Refactor Mixed (modules, regular function names)

1 files changed, 165 insertions, 161 deletions

diff --git a/src/Data/Array/Nested/Internal.hs b/src/Data/Array/Nested/Internal.hs
index 712c5f1..0870789 100644
--- a/src/Data/Array/Nested/Internal.hs
+++ b/src/Data/Array/Nested/Internal.hs
@@ -60,7 +60,11 @@ import Unsafe.Coerce
 
 import Data.Array.Mixed
 import qualified Data.Array.Mixed as X
-import Data.Array.Nested.Internal.Arith
+import Data.Array.Mixed.Lemmas
+import Data.Array.Mixed.Permutation
+import Data.Array.Mixed.Shape
+import Data.Array.Mixed.Internal.Arith
+import Data.Array.Mixed.Types
 
 
 -- Invariant in the API
@@ -123,19 +127,19 @@ lemKnownShX (SUnknown () :!% ssh) | Dict <- lemKnownShX ssh = Dict
 
 ssxFromSNat :: SNat n -> StaticShX (Replicate n Nothing)
 ssxFromSNat SZ = ZKX
-ssxFromSNat (SS (n :: SNat nm1)) | Refl <- X.lemReplicateSucc @(Nothing @Nat) @nm1 = SUnknown () :!% ssxFromSNat n
+ssxFromSNat (SS (n :: SNat nm1)) | Refl <- lemReplicateSucc @(Nothing @Nat) @nm1 = SUnknown () :!% ssxFromSNat n
 
 lemKnownReplicate :: SNat n -> Dict KnownShX (Replicate n Nothing)
 lemKnownReplicate sn = lemKnownShX (ssxFromSNat sn)
 
-lemRankReplicate :: SNat n -> X.Rank (Replicate n (Nothing @Nat)) :~: n
+lemRankReplicate :: SNat n -> Rank (Replicate n (Nothing @Nat)) :~: n
 lemRankReplicate SZ = Refl
 lemRankReplicate (SS (n :: SNat nm1))
-  | Refl <- X.lemReplicateSucc @(Nothing @Nat) @nm1
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @nm1
   , Refl <- lemRankReplicate n
   = Refl
 
-lemRankMapJust :: forall sh. ShS sh -> X.Rank (MapJust sh) :~: X.Rank sh
+lemRankMapJust :: forall sh. ShS sh -> Rank (MapJust sh) :~: Rank sh
 lemRankMapJust ZSS = Refl
 lemRankMapJust (_ :$$ sh') | Refl <- lemRankMapJust sh' = Refl
 
@@ -146,9 +150,9 @@ lemReplicatePlusApp sn _ _ = go sn
     go :: SNat n' -> Replicate (n' + m) a :~: Replicate n' a ++ Replicate m a
     go SZ = Refl
     go (SS (n :: SNat n'm1))
-      | Refl <- X.lemReplicateSucc @a @n'm1
+      | Refl <- lemReplicateSucc @a @n'm1
       , Refl <- go n
-      = sym (X.lemReplicateSucc @a @(n'm1 + m))
+      = sym (lemReplicateSucc @a @(n'm1 + m))
 
 lemLeqPlus :: n <= m => Proxy n -> Proxy m -> Proxy k -> (n <=? (m + k)) :~: 'True
 lemLeqPlus _ _ _ = Refl
@@ -156,17 +160,17 @@ lemLeqPlus _ _ _ = Refl
 lemLeqSuccSucc :: (k + 1 <= n) => Proxy k -> Proxy n -> (k <=? n - 1) :~: True
 lemLeqSuccSucc _ _ = unsafeCoerce Refl
 
-lemDropLenApp :: X.Rank l1 <= X.Rank l2
+lemDropLenApp :: Rank l1 <= Rank l2
               => Proxy l1 -> Proxy l2 -> Proxy rest
-              -> X.DropLen l1 l2 ++ rest :~: X.DropLen l1 (l2 ++ rest)
+              -> DropLen l1 l2 ++ rest :~: DropLen l1 (l2 ++ rest)
 lemDropLenApp _ _ _ = unsafeCoerce Refl
 
-lemTakeLenApp :: X.Rank l1 <= X.Rank l2
+lemTakeLenApp :: Rank l1 <= Rank l2
               => Proxy l1 -> Proxy l2 -> Proxy rest
-              -> X.TakeLen l1 l2 :~: X.TakeLen l1 (l2 ++ rest)
+              -> TakeLen l1 l2 :~: TakeLen l1 (l2 ++ rest)
 lemTakeLenApp _ _ _ = unsafeCoerce Refl
 
-srankSh :: ShX sh f -> SNat (X.Rank sh)
+srankSh :: ShX sh f -> SNat (Rank sh)
 srankSh ZSX = SNat
 srankSh (_ :$% sh) | SNat <- srankSh sh = SNat
 
@@ -585,11 +589,11 @@ class Elt a where
          -> (forall sh' b. Storable b => StaticShX sh' -> XArray (sh1 ++ sh') b -> XArray (sh2 ++ sh') b -> XArray (sh3 ++ sh') b)
          -> Mixed sh1 a -> Mixed sh2 a -> Mixed sh3 a
 
-  mcast :: forall sh1 sh2 sh'. X.Rank sh1 ~ X.Rank sh2
+  mcast :: forall sh1 sh2 sh'. Rank sh1 ~ Rank sh2
         => StaticShX sh1 -> IShX sh2 -> Proxy sh' -> Mixed (sh1 ++ sh') a -> Mixed (sh2 ++ sh') a
 
-  mtranspose :: forall is sh. (X.Permutation is, X.Rank is <= X.Rank sh)
-             => HList SNat is -> Mixed sh a -> Mixed (X.PermutePrefix is sh) a
+  mtranspose :: forall is sh. (IsPermutation is, Rank is <= Rank sh)
+             => Perm is -> Mixed sh a -> Mixed (PermutePrefix is sh) a
 
   -- ====== PRIVATE METHODS ====== --
 
@@ -635,20 +639,20 @@ class Elt a => KnownElt a where
 instance Storable a => Elt (Primitive a) where
   mshape (M_Primitive sh _) = sh
   mindex (M_Primitive _ a) i = Primitive (X.index a i)
-  mindexPartial (M_Primitive sh a) i = M_Primitive (X.shDropIx sh i) (X.indexPartial a i)
+  mindexPartial (M_Primitive sh a) i = M_Primitive (shxDropIx sh i) (X.indexPartial a i)
   mscalar (Primitive x) = M_Primitive ZSX (X.scalar x)
   mfromListOuter l@(arr1 :| _) =
     let sh = SUnknown (length l) :$% mshape arr1
-    in M_Primitive sh (X.fromListOuter (X.staticShapeFrom sh) (map (\(M_Primitive _ a) -> a) (toList l)))
-  mtoListOuter (M_Primitive sh arr) = map (M_Primitive (X.shTail sh)) (X.toListOuter arr)
+    in M_Primitive sh (X.fromListOuter (ssxFromShape sh) (map (\(M_Primitive _ a) -> a) (toList l)))
+  mtoListOuter (M_Primitive sh arr) = map (M_Primitive (shxTail sh)) (X.toListOuter arr)
 
   mlift :: forall sh1 sh2.
            StaticShX sh2
         -> (StaticShX '[] -> XArray (sh1 ++ '[]) a -> XArray (sh2 ++ '[]) a)
         -> Mixed sh1 (Primitive a) -> Mixed sh2 (Primitive a)
   mlift ssh2 f (M_Primitive _ a)
-    | Refl <- X.lemAppNil @sh1
-    , Refl <- X.lemAppNil @sh2
+    | Refl <- lemAppNil @sh1
+    , Refl <- lemAppNil @sh2
     , let result = f ZKX a
     = M_Primitive (X.shape ssh2 result) result
 
