New blog post about Julia parametric types and constructors

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This sentence from the blog post should be corrected, it’s incorrect, or at least highly misleading:

Parametric types can be highly efficient when the type T is concrete (i.e., not abstract).

The issue is that “abstract” is ambiguous, in Julia it sometimes refers to any non-concrete type, but it’s AFAIK more proper to use it to refer merely to types declared with abstract type. The latter meaning is the one used by isabstracttype. Thus isconcretetype and isabstracttype are not opposites.

EDIT (more than three consecutive replies are not allowed):

A visualization of Julia’s subtyping might also be educational. Given these example Julia types:

abstract type PointSupertype0 end
abstract type PointSupertype1{T} <: PointSupertype0 end

struct Point{T} <: PointSupertype1{T} end

types = (
    Point, PointSupertype0, PointSupertype1,
    PointSupertype1{Int}, PointSupertype1{<:Int},
    PointSupertype1{Float64}, PointSupertype1{<:Float64},
    Point{Int}, Point{<:Int}, Point{Float64}, Point{<:Float64},
    Point{Union{Int, Float64}}, Point{<:Union{Int, Float64}},
    Union{Point{Int}, Point{Float64}},
    Union{Point{<:Int}, Point{<:Float64}},
)

… a Julia script makes a digraph from the subtyping relation, does transitive reduction on it, then produces this GraphViz Dot specification for visualizing:

digraph='
digraph {
    "Point" -> "PointSupertype1"
    "PointSupertype1" -> "PointSupertype0"
    "PointSupertype1{<:Float64}" -> "PointSupertype1"
    "PointSupertype1{<:Int64}" -> "PointSupertype1"
    "PointSupertype1{Float64}" -> "PointSupertype1{<:Float64}"
    "PointSupertype1{Int64}" -> "PointSupertype1{<:Int64}"
    "Point{<:Float64}" -> "PointSupertype1{<:Float64}"
    "Point{<:Float64}" -> "Union{Point{<:Int64}, Point{<:Float64}}"
    "Point{<:Int64}" -> "PointSupertype1{<:Int64}"
    "Point{<:Int64}" -> "Union{Point{<:Int64}, Point{<:Float64}}"
    "Point{<:Union{Float64, Int64}}" -> "Point"
    "Point{Float64}" -> "PointSupertype1{Float64}"
    "Point{Float64}" -> "Point{<:Float64}"
    "Point{Float64}" -> "Union{Point{Float64}, Point{Int64}}"
    "Point{Int64}" -> "PointSupertype1{Int64}"
    "Point{Int64}" -> "Point{<:Int64}"
    "Point{Int64}" -> "Union{Point{Float64}, Point{Int64}}"
    "Point{Union{Float64, Int64}}" -> "Point{<:Union{Float64, Int64}}"
    "Union{Point{<:Int64}, Point{<:Float64}}" -> "Point{<:Union{Float64, Int64}}"
    "Union{Point{Float64}, Point{Int64}}" -> "Union{Point{<:Int64}, Point{<:Float64}}"
}
'
printf '%s' "$digraph" | dot -Tpng > /tmp/graphviz.png

This is the result:

graphviz
graphviz1931×635 62.2 KB

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