I want to understand the type system of the Julia language. The following situation I find confusing:
Consider the chain of sub/super-types
Rational{Int64} <: Rational <: Real <: Number <: Any
which (in my mind) corresponds to a path in the type tree starting at the concrete type Rational{Int64} and going up to the top. Now, if I call supertype(Rational) I get Real as expected. However, when I call supertype(Rational{Int64}) I get Real, too. The supertype function seems to 'jump' over Rational. This seems very counter-intuitive to me.
Can anyone explain this behaviour?
In Julia, only DataTypes participate in inheritance. If a type does not have all of its generic type parameters specified, as with Rational (short for Rational{T} where T<:Integer), then it is not a DataType but a UnionAll, and since a UnionAll is not actually a type, it does not participate in inheritance.
julia> Rational === Rational{T} where T<:Integer
true
julia> typeof.((Rational{Int}, Rational, Real))
(DataType, UnionAll, DataType)