@@ -657,36 +661,36 @@ instance Storable a => Elt (Primitive a) where
          -> (StaticShX '[] -> XArray (sh1 ++ '[]) a -> XArray (sh2 ++ '[]) a -> XArray (sh3 ++ '[]) a)
          -> Mixed sh1 (Primitive a) -> Mixed sh2 (Primitive a) -> Mixed sh3 (Primitive a)
   mlift2 ssh3 f (M_Primitive _ a) (M_Primitive _ b)
-    | Refl <- X.lemAppNil @sh1
-    , Refl <- X.lemAppNil @sh2
-    , Refl <- X.lemAppNil @sh3
+    | Refl <- lemAppNil @sh1
+    , Refl <- lemAppNil @sh2
+    , Refl <- lemAppNil @sh3
     , let result = f ZKX a b
     = M_Primitive (X.shape ssh3 result) result
 
-  mcast :: forall sh1 sh2 sh'. X.Rank sh1 ~ X.Rank sh2
+  mcast :: forall sh1 sh2 sh'. Rank sh1 ~ Rank sh2
         => StaticShX sh1 -> IShX sh2 -> Proxy sh' -> Mixed (sh1 ++ sh') (Primitive a) -> Mixed (sh2 ++ sh') (Primitive a)
   mcast ssh1 sh2 _ (M_Primitive sh1' arr) =
-    let (_, sh') = shAppSplit (Proxy @sh') ssh1 sh1'
-    in M_Primitive (shAppend sh2 sh') (X.cast ssh1 sh2 (X.staticShapeFrom sh') arr)
+    let (_, sh') = shxSplitApp (Proxy @sh') ssh1 sh1'
+    in M_Primitive (shxAppend sh2 sh') (X.cast ssh1 sh2 (ssxFromShape sh') arr)
 
   mtranspose perm (M_Primitive sh arr) =
-    M_Primitive (X.shPermutePrefix perm sh)
-                (X.transpose (X.staticShapeFrom sh) perm arr)
+    M_Primitive (shxPermutePrefix perm sh)
+                (X.transpose (ssxFromShape sh) perm arr)
 
   mshapeTree _ = ()
   mshapeTreeEq _ () () = True
   mshapeTreeEmpty _ () = False
   mshowShapeTree _ () = "()"
-  mvecsWrite sh i (Primitive x) (MV_Primitive v) = VSM.write v (X.toLinearIdx sh i) x
+  mvecsWrite sh i (Primitive x) (MV_Primitive v) = VSM.write v (ixxToLinear sh i) x
 
   -- TODO: this use of toVector is suboptimal
   mvecsWritePartial
     :: forall sh' sh s.
        IShX (sh ++ sh') -> IIxX sh -> Mixed sh' (Primitive a) -> MixedVecs s (sh ++ sh') (Primitive a) -> ST s ()
   mvecsWritePartial sh i (M_Primitive sh' arr) (MV_Primitive v) = do
-    let arrsh = X.shape (X.staticShapeFrom sh') arr
-        offset = X.toLinearIdx sh (X.ixAppend i (X.zeroIxX' arrsh))
-    VS.copy (VSM.slice offset (X.shapeSize arrsh) v) (X.toVector arr)
+    let arrsh = X.shape (ssxFromShape sh') arr
+        offset = ixxToLinear sh (ixxAppend i (ixxZero' arrsh))
+    VS.copy (VSM.slice offset (shxSize arrsh) v) (X.toVector arr)
 
   mvecsFreeze sh (MV_Primitive v) = M_Primitive sh . X.fromVector sh <$> VS.freeze v
 
@@ -701,7 +705,7 @@ deriving via Primitive () instance Elt ()
 
 instance Storable a => KnownElt (Primitive a) where
   memptyArray sh = M_Primitive sh (X.empty sh)
-  mvecsUnsafeNew sh _ = MV_Primitive <$> VSM.unsafeNew (X.shapeSize sh)
+  mvecsUnsafeNew sh _ = MV_Primitive <$> VSM.unsafeNew (shxSize sh)
   mvecsNewEmpty _ = MV_Primitive <$> VSM.unsafeNew 0
 
 -- [PRIMITIVE ELEMENT TYPES LIST]
@@ -755,7 +759,7 @@ instance Elt a => Elt (Mixed sh' a) where
   -- moverlongShape method, a prefix of which is mshape.
   mshape :: forall sh. Mixed sh (Mixed sh' a) -> IShX sh
   mshape (M_Nest sh arr)
-    = fst (shAppSplit (Proxy @sh') (X.staticShapeFrom sh) (mshape arr))
+    = fst (shxSplitApp (Proxy @sh') (ssxFromShape sh) (mshape arr))
 
   mindex :: Mixed sh (Mixed sh' a) -> IIxX sh -> Mixed sh' a
   mindex (M_Nest _ arr) i = mindexPartial arr i
@@ -763,8 +767,8 @@ instance Elt a => Elt (Mixed sh' a) where
   mindexPartial :: forall sh1 sh2.
                    Mixed (sh1 ++ sh2) (Mixed sh' a) -> IIxX sh1 -> Mixed sh2 (Mixed sh' a)
   mindexPartial (M_Nest sh arr) i
-    | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
-    = M_Nest (X.shDropIx sh i) (mindexPartial @a @sh1 @(sh2 ++ sh') arr i)
+    | Refl <- lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
+    = M_Nest (shxDropIx sh i) (mindexPartial @a @sh1 @(sh2 ++ sh') arr i)
 
   mscalar = M_Nest ZSX
 
@@ -773,95 +777,95 @@ instance Elt a => Elt (Mixed sh' a) where
     M_Nest (SUnknown (length l) :$% mshape arr)
            (mfromListOuter ((\(M_Nest _ a) -> a) <$> l))
 
