3 files changed, 42 insertions, 4 deletions
diff --git a/src/Data/Array/Mixed.hs b/src/Data/Array/Mixed.hs
index f62d781..b07f120 100644
--- a/src/Data/Array/Mixed.hs
+++ b/src/Data/Array/Mixed.hs
@@ -283,7 +283,7 @@ instance KnownShX sh => IsList (ShX sh Int) where
 
 type family Rank sh where
   Rank '[] = 0
-  Rank (_ : sh) = 1 + Rank sh
+  Rank (_ : sh) = Rank sh + 1
 
 type XArray :: [Maybe Nat] -> Type -> Type
 newtype XArray sh a = XArray (S.Array (Rank sh) a)
diff --git a/src/Data/Array/Nested.hs b/src/Data/Array/Nested.hs
index f712301..438f144 100644
--- a/src/Data/Array/Nested.hs
+++ b/src/Data/Array/Nested.hs
@@ -2,7 +2,7 @@
 {-# LANGUAGE PatternSynonyms #-}
 module Data.Array.Nested (
   -- * Ranked arrays
-  Ranked,
+  Ranked(Ranked),
   ListR(ZR, (:::)),
   IxR(.., ZIR, (:.:)), IIxR,
   ShR(.., ZSR, (:$:)),
@@ -14,9 +14,10 @@ module Data.Array.Nested (
   rlift,
   -- ** Conversions
   rasXArrayPrim, rfromXArrayPrim,
+  rcastToShaped,
 
   -- * Shaped arrays
-  Shaped,
+  Shaped(Shaped),
   ListS(ZS, (::$)),
   IxS(.., ZIS, (:.$)), IIxS,
   ShS(.., ZSS, (:$$)), KnownShS(..),
@@ -28,6 +29,7 @@ module Data.Array.Nested (
   slift,
   -- ** Conversions
   sasXArrayPrim, sfromXArrayPrim,
+  stoRanked,
 
   -- * Mixed arrays
   Mixed,
@@ -37,6 +39,7 @@ module Data.Array.Nested (
   mconstant, mfromList, mtoList, mslice, mrev1, mreshape,
   -- ** Conversions
   masXArrayPrim, mfromXArrayPrim,
+  mtoRanked, mcastToShaped,
 
   -- * Array elements
   Elt(mshape, mindex, mindexPartial, mscalar, mfromList1, mtoList1, mlift, mlift2),
diff --git a/src/Data/Array/Nested/Internal.hs b/src/Data/Array/Nested/Internal.hs
index ef2179c..3863556 100644
--- a/src/Data/Array/Nested/Internal.hs
+++ b/src/Data/Array/Nested/Internal.hs
@@ -28,7 +28,6 @@
 
 {-|
 TODO:
-* Write conversions between Mixed, Ranked and Shaped
 * Write `rerank`
 * Write `rconst :: OR.Array n a -> Ranked n a`
 
@@ -163,6 +162,10 @@ lemTakeLenApp :: X.Rank l1 <= X.Rank l2
               -> X.TakeLen l1 l2 :~: X.TakeLen l1 (l2 ++ rest)
 lemTakeLenApp _ _ _ = unsafeCoerce Refl
 
+srankSh :: ShX sh f -> SNat (X.Rank sh)
+srankSh ZSX = SNat
+srankSh (_ :$% sh) | SNat <- srankSh sh = SNat
+
 
 -- === NEW INDEX TYPES === --
 
@@ -953,6 +956,27 @@ instance (Storable a, Num a, PrimElt a) => Num (Mixed sh a) where
   signum = mliftPrim signum
   fromInteger _ = error "Data.Array.Nested.fromIntegral: No singletons available, use explicit mconstant"
 
+mtoRanked :: forall sh a. Elt a => Mixed sh a -> Ranked (X.Rank sh) a
+mtoRanked arr
+  | Refl <- X.lemAppNil @sh
+  , Refl <- X.lemAppNil @(Replicate (X.Rank sh) (Nothing @Nat))
+  , Refl <- lemRankReplicate (srankSh (mshape arr))
+  = Ranked (mcast (X.staticShapeFrom (mshape arr)) (convSh (mshape arr)) (Proxy @'[]) arr)
+  where
+    convSh :: IShX sh' -> IShX (Replicate (X.Rank sh') Nothing)
+    convSh ZSX = ZSX
+    convSh (smn :$% (sh :: IShX sh'T))
+      | Refl <- X.lemReplicateSucc @(Nothing @Nat) @(X.Rank sh'T)
+      = SUnknown (fromSMayNat' smn) :$% convSh sh
+
+mcastToShaped :: forall sh sh' a. (Elt a, X.Rank sh ~ X.Rank sh')
+              => Mixed sh a -> ShS sh' -> Shaped sh' a
+mcastToShaped arr targetsh
+  | Refl <- X.lemAppNil @sh
+  , Refl <- X.lemAppNil @(MapJust sh')
+  , Refl <- lemRankMapJust targetsh
+  = Shaped (mcast (X.staticShapeFrom (mshape arr)) (shCvtSX targetsh) (Proxy @'[]) arr)
+
 
 -- | A rank-typed array: the number of dimensions of the array (its /rank/) is
 -- represented on the type level as a 'Nat'.
@@ -1408,6 +1432,12 @@ rfromXArrayPrimP sn arr = Ranked (mfromXArrayPrimP (X.staticShapeFrom (X.shape (
 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)
 
+rcastToShaped :: Elt a => Ranked (X.Rank sh) a -> ShS sh -> Shaped sh a
+rcastToShaped (Ranked arr) targetsh
+  | Refl <- lemRankReplicate (srankSh (shCvtSX targetsh))
+  , Refl <- lemRankMapJust targetsh
+  = mcastToShaped arr targetsh
+
 
 -- ====== API OF SHAPED ARRAYS ====== --
 
@@ -1617,3 +1647,8 @@ sfromXArrayPrimP sh arr = Shaped (mfromXArrayPrimP (X.staticShapeFrom (shCvtSX s
 
 sfromXArrayPrim :: PrimElt a => ShS sh -> XArray (MapJust sh) a -> Shaped sh a
 sfromXArrayPrim sh arr = Shaped (mfromXArrayPrim (X.staticShapeFrom (shCvtSX sh)) arr)
+
+stoRanked :: Elt a => Shaped sh a -> Ranked (X.Rank sh) a
+stoRanked sarr@(Shaped arr)
+  | Refl <- lemRankMapJust (sshape sarr)
+  = mtoRanked arr