Continuum indices

So I can define a function f(x)=x^2, x∈[0,1] by

julia> f=Inclusion(0..1).^2
(Inclusion(0..1)) .^ 2

Then I want to do composition, say, g(x)=f(f(x)). But currently I'm not allowed to do:

julia> g=f[f]
ERROR: MethodError: no method matching Int64(::Infinities.InfiniteCardinal{1})
Closest candidates are:
  (::Type{T})(::T) where T<:Number at boot.jl:760
  (::Type{T})(::AbstractChar) where T<:Union{AbstractChar, Number} at char.jl:50
  (::Type{T})(::BigInt) where T<:Union{Int128, Int16, Int32, Int64, Int8} at gmp.jl:356
  ...
Stacktrace:
  [1] union!(s::Set{Float64}, itr::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}})
    @ Base .\abstractset.jl:93
  [2] Set{Float64}(itr::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}})
    @ Base .\set.jl:10
  [3] _Set(itr::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, #unused#::Base.HasEltype)
    @ Base .\set.jl:23
  [4] Set(itr::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}})
    @ Base .\set.jl:21
  [5] issubset(l::QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}}, r::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}})
    @ Base .\abstractset.jl:279
  [6] checkindex(#unused#::Type{Bool}, inds::Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, i::QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}})
    @ QuasiArrays C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\indices.jl:203
  [7] checkbounds_indices
    @ .\abstractarray.jl:642 [inlined]
  [8] checkbounds
    @ C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\abstractquasiarray.jl:275 [inlined]
  [9] checkbounds
    @ C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\abstractquasiarray.jl:287 [inlined]
 [10] view
    @ C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\subquasiarray.jl:68 [inlined]
 [11] layout_getindex
    @ C:\Users\pty\.julia\packages\ArrayLayouts\3lnt1\src\ArrayLayouts.jl:109 [inlined]
 [12] _getindex(#unused#::Type, #unused#::IndexCartesian, A::QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}}, I::Tuple{QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}}})
    @ QuasiArrays C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\abstractquasiarray.jl:384
 [13] _getindex
    @ C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\abstractquasiarray.jl:375 [inlined]
 [14] getindex(A::QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}}, I::QuasiArrays.BroadcastQuasiVector{Float64, typeof(Base.literal_pow), Tuple{Base.RefValue{typeof(^)}, Inclusion{Float64, IntervalSets.ClosedInterval{Int64}}, Base.RefValue{Val{2}}}})
    @ QuasiArrays C:\Users\pty\.julia\packages\QuasiArrays\bxqu9\src\abstractquasiarray.jl:370
 [15] top-level scope
    @ none:1

Can we have this feature?

Reproduce the failure with Inclusion(0..1).^2 and f[f], then inspect the QuasiArrays indexing path shown in src/indices.jl and src/abstractquasiarray.jl, along with the ArrayLayouts call site. The feature is done when composing the continuum-indexed function works without the reported InfiniteCardinal conversion error and existing indexing behavior remains intact.