The code compiles with only GHC nats

3 files changed, 40 insertions, 146 deletions

diff --git a/src/Data/Array/Nested.hs b/src/Data/Array/Nested.hs
index c7d1819..c12d8ad 100644
--- a/src/Data/Array/Nested.hs
+++ b/src/Data/Array/Nested.hs
@@ -37,9 +37,6 @@ module Data.Array.Nested (
   PrimElt,
   Primitive(..),
 
-  -- * Inductive natural numbers
-  module Data.INat,
-
   -- * Further utilities / re-exports
   type (++),
   Storable,
@@ -49,5 +46,4 @@ import Prelude hiding (mappend)
 
 import Data.Array.Mixed
 import Data.Array.Nested.Internal
-import Data.INat
 import Foreign.Storable
diff --git a/src/Data/Array/Nested/Internal.hs b/src/Data/Array/Nested/Internal.hs
index 54b567a..222247b 100644
--- a/src/Data/Array/Nested/Internal.hs
+++ b/src/Data/Array/Nested/Internal.hs
@@ -155,15 +155,26 @@ snatPred snp1 =
       EQI -> Just (SNatPredResult (SNat @(np1 - 1)) Refl)
       GTI -> Nothing
 
+
+-- Stupid things that the type checker should be able to figure out in-line, but can't
+
 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
 
+-- TODO: is this sound? @n@ cannot be negative, surely, but the plugin doesn't see even that.
 lemReplicateSucc :: (a : Replicate n a) :~: Replicate (n + 1) a
 lemReplicateSucc = unsafeCoerce Refl
 
+lemAppLeft :: Proxy l -> a :~: b -> a ++ l :~: b ++ l
+lemAppLeft _ Refl = Refl
+
+knownNatSucc :: KnownNat n => Dict KnownNat (1 + n)
+knownNatSucc = Dict
+
+
 lemKnownReplicate :: forall n. KnownNat n => Proxy n -> Dict KnownShapeX (Replicate n Nothing)
 lemKnownReplicate _ = X.lemKnownShapeX (go (natSing @n))
   where
@@ -947,7 +958,7 @@ type role ListR nominal representational
 type ListR :: Nat -> Type -> Type
 data ListR n i where
   ZR :: ListR 0 i
-  (:::) :: forall n {i}. i -> ListR n i -> ListR (1 + n) i
+  (:::) :: forall n {i}. i -> ListR n i -> ListR (n + 1) 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)
@@ -963,7 +974,7 @@ listRToList (i ::: is) = i : listRToList is
 
 knownListR :: ListR n i -> Dict KnownNat n
 knownListR ZR = Dict
-knownListR (_ ::: l) | Dict <- knownListR l = Dict
+knownListR (_ ::: (l :: ListR m i)) | Dict <- knownListR l = knownNatSucc @m
 
 -- | An index into a rank-typed array.
 type role IxR nominal representational
@@ -1040,11 +1051,11 @@ shCvtXR (n :$? idx) = n :$: shCvtXR idx
 
 ixCvtRX :: IIxR n -> IIxX (Replicate n Nothing)
 ixCvtRX ZIR = ZIX
-ixCvtRX (n :.: idx) = n :.? ixCvtRX idx
+ixCvtRX (n :.: (idx :: IxR m Int)) = castWith (subst2 @IxX @Int (lemReplicateSucc @(Nothing @Nat) @m)) (n :.? ixCvtRX idx)
 
 shCvtRX :: IShR n -> IShX (Replicate n Nothing)
 shCvtRX ZSR = ZSX
-shCvtRX (n :$: idx) = n :$? shCvtRX idx
+shCvtRX (n :$: (idx :: ShR m Int)) = castWith (subst2 @ShX @Int (lemReplicateSucc @(Nothing @Nat) @m)) (n :$? shCvtRX idx)
 
 shapeSizeR :: IShR n -> Int
 shapeSizeR ZSR = 1
@@ -1084,19 +1095,19 @@ rlift f (Ranked arr)
   = Ranked (mlift f arr)
 
 rsumOuter1P :: forall n a.
-               (Storable a, Num a, KnownNat n, 1 <= n)
-            => Ranked n (Primitive a) -> Ranked (n - 1) (Primitive a)
+               (Storable a, Num a, KnownNat n)
+            => Ranked (n + 1) (Primitive a) -> Ranked n (Primitive a)
 rsumOuter1P (Ranked arr)
   | Dict <- lemKnownReplicate (Proxy @n)
+  , Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = Ranked
-    . coerce @(XArray (Replicate (n - 1) 'Nothing) a) @(Mixed (Replicate (n - 1) 'Nothing) (Primitive a))
-    . X.sumOuter (() :!$? ZKSX) (knownShapeX @(Replicate (n - 1) Nothing))
-    . coerce @(Mixed (Replicate n Nothing) (Primitive a)) @(XArray (Replicate n Nothing) a)
+    . coerce @(XArray (Replicate n 'Nothing) a) @(Mixed (Replicate n 'Nothing) (Primitive a))
+    . X.sumOuter (() :!$? ZKSX) (knownShapeX @(Replicate n Nothing))
+    . coerce @(Mixed (Replicate (n + 1) Nothing) (Primitive a)) @(XArray (Replicate (n + 1) Nothing) a)
     $ arr
 
