diff --git a/src/HordeAd/Core/AstSimplify.hs b/src/HordeAd/Core/AstSimplify.hs
index c8590d5ce..550e9f4d1 100644
--- a/src/HordeAd/Core/AstSimplify.hs
+++ b/src/HordeAd/Core/AstSimplify.hs
@@ -116,9 +116,10 @@ import HordeAd.Core.AstFreshId
 import HordeAd.Core.AstTools
 import HordeAd.Core.CarriersConcrete
 import HordeAd.Core.HVectorOps
+import HordeAd.Core.OpsConcrete ()
+import HordeAd.Core.TensorClass
 import HordeAd.Core.TensorKind
 import HordeAd.Core.Types
-import HordeAd.Internal.BackendOX
 import HordeAd.Util.ShapedList qualified as ShapedList
 import HordeAd.Util.SizedList
 
@@ -598,14 +599,14 @@ astIndexKnobsR knobs v0 ix@(i1 :.: (rest1 :: AstIxR AstMethodLet m1)) =
   Ast.AstCastR t -> astCastR $ astIndexKnobsR knobs t ix
   Ast.AstFromIntegralR v -> astFromIntegralR $ astIndexKnobsR knobs v ix
   AstConcrete (FTKR _ x) t ->
-    let unConst :: AstInt AstMethodLet -> Maybe [Int64]
-                -> Maybe [Int64]
-        unConst (AstConcrete _ (RepN i)) (Just l) = Just $ i : l
+    let unConst :: AstInt AstMethodLet -> Maybe [IntOf RepN]
+                -> Maybe [IntOf RepN]
+        unConst (AstConcrete _ i) (Just l) = Just $ i : l
         unConst _ _ = Nothing
     in case foldr unConst (Just []) ix of
       Just ixInt ->
-        let u = tindexZR (unRepN t) $ listToIndex ixInt
-        in AstConcrete (FTKR (Nested.rshape u) x) $ RepN u
+        let u = rindex t (fromList ixInt)
+        in AstConcrete (FTKR (rshape u) x) u
           -- TODO: we'd need mapM for Index to keep this rank-typed
       Nothing -> Ast.AstIndex v0 ix
   Ast.AstProjectR{} -> Ast.AstIndex v0 ix
@@ -854,14 +855,13 @@ astIndexKnobsS knobs v0 ix@((:.$) @in1 i1 (rest1 :: AstIxS AstMethodLet shm1)) |
   Ast.AstCastS t -> astCastS $ astIndexKnobsS knobs t ix
   Ast.AstFromIntegralS v -> astFromIntegralS $ astIndexKnobsS knobs v ix
   AstConcrete (FTKS _ x) t ->
-    let unConst :: AstInt AstMethodLet -> Maybe [Int64]
-                -> Maybe [Int64]
-        unConst (AstConcrete _ (RepN i)) (Just l) = Just $ i : l
+    let unConst :: AstInt AstMethodLet -> Maybe [IntOf RepN]
+                -> Maybe [IntOf RepN]
+        unConst (AstConcrete _ i) (Just l) = Just $ i : l
         unConst _ _ = Nothing
     in case foldr unConst (Just []) ix of
       Just ixInt -> AstConcrete (FTKS knownShS x)
-                    $ RepN $ tindexZS (unRepN t)
-                    $ ShapedList.listToIndex @shm ixInt
+                    $ sindex @_ @_ @shm t (fromList ixInt)
         -- TODO: we'd need mapM for Index to keep this rank-typed
       Nothing -> Ast.AstIndexS v0 ix
   Ast.AstProjectS{} -> Ast.AstIndexS v0 ix
@@ -1523,7 +1523,7 @@ astSum t0 = case shapeAst t0 of
     Ast.AstSlice i 1 v -> astIndexR v (fromIntegral i :.: ZIR)
     Ast.AstReverse v -> astSum v
     AstConcrete (FTKR sh FTKScalar) t ->
-      AstConcrete (FTKR (Nested.Internal.Shape.shrTail sh) FTKScalar) $ RepN $ tsumR $ unRepN t
+      AstConcrete (FTKR (Nested.Internal.Shape.shrTail sh) FTKScalar) $ rsum t
     Ast.AstFromPrimal v -> Ast.AstFromPrimal $ astSum v
     _ -> Ast.AstSum t0
 
