Improve shape inference in cat

`cat` is frequently called with poor inference, since one only has
to concatenate a couple of different container types before inference
punts on the result type. While this does not make the return type
in mixed container types fully inferrable, it does improve the analysis
of the shape.

base/abstractarray.jl

@@ -1437,15 +1437,15 @@ vcat(V::AbstractVector{T}...) where {T} = typed_vcat(T, V...)
 AbstractVecOrTuple{T} = Union{AbstractVector{<:T}, Tuple{Vararg{T}}}
 
 function _typed_vcat(::Type{T}, V::AbstractVecOrTuple{AbstractVector}) where T
-    n::Int = 0
+    n = 0
     for Vk in V
-        n += length(Vk)
+        n += Int(length(Vk))::Int
     end
     a = similar(V[1], T, n)
     pos = 1
-    for k=1:length(V)
+    for k=1:Int(length(V))::Int
         Vk = V[k]
-        p1 = pos+length(Vk)-1
+        p1 = pos + Int(length(Vk))::Int - 1
         a[pos:p1] = Vk
         pos = p1+1
     end
@@ -1507,7 +1507,7 @@ function _typed_vcat(::Type{T}, A::AbstractVecOrTuple{AbstractVecOrMat}) where T
     pos = 1
     for k=1:nargs
         Ak = A[k]
-        p1 = pos+size(Ak,1)-1
+        p1 = pos+size(Ak,1)::Int-1
         B[pos:p1, :] = Ak
         pos = p1+1
     end
@@ -1585,17 +1585,18 @@ end
 _cat(dims, X...) = cat_t(promote_eltypeof(X...), X...; dims=dims)
 
 @inline cat_t(::Type{T}, X...; dims) where {T} = _cat_t(dims, T, X...)
-@inline function _cat_t(dims, T::Type, X...)
+@inline function _cat_t(dims, ::Type{T}, X...) where {T}
     catdims = dims2cat(dims)
-    shape = cat_shape(catdims, map(cat_size, X))
+    shape = cat_shape(catdims, map(cat_size, X)::Tuple{Vararg{Union{Int,Dims}}})::Dims
     A = cat_similar(X[1], T, shape)
-    if count(!iszero, catdims) > 1
+    if count(!iszero, catdims)::Int > 1
         fill!(A, zero(T))
     end
     return __cat(A, shape, catdims, X...)
 end
 
-function __cat(A, shape::NTuple{N}, catdims, X...) where N
+function __cat(A, shape::NTuple{M,Int}, catdims, X...) where M
+    N = M::Int
     offsets = zeros(Int, N)
     inds = Vector{UnitRange{Int}}(undef, N)
     concat = copyto!(zeros(Bool, N), catdims)
@@ -1702,8 +1703,8 @@ julia> hcat(x, [1; 2; 3])
 """
 hcat(X...) = cat(X...; dims=Val(2))
 
-typed_vcat(T::Type, X...) = cat_t(T, X...; dims=Val(1))
-typed_hcat(T::Type, X...) = cat_t(T, X...; dims=Val(2))
+typed_vcat(::Type{T}, X...) where T = cat_t(T, X...; dims=Val(1))
+typed_hcat(::Type{T}, X...) where T = cat_t(T, X...; dims=Val(2))
 
 """
     cat(A...; dims=dims)