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subtype.jl
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subtype.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
using Base.Bottom
using Base.Test
macro UnionAll(var, expr)
Expr(:where, esc(expr), esc(var))
end
const issub = issubtype
issub_strict(x::ANY,y::ANY) = issub(x,y) && !issub(y,x)
isequal_type(x::ANY,y::ANY) = issub(x,y) && issub(y,x)
notequal_type(x::ANY,y::ANY) = !isequal_type(x, y)
_type_intersect(x::ANY, y::ANY) = ccall(:jl_intersect_types, Any, (Any, Any), x, y)
intersection_env(x::ANY, y::ANY) = ccall(:jl_env_from_type_intersection, Any, (Any,Any), x, y)
# level 1: no varags, union, UnionAll
function test_1()
@test issub_strict(Int, Integer)
@test issub_strict(Array{Int,1}, AbstractArray{Int,1})
@test isequal_type(Int, Int)
@test isequal_type(Integer, Integer)
@test isequal_type(Array{Int,1}, Array{Int,1})
@test isequal_type(AbstractArray{Int,1}, AbstractArray{Int,1})
@test issub_strict(Tuple{Int,Int}, Tuple{Integer,Integer})
@test issub_strict(Tuple{Array{Int,1}}, Tuple{AbstractArray{Int,1}})
@test isequal_type(Tuple{Integer,Integer}, Tuple{Integer,Integer})
@test !issub(Tuple{Int,Int}, Tuple{Int})
@test !issub(Tuple{Int}, Tuple{Integer,Integer})
@test !issub(Array{Int,1}, Array{Integer,1})
end
# level 2: varargs
function test_2()
@test issub_strict(Tuple{Int,Int}, Tuple{Vararg{Int}})
@test issub_strict(Tuple{Int,Int}, Tuple{Int,Vararg{Int}})
@test issub_strict(Tuple{Int,Int}, Tuple{Int,Vararg{Integer}})
@test issub_strict(Tuple{Int,Int}, Tuple{Int,Int,Vararg{Integer}})
@test issub_strict(Tuple{Int,Vararg{Int}}, Tuple{Vararg{Int}})
@test issub_strict(Tuple{Int,Int,Int}, Tuple{Vararg{Int}})
@test issub_strict(Tuple{Int,Int,Int}, Tuple{Integer,Vararg{Int}})
@test issub_strict(Tuple{Int}, Tuple{Any})
@test issub_strict(Tuple{}, Tuple{Vararg{Any}})
@test isequal_type(Tuple{Int}, Tuple{Int})
@test isequal_type(Tuple{Vararg{Integer}}, Tuple{Vararg{Integer}})
@test !issub(Tuple{}, Tuple{Int, Vararg{Int}})
@test !issub(Tuple{Int}, Tuple{Int, Int, Vararg{Int}})
@test !issub(Tuple{Int, Tuple{Real, Integer}}, Tuple{Vararg{Int}})
@test isequal_type(Tuple{Int,Int}, Tuple{Vararg{Int,2}})
@test Tuple{Int,Vararg{Int,2}} == Tuple{Int,Int,Int}
@test Tuple{Int,Vararg{Int,2}} === Tuple{Int,Int,Int}
@test Tuple{Any, Any} === Tuple{Vararg{Any,2}}
@test Tuple{Int,Vararg{Int,2}} == Tuple{Int,Int,Vararg{Int,1}}
@test Tuple{Int,Vararg{Int,2}} == Tuple{Int,Int,Int,Vararg{Int,0}}
@test !(Tuple{Int,Vararg{Int,2}} <: Tuple{Int,Int,Int,Vararg{Int,1}})
@test Tuple{Int,Vararg{Int}} == Tuple{Int,Vararg{Int}}
@test (@UnionAll N Tuple{Int,Vararg{Int,N}}) == (@UnionAll N Tuple{Int,Vararg{Int,N}})
@test issub_strict(Tuple{Tuple{Int,Int},Tuple{Int,Int}}, Tuple{NTuple{N,Int},NTuple{N,Int}} where N)
@test !issub(Tuple{Tuple{Int,Int},Tuple{Int,}}, Tuple{NTuple{N,Int},NTuple{N,Int}} where N)
@test NTuple{0} === Tuple{}
@test issub_strict(Tuple{Int,Int}, Tuple{Int,Int,Vararg{Int,N}} where N)
@test issub_strict(Tuple{Int,Int}, Tuple{E,E,Vararg{E,N}} where E where N)
@test issub(Type{Tuple{VecElement{Bool}}}, (Type{Tuple{Vararg{VecElement{T},N}}} where T where N))
@test isequal_type(Type{Tuple{Vararg{Int,N}} where N}, Type{Tuple{Vararg{Int,N} where N}})
@test Type{Tuple{Vararg{Int,N}} where N} !== Type{Tuple{Vararg{Int,N} where N}}
end
function test_diagonal()
@test !issub(Tuple{Integer,Integer}, @UnionAll T Tuple{T,T})
@test issub(Tuple{Integer,Int}, (@UnionAll T @UnionAll S<:T Tuple{T,S}))
@test issub(Tuple{Integer,Int}, (@UnionAll T @UnionAll T<:S<:T Tuple{T,S}))
@test !issub(Tuple{Integer,Int,Int}, (@UnionAll T @UnionAll T<:S<:T Tuple{T,S,S}))
@test issub_strict((@UnionAll R Tuple{R,R}),
(@UnionAll T @UnionAll S Tuple{T,S}))
@test issub_strict((@UnionAll R Tuple{R,R}),
(@UnionAll T @UnionAll S<:T Tuple{T,S}))
@test issub_strict((@UnionAll R Tuple{R,R}),
(@UnionAll T @UnionAll T<:S<:T Tuple{T,S}))
@test issub_strict((@UnionAll R Tuple{R,R}),
(@UnionAll T @UnionAll S>:T Tuple{T,S}))
@test !issub(Tuple{Real,Real}, @UnionAll T<:Real Tuple{T,T})
@test issub((@UnionAll S<:Int (@UnionAll R<:AbstractString Tuple{S,R,Vector{Any}})),
(@UnionAll T Tuple{T, T, Array{T,1}}))
@test issub_strict(Tuple{String, Real, Ref{Number}},
