diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index 327815fde932c..9c88f1f96cc87 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -86,7 +86,7 @@ julia> axes(A)
 """
 function axes(A)
     @_inline_meta
-    map(OneTo, size(A))
+    map(oneto, size(A))
 end
 
 """
@@ -107,10 +107,10 @@ require_one_based_indexing(A...) = !has_offset_axes(A...) || throw(ArgumentError
 # in other applications.
 axes1(A::AbstractArray{<:Any,0}) = OneTo(1)
 axes1(A::AbstractArray) = (@_inline_meta; axes(A)[1])
-axes1(iter) = OneTo(length(iter))
+axes1(iter) = oneto(length(iter))
 
 unsafe_indices(A) = axes(A)
-unsafe_indices(r::AbstractRange) = (OneTo(unsafe_length(r)),) # Ranges use checked_sub for size
+unsafe_indices(r::AbstractRange) = (oneto(unsafe_length(r)),) # Ranges use checked_sub for size
 
 keys(a::AbstractArray) = CartesianIndices(axes(a))
 keys(a::AbstractVector) = LinearIndices(a)
@@ -308,7 +308,7 @@ function eachindex(A::AbstractArray, B::AbstractArray...)
     @_inline_meta
     eachindex(IndexStyle(A,B...), A, B...)
 end
-eachindex(::IndexLinear, A::AbstractArray) = (@_inline_meta; OneTo(length(A)))
+eachindex(::IndexLinear, A::AbstractArray) = (@_inline_meta; oneto(length(A)))
 eachindex(::IndexLinear, A::AbstractVector) = (@_inline_meta; axes1(A))
 function eachindex(::IndexLinear, A::AbstractArray, B::AbstractArray...)
     @_inline_meta
@@ -1483,12 +1483,11 @@ vcat(V::AbstractVector{T}...) where {T} = typed_vcat(T, V...)
 # but that solution currently fails (see #27188 and #27224)
 AbstractVecOrTuple{T} = Union{AbstractVector{<:T}, Tuple{Vararg{T}}}
 
-function _typed_vcat(::Type{T}, V::AbstractVecOrTuple{AbstractVector}) where T
-    n = 0
-    for Vk in V
-        n += Int(length(Vk))::Int
-    end
-    a = similar(V[1], T, n)
+_typed_vcat_similar(V, T, n) = similar(V[1], T, n)
+_typed_vcat(::Type{T}, V::AbstractVecOrTuple{AbstractVector}) where T =
+    _typed_vcat!(_typed_vcat_similar(V, T, mapreduce(length, +, V)), V)
+
+function _typed_vcat!(a::AbstractVector{T}, V::AbstractVecOrTuple{AbstractVector}) where T
     pos = 1
     for k=1:Int(length(V))::Int
         Vk = V[k]
@@ -1634,7 +1633,7 @@ _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, ::Type{T}, X...) where {T}
     catdims = dims2cat(dims)
-    shape = cat_shape(catdims, map(cat_size, X)::Tuple{Vararg{Union{Int,Dims}}})::Dims
+    shape = cat_shape(catdims, map(cat_size, X))
     A = cat_similar(X[1], T, shape)
     if count(!iszero, catdims)::Int > 1
         fill!(A, zero(T))
@@ -1642,7 +1641,7 @@ _cat(dims, X...) = cat_t(promote_eltypeof(X...), X...; dims=dims)
     return __cat(A, shape, catdims, X...)
 end
 
-function __cat(A, shape::NTuple{M,Int}, catdims, X...) where M
+function __cat(A, shape::NTuple{M}, catdims, X...) where M
     N = M::Int
     offsets = zeros(Int, N)
     inds = Vector{UnitRange{Int}}(undef, N)
diff --git a/base/arrayshow.jl b/base/arrayshow.jl
index f355d9e2dd8b4..37adaf13f669e 100644
--- a/base/arrayshow.jl
+++ b/base/arrayshow.jl
@@ -58,9 +58,9 @@ Alignment is reported as a vector of (left,right) tuples, one for each
 column going across the screen.
 """
 function alignment(io::IO, X::AbstractVecOrMat,
-        rows::AbstractVector, cols::AbstractVector,
-        cols_if_complete::Integer, cols_otherwise::Integer, sep::Integer)
-    a = Tuple{Int, Int}[]
+        rows::AbstractVector{T}, cols::AbstractVector{V},
+        cols_if_complete::Integer, cols_otherwise::Integer, sep::Integer) where {T,V}
+    a = Tuple{T, V}[]
     for j in cols # need to go down each column one at a time
         l = r = 0
         for i in rows # plumb down and see what largest element sizes are
@@ -166,6 +166,11 @@ function print_matrix(io::IO, @nospecialize(X::AbstractVecOrMat),
                       vdots::AbstractString = "\u22ee",
                       ddots::AbstractString = "  \u22f1  ",
                       hmod::Integer = 5, vmod::Integer = 5)
+    # use invokelatest to avoid backtracing in type invalidation, ref #37741
+    invokelatest(_print_matrix, io, X, pre, sep, post, hdots, vdots, ddots, hmod, vmod, unitrange(axes(X,1)), unitrange(axes(X,2)))
+end
+
+function _print_matrix(io, @nospecialize(X::AbstractVecOrMat), pre, sep, post, hdots, vdots, ddots, hmod, vmod, rowsA, colsA)
     hmod, vmod = Int(hmod)::Int, Int(vmod)::Int
     if !(get(io, :limit, false)::Bool)
         screenheight = screenwidth = typemax(Int)
@@ -178,7 +183,6 @@ function print_matrix(io::IO, @nospecialize(X::AbstractVecOrMat),
     postsp = ""
     @assert textwidth(hdots) == textwidth(ddots)
     sepsize = length(sep)::Int
-    rowsA, colsA = UnitRange{Int}(axes(X,1)), UnitRange{Int}(axes(X,2))
     m, n = length(rowsA), length(colsA)
     # To figure out alignments, only need to look at as many rows as could
     # fit down screen. If screen has at least as many rows as A, look at A.
diff --git a/base/range.jl b/base/range.jl
index b275e95c7c266..63f4c1aed02e2 100644
--- a/base/range.jl
+++ b/base/range.jl
@@ -295,6 +295,8 @@ unitrange_last(start::T, stop::T) where {T} =
     ifelse(stop >= start, convert(T,start+floor(stop-start)),
                           convert(T,start-oneunit(stop-start)))
 
