#515 replaced permute(compose(permute(A, pA), permute(B, pB)), pAB) with a helper whose signature pins both hom-spaces to one elementary space type S. This breaks contractions of tensors with mixed elementary space types, for example when contracting a BlockTensorMap with a TensorMap (observed when trying to run MPSKit.jl off the current TensorKit.jl main).

For example:

using TensorKit, BlockTensorKit, TensorOperations

V = Vect[FermionParity ⊠ U1Irrep]((0, 0) => 2, (1, 1) => 2, (1, -1) => 2)
Vsum = SumSpace(V, V)

GL = rand(ComplexF64, Vsum ⊗ Vsum ← SumSpace(V))   # BlockTensorMap, (2, 1)
A  = rand(ComplexF64, V ← V ⊗ V)                   # plain TensorMap,  (1, 2)

@tensor y[-1 -2; -3 -4] := GL[-1 -2; 1] * A[1; -3 -4]

results in

MethodError: no method matching _contractedspace(::TensorMapSpace{SumSpace{…}, 2, 1}, …, ::TensorMapSpace{GradedSpace{…}, 1, 2}, …)

This adds a generic fallback for _contractedspace which composes the intermediate spaces.