(@UnionAll T Tuple{Union{T,String}, T, Ref{T}}))
@test issub_strict(Tuple{String, Real},
(@UnionAll T Tuple{Union{T,String}, T}))
@test !issub( Tuple{Real, Real},
(@UnionAll T Tuple{Union{T,String}, T}))
@test issub_strict(Tuple{Int, Int},
(@UnionAll T Tuple{Union{T,String}, T}))
# don't consider a diagonal variable concrete if it already has an abstract lower bound
@test isequal_type(Tuple{Vararg{A}} where A>:Integer,
Tuple{Vararg{A}} where A>:Integer)
end
# level 3: UnionAll
function test_3()
@test issub_strict(Array{Int,1}, @UnionAll T Vector{T})
@test issub_strict((@UnionAll T Pair{T,T}), Pair)
@test issub(Pair{Int,Int8}, Pair)
@test issub(Pair{Int,Int8}, (@UnionAll S Pair{Int,S}))
@test !issub((@UnionAll T<:Real T), (@UnionAll T<:Integer T))
@test isequal_type((@UnionAll T Tuple{T,T}), (@UnionAll R Tuple{R,R}))
@test !issub((@UnionAll T<:Integer @UnionAll S<:Number Tuple{T,S}),
(@UnionAll T<:Integer @UnionAll S<:Number Tuple{S,T}))
@test issub_strict((@UnionAll T Tuple{Array{T},Array{T}}),
Tuple{Array, Array})
AUA = Array{(@UnionAll T Array{T,1}), 1}
UAA = (@UnionAll T Array{Array{T,1}, 1})
@test !issub(AUA, UAA)
@test !issub(UAA, AUA)
@test !isequal_type(AUA, UAA)
@test issub_strict((@UnionAll T Int), (@UnionAll T<:Integer Integer))
@test isequal_type((@UnionAll T @UnionAll S Tuple{T, Tuple{S}}),
(@UnionAll T Tuple{T, @UnionAll S Tuple{S}}))
@test !issub((@UnionAll T Pair{T,T}), Pair{Int,Int8})
@test !issub((@UnionAll T Pair{T,T}), Pair{Int,Int})
@test isequal_type((@UnionAll T Tuple{T}), Tuple{Any})
@test isequal_type((@UnionAll T<:Real Tuple{T}), Tuple{Real})
@test issub(Tuple{Array{Integer,1}, Int},
@UnionAll T<:Integer @UnionAll S<:T Tuple{Array{T,1},S})
@test !issub(Tuple{Array{Integer,1}, Real},
@UnionAll T<:Integer Tuple{Array{T,1},T})
@test !issub(Tuple{Int,String,Vector{Integer}},
@UnionAll T Tuple{T, T, Array{T,1}})
@test !issub(Tuple{String,Int,Vector{Integer}},
@UnionAll T Tuple{T, T, Array{T,1}})
@test !issub(Tuple{Int,String,Vector{Tuple{Integer}}},
@UnionAll T Tuple{T,T,Array{Tuple{T},1}})
@test issub(Tuple{Int,String,Vector{Any}},
@UnionAll T Tuple{T, T, Array{T,1}})
@test isequal_type(Array{Int,1}, Array{(@UnionAll T<:Int T), 1})
@test isequal_type(Array{Tuple{Any},1}, Array{(@UnionAll T Tuple{T}), 1})
@test isequal_type(Array{Tuple{Int,Int},1},
Array{(@UnionAll T<:Int Tuple{T,T}), 1})
@test !issub(Array{Tuple{Int,Integer},1},
Array{(@UnionAll T<:Integer Tuple{T,T}), 1})
@test !issub(Pair{Int,Int8}, (@UnionAll T Pair{T,T}))
@test !issub(Tuple{Array{Int,1}, Integer},
@UnionAll T<:Integer Tuple{Array{T,1},T})
@test !issub(Tuple{Integer, Array{Int,1}},
@UnionAll T<:Integer Tuple{T, Array{T,1}})
@test !issub(Pair{Array{Int,1},Integer}, @UnionAll T Pair{Array{T,1},T})
@test issub(Pair{Array{Int,1},Int}, @UnionAll T Pair{Array{T,1},T})
@test issub(Tuple{Integer,Int}, @UnionAll T<:Integer @UnionAll S<:T Tuple{T,S})
@test !issub(Tuple{Integer,Int}, @UnionAll T<:Int @UnionAll S<:T Tuple{T,S})
@test !issub(Tuple{Integer,Int}, @UnionAll T<:String @UnionAll S<:T Tuple{T,S})
@test issub(Tuple{Float32,Array{Float32,1}},
@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S})
@test !issub(Tuple{Float32,Array{Float64,1}},
@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S})
@test issub(Tuple{Float32,Array{Real,1}},
@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S})
@test !issub(Tuple{Number,Array{Real,1}},
@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S})
@test issub((@UnionAll Int<:T<:Integer T), @UnionAll T<:Real T)
@test issub((@UnionAll Int<:T<:Integer Array{T,1}),
(@UnionAll T<:Real Array{T,1}))
@test issub((@UnionAll Int<:T<:Integer T), (@UnionAll Integer<:T<:Real T))
@test !issub((@UnionAll Int<:T<:Integer Array{T,1}), (@UnionAll Integer<:T<:Real Array{T,1}))
X = (@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S})
Y = (@UnionAll A<:Real @UnionAll B<:AbstractArray{A,1} Tuple{A,B})
@test isequal_type(X,Y)
Z = (@UnionAll A<:Real @UnionAll B<:AbstractArray{A,1} Tuple{Real,B})
@test issub_strict(X,Z)
@test issub_strict((@UnionAll T @UnionAll S<:T Pair{T,S}),
(@UnionAll T @UnionAll S Pair{T,S}))
@test issub_strict((@UnionAll T @UnionAll S>:T Pair{T,S}),
(@UnionAll T @UnionAll S Pair{T,S}))