-  mtoListOuter (M_Nest sh arr) = map (M_Nest (X.shTail sh)) (mtoListOuter arr)
+  mtoListOuter (M_Nest sh arr) = map (M_Nest (shxTail sh)) (mtoListOuter arr)
 
   mlift :: forall sh1 sh2.
            StaticShX sh2
         -> (forall shT b. Storable b => StaticShX shT -> XArray (sh1 ++ shT) b -> XArray (sh2 ++ shT) b)
         -> Mixed sh1 (Mixed sh' a) -> Mixed sh2 (Mixed sh' a)
   mlift ssh2 f (M_Nest sh1 arr) =
-    let result = mlift (X.ssxAppend ssh2 ssh') f' arr
-        (sh2, _) = shAppSplit (Proxy @sh') ssh2 (mshape result)
+    let result = mlift (ssxAppend ssh2 ssh') f' arr
+        (sh2, _) = shxSplitApp (Proxy @sh') ssh2 (mshape result)
     in M_Nest sh2 result
     where
-      ssh' = X.staticShapeFrom (snd (shAppSplit (Proxy @sh') (X.staticShapeFrom sh1) (mshape arr)))
+      ssh' = ssxFromShape (snd (shxSplitApp (Proxy @sh') (ssxFromShape sh1) (mshape arr)))
 
       f' :: forall shT b. Storable b => StaticShX shT -> XArray ((sh1 ++ sh') ++ shT) b -> XArray ((sh2 ++ sh') ++ shT) b
       f' sshT
-        | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh') (Proxy @shT)
-        , Refl <- X.lemAppAssoc (Proxy @sh2) (Proxy @sh') (Proxy @shT)
-        = f (X.ssxAppend ssh' sshT)
+        | Refl <- lemAppAssoc (Proxy @sh1) (Proxy @sh') (Proxy @shT)
+        , Refl <- lemAppAssoc (Proxy @sh2) (Proxy @sh') (Proxy @shT)
+        = f (ssxAppend ssh' sshT)
 
   mlift2 :: forall sh1 sh2 sh3.
             StaticShX sh3
          -> (forall shT b. Storable b => StaticShX shT -> XArray (sh1 ++ shT) b -> XArray (sh2 ++ shT) b -> XArray (sh3 ++ shT) b)
          -> Mixed sh1 (Mixed sh' a) -> Mixed sh2 (Mixed sh' a) -> Mixed sh3 (Mixed sh' a)
   mlift2 ssh3 f (M_Nest sh1 arr1) (M_Nest _ arr2) =
-    let result = mlift2 (X.ssxAppend ssh3 ssh') f' arr1 arr2
-        (sh3, _) = shAppSplit (Proxy @sh') ssh3 (mshape result)
+    let result = mlift2 (ssxAppend ssh3 ssh') f' arr1 arr2
+        (sh3, _) = shxSplitApp (Proxy @sh') ssh3 (mshape result)
     in M_Nest sh3 result
     where
-      ssh' = X.staticShapeFrom (snd (shAppSplit (Proxy @sh') (X.staticShapeFrom sh1) (mshape arr1)))
+      ssh' = ssxFromShape (snd (shxSplitApp (Proxy @sh') (ssxFromShape sh1) (mshape arr1)))
 
       f' :: forall shT b. Storable b => StaticShX shT -> XArray ((sh1 ++ sh') ++ shT) b -> XArray ((sh2 ++ sh') ++ shT) b -> XArray ((sh3 ++ sh') ++ shT) b
       f' sshT
-        | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh') (Proxy @shT)
-        , Refl <- X.lemAppAssoc (Proxy @sh2) (Proxy @sh') (Proxy @shT)
-        , Refl <- X.lemAppAssoc (Proxy @sh3) (Proxy @sh') (Proxy @shT)
-        = f (X.ssxAppend ssh' sshT)
+        | Refl <- lemAppAssoc (Proxy @sh1) (Proxy @sh') (Proxy @shT)
+        , Refl <- lemAppAssoc (Proxy @sh2) (Proxy @sh') (Proxy @shT)
+        , Refl <- lemAppAssoc (Proxy @sh3) (Proxy @sh') (Proxy @shT)
+        = f (ssxAppend ssh' sshT)
 
-  mcast :: forall sh1 sh2 shT. X.Rank sh1 ~ X.Rank sh2
+  mcast :: forall sh1 sh2 shT. Rank sh1 ~ Rank sh2
         => StaticShX sh1 -> IShX sh2 -> Proxy shT -> Mixed (sh1 ++ shT) (Mixed sh' a) -> Mixed (sh2 ++ shT) (Mixed sh' a)
   mcast ssh1 sh2 _ (M_Nest sh1T arr)
-    | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @shT) (Proxy @sh')
-    , Refl <- X.lemAppAssoc (Proxy @sh2) (Proxy @shT) (Proxy @sh')
-    = let (_, shT) = shAppSplit (Proxy @shT) ssh1 sh1T
-      in M_Nest (shAppend sh2 shT) (mcast ssh1 sh2 (Proxy @(shT ++ sh')) arr)
-
-  mtranspose :: forall is sh. (X.Permutation is, X.Rank is <= X.Rank sh)
-             => HList SNat is -> Mixed sh (Mixed sh' a)
-             -> Mixed (X.PermutePrefix is sh) (Mixed sh' a)
+    | Refl <- lemAppAssoc (Proxy @sh1) (Proxy @shT) (Proxy @sh')
+    , Refl <- lemAppAssoc (Proxy @sh2) (Proxy @shT) (Proxy @sh')
+    = let (_, shT) = shxSplitApp (Proxy @shT) ssh1 sh1T
+      in M_Nest (shxAppend sh2 shT) (mcast ssh1 sh2 (Proxy @(shT ++ sh')) arr)
+
+  mtranspose :: forall is sh. (IsPermutation is, Rank is <= Rank sh)
+             => Perm is -> Mixed sh (Mixed sh' a)
+             -> Mixed (PermutePrefix is sh) (Mixed sh' a)
   mtranspose perm (M_Nest sh arr)
-    | let sh' = X.shDropSh @sh @sh' (mshape arr) sh
-    , Refl <- X.lemRankApp (X.staticShapeFrom sh) (X.staticShapeFrom sh')
-    , Refl <- lemLeqPlus (Proxy @(X.Rank is)) (Proxy @(X.Rank sh)) (Proxy @(X.Rank sh'))
-    , Refl <- X.lemAppAssoc (Proxy @(Permute is (TakeLen is (sh ++ sh')))) (Proxy @(DropLen is sh)) (Proxy @sh')
+    | let sh' = shxDropSh @sh @sh' (mshape arr) sh
+    , Refl <- lemRankApp (ssxFromShape sh) (ssxFromShape sh')
+    , Refl <- lemLeqPlus (Proxy @(Rank is)) (Proxy @(Rank sh)) (Proxy @(Rank sh'))
+    , Refl <- lemAppAssoc (Proxy @(Permute is (TakeLen is (sh ++ sh')))) (Proxy @(DropLen is sh)) (Proxy @sh')
     , Refl <- lemDropLenApp (Proxy @is) (Proxy @sh) (Proxy @sh')
     , Refl <- lemTakeLenApp (Proxy @is) (Proxy @sh) (Proxy @sh')
-    = M_Nest (X.shPermutePrefix perm sh)
+    = M_Nest (shxPermutePrefix perm sh)
              (mtranspose perm arr)
 
   mshapeTree :: Mixed sh' a -> ShapeTree (Mixed sh' a)
-  mshapeTree arr = (mshape arr, mshapeTree (mindex arr (X.zeroIxX (X.staticShapeFrom (mshape arr)))))
+  mshapeTree arr = (mshape arr, mshapeTree (mindex arr (ixxZero (ssxFromShape (mshape arr)))))
 
   mshapeTreeEq _ (sh1, t1) (sh2, t2) = sh1 == sh2 && mshapeTreeEq (Proxy @a) t1 t2
 
-  mshapeTreeEmpty _ (sh, t) = X.shapeSize sh == 0 && mshapeTreeEmpty (Proxy @a) t
+  mshapeTreeEmpty _ (sh, t) = shxSize sh == 0 && mshapeTreeEmpty (Proxy @a) t
 
   mshowShapeTree _ (sh, t) = "(" ++ show sh ++ ", " ++ mshowShapeTree (Proxy @a) t ++ ")"
 
