sets.jl

# This file is a part of Julia. License is MIT: https://julialang.org/license

# Set tests
isdefined(Main, :OffsetArrays) || @eval Main include("testhelpers/OffsetArrays.jl")
using .Main.OffsetArrays

using Dates

@testset "Construction, collect" begin
    @test Set([1,2,3]) isa Set{Int}
    @test Set{Int}([3]) isa Set{Int}
    data_in = (1,"banana", ())
    s = Set(data_in)
    data_out = collect(s)
    @test s isa Set{Any}
    @test data_out isa Array{Any,1}
    @test all(map(in(data_out), data_in))
    @test length(data_out) == length(data_in)
    let f17741 = x -> x < 0 ? false : 1
        @test isa(Set(x for x = 1:3), Set{Int})
        @test isa(Set(x for x = 1:3 for j = 1:1), Set{Int})
        @test isa(Set(sin(x) for x = 1:3), Set{Float64})
        @test isa(Set(f17741(x) for x = 1:3), Set{Int})
        @test isa(Set(f17741(x) for x = -1:1), Set{Integer})
    end
    let s1 = Set(["foo", "bar"]), s2 = Set(s1)
        @test s1 == s2
        x = pop!(s1)
        @test s1 != s2
        @test !(x in s1)
        @test x in s2
        push!(s1, "baz")
        push!(s2, "baz2")
        @test "baz" in s1
        @test !("baz" in s2)
        @test !("baz2" in s1)
        @test "baz2" in s2
    end
end

@testset "hash" begin
    s1 = Set(["bar", "foo"])
    s2 = Set(["foo", "bar"])
    s3 = Set(["baz"])
    @test hash(s1) == hash(s2)
    @test hash(s1) != hash(s3)
    d1 = Dict(Set([3]) => 33, Set([2]) => 22)
    d2 = Dict(Set([2]) => 33, Set([3]) => 22)
    @test hash(d1) != hash(d2)
end

@testset "equality" for eq in (isequal, ==)
    @test  eq(Set(), Set())
    @test !eq(Set(), Set([1]))
    @test  eq(Set{Any}(Any[1,2]), Set{Int}([1,2]))
    @test !eq(Set{Any}(Any[1,2]), Set{Int}([1,2,3]))

    # Comparison of unrelated types
    @test  eq(Set{Int}(), Set{AbstractString}())
    @test !eq(Set{Int}(), Set{AbstractString}([""]))
    @test !eq(Set{AbstractString}(), Set{Int}([0]))
    @test !eq(Set{Int}([1]), Set{AbstractString}())
    @test  eq(Set{Any}([1,2,3]), Set{Int}([1,2,3]))
    @test  eq(Set{Int}([1,2,3]), Set{Any}([1,2,3]))
    @test !eq(Set{Any}([1,2,3]), Set{Int}([1,2,3,4]))
    @test !eq(Set{Int}([1,2,3]), Set{Any}([1,2,3,4]))
    @test !eq(Set{Any}([1,2,3,4]), Set{Int}([1,2,3]))
    @test !eq(Set{Int}([1,2,3,4]), Set{Any}([1,2,3]))

    # Special cases
    @test  eq(Set([-0.0]), Set([-0.0]))
    @test !eq(Set([0.0]), Set([-0.0]))
    @test  eq(Set([NaN]), Set([NaN]))
    @test !eq(Set([NaN]), Set([1.0]))
    @test  eq(Set([missing]), Set([missing]))
    @test !eq(Set([missing]), Set([1]))
end

@testset "hash and == for Set/BitSet" begin
    for s = (Set([1]), Set(1:10), Set(-100:7:100))
        b = BitSet(s)
        @test hash(s) == hash(b)
        @test s == b
    end
end

