SumTypes.jl

• Basics
• Pattern matching
• Avoiding namespace clutter
• Performance
• Custom printing

Basics

A julian implementation of sum types. Sum types, sometimes called 'tagged unions' are the type system equivalent of the disjoint union operation (which is not a union in the traditional sense). From a category theory perspective, sum types are interesting because they are dual to Tuples (whatever that means). In the Rust programming language, these are called "Enums".

At the end of the day, a sum type is really just a fancy word for a container that can store data of a few different, pre-declared types and is labelled by how it was instantiated.

Users of statically typed programming languages often prefer Sum types to unions because it makes type checking easier. In a dynamic language like julia, the benefit of these objects is less obvious, but there are cases where they're helpful.

A common use-case for sum types is as a richer version of enums (enum in the julia sense, not in the Rust sense):

julia> @sum_type Fruit begin
           Apple
           Banana
           Orange
       end

julia> Apple
Apple::Fruit

julia> Banana
Banana::Fruit

julia> Orange
Orange::Fruit

julia> typeof(Apple) == typeof(Banana) == typeof(Orange) == Fruit
true

But this isn't particularly interesting. More intesting is sum types which can enclose data. Let's explore a very fundamental sum type (fundamental in the sense that all other sum types may be derived from it):

julia> using SumTypes

julia> @sum_type Either{A, B} begin
           Left{A}(::A)
           Right{B}(::B)
       end

This says that we have a sum type Either{A, B}, and it can hold a value that is either of type A or of type B. Either has two 'constructors' which we have called Left{A} and Right{B}. These exist essentially as a way to have instances of Either carry a record of how they were constructed by being wrapped in dummy structs named Left or Right.

Here is how these constructors behave:

julia> Left(1)
Left(1)::Either{Int64, Uninit}

julia> Right(1.0)
Right(1.0)::Either{Uninit, Float64}

Notice that because both Left{A} and Right{B} each carry one fewer type parameter than Either{A,B}, then simply writing Left(1) is not enough to fully specify the type of the full Either, so the unspecified field is SumTypes.Uninit by default.

In cases like this, you can rely on implicit conversion to get the fully initialized type. E.g.

julia> let x::Either{Int, Float64} = Left(1)
           x
       end
Left(1)::Either{Int64, Float64}

Typically, you'll do this by enforcing a return type on a function:

julia> function foo() :: Either{Int, Float64}
           # Randomly return either a Left(1) or a Right(2.0)
           rand(Bool) ? Left(1) : Right(2.0)
       end;

julia> foo()
Left(1)::Either{Int64, Float64}

julia> foo()
Right(2.0)::Either{Int64, Float64}

This is particularly useful because in this case foo is type stabe!

julia> Base.return_types(foo, Tuple{})
1-element Vector{Any}:
 Either{Int64, Float64}
 
julia> isconcretetype(Either{Int, Float64})
true

Note that unlike Union{A, B}, A <: Either{A,B} is false, and Either{A, A} is distinct from A.

Pattern matching on Sum types

Okay, but how do I actually access the data enclosed in a Fruit or an Either? The answer is pattern matching. SumTypes.jl exposes a @cases macro for efficiently unwrapping and branching on the contents of a sum type:

julia> myfruit = Orange
Orange::Fruit

julia> @cases myfruit begin
           Apple => "Got an apple!"
           Orange => "Got an orange!"
           Banana => throw(error("I'm allergic to bananas!"))
       end
"Got an orange!"

julia> @cases Banana begin
           Apple => "Got an apple!"
           Orange => "Got an orange!"
           Banana => throw(error("I'm allergic to bananas!"))
       end
ERROR: I'm allergic to bananas!
[...]

@cases can automatically detect if you did't give an exhaustive set of cases (with no runtime penalty) and throw an error.

julia> @cases myfruit begin
           Apple => "Got an apple!"
           Orange => "Got an orange!"
       end
ERROR: Inexhaustive @cases specification. Got cases (:Apple, :Orange), expected (:Apple, :Banana, :Orange)
[...]