+unitrange(x) = UnitRange(x)
+
 if isdefined(Main, :Base)
     # Constant-fold-able indexing into tuples to functionally expose Base.tail and Base.front
     function getindex(@nospecialize(t::Tuple), r::UnitRange)
@@ -332,6 +334,7 @@ struct OneTo{T<:Integer} <: AbstractUnitRange{T}
 end
 OneTo(stop::T) where {T<:Integer} = OneTo{T}(stop)
 OneTo(r::AbstractRange{T}) where {T<:Integer} = OneTo{T}(r)
+oneto(r) = OneTo(r)
 
 ## Step ranges parameterized by length
 
diff --git a/base/reshapedarray.jl b/base/reshapedarray.jl
index 3534049a7a10b..d9a9f4eafaa80 100644
--- a/base/reshapedarray.jl
+++ b/base/reshapedarray.jl
@@ -153,7 +153,7 @@ rdims(out::Tuple{}, inds::NTuple{M,Any}) where {M} = ()
 rdims(out::Tuple{Any}, inds::Tuple{}) = out # N == 1, M == 0
 rdims(out::NTuple{N,Any}, inds::Tuple{}) where {N} = out # N > 1, M == 0
 rdims(out::Tuple{Any}, inds::Tuple{Any}) = inds # N == 1, M == 1
-rdims(out::Tuple{Any}, inds::NTuple{M,Any}) where {M} = (OneTo(rdims_trailing(inds...)),) # N == 1, M > 1
+rdims(out::Tuple{Any}, inds::NTuple{M,Any}) where {M} = (oneto(rdims_trailing(inds...)),) # N == 1, M > 1
 rdims(out::NTuple{N,Any}, inds::NTuple{N,Any}) where {N} = inds # N > 1, M == N
 rdims(out::NTuple{N,Any}, inds::NTuple{M,Any}) where {N,M} = (first(inds), rdims(tail(out), tail(inds))...) # N > 1, M > 1, M != N
 
@@ -207,7 +207,7 @@ size(A::ReshapedArray) = A.dims
 similar(A::ReshapedArray, eltype::Type, dims::Dims) = similar(parent(A), eltype, dims)
 IndexStyle(::Type{<:ReshapedArrayLF}) = IndexLinear()
 parent(A::ReshapedArray) = A.parent
-parentindices(A::ReshapedArray) = map(OneTo, size(parent(A)))
+parentindices(A::ReshapedArray) = map(oneto, size(parent(A)))
 reinterpret(::Type{T}, A::ReshapedArray, dims::Dims) where {T} = reinterpret(T, parent(A), dims)
 elsize(::Type{<:ReshapedArray{<:Any,<:Any,P}}) where {P} = elsize(P)
 
diff --git a/base/subarray.jl b/base/subarray.jl
index 3b232d896d3c0..d1207ec094037 100644
--- a/base/subarray.jl
+++ b/base/subarray.jl
@@ -60,7 +60,7 @@ viewindexing(I::Tuple{Vararg{Any}}) = IndexCartesian()
 viewindexing(I::Tuple{AbstractArray, Vararg{Any}}) = IndexCartesian()
 
 # Simple utilities
-size(V::SubArray) = (@_inline_meta; map(n->Int(unsafe_length(n)), axes(V)))
+size(V::SubArray) = (@_inline_meta; map(unsafe_length, axes(V)))
 
 similar(V::SubArray, T::Type, dims::Dims) = similar(V.parent, T, dims)
 