@testset "eltype, empty" begin
    s1 = empty(Set([1,"hello"]))
    @test isequal(s1, Set())
    @test ===(eltype(s1), Any)
    s2 = empty(Set{Float32}([2.0f0,3.0f0,4.0f0]))
    @test isequal(s2, Set())
    @test ===(eltype(s2), Float32)
    s3 = empty(Set([1,"hello"]),Float32)
    @test isequal(s3, Set())
    @test ===(eltype(s3), Float32)
end
@testset "show" begin
    @test sprint(show, Set()) == "Set(Any[])"
    @test sprint(show, Set(['a'])) == "Set(['a'])"
end
@testset "isempty, length, in, push, pop, delete" begin
    # also test for no duplicates
    s = Set(); push!(s,1); push!(s,2); push!(s,3)
    @test !isempty(s)
    @test in(1,s)
    @test in(2,s)
    @test length(s) == 3
    push!(s,1); push!(s,2); push!(s,3)
    @test length(s) == 3
    @test pop!(s,1) == 1
    @test !in(1,s)
    @test in(2,s)
    @test length(s) == 2
    @test_throws KeyError pop!(s,1)
    @test pop!(s,1,:foo) == :foo
    @test length(delete!(s,2)) == 1
    @test !in(1,s)
    @test !in(2,s)
    @test pop!(s) == 3
    @test length(s) == 0
    @test isempty(s)
    @test_throws ArgumentError pop!(s)
    @test length(Set(['x',120])) == 2
end
@testset "copy" begin
    data_in = (1,2,9,8,4)
    s = Set(data_in)
    c = copy(s)
    @test isequal(s,c)
    v = pop!(s)
    @test !in(v,s)
    @test  in(v,c)
    push!(s,100)
    push!(c,200)
    @test !in(100,c)
    @test !in(200,s)
end

@testset "copy!" begin
    for S = (Set, BitSet)
        s = S([1, 2])
        for a = ([1], UInt[1], [3, 4, 5], UInt[3, 4, 5])
            @test s === copy!(s, Set(a)) == S(a)
            @test s === copy!(s, BitSet(a)) == S(a)
        end
    end
end

@testset "sizehint, empty" begin
    s = Set([1])
    @test isequal(sizehint!(s, 10), Set([1]))
    @test isequal(empty!(s), Set())
end
@testset "rehash!" begin
    # Use a pointer type to have defined behavior for uninitialized
    # array element
    s = Set(["a", "b", "c"])
    Base.rehash!(s)
    k = s.dict.keys
    Base.rehash!(s)
    @test length(k) == length(s.dict.keys)
    for i in 1:length(k)
        if isassigned(k, i)
            @test k[i] == s.dict.keys[i]
        else
            @test !isassigned(s.dict.keys, i)
        end
    end
    @test s == Set(["a", "b", "c"])
end

@testset "start, done, next" begin
    for data_in in ((7, 8, 4, 5),
                  ("hello", 23, 2.7, (), [], (1, 8)))
        local data_in, s, t
        s = Set(data_in)

        s_new = Set()
        for el in s
            push!(s_new, el)
        end
        @test isequal(s, s_new)

        t = tuple(s...)
        @test length(t) == length(s)
        for e in t
            @test in(e,s)
        end
    end
end

@testset "union" begin
    for S in (Set, BitSet, Vector)
        s = ∪(S([1,2]), S([3,4]))
        @test s == S([1,2,3,4])
        s = union(S([5,6,7,8]), S([7,8,9]))
        @test s == S([5,6,7,8,9])
        s = S([1,3,5,7])
        union!(s, (2,3,4,5))
        @test s == S([1,3,5,7,2,4]) # order matters for Vector
        let s1 = S([1, 2, 3])
            @test s1 !== union(s1) == s1
            @test s1 !== union(s1, 2:4) == S([1,2,3,4])
            @test s1 !== union(s1, [2,3,4]) == S([1,2,3,4])
            @test s1 !== union(s1, [2,3,4], S([5])) == S([1,2,3,4,5])
            @test s1 === union!(s1, [2,3,4], S([5])) == S([1,2,3,4,5])
        end
    end
    @test union(Set([1]), BitSet()) isa Set{Int}
    @test union(BitSet([1]), Set()) isa BitSet
    @test union([1], BitSet()) isa Vector{Int}
    # union must uniquify
    @test union([1, 2, 1]) == union!([1, 2, 1]) == [1, 2]
    @test union([1, 2, 1], [2, 2]) == union!([1, 2, 1], [2, 2]) == [1, 2]
end

@testset "intersect" begin
    for S in (Set, BitSet, Vector)
        s = S([1,2]) ∩ S([3,4])
        @test s == S()
        s = intersect(S([5,6,7,8]), S([7,8,9]))
        @test s == S([7,8])
        @test intersect(S([2,3,1]), S([4,2,3]), S([5,4,3,2])) == S([2,3])
        let s1 = S([1,2,3])
            @test s1 !== intersect(s1) == s1
            @test s1 !== intersect(s1, 2:10) == S([2,3])
            @test s1 !== intersect(s1, [2,3,4]) == S([2,3])
            @test s1 !== intersect(s1, [2,3,4], 3:4) == S([3])
            @test s1 === intersect!(s1, [2,3,4], 3:4) == S([3])
        end
    end
    @test intersect(Set([1]), BitSet()) isa Set{Int}
    @test intersect(BitSet([1]), Set()) isa BitSet
    @test intersect([1], BitSet()) isa Vector{Int}
    # intersect must uniquify
    @test intersect([1, 2, 1]) == intersect!([1, 2, 1]) == [1, 2]
    @test intersect([1, 2, 1], [2, 2]) == intersect!([1, 2, 1], [2, 2]) == [2]