-  mvecsWrite sh idx val (MV_Nest sh' vecs) = mvecsWritePartial (X.shAppend sh sh') idx val vecs
+  mvecsWrite sh idx val (MV_Nest sh' vecs) = mvecsWritePartial (shxAppend sh sh') idx val vecs
 
   mvecsWritePartial :: forall sh1 sh2 s.
                        IShX (sh1 ++ sh2) -> IIxX sh1 -> Mixed sh2 (Mixed sh' a)
                     -> MixedVecs s (sh1 ++ sh2) (Mixed sh' a)
                     -> ST s ()
   mvecsWritePartial sh12 idx (M_Nest _ arr) (MV_Nest sh' vecs)
-    | Refl <- X.lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
-    = mvecsWritePartial (X.shAppend sh12 sh') idx arr vecs
+    | Refl <- lemAppAssoc (Proxy @sh1) (Proxy @sh2) (Proxy @sh')
+    = mvecsWritePartial (shxAppend sh12 sh') idx arr vecs
 
-  mvecsFreeze sh (MV_Nest sh' vecs) = M_Nest sh <$> mvecsFreeze (X.shAppend sh sh') vecs
+  mvecsFreeze sh (MV_Nest sh' vecs) = M_Nest sh <$> mvecsFreeze (shxAppend sh sh') vecs
 
 instance (KnownShX sh', KnownElt a) => KnownElt (Mixed sh' a) where
-  memptyArray sh = M_Nest sh (memptyArray (X.shAppend sh (X.completeShXzeros (knownShX @sh'))))
+  memptyArray sh = M_Nest sh (memptyArray (shxAppend sh (shxCompleteZeros (knownShX @sh'))))
 
   mvecsUnsafeNew sh example
-    | X.shapeSize sh' == 0 = mvecsNewEmpty (Proxy @(Mixed sh' a))
-    | otherwise = MV_Nest sh' <$> mvecsUnsafeNew (X.shAppend sh sh') (mindex example (X.zeroIxX (X.staticShapeFrom sh')))
+    | shxSize sh' == 0 = mvecsNewEmpty (Proxy @(Mixed sh' a))
+    | otherwise = MV_Nest sh' <$> mvecsUnsafeNew (shxAppend sh sh') (mindex example (ixxZero (ssxFromShape sh')))
     where
       sh' = mshape example
 
-  mvecsNewEmpty _ = MV_Nest (X.completeShXzeros (knownShX @sh')) <$> mvecsNewEmpty (Proxy @a)
+  mvecsNewEmpty _ = MV_Nest (shxCompleteZeros (knownShX @sh')) <$> mvecsNewEmpty (Proxy @a)
 
 
 -- | Create an array given a size and a function that computes the element at a
@@ -882,10 +886,10 @@ instance (KnownShX sh', KnownElt a) => KnownElt (Mixed sh' a) where
 -- array. The type of 'mgenerate' allows this requirement to be broken very
 -- easily, hence the runtime check.
 mgenerate :: forall sh a. KnownElt a => IShX sh -> (IIxX sh -> a) -> Mixed sh a
-mgenerate sh f = case X.enumShape sh of
+mgenerate sh f = case shxEnum sh of
   [] -> memptyArray sh
   firstidx : restidxs ->
-    let firstelem = f (X.zeroIxX' sh)
+    let firstelem = f (ixxZero' sh)
         shapetree = mshapeTree firstelem
     in if mshapeTreeEmpty (Proxy @a) shapetree
          then memptyArray sh
@@ -905,28 +909,28 @@ msumOuter1P :: forall sh n a. (Storable a, NumElt a)
             => Mixed (n : sh) (Primitive a) -> Mixed sh (Primitive a)
 msumOuter1P (M_Primitive (n :$% sh) arr) =
   let nssh = fromSMayNat (\_ -> SUnknown ()) SKnown n :!% ZKX
-  in M_Primitive sh (X.sumOuter nssh (X.staticShapeFrom sh) arr)
+  in M_Primitive sh (X.sumOuter nssh (ssxFromShape sh) arr)
 
 msumOuter1 :: forall sh n a. (NumElt a, PrimElt a)
            => Mixed (n : sh) a -> Mixed sh a
 msumOuter1 = fromPrimitive . msumOuter1P @sh @n @a . toPrimitive
 
 mappend :: forall n m sh a. Elt a
-        => Mixed (n : sh) a -> Mixed (m : sh) a -> Mixed (X.AddMaybe n m : sh) a
+        => Mixed (n : sh) a -> Mixed (m : sh) a -> Mixed (AddMaybe n m : sh) a
 mappend arr1 arr2 = mlift2 (snm :!% ssh) f arr1 arr2
   where
     sn :$% sh = mshape arr1
     sm :$% _ = mshape arr2
-    ssh = X.staticShapeFrom sh
-    snm :: SMayNat () SNat (X.AddMaybe n m)
+    ssh = ssxFromShape sh
+    snm :: SMayNat () SNat (AddMaybe n m)
     snm = case (sn, sm) of
             (SUnknown{}, _) -> SUnknown ()
             (SKnown{}, SUnknown{}) -> SUnknown ()
-            (SKnown n, SKnown m) -> SKnown (X.plusSNat n m)
+            (SKnown n, SKnown m) -> SKnown (snatPlus n m)
 
     f :: forall sh' b. Storable b
-      => StaticShX sh' -> XArray (n : sh ++ sh') b -> XArray (m : sh ++ sh') b -> XArray (X.AddMaybe n m : sh ++ sh') b
-    f ssh' = X.append (X.ssxAppend ssh ssh')
+      => StaticShX sh' -> XArray (n : sh ++ sh') b -> XArray (m : sh ++ sh') b -> XArray (AddMaybe n m : sh ++ sh') b
+    f ssh' = X.append (ssxAppend ssh ssh')
 
 mfromVectorP :: forall sh a. Storable a => IShX sh -> VS.Vector a -> Mixed sh (Primitive a)
 mfromVectorP sh v = M_Primitive sh (X.fromVector sh v)
@@ -971,9 +975,9 @@ mrerankP :: forall sh1 sh2 sh a b. (Storable a, Storable b)
          -> (Mixed sh1 (Primitive a) -> Mixed sh2 (Primitive b))
          -> Mixed (sh ++ sh1) (Primitive a) -> Mixed (sh ++ sh2) (Primitive b)
 mrerankP ssh sh2 f (M_Primitive sh arr) =
-  let sh1 = shDropSSX sh ssh
-  in M_Primitive (X.shAppend (shTakeSSX (Proxy @sh1) sh ssh) sh2)
-                 (X.rerank ssh (X.staticShapeFrom sh1) (X.staticShapeFrom sh2)
+  let sh1 = shxDropSSX sh ssh
+  in M_Primitive (shxAppend (shxTakeSSX (Proxy @sh1) sh ssh) sh2)
+                 (X.rerank ssh (ssxFromShape sh1) (ssxFromShape sh2)
                            (\a -> let M_Primitive _ r = f (M_Primitive sh1 a) in r)
                            arr)
 