@@ -90,7 +90,7 @@ julia> parentindices(V)
 (1, Base.Slice(Base.OneTo(2)))
 ```
 """
-parentindices(a::AbstractArray) = map(OneTo, size(a))
+parentindices(a::AbstractArray) = map(oneto, size(a))
 
 ## Aliasing detection
 dataids(A::SubArray) = (dataids(A.parent)..., _splatmap(dataids, A.indices)...)
@@ -107,7 +107,7 @@ function unaliascopy(V::SubArray{T,N,A,I,LD}) where {T,N,A<:Array,I<:Tuple{Varar
 end
 # Transform indices to be "dense"
 _trimmedindex(i::Real) = oftype(i, 1)
-_trimmedindex(i::AbstractUnitRange) = oftype(i, OneTo(length(i)))
+_trimmedindex(i::AbstractUnitRange) = oftype(i, oneto(length(i)))
 _trimmedindex(i::AbstractArray) = oftype(i, reshape(eachindex(IndexLinear(), i), axes(i)))
 
 ## SubArray creation
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index 958e62e1ecdc1..6d052bfb9a2ae 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -1234,6 +1234,11 @@ end
     @test Base.rest(a, st) == [3, 2, 4]
 end
 
+@testset "issue #37741, non-int cat" begin
+    @test [1; 1:BigInt(5)] == [1; 1:5]
+    @test [1:BigInt(5); 1] == [1:5; 1]
+end
+
 @testset "Base.isstored" begin
     a = rand(3, 4, 5)
     @test Base.isstored(a, 1, 2, 3)
diff --git a/test/subarray.jl b/test/subarray.jl
index 4fd189e2ae441..985b481438c5b 100644
--- a/test/subarray.jl
+++ b/test/subarray.jl
@@ -698,3 +698,17 @@ import InteractiveUtils
     @test M*v == copy(M)*v
     @test (InteractiveUtils.@which M*v) == (InteractiveUtils.@which copy(M)*v)
 end
+
+
+isdefined(Main, :InfiniteArrays) || @eval Main include("testhelpers/InfiniteArrays.jl")
+using .Main.InfiniteArrays, Base64
+
+@testset "PR #37741: non-Int sizes" begin
+    r = BigInt(1):BigInt(100_000_000)^100
+    v = SubArray(r, (r,))
+    @test size(v) == (last(r),)
+
+    v = SubArray(OneToInf(), (OneToInf(),))
+    @test size(v) == (Infinity(),)
+    @test stringmime("text/plain", v; context=(:limit => true)) == "$(Infinity())-element view(::$(OneToInf{Int}), 1:1:$(Infinity())) with eltype $Int with indices 1:1:$(Infinity()):\n  1\n  2\n  3\n  4\n  5\n  6\n  7\n  8\n  9\n 10\n  ⋮"
+end
diff --git a/test/testhelpers/InfiniteArrays.jl b/test/testhelpers/InfiniteArrays.jl
new file mode 100644
index 0000000000000..bc6de1afc5503
--- /dev/null
+++ b/test/testhelpers/InfiniteArrays.jl
@@ -0,0 +1,51 @@
+# This file is a part of Julia. License is MIT: https://julialang.org/license
+
+# InfiniteArrays (arrays with infinite size)
+
+# This test file is designed to exercise support for generic sizing,
+# even though infinite arrays aren't implemented in Base.
+
+module InfiniteArrays
+
+export OneToInf, Infinity
+
+"""
+   Infinity()
+
+represents infinite cardinality. Note that `Infinity <: Integer` to support
+being treated as an index.
+"""
+struct Infinity <: Integer end
+
+Base.:(==)(::Infinity, ::Int) = false
+Base.:(==)(::Int, ::Infinity) = false
+Base.:(<)(::Int, ::Infinity) = true
+Base.:(≤)(::Int, ::Infinity) = true
+Base.:(≤)(::Infinity, ::Int) = false
+Base.:(≤)(::Infinity, ::Infinity) = true
+Base.:(-)(::Infinity, ::Int) = Infinity()
+Base.:(+)(::Infinity, ::Int) = Infinity()
+Base.:(:)(::Infinity, ::Infinity) = 1:0
+
+"""
+    OneToInf(n)
+
+Define an `AbstractInfUnitRange` that behaves like `1:∞`, with the added
+distinction that the limits are guaranteed (by the type system) to
+be 1 and ∞.
+"""
+struct OneToInf{T<:Integer} <: AbstractUnitRange{T} end
+
+OneToInf() = OneToInf{Int}()
+
+Base.axes(r::OneToInf) = (r,)
+Base.unsafe_indices(r::OneToInf) = (r,)
+Base.unsafe_length(r::OneToInf) = Infinity()
+Base.size(r::OneToInf) = (Infinity(),)
+Base.first(r::OneToInf{T}) where {T} = oneunit(T)
+Base.length(r::OneToInf{T}) where {T} = Infinity()
+Base.last(r::OneToInf{T}) where {T} = Infinity()
+Base.unitrange(r::OneToInf) = r
+Base.oneto(::Infinity) = OneToInf()
+
+end
\ No newline at end of file