@@ -1557,7 +1557,7 @@ astSumS t0 = case sameNat (Proxy @n) (Proxy @0) of
     Ast.AstSliceS @i @k v | Just Refl <- sameNat (Proxy @k) (Proxy @1) ->
       astIndexS v (valueOf @i :.$ ZIS)
     Ast.AstReverseS v -> astSumS v
-    AstConcrete _ t -> AstConcrete (FTKS knownShS FTKScalar) $ RepN $ Nested.ssumOuter1 $ unRepN t
+    AstConcrete _ t -> AstConcrete (FTKS knownShS FTKScalar) $ ssum t
     Ast.AstFromPrimal v -> Ast.AstFromPrimal $ astSumS v
     _ -> Ast.AstSumS t0
 
@@ -1609,13 +1609,13 @@ astFromVector :: forall s r n. (KnownNat n, TensorKind2 r, AstSpan s)
 astFromVector v | V.length v == 1 = astReplicate (SNat @1) (v V.! 0)
 astFromVector l | Just Refl <- sameAstSpan @s @PrimalSpan =
   let unConst :: AstTensor AstMethodLet PrimalSpan (TKR2 n r)
-              -> Maybe (FullTensorKind r, Nested.Ranked n (RepORArray r))
-      unConst (AstConcrete (FTKR _ x) (RepN t)) = Just (x, t)
+              -> Maybe (FullTensorKind r, RepN (TKR2 n r))
+      unConst (AstConcrete (FTKR _ x) t) = Just (x, t)
       unConst _ = Nothing
   in case V.mapM unConst l of
     Just l4 | Just ((x, _), _) <- V.uncons l4 ->
       let l3 = V.map snd l4
-      in AstConcrete (FTKR (V.length l :$: Nested.rshape (l3 V.! 0)) x) $ RepN $ tfromVectorR l3
+      in AstConcrete (FTKR (V.length l :$: rshape (l3 V.! 0)) x) $ rfromVector l3
     _ -> Ast.AstFromVector l
 astFromVector l | Just Refl <- sameAstSpan @s @FullSpan =
   let unFromPrimal :: AstTensor AstMethodLet FullSpan (TKR2 n r)
@@ -1635,13 +1635,13 @@ astFromVectorS :: forall s r n sh.
 astFromVectorS v | V.length v == 1 = astReplicate SNat (v V.! 0)
 astFromVectorS l | Just Refl <- sameAstSpan @s @PrimalSpan =
   let unConst :: AstTensor AstMethodLet PrimalSpan (TKS2 sh r)
-              -> Maybe (FullTensorKind r, Nested.Shaped sh (RepORArray r))
-      unConst (AstConcrete (FTKS _ x) (RepN t)) = Just (x, t)
+              -> Maybe (FullTensorKind r, RepN (TKS2 sh r))
+      unConst (AstConcrete (FTKS _ x) t) = Just (x, t)
       unConst _ = Nothing
   in case V.mapM unConst l of
     Just l4 | Just ((x, _), _) <- V.uncons l4 ->
       let l3 = V.map snd l4
-      in AstConcrete (FTKS knownShS x) $ RepN $ tfromVectorS l3
+      in AstConcrete (FTKS knownShS x) $ sfromVector l3
     _ -> Ast.AstFromVectorS l
 astFromVectorS l | Just Refl <- sameAstSpan @s @FullSpan =
   let unFromPrimal :: AstTensor AstMethodLet FullSpan (TKS2 sh r)
@@ -1660,12 +1660,13 @@ astFromVectorX :: forall s r n sh.
                -> AstTensor AstMethodLet s (TKX (Just n ': sh) r)
 astFromVectorX v | V.length v == 1 = astReplicate SNat (v V.! 0)
 astFromVectorX l | Just Refl <- sameAstSpan @s @PrimalSpan =
-  let unConst :: AstTensor AstMethodLet PrimalSpan (TKX sh r) -> Maybe (Nested.Mixed sh r)
-      unConst (AstConcrete _ (RepN t)) = Just t
+  let unConst :: AstTensor AstMethodLet PrimalSpan (TKX sh r)
+              -> Maybe (RepN (TKX sh r))
+      unConst (AstConcrete _ t) = Just t
       unConst _ = Nothing
   in case V.mapM unConst l of
     Just l3 | V.length l3 >= 1 ->
-      AstConcrete (FTKX (SKnown (SNat @n) :$% Nested.mshape (l3 V.! 0)) FTKScalar) $ RepN $ tfromVectorX l3
+      AstConcrete (FTKX (SKnown (SNat @n) :$% xshape (l3 V.! 0)) FTKScalar) $ xfromVector l3
     _ -> Ast.AstFromVectorX l
 astFromVectorX l | Just Refl <- sameAstSpan @s @FullSpan =
   let unFromPrimal :: AstTensor AstMethodLet FullSpan (TKX sh r)
@@ -1734,7 +1735,7 @@ astReplicateNS v =
 