@@ -988,10 +992,10 @@ mrerank ssh sh2 f (toPrimitive -> arr) =
 mreplicate :: forall sh sh' a. Elt a
            => IShX sh -> Mixed sh' a -> Mixed (sh ++ sh') a
 mreplicate sh arr =
-  let ssh' = X.staticShapeFrom (mshape arr)
-  in mlift (X.ssxAppend (X.staticShapeFrom sh) ssh')
+  let ssh' = ssxFromShape (mshape arr)
+  in mlift (ssxAppend (ssxFromShape sh) ssh')
            (\(sshT :: StaticShX shT) ->
-              case X.lemAppAssoc (Proxy @sh) (Proxy @sh') (Proxy @shT) of
+              case lemAppAssoc (Proxy @sh) (Proxy @sh') (Proxy @shT) of
                 Refl -> X.replicate sh (ssxAppend ssh' sshT))
            arr
 
@@ -1005,18 +1009,18 @@ mreplicateScal sh x = fromPrimitive (mreplicateScalP sh x)
 mslice :: Elt a => SNat i -> SNat n -> Mixed (Just (i + n + k) : sh) a -> Mixed (Just n : sh) a
 mslice i n arr =
   let _ :$% sh = mshape arr
-  in mlift (SKnown n :!% X.staticShapeFrom sh) (\_ -> X.slice i n) arr
+  in mlift (SKnown n :!% ssxFromShape sh) (\_ -> X.slice i n) arr
 
 msliceU :: Elt a => Int -> Int -> Mixed (Nothing : sh) a -> Mixed (Nothing : sh) a
-msliceU i n arr = mlift (X.staticShapeFrom (mshape arr)) (\_ -> X.sliceU i n) arr
+msliceU i n arr = mlift (ssxFromShape (mshape arr)) (\_ -> X.sliceU i n) arr
 
 mrev1 :: Elt a => Mixed (n : sh) a -> Mixed (n : sh) a
-mrev1 arr = mlift (X.staticShapeFrom (mshape arr)) (\_ -> X.rev1) arr
+mrev1 arr = mlift (ssxFromShape (mshape arr)) (\_ -> X.rev1) arr
 
 mreshape :: forall sh sh' a. Elt a => IShX sh' -> Mixed sh a -> Mixed sh' a
 mreshape sh' arr =
-  mlift (X.staticShapeFrom sh')
-        (\sshIn -> X.reshapePartial (X.staticShapeFrom (mshape arr)) sshIn sh')
+  mlift (ssxFromShape sh')
+        (\sshIn -> X.reshapePartial (ssxFromShape (mshape arr)) sshIn sh')
         arr
 
 miota :: (Enum a, PrimElt a) => SNat n -> Mixed '[Just n] a
@@ -1095,26 +1099,26 @@ instance (FloatElt a, NumElt a, PrimElt a) => Floating (Mixed sh a) where
   log1pexp = mliftNumElt1 floatEltLog1pexp
   log1mexp = mliftNumElt1 floatEltLog1mexp
 
-mtoRanked :: forall sh a. Elt a => Mixed sh a -> Ranked (X.Rank sh) a
+mtoRanked :: forall sh a. Elt a => Mixed sh a -> Ranked (Rank sh) a
 mtoRanked arr
-  | Refl <- X.lemAppNil @sh
-  , Refl <- X.lemAppNil @(Replicate (X.Rank sh) (Nothing @Nat))
+  | Refl <- lemAppNil @sh
+  , Refl <- lemAppNil @(Replicate (Rank sh) (Nothing @Nat))
   , Refl <- lemRankReplicate (srankSh (mshape arr))
-  = Ranked (mcast (X.staticShapeFrom (mshape arr)) (convSh (mshape arr)) (Proxy @'[]) arr)
+  = Ranked (mcast (ssxFromShape (mshape arr)) (convSh (mshape arr)) (Proxy @'[]) arr)
   where
-    convSh :: IShX sh' -> IShX (Replicate (X.Rank sh') Nothing)
+    convSh :: IShX sh' -> IShX (Replicate (Rank sh') Nothing)
     convSh ZSX = ZSX
     convSh (smn :$% (sh :: IShX sh'T))
-      | Refl <- X.lemReplicateSucc @(Nothing @Nat) @(X.Rank sh'T)
+      | Refl <- lemReplicateSucc @(Nothing @Nat) @(Rank sh'T)
       = SUnknown (fromSMayNat' smn) :$% convSh sh
 
-mcastToShaped :: forall sh sh' a. (Elt a, X.Rank sh ~ X.Rank sh')
+mcastToShaped :: forall sh sh' a. (Elt a, Rank sh ~ Rank sh')
               => Mixed sh a -> ShS sh' -> Shaped sh' a
 mcastToShaped arr targetsh
-  | Refl <- X.lemAppNil @sh
-  , Refl <- X.lemAppNil @(MapJust sh')
+  | Refl <- lemAppNil @sh
+  , Refl <- lemAppNil @(MapJust sh')
   , Refl <- lemRankMapJust targetsh
-  = Shaped (mcast (X.staticShapeFrom (mshape arr)) (shCvtSX targetsh) (Proxy @'[]) arr)
+  = Shaped (mcast (ssxFromShape (mshape arr)) (shCvtSX targetsh) (Proxy @'[]) arr)
 
 
 -- | A rank-typed array: the number of dimensions of the array (its /rank/) is
@@ -1418,7 +1422,7 @@ zeroIxR :: SNat n -> IIxR n
 zeroIxR SZ = ZIR
 zeroIxR (SS n) = 0 :.: zeroIxR n
 
-ixCvtXR :: IIxX sh -> IIxR (X.Rank sh)
+ixCvtXR :: IIxX sh -> IIxR (Rank sh)
 ixCvtXR ZIX = ZIR
 ixCvtXR (n :.% idx) = n :.: ixCvtXR idx
 