    # issue #25801
    x = () ∩ (:something,)
    y = () ∩ (42,)
    @test isempty(x)
    @test isempty(y)
    @test eltype(x) == eltype(y) == Union{}
end

@testset "setdiff" begin
    for S in (Set, BitSet, Vector)
        @test setdiff(S([1,2,3]), S())        == S([1,2,3])
        @test setdiff(S([1,2,3]), S([1]))     == S([2,3])
        @test setdiff(S([1,2,3]), S([1,2]))   == S([3])
        @test setdiff(S([1,2,3]), S([1,2,3])) == S()
        @test setdiff(S([1,2,3]), S([4]))     == S([1,2,3])
        @test setdiff(S([1,2,3]), S([4,1]))   == S([2,3])
        let s1 = S([1, 2, 3])
            @test s1 !== setdiff(s1) == s1
            @test s1 !== setdiff(s1, 2:10) == S([1])
            @test s1 !== setdiff(s1, [2,3,4]) == S([1])
            @test s1 !== setdiff(s1, S([2,3,4]), S([1])) == S()
            @test s1 === setdiff!(s1, S([2,3,4]), S([1])) == S()
        end
    end

    @test setdiff(Set([1]), BitSet()) isa Set{Int}
    @test setdiff(BitSet([1]), Set()) isa BitSet
    @test setdiff([1], BitSet()) isa Vector{Int}
    # setdiff must uniquify
    @test setdiff([1, 2, 1]) == setdiff!([1, 2, 1]) == [1, 2]
    @test setdiff([1, 2, 1], [2, 2]) == setdiff!([1, 2, 1], [2, 2]) == [1]

    s = Set([1,3,5,7])
    setdiff!(s,(3,5))
    @test isequal(s,Set([1,7]))
    s = Set([1,2,3,4])
    setdiff!(s, Set([2,4,5,6]))
    @test isequal(s,Set([1,3]))

    # setdiff iterates the shorter set - make sure this algorithm works
    sa, sb = Set([1,2,3,4,5,6,7]), Set([2,3,9])
    @test Set([1,4,5,6,7]) == setdiff(sa, sb) !== sa
    @test Set([1,4,5,6,7]) == setdiff!(sa, sb) === sa
    sa, sb = Set([1,2,3,4,5,6,7]), Set([2,3,9])
    @test Set([9]) == setdiff(sb, sa) !== sb
    @test Set([9]) == setdiff!(sb, sa) === sb
end

@testset "ordering" begin
    @test Set() < Set([1])
    @test Set([1]) < Set([1,2])
    @test !(Set([3]) < Set([1,2]))
    @test !(Set([3]) > Set([1,2]))
    @test Set([1,2,3]) > Set([1,2])
    @test !(Set([3]) <= Set([1,2]))
    @test !(Set([3]) >= Set([1,2]))
    @test Set([1]) <= Set([1,2])
    @test Set([1,2]) <= Set([1,2])
    @test Set([1,2]) >= Set([1,2])
    @test Set([1,2,3]) >= Set([1,2])
    @test !(Set([1,2,3]) >= Set([1,2,4]))
    @test !(Set([1,2,3]) <= Set([1,2,4]))
end