-rsumOuter1 :: forall n a.
-  (Storable a, Num a, PrimElt a, KnownNat n, 1 <= n)
-           => Ranked n a -> Ranked (n - 1) a
+rsumOuter1 :: forall n a. (Storable a, Num a, PrimElt a, KnownNat n)
+           => Ranked (1 + n) a -> Ranked n a
 rsumOuter1 = coerce fromPrimitive . rsumOuter1P @n @a . coerce toPrimitive
 
 rtranspose :: forall n a. (KnownNat n, Elt a) => [Int] -> Ranked n a -> Ranked n a
@@ -1104,9 +1115,12 @@ rtranspose perm (Ranked arr)
   | Dict <- lemKnownReplicate (Proxy @n)
   = Ranked (mtranspose perm arr)
 
-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
+rappend :: forall n a. (KnownNat n, Elt a)
+        => Ranked (n + 1) a -> Ranked (n + 1) a -> Ranked (n + 1) a
+rappend
+  | Dict <- lemKnownReplicate (Proxy @n)
+  , Refl <- lemReplicateSucc @(Nothing @Nat) @n
+  = coerce (mappend @Nothing @Nothing @(Replicate n Nothing))
 
 rscalar :: Elt a => a -> Ranked 0 a
 rscalar x = Ranked (mscalar x)
@@ -1125,16 +1139,19 @@ rtoVectorP = coerce mtoVectorP
 rtoVector :: (Storable a, PrimElt a) => Ranked n a -> VS.Vector a
 rtoVector = coerce mtoVector
 
-rfromList1 :: forall n a. (KnownNat n, Elt a) => NonEmpty (Ranked n a) -> Ranked (1 + n) a
+rfromList1 :: forall n a. (KnownNat n, Elt a) => NonEmpty (Ranked n a) -> Ranked (n + 1) a
 rfromList1 l
   | Dict <- lemKnownReplicate (Proxy @n)
-  = Ranked (mfromList1 (coerce l))
+  , Refl <- lemReplicateSucc @(Nothing @Nat) @n
+  = Ranked (mfromList1 @a @Nothing @(Replicate n Nothing) (coerce l))
 
 rfromList :: Elt a => NonEmpty a -> Ranked 1 a
 rfromList = Ranked . mfromList1 . fmap mscalar
 
-rtoList :: Elt a => Ranked (1 + n) a -> [Ranked n a]
-rtoList (Ranked arr) = coerce (mtoList1 arr)
+rtoList :: forall n a. Elt a => Ranked (n + 1) a -> [Ranked n a]
+rtoList (Ranked arr)
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @n
+  = coerce (mtoList1 @a @Nothing @(Replicate n Nothing) arr)
 
 rtoList1 :: Elt a => Ranked 1 a -> [a]
 rtoList1 = map runScalar . rtoList
@@ -1154,8 +1171,10 @@ rconstant sh x = coerce fromPrimitive (rconstantP sh x)
 rslice :: (KnownNat n, Elt a) => [(Int, Int)] -> Ranked n a -> Ranked n a
 rslice ivs = rlift $ \_ -> X.slice ivs
 
-rrev1 :: (KnownNat n, Elt a, 1 <= n) => Ranked n a -> Ranked n a
-rrev1 = rlift $ \_ -> X.rev1
+rrev1 :: forall n a. (KnownNat n, Elt a) => Ranked (n + 1) a -> Ranked (n + 1) a
+rrev1 = rlift $ \(Proxy @sh') ->
+  case lemReplicateSucc @(Nothing @Nat) @n of
+    Refl -> X.rev1 @Nothing @(Replicate n Nothing ++ sh')
 