 astReplicate0N :: forall n s r. (GoodScalar r, AstSpan s)
                => IShR n -> r -> AstTensor AstMethodLet s (TKR n r)
-astReplicate0N sh = astReplicate0NT sh . fromPrimal . AstConcrete (FTKR ZSR FTKScalar) . RepN . Nested.rscalar
+astReplicate0N sh = astReplicate0NT sh . fromPrimal . AstConcrete (FTKR ZSR FTKScalar) . rscalar
 
 astReplicate0NS :: forall shn s r. (KnownShS shn, GoodScalar r, AstSpan s)
                 => r -> AstTensor AstMethodLet s (TKS shn r)
@@ -1742,7 +1743,7 @@ astReplicate0NS =
   let go :: ShS sh' -> AstTensor AstMethodLet s (TKS '[] r) -> AstTensor AstMethodLet s (TKS sh' r)
       go ZSS v = v
       go ((:$$) SNat sh') v | Dict <- sshapeKnown sh' = astReplicate SNat $ go sh' v
-  in go (knownShS @shn) . fromPrimal . AstConcrete (FTKS ZSS FTKScalar) . RepN . Nested.sscalar
+  in go (knownShS @shn) . fromPrimal . AstConcrete (FTKS ZSS FTKScalar) . sscalar
 