@testset "issubset, symdiff" begin
    for S in (Set, BitSet, Vector)
        for (l,r) in ((S([1,2]),     S([3,4])),
                      (S([5,6,7,8]), S([7,8,9])),
                      (S([1,2]),     S([3,4])),
                      (S([5,6,7,8]), S([7,8,9])),
                      (S([1,2,3]),   S()),
                      (S([1,2,3]),   S([1])),
                      (S([1,2,3]),   S([1,2])),
                      (S([1,2,3]),   S([1,2,3])),
                      (S([1,2,3]),   S([4])),
                      (S([1,2,3]),   S([4,1])))
            @test issubset(intersect(l,r), l)
            @test issubset(intersect(l,r), r)
            @test issubset(l, union(l,r))
            @test issubset(r, union(l,r))
            if S === Vector
                @test sort(union(intersect(l,r),symdiff(l,r))) == sort(union(l,r))
            else
                @test union(intersect(l,r),symdiff(l,r)) == union(l,r)
            end
        end
        if S !== Vector
            @test ⊆(S([1]), S([1,2]))
            @test ⊊(S([1]), S([1,2]))
            @test !⊊(S([1]), S([1]))
            @test ⊈(S([1]), S([2]))
            @test ⊇(S([1,2]), S([1]))
            @test ⊋(S([1,2]), S([1]))
            @test !⊋(S([1]), S([1]))
            @test ⊉(S([1]), S([2]))
        end
        let s1 = S([1,2,3,4])
            @test s1 !== symdiff(s1) == s1
            @test s1 !== symdiff(s1, S([2,4,5,6])) == S([1,3,5,6])
            @test s1 !== symdiff(s1, S([2,4,5,6]), [1,6,7]) == S([3,5,7])
            @test s1 === symdiff!(s1, S([2,4,5,6]), [1,6,7]) == S([3,5,7])
        end
    end
    @test symdiff(Set([1,2,3,4]), Set([2,4,5,6])) == Set([1,3,5,6])
    @test symdiff(Set([1]), BitSet()) isa Set{Int}
    @test symdiff(BitSet([1]), Set{Int}()) isa BitSet
    @test symdiff([1], BitSet()) isa Vector{Int}
    # symdiff must NOT uniquify
    @test symdiff([1, 2, 1]) == symdiff!([1, 2, 1]) == [2]
    @test symdiff([1, 2, 1], [2, 2]) == symdiff!([1, 2, 1], [2, 2]) == [2]
end

@testset "unique" begin
    u = unique([1, 1, 2])
    @test in(1, u)
    @test in(2, u)
    @test length(u) == 2
    @test unique(iseven, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6]) == [5, 8]
    @test unique(n -> n % 3, [5, 1, 8, 9, 3, 4, 10, 7, 2, 6]) == [5, 1, 9]
end

@testset "issue 20105" begin
    @test @inferred(unique(x for x in 1:1)) == [1]
    @test unique(x for x in Any[1, 1.0])::Vector{Real} == [1]
    @test unique(x for x in Real[1, 1.0])::Vector{Real} == [1]
    @test unique(Integer[1, 1, 2])::Vector{Integer} == [1, 2]
end

@testset "unique!" begin
    u = [1,1,3,2,1]
    unique!(u)
    @test u == [1,3,2]
    @test unique!([]) == []
    @test unique!(Float64[]) == Float64[]
    u = [1,2,2,3,5,5]
    @test unique!(u) === u
    @test u == [1,2,3,5]
    u = [6,5,5,3,3,2,1]
    @test unique!(u) === u
    @test u == [6,5,3,2,1]
    u = OffsetArray([1,2,2,3,5,5], -1)
    @test unique!(u) === u
    @test u == OffsetArray([1,2,3,5], -1)
    u = OffsetArray([5,5,4,4,2,2,0,-1,-1], -1)
    @test unique!(u) === u
    @test u == OffsetArray([5,4,2,0,-1], -1)
    u = OffsetArray(["w","we","w",5,"r",5,5], -1)
    @test unique!(u) === u
    @test u == OffsetArray(["w","we",5,"r"], -1)
    u = [0.0,-0.0,1.0,2]
    @test unique!(u) === u
    @test u == [0.0,-0.0,1.0,2.0]
    u = [1,NaN,NaN,3]
    @test unique!(u) === u
    @test u[1] == 1
    @test isnan(u[2])
    @test u[3] == 3
    u = [5,"w","we","w","r",5,"w"]
    unique!(u)
    @test u == [5,"w","we","r"]
    u = [1,2,5,1,3,2]
end