@@ -1429,7 +1433,7 @@ shCvtXR' ZSX =
 shCvtXR' (n :$% (idx :: IShX sh))
   | Refl <- lemReplicateSucc @(Nothing @Nat) @(n - 1) =
   castWith (subst2 (lem1 @sh Refl))
-    (X.fromSMayNat' n :$: shCvtXR' (castWith (subst2 (lem2 Refl)) idx))
+    (fromSMayNat' n :$: shCvtXR' (castWith (subst2 (lem2 Refl)) idx))
   where
     lem1 :: forall sh' n' k.
             k : sh' :~: Replicate n' Nothing
@@ -1443,13 +1447,13 @@ shCvtXR' (n :$% (idx :: IShX sh))
 ixCvtRX :: IIxR n -> IIxX (Replicate n Nothing)
 ixCvtRX ZIR = ZIX
 ixCvtRX (n :.: (idx :: IxR m Int)) =
-  castWith (subst2 @IxX @Int (X.lemReplicateSucc @(Nothing @Nat) @m))
+  castWith (subst2 @IxX @Int (lemReplicateSucc @(Nothing @Nat) @m))
     (n :.% ixCvtRX idx)
 
 shCvtRX :: IShR n -> IShX (Replicate n Nothing)
 shCvtRX ZSR = ZSX
 shCvtRX (n :$: (idx :: ShR m Int)) =
-  castWith (subst2 @ShX @Int (X.lemReplicateSucc @(Nothing @Nat) @m))
+  castWith (subst2 @ShX @Int (lemReplicateSucc @(Nothing @Nat) @m))
     (SUnknown n :$% shCvtRX idx)
 
 shapeSizeR :: IShR n -> Int
@@ -1506,7 +1510,7 @@ rsumOuter1P :: forall n a.
                (Storable a, NumElt a)
             => Ranked (n + 1) (Primitive a) -> Ranked n (Primitive a)
 rsumOuter1P (Ranked arr)
-  | Refl <- X.lemReplicateSucc @(Nothing @Nat) @n
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = Ranked (msumOuter1P arr)
 
 rsumOuter1 :: forall n a. (NumElt a, PrimElt a)
@@ -1559,7 +1563,7 @@ rappend :: forall n a. Elt a
 rappend arr1 arr2
   | sn@SNat <- snatFromShR (rshape arr1)
   , Dict <- lemKnownReplicate sn
-  , Refl <- X.lemReplicateSucc @(Nothing @Nat) @n
+  , Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = coerce (mappend @Nothing @Nothing @(Replicate n Nothing))
       arr1 arr2
 
@@ -1582,7 +1586,7 @@ rtoVector = coerce mtoVector
 
 rfromListOuter :: forall n a. Elt a => NonEmpty (Ranked n a) -> Ranked (n + 1) a
 rfromListOuter l
-  | Refl <- X.lemReplicateSucc @(Nothing @Nat) @n
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = Ranked (mfromListOuter (coerce l :: NonEmpty (Mixed (Replicate n Nothing) a)))
 
 rfromList1 :: Elt a => NonEmpty a -> Ranked 1 a
@@ -1593,7 +1597,7 @@ rfromList1Prim l = Ranked (mfromList1Prim l)
 
 rtoListOuter :: forall n a. Elt a => Ranked (n + 1) a -> [Ranked n a]
 rtoListOuter (Ranked arr)
-  | Refl <- X.lemReplicateSucc @(Nothing @Nat) @n
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = coerce (mtoListOuter @a @Nothing @(Replicate n Nothing) arr)
 
 rtoList1 :: Elt a => Ranked 1 a -> [a]
@@ -1677,7 +1681,7 @@ rreplicateScal sh x = rfromPrimitive (rreplicateScalP sh x)
 
 rslice :: forall n a. Elt a => Int -> Int -> Ranked (n + 1) a -> Ranked (n + 1) a
 rslice i n arr
-  | Refl <- X.lemReplicateSucc @(Nothing @Nat) @n
+  | Refl <- lemReplicateSucc @(Nothing @Nat) @n
   = rlift (snatFromShR (rshape arr))
           (\_ -> X.sliceU i n)
           arr
@@ -1686,7 +1690,7 @@ rrev1 :: forall n a. Elt a => Ranked (n + 1) a -> Ranked (n + 1) a
 rrev1 arr =
   rlift (snatFromShR (rshape arr))
         (\(_ :: StaticShX sh') ->
-          case X.lemReplicateSucc @(Nothing @Nat) @n of
+          case lemReplicateSucc @(Nothing @Nat) @n of
             Refl -> X.rev1 @Nothing @(Replicate n Nothing ++ sh'))
         arr
 
@@ -1707,12 +1711,12 @@ rasXArrayPrim :: PrimElt a => Ranked n a -> (IShR n, XArray (Replicate n Nothing
 rasXArrayPrim (Ranked arr) = first shCvtXR' (masXArrayPrim arr)
 
 rfromXArrayPrimP :: SNat n -> XArray (Replicate n Nothing) a -> Ranked n (Primitive a)
-rfromXArrayPrimP sn arr = Ranked (mfromXArrayPrimP (X.staticShapeFrom (X.shape (ssxFromSNat sn) arr)) arr)
+rfromXArrayPrimP sn arr = Ranked (mfromXArrayPrimP (ssxFromShape (X.shape (ssxFromSNat sn) arr)) arr)
 
 rfromXArrayPrim :: PrimElt a => SNat n -> XArray (Replicate n Nothing) a -> Ranked n a
-rfromXArrayPrim sn arr = Ranked (mfromXArrayPrim (X.staticShapeFrom (X.shape (ssxFromSNat sn) arr)) arr)
+rfromXArrayPrim sn arr = Ranked (mfromXArrayPrim (ssxFromShape (X.shape (ssxFromSNat sn) arr)) arr)
 
-rcastToShaped :: Elt a => Ranked (X.Rank sh) a -> ShS sh -> Shaped sh a
+rcastToShaped :: Elt a => Ranked (Rank sh) a -> ShS sh -> Shaped sh a
 rcastToShaped (Ranked arr) targetsh
   | Refl <- lemRankReplicate (srankSh (shCvtSX targetsh))
   , Refl <- lemRankMapJust targetsh
@@ -1809,7 +1813,7 @@ shCvtSX (n :$$ sh) = SKnown n :$% shCvtSX sh
 
 shapeSizeS :: ShS sh -> Int
 shapeSizeS ZSS = 1
-shapeSizeS (n :$$ sh) = X.fromSNat' n * shapeSizeS sh
+shapeSizeS (n :$$ sh) = fromSNat' n * shapeSizeS sh
 
 
 sshape :: forall sh a. Elt a => Shaped sh a -> ShS sh
@@ -1838,14 +1842,14 @@ slift :: forall sh1 sh2 a. Elt a
       => ShS sh2
       -> (forall sh' b. Storable b => StaticShX sh' -> XArray (MapJust sh1 ++ sh') b -> XArray (MapJust sh2 ++ sh') b)
       -> Shaped sh1 a -> Shaped sh2 a
-slift sh2 f (Shaped arr) = Shaped (mlift (X.staticShapeFrom (shCvtSX sh2)) f arr)
+slift sh2 f (Shaped arr) = Shaped (mlift (ssxFromShape (shCvtSX sh2)) f arr)
 