 astReplicate0NT :: forall n s r. (GoodScalar r, AstSpan s)
                 => IShR n -> AstTensor AstMethodLet s (TKR 0 r) -> AstTensor AstMethodLet s (TKR n r)
@@ -1758,7 +1759,7 @@ astAppend :: (KnownNat n, GoodScalar r, AstSpan s)
           -> AstTensor AstMethodLet s (TKR (1 + n) r)
 astAppend (AstConcrete (FTKR (ulen :$: sh) FTKScalar) u)
           (AstConcrete (FTKR (vlen :$: _) FTKScalar) v) =
-  AstConcrete (FTKR (ulen + vlen :$: sh) FTKScalar) $ RepN $ tappendR (unRepN u) (unRepN v)
+  AstConcrete (FTKR (ulen + vlen :$: sh) FTKScalar) $ rappend u v
 astAppend (Ast.AstFromPrimal u) (Ast.AstFromPrimal v) =
   Ast.AstFromPrimal $ astAppend u v
 astAppend (Ast.AstFromVector l1) (Ast.AstFromVector l2) =
@@ -1769,7 +1770,7 @@ astAppendS :: (KnownNat m, KnownNat n, KnownShS sh, GoodScalar r, AstSpan s)
            => AstTensor AstMethodLet s (TKS (m ': sh) r) -> AstTensor AstMethodLet s (TKS (n ': sh) r)
            -> AstTensor AstMethodLet s (TKS ((m + n) ': sh) r)
 astAppendS (AstConcrete _ u) (AstConcrete _ v) =
-  AstConcrete (FTKS knownShS FTKScalar) $ RepN $ tappendS (unRepN u) (unRepN v)
+  AstConcrete (FTKS knownShS FTKScalar) $ sappend u v
 astAppendS (Ast.AstFromPrimal u) (Ast.AstFromPrimal v) =
   Ast.AstFromPrimal $ astAppendS u v
 astAppendS (Ast.AstFromVectorS l1) (Ast.AstFromVectorS l2) =
@@ -1780,7 +1781,7 @@ astSlice :: forall k s r. (KnownNat k, GoodScalar r, AstSpan s)
          => Int -> Int -> AstTensor AstMethodLet s (TKR (1 + k) r)
          -> AstTensor AstMethodLet s (TKR (1 + k) r)
 astSlice i n (AstConcrete (FTKR (_ :$: sh) FTKScalar) t) =
-  AstConcrete (FTKR (n :$: sh) FTKScalar) $ RepN $ tsliceR i n (unRepN t)
+  AstConcrete (FTKR (n :$: sh) FTKScalar) $ rslice i n t
 astSlice i n (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astSlice i n v
 astSlice 0 n v | n == lengthAst v = v
 astSlice _i n (Ast.AstReplicate @y2 _ v) = case stensorKind @y2 of
@@ -1817,7 +1818,7 @@ astSliceS :: forall i n k sh s r.
           => AstTensor AstMethodLet s (TKS (i + n + k ': sh) r)
           -> AstTensor AstMethodLet s (TKS (n ': sh) r)
 astSliceS (AstConcrete _ t) =
-  AstConcrete (FTKS knownShS FTKScalar) $ RepN $ tsliceS @i @n (unRepN t)
+  AstConcrete (FTKS knownShS FTKScalar) $ sslice (Proxy @i) (Proxy @n) t
 astSliceS (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astSliceS @i @n v
 astSliceS v | Just Refl <- sameNat (Proxy @i) (Proxy @0)
             , Just Refl <- sameNat (Proxy @k) (Proxy @0) = v
@@ -1857,7 +1858,7 @@ astSliceS v = Ast.AstSliceS @i v
 astReverse :: forall n s r. (KnownNat n, TensorKind2 r, AstSpan s)
            => AstTensor AstMethodLet s (TKR2 (1 + n) r)
            -> AstTensor AstMethodLet s (TKR2 (1 + n) r)
-astReverse (AstConcrete ftk t) = AstConcrete ftk $ RepN $ treverseR (unRepN t)
+astReverse (AstConcrete ftk t) = AstConcrete ftk $ rreverse t
 astReverse (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astReverse v
 astReverse (Ast.AstReplicate k v) = astReplicate k v
 astReverse (Ast.AstFromVector l) = astFromVector $ V.reverse l
@@ -1872,7 +1873,7 @@ astReverse v = Ast.AstReverse v
 astReverseS :: forall n sh s r. (KnownNat n, KnownShS sh, TensorKind2 r, AstSpan s)
             => AstTensor AstMethodLet s (TKS2 (n ': sh) r)
             -> AstTensor AstMethodLet s (TKS2 (n ': sh) r)
-astReverseS (AstConcrete ftk t) = AstConcrete ftk $ RepN $ treverseS (unRepN t)
+astReverseS (AstConcrete ftk t) = AstConcrete ftk $ sreverse t
 astReverseS (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astReverseS v
 astReverseS (Ast.AstReplicate k v) = astReplicate k v
 astReverseS (Ast.AstFromVectorS l) = astFromVectorS $ V.reverse l
@@ -1918,7 +1919,7 @@ astTranspose perm = \case
     -- TODO: should the below be backpermute or permute?
     astGatherR (Nested.Internal.Shape.shrPermutePrefix perm sh) v
                (Nested.Internal.Shape.listrPermutePrefix perm vars, ix)
-  AstConcrete (FTKR sh FTKScalar) t -> AstConcrete (FTKR (Nested.Internal.Shape.shrPermutePrefix perm sh) FTKScalar) $ RepN $ ttransposeR perm (unRepN t)
+  AstConcrete (FTKR sh FTKScalar) t -> AstConcrete (FTKR (Nested.Internal.Shape.shrPermutePrefix perm sh) FTKScalar) $ rtranspose perm t
   Ast.AstFromPrimal v -> Ast.AstFromPrimal $ astTranspose perm v
   u -> Ast.AstTranspose perm u
     -- we don't go inside AstSumOfList, because they are usually long
@@ -2074,7 +2075,7 @@ astReshape shOut = \case
   Ast.AstFromVector l | [x] <- V.toList l -> astReshape shOut x
   Ast.AstReshape _ v -> astReshape shOut v
   AstConcrete (FTKR _ x) t -> AstConcrete (FTKR shOut x)
-                              $ RepN $ Nested.rreshape shOut (unRepN t)
+                              $ rreshape shOut t
   Ast.AstFromPrimal v -> Ast.AstFromPrimal $ astReshape shOut v
   v -> let shIn = shapeAst v
        in case sameNat (Proxy @p) (Proxy @m) of
@@ -2104,7 +2105,7 @@ astReshapeS = \case
     astReshapeS $ l V.! 0
   Ast.AstReshapeS v -> astReshapeS @_ @sh2 v
   AstConcrete (FTKS _ x) t -> AstConcrete (FTKS knownShS x)
-                              $ RepN $ treshapeS (unRepN t)
+                              $ sreshape t
   Ast.AstFromPrimal v -> Ast.AstFromPrimal $ astReshapeS v
   v -> case sameShape @sh @sh2 of
          Just Refl -> v
@@ -2112,7 +2113,7 @@ astReshapeS = \case
 