# these would be correct if the diagonal rule applied to type vars occurring
# only once in covariant position.
#@test issub_strict((@UnionAll T Tuple{Ref{T}, T}),
# (@UnionAll T @UnionAll S<:T Tuple{Ref{T},S}))
#@test issub_strict((@UnionAll T Tuple{Ref{T}, T}),
# (@UnionAll T @UnionAll S<:T @UnionAll R<:S Tuple{Ref{T},R}))
@test isequal_type((@UnionAll T Tuple{Ref{T}, T}),
(@UnionAll T @UnionAll T<:S<:T Tuple{Ref{T},S}))
@test issub_strict((@UnionAll T Tuple{Ref{T}, T}),
(@UnionAll T @UnionAll S>:T Tuple{Ref{T}, S}))
A = @UnionAll T Tuple{T,Ptr{T}}
B = @UnionAll T Tuple{Ptr{T},T}
C = @UnionAll T>:Ptr @UnionAll S>:Ptr Tuple{Ptr{T},Ptr{S}}
D = @UnionAll T>:Ptr @UnionAll S>:Ptr{T} Tuple{Ptr{T},Ptr{S}}
E = @UnionAll T>:Ptr @UnionAll S>:Ptr{T} Tuple{Ptr{S},Ptr{T}}
@test !issub(A, B)
@test !issub(B, A)
@test issub_strict(C, A)
@test issub_strict(C, B)
@test issub_strict(C, D)
@test issub_strict(Union{D,E}, A)
@test issub_strict(Union{D,E}, B)
@test issub_strict((@UnionAll T>:Ptr @UnionAll Ptr<:S<:Ptr Tuple{Ptr{T},Ptr{S}}),
(@UnionAll T>:Ptr @UnionAll S>:Ptr{T} Tuple{Ptr{T},Ptr{S}}))
@test !issub((@UnionAll T>:Ptr @UnionAll S>:Ptr Tuple{Ptr{T},Ptr{S}}),
(@UnionAll T>:Ptr @UnionAll Ptr{T}<:S<:Ptr Tuple{Ptr{T},Ptr{S}}))
@test !issub((@UnionAll T>:Integer @UnionAll S>:Ptr Tuple{Ptr{T},Ptr{S}}), B)
@test issub((@UnionAll T>:Ptr @UnionAll S>:Integer Tuple{Ptr{T},Ptr{S}}), B)
end
# level 4: Union
function test_4()
@test isequal_type(Union{Bottom,Bottom}, Bottom)
@test issub_strict(Int, Union{Int,String})
@test issub_strict(Union{Int,Int8}, Integer)
@test isequal_type(Union{Int,Int8}, Union{Int,Int8})
@test isequal_type(Union{Int,Integer}, Integer)
@test isequal_type(Tuple{Union{Int,Int8},Int16}, Union{Tuple{Int,Int16},Tuple{Int8,Int16}})
@test issub_strict(Tuple{Int,Int8,Int}, Tuple{Vararg{Union{Int,Int8}}})
@test issub_strict(Tuple{Int,Int8,Int}, Tuple{Vararg{Union{Int,Int8,Int16}}})
# nested unions
@test !issub(Union{Int,Ref{Union{Int,Int8}}}, Union{Int,Ref{Union{Int8,Int16}}})
A = Int64; B = Int8
C = Int16; D = Int32
@test issub(Union{Union{A,Union{A,Union{B,C}}}, Union{D,Bottom}},
Union{Union{A,B},Union{C,Union{B,D}}})
@test !issub(Union{Union{A,Union{A,Union{B,C}}}, Union{D,Bottom}},
Union{Union{A,B},Union{C,Union{B,A}}})
@test isequal_type(Union{Union{A,B,C}, Union{D}}, Union{A,B,C,D})
@test isequal_type(Union{Union{A,B,C}, Union{D}}, Union{A,Union{B,C},D})
@test isequal_type(Union{Union{Union{Union{A}},B,C}, Union{D}},
Union{A,Union{B,C},D})
@test issub_strict(Union{Union{A,C}, Union{D}}, Union{A,B,C,D})
@test !issub(Union{Union{A,B,C}, Union{D}}, Union{A,C,D})
# obviously these unions can be simplified, but when they aren't there's trouble
X = Union{Union{A,B,C},Union{A,B,C},Union{A,B,C},Union{A,B,C},
Union{A,B,C},Union{A,B,C},Union{A,B,C},Union{A,B,C}}
Y = Union{Union{D,B,C},Union{D,B,C},Union{D,B,C},Union{D,B,C},
Union{D,B,C},Union{D,B,C},Union{D,B,C},Union{A,B,C}}
@test issub_strict(X,Y)
end
# level 5: union and UnionAll
function test_5()
u = Union{Int8,Int}
@test issub(Tuple{String,Array{Int,1}},
(@UnionAll T Union{Tuple{T,Array{T,1}}, Tuple{T,Array{Int,1}}}))
@test issub(Tuple{Union{Vector{Int},Vector{Int8}}},
@UnionAll T Tuple{Array{T,1}})
@test !issub(Tuple{Union{Vector{Int},Vector{Int8}},Vector{Int}},
@UnionAll T Tuple{Array{T,1}, Array{T,1}})
@test !issub(Tuple{Union{Vector{Int},Vector{Int8}},Vector{Int8}},
@UnionAll T Tuple{Array{T,1}, Array{T,1}})
@test !issub(Vector{Int}, @UnionAll T>:u Array{T,1})
@test issub(Vector{Integer}, @UnionAll T>:u Array{T,1})
@test issub(Vector{Union{Int,Int8}}, @UnionAll T>:u Array{T,1})
@test issub((@UnionAll Int<:T<:u Array{T,1}), (@UnionAll Int<:T<:u Array{T,1}))
# with varargs
@test !issub(Array{Tuple{Array{Int},Array{Vector{Int16}},Array{Vector{Int}},Array{Int}}},
@UnionAll T<:(@UnionAll S Tuple{Vararg{Union{Array{S}, Array{Array{S,1}}}}}) Array{T})
@test issub(Array{Tuple{Array{Int},Array{Vector{Int}},Array{Vector{Int}},Array{Int}}},
@UnionAll T<:(@UnionAll S Tuple{Vararg{Union{Array{S}, Array{Array{S,1}}}}}) Array{T})
@test !issub(Tuple{Array{Int},Array{Vector{Int16}},Array{Vector{Int}},Array{Int}},
@UnionAll S Tuple{Vararg{Union{Array{S},Array{Array{S,1}}}}})
@test issub(Tuple{Array{Int},Array{Vector{Int}},Array{Vector{Int}},Array{Int}},
@UnionAll S Tuple{Vararg{Union{Array{S},Array{Array{S,1}}}}})
B = @UnionAll S<:u Tuple{S, Tuple{Any,Any,Any}, Ref{S}}
# these tests require renaming in issub_unionall
@test issub((@UnionAll T<:B Tuple{Int8, T, Ref{Int8}}), B)
@test !issub((@UnionAll T<:B Tuple{Int8, T, Ref{T}}), B)
# the `convert(Type{T},T)` pattern, where T is a Union
# required changing priority of unions and vars
@test issub(Tuple{Array{u,1},Int}, @UnionAll T Tuple{Array{T,1}, T})
@test issub(Tuple{Array{u,1},Int}, @UnionAll T @UnionAll S<:T Tuple{Array{T,1}, S})
@test !issub(Ref{Union{Ref{Int},Ref{Int8}}}, @UnionAll T Ref{Ref{T}})
