4 files changed, 80 insertions, 16 deletions
diff --git a/src/Data/Array/Nested/Internal/Mixed.hs b/src/Data/Array/Nested/Internal/Mixed.hs
index 215313e..50202ba 100644
--- a/src/Data/Array/Nested/Internal/Mixed.hs
+++ b/src/Data/Array/Nested/Internal/Mixed.hs
@@ -104,7 +104,7 @@ newtype Primitive a = Primitive a
 
 -- | Element types that are primitive; arrays of these types are just a newtype
 -- wrapper over an array.
-class Storable a => PrimElt a where
+class (Storable a, Elt a) => PrimElt a where
   fromPrimitive :: Mixed sh (Primitive a) -> Mixed sh a
   toPrimitive :: Mixed sh a -> Mixed sh (Primitive a)
 
@@ -854,15 +854,26 @@ mmaxIndexPrim :: (PrimElt a, NumElt a) => Mixed sh a -> IIxX sh
 mmaxIndexPrim (toPrimitive -> M_Primitive sh (XArray arr)) =
   ixxFromList (ssxFromShape sh) (numEltMaxIndex arr)
 
-mdot1 :: (PrimElt a, NumElt a) => Mixed '[n] a -> Mixed '[n] a -> a
-mdot1 (toPrimitive -> M_Primitive _ (XArray arr1)) (toPrimitive -> M_Primitive _ (XArray arr2)) =
-  numEltDotprod arr1 arr2
+mdot1Inner :: forall sh n a. (PrimElt a, NumElt a)
+           => Proxy n -> Mixed (sh ++ '[n]) a -> Mixed (sh ++ '[n]) a -> Mixed sh a
+mdot1Inner _ (toPrimitive -> M_Primitive sh1 (XArray a)) (toPrimitive -> M_Primitive sh2 (XArray b))
+  | Refl <- lemInitApp (Proxy @sh) (Proxy @n)
+  , Refl <- lemLastApp (Proxy @sh) (Proxy @n)
+  = case sh1 of
+      _ :$% _
+        | sh1 == sh2
+        , Refl <- lemRankApp (ssxInit (ssxFromShape sh1)) (ssxLast (ssxFromShape sh1) :!% ZKX) ->
+            fromPrimitive $ M_Primitive (shxInit sh1) (XArray (numEltDotprodInner (shxRank (shxInit sh1)) a b))
+        | otherwise -> error "mdot1Inner: Unequal shapes"
+      ZSX -> error "unreachable"
 
 -- | This has a temporary, suboptimal implementation in terms of 'mflatten'.
--- Prefer 'mdot1' if applicable.
+-- Prefer 'mdot1Inner' if applicable.
 mdot :: (PrimElt a, NumElt a) => Mixed sh a -> Mixed sh a -> a
-mdot a b = mdot1 (fromPrimitive (mflatten (toPrimitive a)))
-                 (fromPrimitive (mflatten (toPrimitive b)))
+mdot a b =
+  munScalar $
+    mdot1Inner Proxy (fromPrimitive (mflatten (toPrimitive a)))
+                     (fromPrimitive (mflatten (toPrimitive b)))
 
 mtoXArrayPrimP :: Mixed sh (Primitive a) -> (IShX sh, XArray sh a)
 mtoXArrayPrimP (M_Primitive sh arr) = (sh, arr)
diff --git a/src/Data/Array/Nested/Internal/Ranked.hs b/src/Data/Array/Nested/Internal/Ranked.hs
index 74b2186..735d1a3 100644
--- a/src/Data/Array/Nested/Internal/Ranked.hs
+++ b/src/Data/Array/Nested/Internal/Ranked.hs
@@ -483,11 +483,14 @@ rmaxIndexPrim rarr@(Ranked arr)
   | Refl <- lemRankReplicate (rrank (rtoPrimitive rarr))
   = ixCvtXR (mmaxIndexPrim arr)
 
