go n + = Refl + +lemReplicatePlusApp :: forall n m a. KnownNat n => Proxy n -> Proxy m -> Proxy a + -> Replicate (n + m) a :~: Replicate n a ++ Replicate m a +lemReplicatePlusApp _ _ _ = go (natSing @n) where - go :: SINat n' -> Replicate (n' +! m) a :~: Replicate n' a ++ Replicate m a + go :: SNat n' -> Replicate (n' + m) a :~: Replicate n' a ++ Replicate m a go SZ = Refl - go (SS n) | Refl <- go n = Refl + go (SS (n :: SNat n'm1)) + | Refl <- lemReplicateSucc @a @n'm1 + , Refl <- go n + = sym (lemReplicateSucc @a @(n'm1 + m)) shAppSplit :: Proxy sh' -> StaticShX sh -> IShX (sh ++ sh') -> (IShX sh, IShX sh') shAppSplit _ ZKSX idx = (ZSX, idx) @@ -575,18 +647,15 @@ deriving via Mixed sh (Primitive Double) instance KnownShapeX sh => Num (Mixed s -- | A rank-typed array: the number of dimensions of the array (its /rank/) is --- represented on the type level as a 'INat'. +-- represented on the type level as a 'Nat'. -- -- Valid elements of a ranked arrays are described by the 'Elt' type class. -- Because 'Ranked' itself is also an instance of 'Elt', nested arrays are -- supported (and are represented as a single, flattened, struct-of-arrays -- array internally). -- --- Note that this 'INat' is not a "GHC.TypeLits" natural, because we want a --- type-level natural that supports induction. --- -- 'Ranked' is a newtype around a 'Mixed' of 'Nothing's. -type Ranked :: INat -> Type -> Type +type Ranked :: Nat -> Type -> Type newtype Ranked n a = Ranked (Mixed (Replicate n Nothing) a) deriving instance Show (Mixed (Replicate n Nothing) a) => Show (Ranked n a) @@ -616,7 +685,7 @@ newtype instance MixedVecs s sh (Shaped sh' a) = MV_Shaped (MixedVecs s sh (Mixe -- 'Ranked' and 'Shaped' can already be used at the top level of an array nest; -- these instances allow them to also be used as elements of arrays, thus -- making them first-class in the API. -instance (Elt a, KnownINat n) => Elt (Ranked n a) where +instance (Elt a, KnownNat n) => Elt (Ranked n a) where mshape (M_Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) = mshape arr mindex (M_Ranked arr) i | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mindex arr i) @@ -848,37 +917,37 @@ rewriteMixed Refl x = x -- ====== API OF RANKED ARRAYS ====== -- -arithPromoteRanked :: forall n a. KnownINat n +arithPromoteRanked :: forall n a. KnownNat n => (forall sh. KnownShapeX sh => Mixed sh a -> Mixed sh a) -> Ranked n a -> Ranked n a arithPromoteRanked | Dict <- lemKnownReplicate (Proxy @n) = coerce -arithPromoteRanked2 :: forall n a. KnownINat n +arithPromoteRanked2 :: forall n a. KnownNat n => (forall sh. KnownShapeX sh => Mixed sh a -> Mixed sh a -> Mixed sh a) -> Ranked n a -> Ranked n a -> Ranked n a arithPromoteRanked2 | Dict <- lemKnownReplicate (Proxy @n) = coerce -instance (KnownINat n, Storable a, Num a) => Num (Ranked n (Primitive a)) where +instance (KnownNat n, Storable a, Num a) => Num (Ranked n (Primitive a)) where (+) = arithPromoteRanked2 (+) (-) = arithPromoteRanked2 (-) (*) = arithPromoteRanked2 (*) negate = arithPromoteRanked negate abs = arithPromoteRanked abs signum = arithPromoteRanked signum - fromInteger