 -- | See the documentation of 'mlift'.
 slift2 :: forall sh1 sh2 sh3 a. Elt a
        => ShS sh3
        -> (forall sh' b. Storable b => StaticShX sh' -> XArray (MapJust sh1 ++ sh') b -> XArray (MapJust sh2 ++ sh') b -> XArray (MapJust sh3 ++ sh') b)
        -> Shaped sh1 a -> Shaped sh2 a -> Shaped sh3 a
-slift2 sh3 f (Shaped arr1) (Shaped arr2) = Shaped (mlift2 (X.staticShapeFrom (shCvtSX sh3)) f arr1 arr2)
+slift2 sh3 f (Shaped arr1) (Shaped arr2) = Shaped (mlift2 (ssxFromShape (shCvtSX sh3)) f arr1 arr2)
 
 ssumOuter1P :: forall sh n a. (Storable a, NumElt a)
             => Shaped (n : sh) (Primitive a) -> Shaped sh (Primitive a)
@@ -1855,28 +1859,28 @@ ssumOuter1 :: forall sh n a. (NumElt a, PrimElt a)
            => Shaped (n : sh) a -> Shaped sh a
 ssumOuter1 = sfromPrimitive . ssumOuter1P . stoPrimitive
 
-lemCommMapJustTakeLen :: HList SNat is -> ShS sh -> X.TakeLen is (MapJust sh) :~: MapJust (X.TakeLen is sh)
-lemCommMapJustTakeLen HNil _ = Refl
-lemCommMapJustTakeLen (_ `HCons` is) (_ :$$ sh) | Refl <- lemCommMapJustTakeLen is sh = Refl
-lemCommMapJustTakeLen (_ `HCons` _) ZSS = error "TakeLen of empty"
+lemCommMapJustTakeLen :: Perm is -> ShS sh -> TakeLen is (MapJust sh) :~: MapJust (TakeLen is sh)
+lemCommMapJustTakeLen PNil _ = Refl
+lemCommMapJustTakeLen (_ `PCons` is) (_ :$$ sh) | Refl <- lemCommMapJustTakeLen is sh = Refl
+lemCommMapJustTakeLen (_ `PCons` _) ZSS = error "TakeLen of empty"
 
-lemCommMapJustDropLen :: HList SNat is -> ShS sh -> X.DropLen is (MapJust sh) :~: MapJust (X.DropLen is sh)
-lemCommMapJustDropLen HNil _ = Refl
-lemCommMapJustDropLen (_ `HCons` is) (_ :$$ sh) | Refl <- lemCommMapJustDropLen is sh = Refl
-lemCommMapJustDropLen (_ `HCons` _) ZSS = error "DropLen of empty"
+lemCommMapJustDropLen :: Perm is -> ShS sh -> DropLen is (MapJust sh) :~: MapJust (DropLen is sh)
+lemCommMapJustDropLen PNil _ = Refl
+lemCommMapJustDropLen (_ `PCons` is) (_ :$$ sh) | Refl <- lemCommMapJustDropLen is sh = Refl
+lemCommMapJustDropLen (_ `PCons` _) ZSS = error "DropLen of empty"
 
-lemCommMapJustIndex :: SNat i -> ShS sh -> X.Index i (MapJust sh) :~: Just (X.Index i sh)
+lemCommMapJustIndex :: SNat i -> ShS sh -> Index i (MapJust sh) :~: Just (Index i sh)
 lemCommMapJustIndex SZ (_ :$$ _) = Refl
 lemCommMapJustIndex (SS (i :: SNat i')) ((_ :: SNat n) :$$ (sh :: ShS sh'))
   | Refl <- lemCommMapJustIndex i sh
-  , Refl <- X.lemIndexSucc (Proxy @i') (Proxy @(Just n)) (Proxy @(MapJust sh'))
-  , Refl <- X.lemIndexSucc (Proxy @i') (Proxy @n) (Proxy @sh')
+  , Refl <- lemIndexSucc (Proxy @i') (Proxy @(Just n)) (Proxy @(MapJust sh'))
+  , Refl <- lemIndexSucc (Proxy @i') (Proxy @n) (Proxy @sh')
   = Refl
 lemCommMapJustIndex _ ZSS = error "Index of empty"
 
-lemCommMapJustPermute :: HList SNat is -> ShS sh -> X.Permute is (MapJust sh) :~: MapJust (X.Permute is sh)
-lemCommMapJustPermute HNil _ = Refl
-lemCommMapJustPermute (i `HCons` is) sh
+lemCommMapJustPermute :: Perm is -> ShS sh -> Permute is (MapJust sh) :~: MapJust (Permute is sh)
+lemCommMapJustPermute PNil _ = Refl
+lemCommMapJustPermute (i `PCons` is) sh
   | Refl <- lemCommMapJustPermute is sh
   , Refl <- lemCommMapJustIndex i sh
   = Refl
@@ -1885,53 +1889,53 @@ listsAppend :: ListS sh f -> ListS sh' f -> ListS (sh ++ sh') f
 listsAppend ZS idx' = idx'
 listsAppend (i ::$ idx) idx' = i ::$ listsAppend idx idx'
 
-listsTakeLen :: forall f is sh. HList SNat is -> ListS sh f -> ListS (X.TakeLen is sh) f
-listsTakeLen HNil _ = ZS
-listsTakeLen (_ `HCons` is) (n ::$ sh) = n ::$ listsTakeLen is sh
-listsTakeLen (_ `HCons` _) ZS = error "Permutation longer than shape"
+listsTakeLen :: forall f is sh. Perm is -> ListS sh f -> ListS (TakeLen is sh) f
+listsTakeLen PNil _ = ZS
+listsTakeLen (_ `PCons` is) (n ::$ sh) = n ::$ listsTakeLen is sh
+listsTakeLen (_ `PCons` _) ZS = error "Permutation longer than shape"
 
-listsDropLen :: forall f is sh. HList SNat is -> ListS sh f -> ListS (DropLen is sh) f
-listsDropLen HNil sh = sh
-listsDropLen (_ `HCons` is) (_ ::$ sh) = listsDropLen is sh
-listsDropLen (_ `HCons` _) ZS = error "Permutation longer than shape"
+listsDropLen :: forall f is sh. Perm is -> ListS sh f -> ListS (DropLen is sh) f
+listsDropLen PNil sh = sh
+listsDropLen (_ `PCons` is) (_ ::$ sh) = listsDropLen is sh
+listsDropLen (_ `PCons` _) ZS = error "Permutation longer than shape"
 
-listsPermute :: forall f is sh. HList SNat is -> ListS sh f -> ListS (X.Permute is sh) f
-listsPermute HNil _ = ZS
-listsPermute (i `HCons` (is :: HList SNat is')) (sh :: ListS sh f) = listsIndex (Proxy @is') (Proxy @sh) i sh (listsPermute is sh)
+listsPermute :: forall f is sh. Perm is -> ListS sh f -> ListS (Permute is sh) f
+listsPermute PNil _ = ZS
+listsPermute (i `PCons` (is :: Perm is')) (sh :: ListS sh f) = listsIndex (Proxy @is') (Proxy @sh) i sh (listsPermute is sh)
 