 astCast :: (GoodScalar r1, GoodScalar r2, RealFrac r1, RealFrac r2)
         => AstTensor ms s (TKScalar r1) -> AstTensor ms s (TKScalar r2)
-astCast (AstConcrete FTKScalar t) = AstConcrete FTKScalar $ RepN $ realToFrac (unRepN t)
+astCast (AstConcrete FTKScalar t) = AstConcrete FTKScalar $ kcast t
 astCast (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astCast v
 astCast (Ast.AstCast v) = astCast v
 astCast (Ast.AstFromIntegral v) = astFromIntegral v
@@ -2120,7 +2121,7 @@ astCast v = Ast.AstCast v
 
 astCastR :: (KnownNat n, GoodScalar r1, GoodScalar r2, RealFrac r1, RealFrac r2)
         => AstTensor AstMethodLet s (TKR n r1) -> AstTensor AstMethodLet s (TKR n r2)
-astCastR (AstConcrete (FTKR sh FTKScalar) t) = AstConcrete (FTKR sh FTKScalar) $ RepN $ tcastR (unRepN t)
+astCastR (AstConcrete (FTKR sh FTKScalar) t) = AstConcrete (FTKR sh FTKScalar) $ rcast t
 astCastR (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astCastR v
 astCastR (Ast.AstCastR v) = astCastR v
 astCastR (Ast.AstFromIntegralR v) = astFromIntegralR v
@@ -2129,7 +2130,7 @@ astCastR v = Ast.AstCastR v
 astCastS :: ( KnownShS sh, GoodScalar r1, GoodScalar r2, RealFrac r1
             , RealFrac r2 )
          => AstTensor AstMethodLet s (TKS sh r1) -> AstTensor AstMethodLet s (TKS sh r2)
-astCastS (AstConcrete (FTKS sh FTKScalar) t) = AstConcrete (FTKS sh FTKScalar) $ RepN $ tcastS (unRepN t)
+astCastS (AstConcrete (FTKS sh FTKScalar) t) = AstConcrete (FTKS sh FTKScalar) $ scast t
 astCastS (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astCastS v
 astCastS (Ast.AstCastS v) = astCastS v
 astCastS (Ast.AstFromIntegralS v) = astFromIntegralS v
@@ -2138,21 +2139,21 @@ astCastS v = Ast.AstCastS v
 astFromIntegral :: (GoodScalar r1, GoodScalar r2, Integral r1)
                 => AstTensor ms PrimalSpan (TKScalar r1)
                 -> AstTensor ms PrimalSpan (TKScalar r2)
-astFromIntegral (AstConcrete FTKScalar t) = AstConcrete FTKScalar $ RepN $ fromIntegral (unRepN t)
+astFromIntegral (AstConcrete FTKScalar t) = AstConcrete FTKScalar $ kfromIntegral t
 astFromIntegral (Ast.AstFromIntegral v) = astFromIntegral v
 astFromIntegral v = Ast.AstFromIntegral v
 
