diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index 0ba8fbebacf91..e26eb5be263b0 100644
--- a/base/abstractarray.jl
+++ b/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)