-listsIndex :: forall f i is sh shT. Proxy is -> Proxy shT -> SNat i -> ListS sh f -> ListS (X.Permute is shT) f -> ListS (X.Index i sh : X.Permute is shT) f
+listsIndex :: forall f i is sh shT. Proxy is -> Proxy shT -> SNat i -> ListS sh f -> ListS (Permute is shT) f -> ListS (Index i sh : Permute is shT) f
 listsIndex _ _ SZ (n ::$ _) rest = n ::$ rest
 listsIndex p pT (SS (i :: SNat i')) ((_ :: f n) ::$ (sh :: ListS sh' f)) rest
-  | Refl <- X.lemIndexSucc (Proxy @i') (Proxy @n) (Proxy @sh')
+  | Refl <- lemIndexSucc (Proxy @i') (Proxy @n) (Proxy @sh')
   = listsIndex p pT i sh rest
 listsIndex _ _ _ ZS _ = error "Index into empty shape"
 
-shsTakeLen :: HList SNat is -> ShS sh -> ShS (X.TakeLen is sh)
+shsTakeLen :: Perm is -> ShS sh -> ShS (TakeLen is sh)
 shsTakeLen = coerce (listsTakeLen @SNat)
 
-shsPermute :: HList SNat is -> ShS sh -> ShS (X.Permute is sh)
+shsPermute :: Perm is -> ShS sh -> ShS (Permute is sh)
 shsPermute = coerce (listsPermute @SNat)
 
-shsIndex :: Proxy is -> Proxy shT -> SNat i -> ShS sh -> ShS (X.Permute is shT) -> ShS (X.Index i sh : X.Permute is shT)
+shsIndex :: Proxy is -> Proxy shT -> SNat i -> ShS sh -> ShS (Permute is shT) -> ShS (Index i sh : Permute is shT)
 shsIndex pis pshT = coerce (listsIndex @SNat pis pshT)
 
-applyPermS :: forall f is sh. HList SNat is -> ListS sh f -> ListS (PermutePrefix is sh) f
+applyPermS :: forall f is sh. Perm is -> ListS sh f -> ListS (PermutePrefix is sh) f
 applyPermS perm sh = listsAppend (listsPermute perm (listsTakeLen perm sh)) (listsDropLen perm sh)
 
-applyPermIxS :: forall i is sh. HList SNat is -> IxS sh i -> IxS (PermutePrefix is sh) i
+applyPermIxS :: forall i is sh. Perm is -> IxS sh i -> IxS (PermutePrefix is sh) i
 applyPermIxS = coerce (applyPermS @(Const i))
 
-applyPermShS :: forall is sh. HList SNat is -> ShS sh -> ShS (PermutePrefix is sh)
+applyPermShS :: forall is sh. Perm is -> ShS sh -> ShS (PermutePrefix is sh)
 applyPermShS = coerce (applyPermS @SNat)
 
-stranspose :: forall is sh a. (X.Permutation is, X.Rank is <= X.Rank sh, Elt a)
-           => HList SNat is -> Shaped sh a -> Shaped (X.PermutePrefix is sh) a
+stranspose :: forall is sh a. (IsPermutation is, Rank is <= Rank sh, Elt a)
+           => Perm is -> Shaped sh a -> Shaped (PermutePrefix is sh) a
 stranspose perm sarr@(Shaped arr)
   | Refl <- lemRankMapJust (sshape sarr)
   , Refl <- lemCommMapJustTakeLen perm (sshape sarr)
   , Refl <- lemCommMapJustDropLen perm (sshape sarr)
   , Refl <- lemCommMapJustPermute perm (shsTakeLen perm (sshape sarr))
-  , Refl <- lemCommMapJustApp (shsPermute perm (shsTakeLen perm (sshape sarr))) (Proxy @(X.DropLen is sh))
+  , Refl <- lemCommMapJustApp (shsPermute perm (shsTakeLen perm (sshape sarr))) (Proxy @(DropLen is sh))
   = Shaped (mtranspose perm arr)
 
 sappend :: Elt a => Shaped (n : sh) a -> Shaped (m : sh) a -> Shaped (n + m : sh) a
@@ -1969,7 +1973,7 @@ stoList1 = map sunScalar . stoListOuter
 
 sfromListPrim :: forall n a. PrimElt a => SNat n -> [a] -> Shaped '[n] a
 sfromListPrim sn l
-  | Refl <- X.lemAppNil @'[Just n]
+  | Refl <- lemAppNil @'[Just n]
   = let ssh = SUnknown () :!% ZKX
         xarr = X.cast ssh (SKnown sn :$% ZSX) ZKX (X.fromList1 ssh l)
     in Shaped $ fromPrimitive $ M_Primitive (X.shape (SKnown sn :!% ZKX) xarr) xarr
@@ -1989,7 +1993,7 @@ srerankP :: forall sh1 sh2 sh a b. (Storable a, Storable b)
 srerankP sh sh2 f sarr@(Shaped arr)
   | Refl <- lemCommMapJustApp sh (Proxy @sh1)
   , Refl <- lemCommMapJustApp sh (Proxy @sh2)
-  = Shaped (mrerankP (X.staticShapeFrom (shTakeSSX (Proxy @(MapJust sh1)) (shCvtSX (sshape sarr)) (X.staticShapeFrom (shCvtSX sh))))
+  = Shaped (mrerankP (ssxFromShape (shxTakeSSX (Proxy @(MapJust sh1)) (shCvtSX (sshape sarr)) (ssxFromShape (shCvtSX sh))))
                      (shCvtSX sh2)
                      (\a -> let Shaped r = f (Shaped a) in r)
                      arr)
@@ -2033,12 +2037,12 @@ sasXArrayPrim :: PrimElt a => Shaped sh a -> (ShS sh, XArray (MapJust sh) a)
 sasXArrayPrim (Shaped arr) = first shCvtXS' (masXArrayPrim arr)
 
 sfromXArrayPrimP :: ShS sh -> XArray (MapJust sh) a -> Shaped sh (Primitive a)
-sfromXArrayPrimP sh arr = Shaped (mfromXArrayPrimP (X.staticShapeFrom (shCvtSX sh)) arr)
+sfromXArrayPrimP sh arr = Shaped (mfromXArrayPrimP (ssxFromShape (shCvtSX sh)) arr)
 
 sfromXArrayPrim :: PrimElt a => ShS sh -> XArray (MapJust sh) a -> Shaped sh a
-sfromXArrayPrim sh arr = Shaped (mfromXArrayPrim (X.staticShapeFrom (shCvtSX sh)) arr)
+sfromXArrayPrim sh arr = Shaped (mfromXArrayPrim (ssxFromShape (shCvtSX sh)) arr)
 
-stoRanked :: Elt a => Shaped sh a -> Ranked (X.Rank sh) a
+stoRanked :: Elt a => Shaped sh a -> Ranked (Rank sh) a
 stoRanked sarr@(Shaped arr)
   | Refl <- lemRankMapJust (sshape sarr)
   = mtoRanked arr