 astFromIntegralR :: (KnownNat n, GoodScalar r1, GoodScalar r2, Integral r1)
                 => AstTensor AstMethodLet PrimalSpan (TKR n r1)
                 -> AstTensor AstMethodLet PrimalSpan (TKR n r2)
-astFromIntegralR (AstConcrete (FTKR sh FTKScalar) t) = AstConcrete (FTKR sh FTKScalar) $ RepN $ tfromIntegralR (unRepN t)
+astFromIntegralR (AstConcrete (FTKR sh FTKScalar) t) = AstConcrete (FTKR sh FTKScalar) $ rfromIntegral t
 astFromIntegralR (Ast.AstFromIntegralR v) = astFromIntegralR v
 astFromIntegralR v = Ast.AstFromIntegralR v
 
 astFromIntegralS :: (KnownShS sh, GoodScalar r1, GoodScalar r2, Integral r1)
                  => AstTensor AstMethodLet PrimalSpan (TKS sh r1)
                  -> AstTensor AstMethodLet PrimalSpan (TKS sh r2)
-astFromIntegralS (AstConcrete (FTKS sh FTKScalar) t) = AstConcrete (FTKS sh FTKScalar) $ RepN $ tfromIntegralS (unRepN t)
+astFromIntegralS (AstConcrete (FTKS sh FTKScalar) t) = AstConcrete (FTKS sh FTKScalar) $ sfromIntegral t
 astFromIntegralS (Ast.AstFromIntegralS v) = astFromIntegralS v
 astFromIntegralS v = Ast.AstFromIntegralS v
 