@testset "allunique" begin
    @test allunique([])
    @test allunique(Set())
    @test allunique([1,2,3])
    @test allunique([:a,:b,:c])
    @test allunique(Set([1,2,3]))
    @test !allunique([1,1,2])
    @test !allunique([:a,:b,:c,:a])
    @test allunique(4:7)
    @test allunique(1:1)
    @test allunique(4.0:0.3:7.0)
    @test allunique(4:-1:5)       # empty range
    @test allunique(7:-1:1)       # negative step
    @test allunique(Date(2018, 8, 7):Day(1):Date(2018, 8, 11))  # JuliaCon 2018
    @test allunique(DateTime(2018, 8, 7):Hour(1):DateTime(2018, 8, 11))
end
@testset "filter(f, ::$S)" for S = (Set, BitSet)
    s = S([1,2,3,4])
    @test s !== filter( isodd, s) == S([1,3])
    @test s === filter!(isodd, s) == S([1,3])
end
@testset "first" begin
    @test_throws ArgumentError first(Set())
    @test first(Set(2)) == 2
end
@testset "pop!" begin
    s = Set(1:5)
    @test 2 in s
    @test pop!(s, 2) == 2
    @test !(2 in s)
    @test_throws KeyError pop!(s, 2)
    @test pop!(s, 2, ()) == ()
    @test 3 in s
    @test pop!(s, 3, ()) == 3
    @test !(3 in s)
    @test pop!(Set(1:2), 2, nothing) == 2
end

@testset "convert" begin
    iset = Set([17, 4711])
    cfset = convert(Set{Float64}, iset)
    @test typeof(cfset) == Set{Float64}
    @test cfset == iset
    fset = Set([17.0, 4711.0])
    ciset = convert(Set{Int}, fset)
    @test typeof(ciset) == Set{Int}
    @test ciset == fset
    ssset = Set(split("foo bar"))
    cssset = convert(Set{String}, ssset)
    @test typeof(cssset) == Set{String}
    @test cssset == Set(["foo", "bar"])
end

@testset "fuzzy testing Set & BitSet" begin
    b1, b2 = rand(-1000:1000, 2)
    e1 = rand(b1-9:1000) # -9 to have an empty list sometimes
    e2 = rand(b2-9:1000)
    l1, l2 = rand(1:1000, 2)
    a1 = b1 <= e1 ? rand(b1:e1, l1) : Int[]
    a2 = b2 <= e2 ? rand(b2:e2, l2) : Int[]
    s1, s2 = Set(a1), Set(a2)
    t1, t2 = BitSet(a1), BitSet(a2)

    for (s, t) = ((s1, t1), (s2, t2))
        @test length(s) == length(t)
        @test issubset(s, t)
        @test issubset(t, s)
        @test isempty(s) == isempty(t)
        isempty(s) && continue
        @test maximum(s) == maximum(t)
        @test minimum(s) == minimum(t)
        @test extrema(s) == extrema(t)
        rs, rt = rand(s), rand(t)
        @test rs in s
        @test rt in s
        @test rs in t
        @test rt in t
        for y in (rs, rt)
            ss = copy(s)
            tt = copy(t)
            pop!(ss, y)
            pop!(tt, y)
            @test BitSet(ss) == tt
            @test Set(tt) == ss
            z = rand(1001:1100) # z ∉ s or t
            push!(ss, z)
            push!(tt, z)
            @test BitSet(ss) == tt
            @test Set(tt) == ss
        end
    end

    res = Dict{String,Union{Bool,Vector{Int}}}()
    function check(desc, val)
        n = val isa Bool ? val : sort!(collect(val))
        r = get!(res, desc, n)
        if n isa Bool || r !== n
            @test r == n
        end
    end
    asbitset(x) = x isa BitSet ? x : BitSet(x)
    asset(x) = x isa Set ? x : Set(x)

    for x1 = (s1, t1), x2 = (s2, t2)
        check("union", union(x1, x2))
        check("intersect", intersect(x1, x2))
        check("symdiff", symdiff(x1, x2))
        check("setdiff", setdiff(x1, x2))
        check("== as Bitset", asbitset(x1) == asbitset(x2))
        check("== as Set", asset(x1) == asset(x2))
        check("issubset", issubset(x1, x2))
        if typeof(x1) == typeof(x2)
            check("<", x1 < x2)
            check("<=", x1 > x2)
            check("union!", union!(copy(x1), x2))
            check("setdiff!", setdiff!(copy(x1), x2))
            x1 isa Set && continue
            check("intersect!", intersect!(copy(x1), x2))
            check("symdiff!", symdiff!(copy(x1), x2))
        end
    end
end

