Base.isconcretetype incorrect for Type{T}?

[MilesCranmer]

I saw the following weird behaviour on https://discourse.julialang.org/t/ann-dispatchdoctor-jl-offers-you-a-prescription-for-type-stability/114837/35

julia> Base.isconcretetype(Type{Float32})
false

I think this could be a bug? The definition states:

Determine whether type T is a concrete type, meaning it could have direct instances (values x such that typeof(x) === T).

However, typeof(T) returns a DataType rather than Type{Float32}. But the docstring for DataType says DataType <: Type{T}. So I'm confused.

If this indeed a bug I think it's because the @nospecialize here was implemented without expecting such an input:

isconcretetype(@nospecialize(t)) = (@_total_meta; isa(t, DataType) && (t.flags & 0x0002) == 0x0002)

The solution would be to add a

isconcretetype(::Type{Type{T}}) where {T} = isconcretetype(T)

whose recursion would automatically deal with Type{Type{Float32}} and so on.

But obviously this would be a massive breaking change so wouldn't be possible. So I guess I'm just looking for some clarification :)

[martinholters]

The subtyping relationship is Type{Float32} <: DataType <: Type, and as you've discovered yourself, typeof(Float32)==DataType, so neither Type{Float32} nor Type are concrete, but DataType is.

What's confusing indeed is the DataType <: Type{T} in the docstring. While DataType <: Type{T} where T is true (and just a more verbose form of DataType <: Type), for any actual T, DataType <: Type{T} does not hold.

[MilesCranmer]

Got it, thanks.