@test issub(Tuple{Union{Ref{Int},Ref{Int8}}}, @UnionAll T Tuple{Ref{T}})
@test !issub(Ref{Union{Ref{Int},Ref{Int8}}}, Union{Ref{Ref{Int}}, Ref{Ref{Int8}}})
@test isequal_type(Ref{Tuple{Union{Int,Int8},Int16}}, Ref{Union{Tuple{Int,Int16},Tuple{Int8,Int16}}})
@test isequal_type(Ref{T} where T<:Tuple{Union{Int,Int8},Int16},
Ref{T} where T<:Union{Tuple{Int,Int16},Tuple{Int8,Int16}})
@test isequal_type(Ref{Tuple{Union{Int,Int8},Int16,T}} where T,
Ref{Union{Tuple{Int,Int16,S},Tuple{Int8,Int16,S}}} where S)
end
# tricky type variable lower bounds
function test_6()
@test issub((@UnionAll S<:Int (@UnionAll R<:String Tuple{S,R,Vector{Any}})),
(@UnionAll T Tuple{T, T, Array{T,1}}))
@test !issub((@UnionAll S<:Int (@UnionAll R<:String Tuple{S,R,Vector{Integer}})),
(@UnionAll T Tuple{T, T, Array{T,1}}))
t = @UnionAll T Tuple{T,T,Ref{T}}
@test isequal_type(t, @UnionAll S Tuple{S,S,Ref{S}})
@test !issub((@UnionAll T Tuple{T,String,Ref{T}}), (@UnionAll T Tuple{T,T,Ref{T}}))
@test !issub((@UnionAll T Tuple{T,Ref{T},String}), (@UnionAll T Tuple{T,Ref{T},T}))
i = Int; ai = Integer
@test isequal_type((@UnionAll i<:T<:i Ref{T}), Ref{i})
@test isequal_type((@UnionAll ai<:T<:ai Ref{T}), Ref{ai})
# Pair{T,S} <: Pair{T,T} can be true with certain bounds
@test issub_strict((@UnionAll i<:T<:i @UnionAll i<:S<:i Pair{T,S}),
@UnionAll T Pair{T,T})
@test issub_strict(Tuple{i, Ref{i}},
(@UnionAll T @UnionAll S<:T Tuple{S,Ref{T}}))
@test !issub(Tuple{Real, Ref{i}},
(@UnionAll T @UnionAll S<:T Tuple{S,Ref{T}}))
# S >: T
@test issub_strict(Tuple{Real, Ref{i}},
(@UnionAll T @UnionAll S>:T Tuple{S,Ref{T}}))
@test !issub(Tuple{Ref{i}, Ref{ai}},
(@UnionAll T @UnionAll S>:T Tuple{Ref{S},Ref{T}}))
@test issub_strict(Tuple{Ref{Real}, Ref{ai}},
(@UnionAll T @UnionAll S>:T Tuple{Ref{S},Ref{T}}))
@test issub_strict(Tuple{Real, Ref{Tuple{i}}},
(@UnionAll T @UnionAll S>:T Tuple{S,Ref{Tuple{T}}}))
@test !issub(Tuple{Ref{Tuple{i}}, Ref{Tuple{ai}}},
(@UnionAll T @UnionAll S>:T Tuple{Ref{Tuple{S}},Ref{Tuple{T}}}))
@test issub_strict(Tuple{Ref{Tuple{Real}}, Ref{Tuple{ai}}},
(@UnionAll T @UnionAll S>:T Tuple{Ref{Tuple{S}},Ref{Tuple{T}}}))
# (@UnionAll x<:T<:x Q{T}) == Q{x}
@test isequal_type(Ref{Ref{i}}, Ref{@UnionAll i<:T<:i Ref{T}})
@test isequal_type(Ref{Ref{i}}, @UnionAll i<:T<:i Ref{Ref{T}})
@test isequal_type((@UnionAll i<:T<:i Ref{Ref{T}}), Ref{@UnionAll i<:T<:i Ref{T}})
@test !issub((@UnionAll i<:T<:i Ref{Ref{T}}), Ref{@UnionAll T<:i Ref{T}})
u = Union{Int8,Int64}
A = Ref{Bottom}
B = @UnionAll S<:u Ref{S}
@test issub(Ref{B}, @UnionAll A<:T<:B Ref{T})
C = @UnionAll S<:u S
@test issub(Ref{C}, @UnionAll u<:T<:u Ref{T})
BB = @UnionAll S<:Bottom S
@test issub(Ref{B}, @UnionAll BB<:U<:B Ref{U})
end
# uncategorized
function test_7()
@test isequal_type(Ref{Union{Int16, T}} where T, Ref{Union{Int16, S}} where S)
@test isequal_type(Pair{Union{Int16, T}, T} where T, Pair{Union{Int16, S}, S} where S)
end
function test_Type()
@test issub_strict(DataType, Type)
@test issub_strict(Union, Type)
@test issub_strict(UnionAll, Type)
@test issub_strict(typeof(Bottom), Type)
@test !issub(TypeVar, Type)
@test !issub(Type, TypeVar)
@test !issub(DataType, @UnionAll T<:Number Type{T})
@test issub_strict(Type{Int}, DataType)
@test !issub((@UnionAll T<:Integer Type{T}), DataType)
@test isequal_type(Type{AbstractArray}, Type{AbstractArray})
@test !issub(Type{Int}, Type{Integer})
@test issub((@UnionAll T<:Integer Type{T}), (@UnionAll T<:Number Type{T}))
@test isa(Int, @UnionAll T<:Number Type{T})
@test !isa(DataType, @UnionAll T<:Number Type{T})
@test DataType <: (@UnionAll T<:Type Type{T})
@test isa(Tuple{},Type{Tuple{}})
@test !(Tuple{Int,} <: (@UnionAll T<:Tuple Type{T}))
@test isa(Tuple{Int}, (@UnionAll T<:Tuple Type{T}))
# this matches with T==DataType, since DataType is concrete
@test issub(Tuple{Type{Int},Type{Int8}}, Tuple{T,T} where T)
@test !issub(Tuple{Type{Int},Type{Union{}}}, Tuple{T,T} where T)
# issue #20476
@test issub(Tuple{Type{Union{Type{UInt32}, Type{UInt64}}}, Type{UInt32}}, Tuple{Type{T},T} where T)
@test isequal_type(Core.TypeofBottom, Type{Union{}})
@test issub(Core.TypeofBottom, Type{T} where T<:Real)
end
# old subtyping tests from test/core.jl
function test_old()
@test Int8 <: Integer
@test Int32 <: Integer
@test Tuple{Int8,Int8} <: Tuple{Integer,Integer}
@test !(AbstractArray{Float64,2} <: AbstractArray{Number,2})
@test !(AbstractArray{Float64,1} <: AbstractArray{Float64,2})
@test Tuple{Integer,Vararg{Integer}} <: Tuple{Integer,Vararg{Real}}
@test Tuple{Integer,Float64,Vararg{Integer}} <: Tuple{Integer,Vararg{Number}}
@test Tuple{Integer,Float64} <: Tuple{Integer,Vararg{Number}}
@test Tuple{Int32,} <: Tuple{Vararg{Number}}
@test Tuple{} <: Tuple{Vararg{Number}}
@test !(Tuple{Vararg{Int32}} <: Tuple{Int32,})
@test !(Tuple{Vararg{Int32}} <: Tuple{Number,Integer})
@test !(Tuple{Vararg{Integer}} <: Tuple{Integer,Integer,Vararg{Integer}})
@test !(Array{Int8,1} <: Array{Any,1})