-rdot1 :: (PrimElt a, NumElt a) => Ranked 1 a -> Ranked 1 a -> a
-rdot1 = coerce mdot1
+rdot1Inner :: forall n a. (PrimElt a, NumElt a) => Ranked (n + 1) a -> Ranked (n + 1) a -> Ranked n a
+rdot1Inner arr1 arr2
+  | SNat <- rrank arr1
+  , Refl <- lemReplicatePlusApp (SNat @n) (Proxy @1) (Proxy @(Nothing @Nat))
+  = coerce (mdot1Inner (Proxy @(Nothing @Nat))) arr1 arr2
 
 -- | This has a temporary, suboptimal implementation in terms of 'mflatten'.
--- Prefer 'rdot1' if applicable.
+-- Prefer 'rdot1Inner' if applicable.
 rdot :: (PrimElt a, NumElt a) => Ranked n a -> Ranked n a -> a
 rdot = coerce mdot
 
diff --git a/src/Data/Array/Nested/Internal/Shape.hs b/src/Data/Array/Nested/Internal/Shape.hs
index ca04840..7077053 100644
--- a/src/Data/Array/Nested/Internal/Shape.hs
+++ b/src/Data/Array/Nested/Internal/Shape.hs
@@ -87,6 +87,16 @@ listrTail :: ListR (n + 1) i -> ListR n i
 listrTail (_ ::: sh) = sh
 listrTail ZR = error "unreachable"
 
+listrInit :: ListR (n + 1) i -> ListR n i
+listrInit (n ::: sh@(_ ::: _)) = n ::: listrInit sh
+listrInit (_ ::: ZR) = ZR
+listrInit ZR = error "unreachable"
+
+listrLast :: ListR (n + 1) i -> i
+listrLast (_ ::: sh@(_ ::: _)) = listrLast sh
+listrLast (n ::: ZR) = n
+listrLast ZR = error "unreachable"
+
 listrIndex :: forall k n i. (k + 1 <= n) => SNat k -> ListR n i -> i
 listrIndex SZ (x ::: _) = x
 listrIndex (SS i) (_ ::: xs) | Refl <- lemLeqSuccSucc (Proxy @k) (Proxy @n) = listrIndex i xs
@@ -166,6 +176,12 @@ ixrHead (IxR list) = listrHead list
 ixrTail :: IxR (n + 1) i -> IxR n i
 ixrTail (IxR list) = IxR (listrTail list)
 
+ixrInit :: IxR (n + 1) i -> IxR n i
+ixrInit (IxR list) = IxR (listrInit list)
+
+ixrLast :: IxR (n + 1) i -> i
+ixrLast (IxR list) = listrLast list
+
 ixrAppend :: forall n m i. IxR n i -> IxR m i -> IxR (n + m) i
 ixrAppend = coerce (listrAppend @_ @i)
 
@@ -235,6 +251,12 @@ shrHead (ShR list) = listrHead list
 shrTail :: ShR (n + 1) i -> ShR n i
 shrTail (ShR list) = ShR (listrTail list)
 
+shrInit :: ShR (n + 1) i -> ShR n i
+shrInit (ShR list) = ShR (listrInit list)
+
+shrLast :: ShR (n + 1) i -> i
+shrLast (ShR list) = listrLast list
+
 shrAppend :: forall n m i. ShR n i -> ShR m i -> ShR (n + m) i
 shrAppend = coerce (listrAppend @_ @i)
 
@@ -310,17 +332,25 @@ listsToList :: ListS sh (Const i) -> [i]
 listsToList ZS = []
 listsToList (Const i ::$ is) = i : listsToList is
 
-listsHead :: ListS (n : sh) i -> i n
+listsHead :: ListS (n : sh) f -> f n
 listsHead (i ::$ _) = i
 
-listsTail :: ListS (n : sh) i -> ListS sh i
+listsTail :: ListS (n : sh) f -> ListS sh f
 listsTail (_ ::$ sh) = sh
 