@testset "replace! & replace" begin
    a = [1, 2, 3, 1]
    @test replace(x -> iseven(x) ? 2x : x, a) == [1, 4, 3, 1]
    @test replace!(x -> iseven(x) ? 2x : x, a) === a
    @test a == [1, 4, 3, 1]
    @test replace(a, 1=>0) == [0, 4, 3, 0]
    for count = (1, 0x1, big(1))
        @test replace(a, 1=>0, count=count) == [0, 4, 3, 1]
    end
    @test replace!(a, 1=>2) === a
    @test a == [2, 4, 3, 2]
    @test replace!(x->2x, a, count=0x2) == [4, 8, 3, 2]

    d = Dict(1=>2, 3=>4)
    @test replace!(x -> x.first > 2 ? x.first=>2*x.second : x, d) === d
    @test d == Dict(1=>2, 3=>8)
    @test replace(d, (3=>8)=>(0=>0)) == Dict(1=>2, 0=>0)
    @test replace!(d, (3=>8)=>(2=>2)) === d
    @test d == Dict(1=>2, 2=>2)

    s = Set([1, 2, 3])
    @test replace(x -> x > 1 ? 2x : x, s) == Set([1, 4, 6])
    for count = (1, 0x1, big(1))
        @test replace(x -> x > 1 ? 2x : x, s, count=count) in [Set([1, 4, 3]), Set([1, 2, 6])]
    end
    @test replace(s, 1=>4) == Set([2, 3, 4])
    @test replace!(s, 1=>2) === s
    @test s == Set([2, 3])
    @test replace!(x->2x, s, count=0x1) in [Set([4, 3]), Set([2, 6])]

    for count = (0, 0x0, big(0))
        @test replace([1, 2], 1=>0, 2=>0, count=count) == [1, 2] # count=0 --> no replacements
    end

    # test collisions with AbstractSet/AbstractDict
    @test replace!(x->2x, Set([3, 6])) == Set([6, 12])
    @test replace!(x->2x, Set([1:20;])) == Set([2:2:40;])
    @test replace!(kv -> (2kv[1] => kv[2]), Dict(1=>2, 2=>4, 4=>8, 8=>16)) == Dict(2=>2, 4=>4, 8=>8, 16=>16)

    # avoid recursive call issue #25384
    @test_throws MethodError replace!("")

    # test eltype promotion
    x = @inferred replace([1, 2], 2=>2.5)
    @test x == [1, 2.5] && x isa Vector{Float64}

    x = @inferred replace([1, 2], 2=>missing)
    @test isequal(x, [1, missing]) && x isa Vector{Union{Int, Missing}}

    @test_broken @inferred replace([1, missing], missing=>2)
    x = replace([1, missing], missing=>2)
    @test x == [1, 2] && x isa Vector{Int}
    x = @inferred replace([1, missing], missing=>2, count=1)
    @test x == [1, 2] && x isa Vector{Union{Int, Missing}}
    x = @inferred replace([1, missing], missing=>missing)
    @test isequal(x, [1, missing]) && x isa Vector{Union{Int, Missing}}
    x = @inferred replace([1, missing], missing=>2, 1=>missing)
    @test isequal(x, [missing, 2]) && x isa Vector{Union{Int, Missing}}

    # test that isequal is used
    @test replace([NaN, 1.0], NaN=>0.0) == [0.0, 1.0]
    @test replace([1, missing], missing=>0) == [1, 0]
end

@testset "⊆, ⊊, ⊈, ⊇, ⊋, ⊉, <, <=, issetequal" begin
    a = [1, 2]
    b = [2, 1, 3]
    for C = (Tuple, identity, Set, BitSet, Base.IdSet{Int})
        A = C(a)
        B = C(b)
        @test A ⊆ B
        @test A ⊊ B
        @test !(A ⊈ B)
        @test !(A ⊇ B)
        @test !(A ⊋ B)
        @test A ⊉ B
        @test !(B ⊆ A)
        @test !(B ⊊ A)
        @test B ⊈ A
        @test B ⊇ A
        @test B ⊋ A
        @test !(B ⊉ A)
        @test !issetequal(A, B)
        @test !issetequal(B, A)
        if A isa AbstractSet && B isa AbstractSet
            @test A <= B
            @test A <  B
            @test !(A >= B)
            @test !(A >  B)
            @test !(B <= A)
            @test !(B <  A)
            @test B >= A
            @test B >  A
        end
        for D = (Tuple, identity, Set, BitSet)
            @test issetequal(A, D(A))
            @test !issetequal(A, D(B))
        end
    end
end

struct OpenInterval{T}
    lower::T
    upper::T
end
Base.in(x, i::OpenInterval) = i.lower < x < i.upper
Base.IteratorSize(::Type{<:OpenInterval}) = Base.SizeUnknown()

@testset "Continuous sets" begin
    i = OpenInterval(2, 4)
    @test 3 ∈ i
    @test issubset(3, i)
end