@test !(Array{Any,1} <: Array{Int8,1})
@test Array{Int8,1} <: Array{Int8,1}
@test !(Type{Bottom} <: Type{Int32})
@test !(Vector{Float64} <: Vector{Union{Float64,Float32}})
@test !isa(Array,Type{Any})
@test Type{Complex} <: UnionAll
@test isa(Complex,Type{Complex})
@test !(Type{Ptr{Bottom}} <: Type{Ptr})
@test !(Type{Rational{Int}} <: Type{Rational})
@test Tuple{} <: Tuple{Vararg}
@test Tuple{Int,Int} <: Tuple{Vararg}
@test Tuple{} <: @UnionAll N NTuple{N}
@test !(Type{Tuple{}} <: Type{Tuple{Vararg}})
@test Type{Tuple{}} <: (@UnionAll N Type{NTuple{N}})
@test !(Type{Array{Integer}} <: Type{AbstractArray{Integer}})
@test !(Type{Array{Integer}} <: Type{@UnionAll T<:Integer Array{T}})
# issue #6561
# TODO: note that NTuple now means "tuples of all the same type"
#@test issubtype(Array{Tuple}, Array{NTuple})
@test issub_strict(NTuple, Tuple)
@test issub_strict(NTuple, Tuple{Vararg})
@test isequal_type(Tuple, Tuple{Vararg})
#@test issubtype(Array{Tuple{Vararg{Any}}}, Array{NTuple})
#@test issubtype(Array{Tuple{Vararg}}, Array{NTuple})
@test !issubtype(Type{Tuple{Void}}, Tuple{Type{Void}})
end
const menagerie =
Any[Bottom, Any, Int, Int8, Integer, Real,
Array{Int,1}, AbstractArray{Int,1},
Tuple{Int,Vararg{Integer}}, Tuple{Integer,Vararg{Int}}, Tuple{},
Union{Int,Int8},
(@UnionAll T Array{T,1}),
(@UnionAll T Pair{T,T}),
(@UnionAll T @UnionAll S Pair{T,S}),
Pair{Int,Int8},
(@UnionAll S Pair{Int,S}),
(@UnionAll T Tuple{T,T}),
(@UnionAll T<:Integer Tuple{T,T}),
(@UnionAll T @UnionAll S Tuple{T,S}),
(@UnionAll T<:Integer @UnionAll S<:Number Tuple{T,S}),
(@UnionAll T<:Integer @UnionAll S<:Number Tuple{S,T}),
Array{(@UnionAll T Array{T,1}),1},
(@UnionAll T Array{Array{T,1},1}),
Array{(@UnionAll T<:Int T), 1},
(@UnionAll T<:Real @UnionAll S<:AbstractArray{T,1} Tuple{T,S}),
Union{Int,Ref{Union{Int,Int8}}},
(@UnionAll T Union{Tuple{T,Array{T,1}}, Tuple{T,Array{Int,1}}}),
]
let new = Any[]
# add variants of each type
for T in menagerie
push!(new, Ref{T})
push!(new, Tuple{T})
push!(new, Tuple{T,T})
push!(new, Tuple{Vararg{T}})
push!(new, @UnionAll S<:T S)
push!(new, @UnionAll S<:T Ref{S})
end
append!(menagerie, new)
end
function test_properties()
x→y = !x || y
¬T = @UnionAll X>:T Ref{X}
for T in menagerie
# top and bottom identities
@test issub(Bottom, T)
@test issub(T, Any)
@test issub(T, Bottom) → isequal_type(T, Bottom)
@test issub(Any, T) → isequal_type(T, Any)
# unionall identity
@test isequal_type(T, @UnionAll S<:T S)
@test isequal_type(Ref{T}, @UnionAll T<:U<:T Ref{U})
# equality under renaming
if isa(T, UnionAll)
lb, ub = T.var.lb, T.var.ub
@test isequal_type(T, (@UnionAll lb<:Y<:ub T{Y}))
end
# inequality under wrapping
@test !isequal_type(T, Ref{T})
for S in menagerie
issubTS = issub(T, S)
# transitivity
if issubTS
for R in menagerie
if issub(S, R)
@test issub(T, R) # issub(T,S) ∧ issub(S,R) → issub(T,R)
@test issub(Ref{S}, @UnionAll T<:U<:R Ref{U})
end
end
end
# union subsumption
@test isequal_type(T, Union{T,S}) → issub(S, T)
# invariance
@test isequal_type(T, S) == isequal_type(Ref{T}, Ref{S})
# covariance
@test issubTS == issub(Tuple{T}, Tuple{S})
@test issubTS == issub(Tuple{Vararg{T}}, Tuple{Vararg{S}})
@test issubTS == issub(Tuple{T}, Tuple{Vararg{S}})
# pseudo-contravariance
@test issubTS == issub(¬S, ¬T)
end
end
end
macro testintersect(a, b, result)
if isa(result,Expr) && result.head === :call && length(result.args)==2 && result.args[1] === :!
result = result.args[2]
cmp = :notequal_type
else
cmp = :isequal_type
end
Base.remove_linenums!(quote
@test $(esc(cmp))(_type_intersect($(esc(a)), $(esc(b))), $(esc(result)))
@test $(esc(cmp))(_type_intersect($(esc(b)), $(esc(a))), $(esc(result)))
end)
end
abstract type IT4805_2{N, T} end
abstract type AbstractThing{T,N} end
mutable struct ConcreteThing{T<:AbstractFloat,N} <: AbstractThing{T,N}
end
mutable struct A11136 end
mutable struct B11136 end
abstract type Foo11367 end
abstract type AbstractTriangular{T,S<:AbstractMatrix} <: AbstractMatrix{T} end
struct UpperTriangular{T,S<:AbstractMatrix} <: AbstractTriangular{T,S} end
struct UnitUpperTriangular{T,S<:AbstractMatrix} <: AbstractTriangular{T,S} end
struct SIQ20671{T<:Number,m,kg,s,A,K,mol,cd,rad,sr} <: Number
val::T
end
function test_intersection()
@testintersect(Vector{Float64}, Vector{Union{Float64,Float32}}, Bottom)
@testintersect(Array{Bottom}, (@UnionAll T AbstractArray{T}), !Bottom)
@testintersect(Tuple{Type{Ptr{UInt8}}, Ptr{Bottom}},
(@UnionAll T Tuple{Type{Ptr{T}},Ptr{T}}), Bottom)
@testintersect(Tuple{Range{Int},Tuple{Int,Int}}, (@UnionAll T Tuple{AbstractArray{T},Dims}),
Tuple{Range{Int},Tuple{Int,Int}})
@testintersect((@UnionAll Integer<:T<:Number Array{T}), (@UnionAll T<:Number Array{T}),
(@UnionAll Integer<:T<:Number Array{T}))
@testintersect((@UnionAll Integer<:T<:Number Array{T}), (@UnionAll T<:Real Array{T}),
(@UnionAll Integer<:T<:Real Array{T}))
