What is difference between Type{T} and T

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Am I right in thinking that Type{<:T} is equivalent to the set of objects that are either at level T or lower according to <: ?
For instance

julia> DataType isa Type{Any}
false

julia> DataType isa Type{<:Any}
true

Assuming you are right, then you have shown that, the restriction of isa to the image of Type{<: } is isomorphic to <: . In other words, you have succeeded in “embedding” <: in isa. This is nice. What it does not provide is a characterisation of isa.

@goretkin

Note that it’s not the case that all the nodes have that self-loop, rather DataType is unique in that way. So it’s not that the relation R(a, b) = (a == typeof(b)) is reflexive. It is most certainly not.

Great, so this establishes that <: is not a partial order. Further clarification on what you mean by “unique” would be useful:

julia> DataType <: DataType
true

julia> Any <: Any
true

julia> Type <: Type
true

julia> Int <: Int
true

Is isa is characterised by typeof? if so, then we get reflexivity in the sense that, for every object x

julia> x isa typeof(x)
true