+listsInit :: ListS (n : sh) f -> ListS (Init (n : sh)) f
+listsInit (n ::$ sh@(_ ::$ _)) = n ::$ listsInit sh
+listsInit (_ ::$ ZS) = ZS
+
+listsLast :: ListS (n : sh) f -> f (Last (n : sh))
+listsLast (_ ::$ sh@(_ ::$ _)) = listsLast sh
+listsLast (n ::$ ZS) = n
+
 listsAppend :: ListS sh f -> ListS sh' f -> ListS (sh ++ sh') f
 listsAppend ZS idx' = idx'
 listsAppend (i ::$ idx) idx' = i ::$ listsAppend idx idx'
 
-listsRank :: ListS sh i -> SNat (Rank sh)
+listsRank :: ListS sh f -> SNat (Rank sh)
 listsRank ZS = SNat
 listsRank (_ ::$ sh) = snatSucc (listsRank sh)
 
@@ -403,6 +433,12 @@ ixsHead (IxS list) = getConst (listsHead list)
 ixsTail :: IxS (n : sh) i -> IxS sh i
 ixsTail (IxS list) = IxS (listsTail list)
 
+ixsInit :: IxS (n : sh) i -> IxS (Init (n : sh)) i
+ixsInit (IxS list) = IxS (listsInit list)
+
+ixsLast :: IxS (n : sh) i -> i
+ixsLast (IxS list) = getConst (listsLast list)
+
 ixsAppend :: forall sh sh' i. IxS sh i -> IxS sh' i -> IxS (sh ++ sh') i
 ixsAppend = coerce (listsAppend @_ @(Const i))
 
@@ -469,6 +505,12 @@ shsHead (ShS list) = listsHead list
 shsTail :: ShS (n : sh) -> ShS sh
 shsTail (ShS list) = ShS (listsTail list)
 
+shsInit :: ShS (n : sh) -> ShS (Init (n : sh))
+shsInit (ShS list) = ShS (listsInit list)
+
+shsLast :: ShS (n : sh) -> SNat (Last (n : sh))
+shsLast (ShS list) = listsLast list
+
 shsAppend :: forall sh sh'. ShS sh -> ShS sh' -> ShS (sh ++ sh')
 shsAppend = coerce (listsAppend @_ @SNat)
 
diff --git a/src/Data/Array/Nested/Internal/Shaped.hs b/src/Data/Array/Nested/Internal/Shaped.hs
index d013959..995507f 100644
--- a/src/Data/Array/Nested/Internal/Shaped.hs
+++ b/src/Data/Array/Nested/Internal/Shaped.hs
@@ -418,11 +418,19 @@ sminIndexPrim sarr@(Shaped arr) = ixCvtXS (sshape (stoPrimitive sarr)) (mminInde
 smaxIndexPrim :: (PrimElt a, NumElt a) => Shaped sh a -> IIxS sh
 smaxIndexPrim sarr@(Shaped arr) = ixCvtXS (sshape (stoPrimitive sarr)) (mmaxIndexPrim arr)
 
-sdot1 :: (PrimElt a, NumElt a) => Shaped '[n] a -> Shaped '[n] a -> a
-sdot1 = coerce mdot1
+sdot1Inner :: forall sh n a. (PrimElt a, NumElt a)
+           => Proxy n -> Shaped (sh ++ '[n]) a -> Shaped (sh ++ '[n]) a -> Shaped sh a
+sdot1Inner Proxy sarr1@(Shaped arr1) (Shaped arr2)
+  | Refl <- lemInitApp (Proxy @sh) (Proxy @n)
+  , Refl <- lemLastApp (Proxy @sh) (Proxy @n)
+  = case sshape sarr1 of
+      _ :$$ _
+        | Refl <- lemMapJustApp (shsInit (sshape sarr1)) (Proxy @'[n])
+        -> Shaped (mdot1Inner (Proxy @(Just n)) arr1 arr2)
+      _ -> error "unreachable"
 
 -- | This has a temporary, suboptimal implementation in terms of 'mflatten'.
--- Prefer 'sdot1' if applicable.
+-- Prefer 'sdot1Inner' if applicable.
 sdot :: (PrimElt a, NumElt a) => Shaped sh a -> Shaped sh a -> a
 sdot = coerce mdot