@testintersect((@UnionAll Integer<:T<:Number Array{T}), (@UnionAll T<:String Array{T}),
Bottom)
@testintersect((@UnionAll Integer<:T<:Number Array{T}), (@UnionAll String<:T<:AbstractString Array{T}),
Bottom)
@testintersect((@UnionAll T<:Number Array{T}), (@UnionAll T<:String Array{T}),
Array{Bottom})
@testintersect((@UnionAll T Tuple{T, AbstractArray{T}}), Tuple{Number, Array{Int,1}},
Tuple{Int, Array{Int,1}})
@testintersect((@UnionAll T Tuple{T, AbstractArray{T}}), Tuple{Int, Array{Number,1}},
Tuple{Int, Array{Number,1}})
@testintersect((@UnionAll S Tuple{S,Vector{S}}), (@UnionAll T<:Real Tuple{T,AbstractVector{T}}),
(@UnionAll S<:Real Tuple{S,Vector{S}}))
# typevar corresponding to a type it will end up being neither greater than nor
# less than
@testintersect((@UnionAll T Tuple{T, Ref{T}}), Tuple{Array{Int}, Ref{AbstractVector}},
Tuple{Array{Int,1}, Ref{AbstractVector}})
@testintersect((@UnionAll T Tuple{T, AbstractArray{T}}), Tuple{Any, Array{Number,1}},
Tuple{Number, Array{Number,1}})
@testintersect((@UnionAll T Tuple{Array{T}, Array{T}}), Tuple{Array, Array{Any}}, !Bottom)
@testintersect((@UnionAll T Tuple{T,T}), Tuple{Real, Real}, (@UnionAll T<:Real Tuple{T,T}))
@testintersect((@UnionAll T Tuple{T}), Tuple{Real}, Tuple{Real})
@testintersect((@UnionAll T Tuple{T,T}), Tuple{Union{Float64,Int64},Int64}, Tuple{Int64,Int64})
@testintersect((@UnionAll T Tuple{T,T}), Tuple{Int64,Union{Float64,Int64}}, Tuple{Int64,Int64})
@testintersect((@UnionAll Z Tuple{Z,Z}), (@UnionAll T<:Integer @UnionAll S<:Number Tuple{T,S}),
@UnionAll Z<:Integer Tuple{Z,Z})
@testintersect((@UnionAll Z Pair{Z,Z}), (@UnionAll T<:Integer @UnionAll S<:Number Pair{T,S}),
@UnionAll Z<:Integer Pair{Z,Z})
@testintersect((@UnionAll T<:Vector Type{T}), (@UnionAll N Type{@UnionAll S<:Number Array{S,N}}),
Type{@UnionAll S<:Number Array{S,1}})
@testintersect((@UnionAll T Tuple{Type{Array{T,1}},Array{T,1}}),
Tuple{Type{AbstractVector},Vector{Int}}, Bottom)
@testintersect(Tuple{Type{Vector{Complex128}}, AbstractVector},
(@UnionAll T @UnionAll S @UnionAll N Tuple{Type{Array{T,N}}, Array{S,N}}),
Tuple{Type{Vector{Complex128}},Vector})
@testintersect(Tuple{Type{Vector{Complex128}}, AbstractArray},
(@UnionAll T @UnionAll S @UnionAll N Tuple{Type{Array{T,N}}, Array{S,N}}),
Tuple{Type{Vector{Complex128}},Vector})
@testintersect(Type{Array}, Type{AbstractArray}, Bottom)
@testintersect(Type{Tuple{Bool,Vararg{Int}}}, Type{@UnionAll T Tuple{Vararg{T}}}, Bottom)
@testintersect(Type{Tuple{Bool,Vararg{Int}}}, Type{@UnionAll T Tuple{T,Vararg{T}}}, Bottom)
@testintersect((@UnionAll T Tuple{Vararg{T}}), Tuple{Float64,Int}, Bottom)
@testintersect((@UnionAll T Tuple{Rational{T},T}), Tuple{Rational{Integer},Int}, Tuple{Rational{Integer},Int})
@testintersect((@UnionAll T Pair{T,Ptr{T}}), (@UnionAll S Pair{Ptr{S},S}), Bottom)
@testintersect((@UnionAll T Tuple{T,Ptr{T}}), (@UnionAll S Tuple{Ptr{S},S}),
Union{(@UnionAll T>:Ptr @UnionAll S>:Ptr{T} Tuple{Ptr{T},Ptr{S}}),
(@UnionAll T>:Ptr @UnionAll S>:Ptr{T} Tuple{Ptr{S},Ptr{T}})})
@testintersect((@UnionAll N Tuple{NTuple{N,Integer},NTuple{N,Integer}}),
Tuple{Tuple{Integer,Integer}, Tuple{Vararg{Integer}}},
Tuple{Tuple{Integer,Integer}, Tuple{Integer,Integer}})
@testintersect((@UnionAll N Tuple{NTuple{N,Integer},NTuple{N,Integer}}),
Tuple{Tuple{Vararg{Integer}}, Tuple{Integer,Integer}},
Tuple{Tuple{Integer,Integer}, Tuple{Integer,Integer}})
#@test isequal_type(typeintersect((@UnionAll N Tuple{NTuple{N,Any},Array{Int,N}}),
# Tuple{Tuple{Int,Vararg{Int}},Array}),
# Tuple{Tuple{Int,Vararg{Int}},Array{Int,N}})
@testintersect((@UnionAll N Tuple{NTuple{N,Any},Array{Int,N}}),
Tuple{Tuple{Int,Vararg{Int}},Array{Int,2}},
Tuple{Tuple{Int,Int}, Array{Int,2}})
@testintersect(Type{Any},Type{Complex}, Bottom)
@testintersect(Type{Any},(@UnionAll T<:Real Type{T}), Bottom)
@testintersect(Type{Function},Union,Bottom)
@testintersect(Type{Int32}, DataType, Type{Int32})
@testintersect(DataType, Type, !Bottom)
@testintersect(Union, Type, !Bottom)
@testintersect(DataType, Type{Int}, !Bottom)
@testintersect(DataType, (@UnionAll T<:Int Type{T}), !Bottom)
@testintersect(DataType, (@UnionAll T<:Integer Type{T}), !Bottom)
@testintersect(Tuple{Vararg{Int}}, Tuple{Vararg{Bool}}, Tuple{})
@testintersect(Type{Tuple{Vararg{Int}}}, Type{Tuple{Vararg{Bool}}}, Bottom)
@testintersect(Tuple{Bool,Vararg{Int}}, Tuple{Vararg{Bool}}, Tuple{Bool})
let M = @UnionAll T<:Union{Float32,Float64} Matrix{T}
@testintersect(AbstractArray, M, M)
end
@testintersect((@UnionAll N Tuple{Array{Int,N},Vararg{Int,N}}), Tuple{Vector{Int},Real,Real,Real}, Bottom)
@testintersect((@UnionAll N Tuple{Array{Int,N},Vararg{Int,N}}), Tuple{Array{Int,0}}, Tuple{Array{Int,0}})
@testintersect((@UnionAll N Tuple{Array{Int,N},Vararg{Int,N}}), Tuple{Array{Int,2}}, Bottom)
@testintersect(Tuple{Int,Vararg{Int}}, Tuple{Int,Int,Int,Vararg{Float64}}, Tuple{Int,Int,Int})
@testintersect(Tuple{Int,Vararg{Int}}, Tuple{Int,Vararg{Float64}}, Tuple{Int})