@@ -2215,8 +2216,8 @@ astRFromS :: forall sh s r. (TensorKind1 r, KnownShS sh)
 astRFromS (AstConcrete ftk t)
  | Dict <- lemKnownNatRankS (knownShS @sh) = case ftk of
   FTKS _ x ->
-    let u = Nested.stoRanked (unRepN t)
-    in AstConcrete (FTKR (Nested.rshape u) x) (RepN u)
+    let u = rfromS t
+    in AstConcrete (FTKR (rshape u) x) u
 astRFromS (Ast.AstFromPrimal v)
  | Dict <- lemKnownNatRankS (knownShS @sh) =
   Ast.AstFromPrimal $ astRFromS v
@@ -2229,8 +2230,8 @@ astRFromX :: forall sh s r. (TensorKind1 r, KnownShX sh)
 astRFromX (AstConcrete ftk t)
  | Dict <- lemKnownNatRankX (knownShX @sh) = case ftk of
   FTKX _ x ->
-    let u = Nested.mtoRanked (unRepN t)
-    in AstConcrete (FTKR (Nested.rshape u) x) (RepN u)
+    let u = rfromX t
+    in AstConcrete (FTKR (rshape u) x) u
 astRFromX (Ast.AstFromPrimal v)
  | Dict <- lemKnownNatRankX (knownShX @sh) =
   Ast.AstFromPrimal $ astRFromX v
@@ -2242,8 +2243,8 @@ astSFromR :: forall sh s r. (TensorKind1 r, KnownShS sh, KnownNat (Rank sh))
           -> AstTensor AstMethodLet s (TKS2 sh r)
 astSFromR (AstConcrete ftk t) = case ftk of
   FTKR _ x ->
-    AstConcrete (FTKS knownShS x) $ RepN
-    $ Nested.rcastToShaped (unRepN t) Nested.knownShS
+    let u = sfromR t
+    in AstConcrete (FTKS knownShS x) u
 astSFromR (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astSFromR v
 astSFromR (Ast.AstRFromS @sh1 v) =
   case sameShape @sh1 @sh of
@@ -2257,8 +2258,8 @@ astSFromX :: forall sh sh' s r.
           -> AstTensor AstMethodLet s (TKS2 sh r)
 astSFromX (AstConcrete ftk t) = case ftk of
   FTKX _ x ->
-    AstConcrete (FTKS knownShS x)
-    $ RepN $ Nested.mcastToShaped (unRepN t) Nested.knownShS
+    let u = sfromX t
+    in AstConcrete (FTKS knownShS x) u
 astSFromX (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astSFromX v
 astSFromX (Ast.AstXFromS @sh1 v) =
   case sameShape @sh1 @sh of
@@ -2272,8 +2273,8 @@ astXFromR :: forall sh s r.
           -> AstTensor AstMethodLet s (TKX2 sh r)
 astXFromR (AstConcrete ftk t) = case ftk of
   FTKR _ x ->
-    let u = Nested.rcastToMixed (knownShX @sh) (unRepN t)
-    in AstConcrete (FTKX (Nested.mshape u) x) (RepN u)
+    let u = xfromR t
+    in AstConcrete (FTKX (xshape u) x) u
 astXFromR (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astXFromR v
 astXFromR v = Ast.AstXFromR v
 
@@ -2283,8 +2284,8 @@ astXFromS :: forall sh sh' s r.
           -> AstTensor AstMethodLet s (TKX2 sh' r)
 astXFromS (AstConcrete ftk t) = case ftk of
   FTKS _ x ->
-    let u = Nested.scastToMixed (knownShX @sh') (unRepN t)
-    in AstConcrete (FTKX (Nested.mshape u) x) (RepN u)
+    let u = xfromS t
+    in AstConcrete (FTKX (xshape u) x) u
 astXFromS (Ast.AstFromPrimal v) = Ast.AstFromPrimal $ astXFromS v
 -- impossible, shapes may differ: astXFromS (Ast.AstSFromX v) = v
 astXFromS v = Ast.AstXFromS v
@@ -2763,7 +2764,7 @@ astFromScalar t = case t of
   Ast.AstToScalar u -> u
   Ast.AstCond b a2 a3 -> Ast.AstCond b (astFromScalar a2) (astFromScalar a3)
   AstConcrete FTKScalar (RepN v) ->
-    AstConcrete (FTKS ZSS FTKScalar) $ RepN $ Nested.sscalar v
+    AstConcrete (FTKS ZSS FTKScalar) $ sscalar v
   AstN1 opCode u -> AstN1S opCode (astFromScalar u)
   AstN2 opCode u v -> AstN2S opCode (astFromScalar u) (astFromScalar v)
 -- TODO:  Ast.AstR1 opCode u -> Ast.AstR1S opCode (astFromScalar u)
diff --git a/src/HordeAd/Core/TensorClass.hs b/src/HordeAd/Core/TensorClass.hs
index e48f5da66..22abe0e40 100644
--- a/src/HordeAd/Core/TensorClass.hs
+++ b/src/HordeAd/Core/TensorClass.hs
@@ -175,7 +175,7 @@ class ( Num (IntOf target)
       => BaseTensor (target :: Target) where
 
   -- Integer codomain
-  rshape :: TensorKind2 r => target (TKR2 n r) -> IShR n
+  rshape :: TensorKind1 r => target (TKR2 n r) -> IShR n
   rrank :: forall r n. (TensorKind2 r, KnownNat n) => target (TKR2 n r) -> Int
   rrank _ = valueOf @n
   rsize :: TensorKind2 r => target (TKR2 n r) -> Int