n = case inatSing @n of + fromInteger n = case natSing @n of SZ -> Ranked (M_Primitive (X.scalar (fromInteger n))) - SS _ -> error "Data.Array.Nested.fromIntegral(Ranked): \ - \Rank non-zero, use explicit mconstant" + _ -> error "Data.Array.Nested.fromIntegral(Ranked): \ + \Rank non-zero, use explicit mconstant" -- [PRIMITIVE ELEMENT TYPES LIST] (really, a partial list of just the numeric types) -deriving via Ranked n (Primitive Int) instance KnownINat n => Num (Ranked n Int) -deriving via Ranked n (Primitive Double) instance KnownINat n => Num (Ranked n Double) +deriving via Ranked n (Primitive Int) instance KnownNat n => Num (Ranked n Int) +deriving via Ranked n (Primitive Double) instance KnownNat n => Num (Ranked n Double) type role ListR nominal representational -type ListR :: INat -> Type -> Type +type ListR :: Nat -> Type -> Type data ListR n i where - ZR :: ListR Z i - (:::) :: forall n {i}. i -> ListR n i -> ListR (S n) i + ZR :: ListR 0 i + (:::) :: forall n {i}. i -> ListR n i -> ListR (1 + n) i deriving instance Show i => Show (ListR n i) deriving instance Eq i => Eq (ListR n i) deriving instance Ord i => Ord (ListR n i) @@ -892,23 +961,23 @@ listRToList :: ListR n i -> [i] listRToList ZR = [] listRToList (i ::: is) = i : listRToList is -knownListR :: ListR n i -> Dict KnownINat n +knownListR :: ListR n i -> Dict KnownNat n knownListR ZR = Dict knownListR (_ ::: l) | Dict <- knownListR l = Dict -- | An index into a rank-typed array. type role IxR nominal representational -type IxR :: INat -> Type -> Type +type IxR :: Nat -> Type -> Type newtype IxR n i = IxR (ListR n i) deriving (Show, Eq, Ord) deriving newtype (Functor, Foldable) -pattern ZIR :: forall n i. () => n ~ Z => IxR n i +pattern ZIR :: forall n i. () => n ~ 0 => IxR n i pattern ZIR = IxR ZR pattern (:.:) :: forall {n1} {i}. - forall n. (S n ~ n1) + forall n. (1 + n ~ n1) => i -> IxR n i -> IxR n1 i pattern i :.: sh <- (unconsIxR -> Just (UnconsIxRRes sh i)) where i :.: IxR sh = IxR (i ::: sh) @@ -916,30 +985,30 @@ pattern i :.: sh <- (unconsIxR -> Just (UnconsIxRRes sh i)) infixr 3 :.: data UnconsIxRRes i n1 = - forall n. ((S n) ~ n1) => UnconsIxRRes (IxR n i) i + forall n. (1 + n ~ n1) => UnconsIxRRes (IxR n i) i unconsIxR :: IxR n1 i -> Maybe (UnconsIxRRes i n1) unconsIxR (IxR (i ::: sh')) = Just (UnconsIxRRes (IxR sh') i) unconsIxR (IxR ZR) = Nothing type IIxR n = IxR n Int -knownIxR :: IxR n i -> Dict KnownINat n +knownIxR :: IxR n i -> Dict KnownNat n knownIxR (IxR sh) = knownListR sh type role ShR nominal representational -type ShR :: INat -> Type -> Type +type ShR :: Nat -> Type -> Type newtype ShR n i = ShR (ListR n i) deriving (Show, Eq, Ord) deriving newtype (Functor, Foldable) type IShR n = ShR n Int -pattern ZSR :: forall n i. () => n ~ Z => ShR n i +pattern ZSR :: forall n i. () => n ~ 0 => ShR n i pattern ZSR = ShR ZR pattern (:$:) :: forall {n1} {i}. - forall n. (S n ~ n1) + forall n. (1 + n ~ n1) => i -> ShR n i -> ShR n1 i pattern i :$: sh <- (unconsShR -> Just (UnconsShRRes sh i)) where i :$: (ShR sh) = ShR (i ::: sh) @@ -947,15 +1016,15 @@ pattern i :$: sh <- (unconsShR -> Just (UnconsShRRes sh i)) infixr 3 :$: data UnconsShRRes i n1 = - forall n. S n ~ n1 => UnconsShRRes (ShR n i) i + forall n. 1 + n ~ n1 => UnconsShRRes (ShR n i) i unconsShR :: ShR n1 i -> Maybe (UnconsShRRes i n1) unconsShR (ShR (i ::: sh')) = Just (UnconsShRRes (ShR sh') i) unconsShR (ShR ZR) = Nothing -knownShR :: ShR n i -> Dict KnownINat n +knownShR :: ShR n i -> Dict KnownNat n knownShR (ShR sh) = knownListR sh -zeroIxR :: SINat n -> IIxR n +zeroIxR :: SNat n -> IIxR n zeroIxR SZ = ZIR zeroIxR (SS n) = 0 :.: zeroIxR n @@ -982,7 +1051,7 @@ shapeSizeR ZSR = 1 shapeSizeR (n :$: sh) = n * shapeSizeR sh -rshape :: forall n a. (KnownINat n, Elt a) => Ranked n a -> IShR n +rshape :: forall n a. (KnownNat n, Elt a) => Ranked n a -> IShR n rshape (Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) , Refl <- lemRankReplicate (Proxy @n) @@ -991,7 +1060,7 @@ rshape (Ranked arr) rindex :: Elt a => Ranked n a -> IIxR n -> a rindex (Ranked arr) idx = mindex arr (ixCvtRX idx) -rindexPartial :: forall n m a. (KnownINat n, Elt a) => Ranked (n +! m) a -> IIxR n -> Ranked m a +rindexPartial :: forall n m a. (KnownNat n, Elt a) => Ranked (n + m) a -> IIxR n -> Ranked m a rindexPartial (Ranked arr) idx = Ranked (mindexPartial @a @(Replicate n Nothing) @(Replicate m Nothing) (rewriteMixed (lemReplicatePlusApp (Proxy @n) (Proxy @m) (Proxy @Nothing)) arr) @@ -1007,7 +1076,7 @@ rgenerate sh f = Ranked (mgenerate (shCvtRX sh) (f . ixCvtXR)) -- | See the documentation of 'mlift'. -rlift :: forall n1 n2 a. (KnownINat n2, Elt a) +rlift :: forall n1 n2 a. (KnownNat n2, Elt a) => (forall sh' b. KnownShapeX sh' => Proxy sh' -> XArray (Replicate n1 Nothing ++ sh') b -> XArray (Replicate n2 Nothing ++ sh') b) -> Ranked n1 a -> Ranked n2 a rlift f (Ranked arr) @@ -1015,39 +1084,39 @@ rlift f (Ranked arr) = Ranked (mlift f arr) rsumOuter1P :: forall n a. - (Storable a, Num a, KnownINat n) - => Ranked (S n) (Primitive a) -> Ranked n (Primitive a) + (Storable a, Num a, KnownNat n, 1 <= n) + => Ranked n (Primitive a) -> Ranked (n - 1) (Primitive a) rsumOuter1P (Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) = Ranked - . coerce @(XArray (Replicate n 'Nothing) a) @(Mixed (Replicate n 'Nothing) (Primitive a)) - . X.sumOuter (() :!$? ZKSX) (knownShapeX @(Replicate n Nothing)) - . coerce @(Mixed (Replicate (S n) Nothing) (Primitive a)) @(XArray (Replicate (S n) Nothing) a) + . coerce @(XArray (Replicate (n - 1) 'Nothing) a) @(Mixed (Replicate (n - 1) 'Nothing) (Primitive a)) + . X.sumOuter (() :!$? ZKSX) (knownShapeX @(Replicate (n - 1) Nothing)) + . coerce @(Mixed (Replicate n Nothing) (Primitive a)) @(XArray (Replicate n Nothing) a) $ arr rsumOuter1 :: forall n a. - (Storable a, Num a, PrimElt a, KnownINat n) - => Ranked (S n) a -> Ranked n a + (Storable a, Num a, PrimElt a, KnownNat n, 1 <= n) + => Ranked n a -> Ranked (n - 1) a rsumOuter1 = coerce fromPrimitive . rsumOuter1P @n @a . coerce toPrimitive -rtranspose :: forall n a. (KnownINat n, Elt a) => [Int] -> Ranked n a -> Ranked n a +rtranspose :: forall n a. (KnownNat n, Elt a) => [Int] -> Ranked n a -> Ranked n a rtranspose perm (Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mtranspose perm arr) -rappend :: forall n a. (KnownINat n, Elt a) - => Ranked (S n) a -> Ranked (S n) a -> Ranked (S n) a +rappend :: forall n a. (KnownNat n, Elt a, 1 <= n) + => Ranked n a -> Ranked n a -> Ranked n a rappend | Dict <- lemKnownReplicate (Proxy @n) = coerce mappend -rscalar :: Elt a => a -> Ranked I0 a +rscalar :: Elt a => a -> Ranked 0 a rscalar x = Ranked (mscalar x) -rfromVectorP :: forall n a. (KnownINat n, Storable a) => IShR n -> VS.Vector a -> Ranked n (Primitive a) +rfromVectorP :: forall n a. (KnownNat n, Storable a) => IShR n -> VS.Vector a -> Ranked n (Primitive a) rfromVectorP sh v | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mfromVectorP (shCvtRX sh) v) -rfromVector :: forall n a. (KnownINat n, Storable a, PrimElt a) => IShR n -> VS.Vector a -> Ranked n a +rfromVector :: forall n a. (KnownNat n, Storable a, PrimElt a) => IShR n -> VS.Vector a -> Ranked n a rfromVector sh v = coerce fromPrimitive (rfromVectorP sh v) rtoVectorP :: Storable a => Ranked n (Primitive a) -> VS.Vector a @@ -1056,39 +1125,39 @@ rtoVectorP = coerce mtoVectorP rtoVector :: (Storable a, PrimElt a) => Ranked n a -> VS.Vector a rtoVector = coerce mtoVector -rfromList1 :: forall n a. (KnownINat n, Elt a) => NonEmpty (Ranked n a) -> Ranked (S n) a +rfromList1 :: forall n a. (KnownNat n, Elt a) => NonEmpty (Ranked n a) -> Ranked (1 + n) a rfromList1 l | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mfromList1 (coerce l)) -rfromList :: Elt a => NonEmpty a -> Ranked I1 a +rfromList :: Elt a => NonEmpty a -> Ranked 1 a rfromList = Ranked . mfromList1 . fmap mscalar -rtoList :: Elt a => Ranked (S n) a -> [Ranked n a] +rtoList :: Elt a => Ranked (1 + n) a -> [Ranked n a] rtoList (Ranked arr) = coerce (mtoList1 arr) -rtoList1 :: Elt a => Ranked I1 a -> [a] +rtoList1 :: Elt a => Ranked 1 a -> [a] rtoList1 = map runScalar . rtoList -runScalar :: Elt a => Ranked I0 a -> a +runScalar :: Elt a => Ranked 0 a -> a runScalar arr = rindex arr ZIR -rconstantP :: forall n a. (KnownINat n, Storable a) => IShR n -> a -> Ranked n (Primitive a) +rconstantP :: forall n a. (KnownNat n, Storable a) => IShR n -> a -> Ranked n (Primitive a) rconstantP sh x | Dict <- lemKnownReplicate (Proxy @n) = Ranked (mconstantP (shCvtRX sh) x) -rconstant :: forall n a. (KnownINat n, Storable a, PrimElt a) +rconstant :: forall n a. (KnownNat n, Storable a, PrimElt a) => IShR n -> a -> Ranked n a rconstant sh x = coerce fromPrimitive (rconstantP sh x) -rslice :: (KnownINat n, Elt a) => [(Int, Int)] -> Ranked n a -> Ranked n a +rslice :: (KnownNat n, Elt a) => [(Int, Int)] -> Ranked n a -> Ranked n a rslice ivs = rlift $ \_ -> X.slice ivs -rrev1 :: (KnownINat n, Elt a) => Ranked (S n) a -> Ranked (S n) a +rrev1 :: (KnownNat n, Elt a, 1 <= n) => Ranked n a -> Ranked n a rrev1 = rlift $ \_ -> X.rev1 -rreshape :: forall n n' a. (KnownINat n, KnownINat n', Elt a) +rreshape :: forall n n' a. (KnownNat n, KnownNat n', Elt a) => IShR n' -> Ranked n a -> Ranked n' a rreshape sh' (Ranked arr) | Dict <- lemKnownReplicate (Proxy @n) -- cgit v1.2.3-70-g09d2