@testintersect((@UnionAll N Tuple{Array{Int,N},Vararg{Int,N}}),
Tuple{Matrix{Int},Int,Int,Vararg{Float64}},
Tuple{Matrix{Int},Int,Int})
@testintersect((@UnionAll N Tuple{Array{Int,N},Vararg{Int,N}}),
Tuple{Matrix{Int},Int,Vararg{Float64}}, Bottom)
@testintersect(Tuple{Array{Any,1}, Tuple{Int64, Int64, Vararg{Int64, N} where N}},
Tuple{Array{T,N}, Tuple{Vararg{Int64,N}}} where N where T,
Bottom)
@testintersect((@UnionAll T<:Union{Float64,Array{Float64,1}} T), Real, Float64)
# issue #4805
@testintersect((@UnionAll T<:Int Type{IT4805_2{1,T}}),
(@UnionAll S<:(@UnionAll N IT4805_2{N,Int}) Type{S}),
!Bottom)
# issue #8851
@testintersect((@UnionAll T AbstractThing{T,2}),
ConcreteThing,
(@UnionAll T<:AbstractFloat ConcreteThing{T,2}))
# issue #11136 and #11367
@testintersect((@UnionAll T Tuple{T, T}), (@UnionAll TB<:B11136 Tuple{A11136, TB}), Bottom)
@testintersect((@UnionAll T Tuple{T, T}), (@UnionAll T2<:Foo11367 Tuple{Type{BigInt}, T2}), Bottom)
# PR #12058
@testintersect((@UnionAll N NTuple{N,Int}), (@UnionAll N NTuple{N,Float64}), Tuple{})
@testintersect((@UnionAll T Tuple{Type{T},T}), Tuple{Type{Type{Float64}},Type{Int}}, Bottom)
@testintersect((@UnionAll T T), Type{Int8}, Type{Int8})
# issue #14482
@testintersect((@UnionAll T Tuple{T}), Tuple{Type{Int8}}, Tuple{Type{Int8}})
@testintersect((@UnionAll T Tuple{Union{Int,T}, Union{Vector{T},Vector{String}}}),
Tuple{Integer, Vector{Int8}},
Tuple{Union{Int,Int8}, Vector{Int8}})
@testintersect((@UnionAll T Tuple{Union{Int,T}, Union{Vector{T},Vector{String}}}),
Tuple{Int8, Vector{String}},
Tuple{Int8, Vector{String}})
@testintersect((@UnionAll T Tuple{Union{Int,T}, Union{Vector{T},Vector{String}}}),
Tuple{Int, Vector{Int8}},
Tuple{Int, Vector{Int8}})
@testintersect(( Tuple{Union{Int,String}, Union{Ref{Int}, Ref{String}}}),
(@UnionAll T Tuple{T, Union{Ref{T}, Ref{String}}}),
Union{Tuple{Int, Union{Ref{Int},Ref{String}}},
Tuple{String, Ref{String}}})
@testintersect((@UnionAll Z<:(@UnionAll T @UnionAll S Tuple{T,S}) Ref{Z}),
(@UnionAll X<:(@UnionAll T Tuple{T,T}) Ref{X}),
(@UnionAll X<:(@UnionAll T Tuple{T,T}) Ref{X}))
@testintersect(Ref{@UnionAll T @UnionAll S Tuple{T,S}},
Ref{@UnionAll T Tuple{T,T}}, Bottom)
@testintersect(Tuple{T,T} where T<:Union{UpperTriangular, UnitUpperTriangular},
Tuple{AbstractArray{T,N}, AbstractArray{T,N}} where N where T,
Union{Tuple{T,T} where T<:UpperTriangular,
Tuple{T,T} where T<:UnitUpperTriangular})
@testintersect(DataType, Type, DataType)
@testintersect(DataType, Type{T} where T<:Integer, Type{T} where T<:Integer)
@testintersect(Union{DataType,Int}, Type, DataType)
@testintersect(Union{DataType,Int}, Type{T} where T, DataType)
# test typeintersect wrapper as well as _type_intersect
@test typeintersect(Union{DataType,Int}, Type) === DataType
@test typeintersect(Union{DataType,Int}, Type{T} where T) === DataType
# since TypeofBottom is a singleton we can deduce its intersection with Type{...}
@testintersect(Core.TypeofBottom, (Type{T} where T<:Tuple), Type{Union{}})
@testintersect((Type{Tuple{Vararg{T}}} where T), Type{Tuple}, Bottom)
@testintersect(Tuple{Type{S}, Tuple{Any, Vararg{Any}}} where S<:Tuple{Any, Vararg{Any}},
Tuple{Type{T}, T} where T,
Tuple{Type{S},S} where S<:Tuple{Any,Vararg{Any,N} where N})
# part of issue #20450
@testintersect(Tuple{Array{Ref{T}, 1}, Array{Pair{M, V}, 1}} where V where T where M,
Tuple{Array{Ref{T}, 1}, Array{Pair{M, T}, 1}, SS} where T where M where SS,
Union{})
@testintersect(Tuple{Array{Ref{T}, 1}, Array{Pair{M, V}, 1}, Int} where V where T where M,
Tuple{Array{Ref{T}, 1}, Array{Pair{M, T}, 1}, Any} where T where M,
Tuple{Array{Ref{T}, 1}, Array{Pair{M, T}, 1}, Int} where T where M)
@testintersect(Tuple{Int, Ref{Pair{K,V}}} where V where K,
Tuple{Any, Ref{Pair{T,T}} where T },
Tuple{Int, Ref{Pair{T,T}} where T })
@test_broken isequal_type(_type_intersect(Tuple{T,T} where T,
Union{Tuple{S,Array{Int64,1}},Tuple{S,Array{S,1}}} where S),
Union{Tuple{Vector{Int64},Vector{Int64}},
Tuple{Vector{T},Vector{T}} where T>:Vector})
# part of issue #20344
@testintersect(Tuple{Type{Tuple{Vararg{T, N} where N}}, Tuple} where T,
Tuple{Type{Tuple{Vararg{T, N}}} where N where T, Any},
Bottom)
@testintersect(Type{NTuple{N,UnitRange}} where N,
Type{Tuple{Vararg{UnitRange}}},
Bottom)
@testintersect(Type{NTuple{Z,UnitRange}} where Z,
Type{NTuple{Z,String}} where Z,
Type{Tuple{}})
# first union component sets N==0, but for the second N is unknown
_, E = intersection_env(Tuple{Tuple{Vararg{Int}}, Any},
Tuple{Union{Base.DimsInteger{N},Base.Indices{N}}, Int} where N)
@test length(E)==1 && isa(E[1],TypeVar)
@testintersect(Tuple{Dict{Int,Int}, Ref{Pair{K,V}}} where V where K,
Tuple{Associative{Int,Int}, Ref{Pair{T,T}} where T},
Tuple{Dict{Int,Int}, Ref{Pair{K,K}}} where K)
# issue #20643
@testintersect(Tuple{Ref{Pair{p2,T2}}, Pair{p1,Pair}} where T2 where p2 where p1,