 rreshape :: forall n n' a. (KnownNat n, KnownNat n', Elt a)
          => IShR n' -> Ranked n a -> Ranked n' a
diff --git a/src/Data/INat.hs b/src/Data/INat.hs
deleted file mode 100644
index af8f18b..0000000
--- a/src/Data/INat.hs
+++ /dev/null
@@ -1,121 +0,0 @@
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE GADTs #-}
-{-# LANGUAGE PatternSynonyms #-}
-{-# LANGUAGE PolyKinds #-}
-{-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE StandaloneDeriving #-}
-{-# LANGUAGE TypeAbstractions #-}
-{-# LANGUAGE TypeApplications #-}
-{-# LANGUAGE TypeFamilies #-}
-{-# LANGUAGE TypeOperators #-}
-{-# LANGUAGE UndecidableInstances #-}
-{-# LANGUAGE ViewPatterns #-}
-{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver #-}
-module Data.INat where
-
-import Data.Proxy
-import Data.Type.Equality ((:~:) (Refl))
-import Numeric.Natural
-import GHC.TypeLits
-import Unsafe.Coerce (unsafeCoerce)
-
--- | Evidence for the constraint @c a@.
-data Dict c a where
-  Dict :: c a => Dict c a
-
--- | An inductive peano natural number. Intended to be used at the type level.
-data INat = Z | S INat
-  deriving (Show)
-
--- | Singleton for a 'INat'.
-data SINat n where
-  SZ :: SINat Z
-  SS :: SINat n -> SINat (S n)
-deriving instance Show (SINat n)
-
--- | A singleton 'SINat' corresponding to @n@.
-class KnownINat n where inatSing :: SINat n
-instance KnownINat Z where inatSing = SZ
-instance KnownINat n => KnownINat (S n) where inatSing = SS inatSing
-
--- | Explicitly bidirectional pattern synonym that converts between a singleton
--- 'SINat' and evidence of a 'KnownINat' constraint. Analogous to 'GHC.SNat'.
-pattern SINat' :: () => KnownINat n => SINat n
-pattern SINat' <- (snatKnown -> Dict)
-  where SINat' = inatSing
-
--- | A 'KnownINat' dictionary is just a singleton natural, so we can create
--- evidence of 'KnownINat' given an 'SINat'.
-snatKnown :: SINat n -> Dict KnownINat n
-snatKnown SZ = Dict
-snatKnown (SS n) | Dict <- snatKnown n = Dict
-
--- | Convert a 'INat' to a normal number.
-fromINat :: INat -> Natural
-fromINat Z = 0
-fromINat (S n) = 1 + fromINat n
-
--- | Convert an 'SINat' to a normal number.
-fromSINat :: SINat n -> Natural
-fromSINat SZ = 0
-fromSINat (SS n) = 1 + fromSINat n
-
--- | The value of a known inductive natural as a value-level integer.
-inatVal :: forall n. KnownINat n => Proxy n -> Natural
-inatVal _ = fromSINat (inatSing @n)
-
--- | Add two 'INat's
-type family n +! m where
-  Z +! m = m
-  S n +! m = S (n +! m)
-
--- | Convert a 'INat' to a "GHC.TypeLits" 'G.Nat'.
-type family FromINat n where
-  FromINat Z = 0
-  FromINat (S n) = 1 + FromINat n
-
--- | Convert a "GHC.TypeLits" 'G.Nat' to a 'INat'.
-type family ToINat (n :: Nat) where
-  ToINat 0 = Z
-  ToINat n = S (ToINat (n - 1))
-
-lemInjectiveFromINat :: n :~: ToINat (FromINat n)
-lemInjectiveFromINat = unsafeCoerce Refl
-
-lemSuccFromINat :: Proxy n -> 1 + FromINat n :~: FromINat (S n)
-lemSuccFromINat _ = unsafeCoerce Refl
-
-lemAddFromINat :: Proxy m -> Proxy n
-               -> FromINat m + FromINat n :~: FromINat (m +! n)
-lemAddFromINat _ = unsafeCoerce Refl
-
-lemInjectiveToINat :: n :~: FromINat (ToINat n)
-lemInjectiveToINat = unsafeCoerce Refl
-
-lemSuccToINat :: Proxy n -> ToINat (1 + n) :~: S (ToINat n)
-lemSuccToINat _ = unsafeCoerce Refl
-
-lemAddToINat :: Proxy m -> Proxy n -> ToINat (m + n) :~: ToINat m +! ToINat n
-lemAddToINat _ _ = unsafeCoerce Refl
-
--- | If an inductive 'INat' is known, then the corresponding "GHC.TypeLits"
--- 'G.Nat' is also known.
-knownNatFromINat :: KnownINat n => Proxy n -> Dict KnownNat (FromINat n)
-knownNatFromINat (Proxy @n) = go (SINat' @n)
-  where
-    go :: SINat m -> Dict KnownNat (FromINat m)
-    go SZ = Dict
-    go (SS n) | Dict <- go n = Dict
-
--- * Some type-level inductive naturals
-
-type I0 = Z
-type I1 = S I0
-type I2 = S I1
-type I3 = S I2
-type I4 = S I3
-type I5 = S I4
-type I6 = S I5
-type I7 = S I6
-type I8 = S I7
-type I9 = S I8