Tuple{Ref{Pair{p3,T3}}, Pair{p3}} where T3 where p3,
Tuple{Ref{Pair{p1,T2}}, Pair{p1,Pair}} where T2 where p1)
# issue #20998
_, E = intersection_env(Tuple{Int,Any,Any}, Tuple{T,T,S} where {T,S})
@test length(E) == 2 && E[1] == Int && isa(E[2], TypeVar)
_, E = intersection_env(Tuple{Dict{Int,Type}, Type, Any},
Tuple{Dict{K,V}, Any, Int} where {K,V})
@test E[2] == Type
# issue #20611
I, E = intersection_env(Tuple{Ref{Integer},Int,Any}, Tuple{Ref{Z},Z,Z} where Z)
@test isequal_type(I, Tuple{Ref{Integer},Int,Integer})
@test E[1] == Integer
# issue #21118
A = Tuple{Ref, Vararg{Any}}
B = Tuple{Vararg{Union{Z,Ref,Void}}} where Z<:Union{Ref,Void}
@test B <: _type_intersect(A, B)
@testintersect(Tuple{Int,Any,Vararg{A}} where A>:Integer,
Tuple{Any,Int,Vararg{A}} where A>:Integer,
Tuple{Int,Int,Vararg{A}} where A>:Integer)
# issue #21132
@testintersect(Pair{L,Tuple{L,Pair{L,HL}}} where {L,HL},
Pair{R,Tuple{Pair{R,HR},R}} where {R,HR},
Bottom) # X == Pair{X,...} is not satisfiable
# issue #20671 --- this just took too long
@testintersect(Tuple{Type{SIQ20671{T, mT, kgT, sT, AT, KT, molT, cdT, radT, srT}},
SIQ20671{S, mS, kgS, sS, AS, KS, molS, cdS, radS, srS}} where {T, mT, kgT, sT, AT, KT, molT, cdT, radT, srT,
S, mS, kgS, sS, AS, KS, molS, cdS, radS, srS},
Tuple{Type{T}, T} where T,
Tuple{Type{SIQ20671{T,mS,kgS,sS,AS,KS,molS,cdS,radS,srS}},
SIQ20671{T,mS,kgS,sS,AS,KS,molS,cdS,radS,srS}} where {T,mS,kgS,sS,AS,KS,molS,cdS,radS,srS})
# issue #21243
@testintersect(Tuple{Ref{Ref{T}} where T, Ref},
Tuple{Ref{T}, Ref{T}} where T,
Tuple{Ref{Ref{T}}, Ref{Ref{T}}} where T)
end
function test_intersection_properties()
for T in menagerie
for S in menagerie
I = _type_intersect(T,S)
I2 = _type_intersect(S,T)
@test isequal_type(I, I2)
@test issub(I, T) && issub(I, S)
if issub(T, S)
@test isequal_type(I, T)
end
end
end
end
test_1()
test_2()
test_diagonal()
test_3()
test_4()
test_5()
test_6()
test_7()
test_Type()
test_old()
test_intersection()
test_properties()
test_intersection_properties()
# issue #20121
@test NTuple{170,Matrix{Int}} <: (Tuple{Vararg{Union{Array{T,1},Array{T,2},Array{T,3}}}} where T)
# Issue #12580
abstract type AbstractMyType12580{T} end
struct MyType12580{T}<:AbstractMyType12580{T} end
tpara{A<:AbstractMyType12580}(::Type{A}) = tpara(supertype(A))
tpara{I}(::Type{AbstractMyType12580{I}}) = I
@test tpara(MyType12580{true})
# Issue #18348
f18348{T<:Any}(::Type{T}, x) = 1
f18348{T<:Any}(::Type{T}, x::T) = 2
@test length(methods(f18348, Tuple{Type{Any},Any})) == 1
# Issue #13165
@test Symmetric{Float64,Matrix{Float64}} <: LinAlg.RealHermSymComplexHerm
@test Hermitian{Float64,Matrix{Float64}} <: LinAlg.RealHermSymComplexHerm
@test Hermitian{Complex{Float64},Matrix{Complex{Float64}}} <: LinAlg.RealHermSymComplexHerm
# Issue #12721
f12721{T<:Type{Int}}(::T) = true
@test_throws MethodError f12721(Float64)
# implicit "covariant" type parameters:
mutable struct TwoParams{S,T}; x::S; y::T; end
@test TwoParams{<:Real,<:Number} == (TwoParams{S,T} where S<:Real where T<:Number) ==
(TwoParams{S,<:Number} where S<:Real) == (TwoParams{<:Real,T} where T<:Number)
@test TwoParams(3,0im) isa TwoParams{<:Real,<:Number}
@test TwoParams(3,"foo") isa TwoParams{<:Real}
@test !(TwoParams(3im,0im) isa TwoParams{<:Real,<:Number})
@test !(TwoParams(3,"foo") isa TwoParams{<:Real,<:Number})
ftwoparams(::TwoParams) = 1
ftwoparams(::TwoParams{<:Real}) = 2
ftwoparams(::TwoParams{<:Real,<:Real}) = 3
@test ftwoparams(TwoParams('x',3)) == 1
@test ftwoparams(TwoParams(3,'x')) == 2
@test ftwoparams(TwoParams(3,4)) == 3
@test !([TwoParams(3,4)] isa Vector{TwoParams{<:Real,<:Real}})
@test TwoParams{<:Real,<:Real}[TwoParams(3,4)] isa Vector{TwoParams{<:Real,<:Real}}
@test [TwoParams(3,4)] isa Vector{<:TwoParams{<:Real,<:Real}}
@test [TwoParams(3,4)] isa (Vector{TwoParams{T,T}} where T<:Real)
# implicit "contravariant" type parameters:
@test TwoParams{>:Int,<:Number} == (TwoParams{S,T} where S>:Int where T<:Number) ==
(TwoParams{S,<:Number} where S>:Int) == (TwoParams{>:Int,T} where T<:Number)
@test TwoParams(3,0im) isa TwoParams{>:Int,<:Number}
@test TwoParams{Real,Complex}(3,0im) isa TwoParams{>:Int,<:Number}
@test !(TwoParams(3.0,0im) isa TwoParams{>:Int,<:Number})
@test !(TwoParams(3,'x') isa TwoParams{>:Int,<:Number})
# supertype operator
@test !(Int >: Integer)
@test Integer >: Int
# tolerate non-types in Tuples
@test typeintersect(Tuple{0}, Tuple{T} where T) === Tuple{0}
# TypeVars deduced as non-type constants (#20869)
@testintersect(Tuple{Val{0}, Val{Val{N}}} where N, Tuple{Val{N}, Val{Val{N}}} where N, Tuple{Val{0},Val{Val{0}}})
@testintersect(Tuple{Val{N}, Val{Val{0}}} where N, Tuple{Val{N}, Val{Val{N}}} where N, Tuple{Val{0},Val{Val{0}}})
@testintersect(Tuple{Val{Val{0}}, Val{N}} where N, Tuple{Val{Val{N}}, Val{N}} where N, Tuple{Val{Val{0}},Val{0}})
@testintersect(Tuple{Val{Val{N}}, Val{0}} where N, Tuple{Val{Val{N}}, Val{N}} where N, Tuple{Val{Val{0}},Val{0}})