Furthermore, @cases can destructure sum types which hold data:

julia> let x::Either{Int, Float64} = rand(Bool) ? Left(1) : Right(2.0)
           @cases x begin
               Left(l) => l + 1.0
               Right(r) => r - 1
           end
       end
2.0

i.e. in this example, @cases took in an Either{Int,Float64} and if it contained a Left, it took the wrapped data (an Int) bound it do the variable l and added 1.0 to l, whereas if it was a Right, it took the Float64 and bound it to a variable r and subtracted 1 from r.

Avoiding namespace clutter

A common complaint about Enums and Sum Types is that sometimes they can contribute to clutter in the namespace. If you want to avoid having all the variants being available as top-level constant variables, then you can use the hide_variants=true option:

julia> @sum_type Foo{T} begin
           A
           B{T}(::T)
       end hide_variants=true

julia> A
ERROR: UndefVarError: A not defined

julia> B
ERROR: UndefVarError: B not defined

These 'hidden' variants can be accessed by applying the ' operator to the type Foo, which returns a named tuple of the variants:

julia> Foo'
(A = A::Foo{Uninit}, B = var"#Foo#B")

And then you can access this named tuple as normal:

julia> Foo'.A
A::Foo{Uninit}

julia> Foo'.B(1)
B(1)::Foo{Int64}

You can even do fancy things like

julia> let (; B) = Foo'
           B(1)
       end
B(1)::Foo{Int64}

Note that property-destructuring syntax is only available on julia version 1.7 and higher https://github.com/JuliaLang/julia/issues/39285

Performance

In the same way as Unityper.jl is able to provide a dramatic speedup versus manual union splitting, SumTypes.jl can do this too:

Branching on abstractly typed data

module AbstractTypeTest

using BenchmarkTools

abstract type AT end
Base.@kwdef struct A <: AT
    common_field::Int = 0
    a::Bool = true
    b::Int = 10
end
Base.@kwdef struct B <: AT
    common_field::Int = 0
    a::Int = 1
    b::Float64 = 1.0
    d::Complex = 1 + 1.0im # not isbits
end
Base.@kwdef struct C <: AT
    common_field::Int = 0
    b::Float64 = 2.0
    d::Bool = false
    e::Float64 = 3.0
    k::Complex{Real} = 1 + 2im # not isbits
end
Base.@kwdef struct D <: AT
    common_field::Int = 0
    b::Any = :hi # not isbits
end

foo!(xs) = for i in eachindex(xs)
    @inbounds x = xs[i]
    @inbounds xs[i] = x isa A ? B() :
                      x isa B ? C() :
                      x isa C ? D() :
                      x isa D ? A() : error()
end


xs = rand((A(), B(), C(), D()), 10000);
display(@benchmark foo!($xs);)

end

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  393.061 μs …   6.725 ms  ┊ GC (min … max): 0.00% … 90.92%
 Time  (median):     434.257 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   483.461 μs ± 435.758 μs  ┊ GC (mean ± σ):  9.38% ±  9.39%

  █▅▃▁                                                          ▁
  █████▆▆▃▃▁▁▃▁▁▁▁▁▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▄▃▅ █
  393 μs        Histogram: log(frequency) by time        4.2 ms <

 Memory estimate: 654.16 KiB, allocs estimate: 21950.

SumTypes.jl

module SumTypeTest

using SumTypes,  BenchmarkTools
@sum_type AT begin
    A(common_field::Int, a::Bool, b::Int)
    B(common_field::Int, a::Int, b::Float64, d::Complex)
    C(common_field::Int, b::Float64, d::Bool, e::Float64, k::Complex{Real})
    D(common_field::Int, b::Any)
end

A(;common_field=1, a=true, b=10) = A(common_field, a, b) 
B(;common_field=1, a=1, b=1.0, d=1 + 1.0im) = B(common_field, a, b, d)
C(;common_field=1, b=2.0, d=false, e=3.0, k=Complex{Real}(1 + 2im)) = C(common_field, b, d, e, k)
D(;common_field=1, b=:hi) = D(common_field, b)

foo!(xs) = for i in eachindex(xs)
    xs[i] = @cases xs[i] begin
        A => B()
        B => C()
        C => D()
        D => A()
    end
end

xs = rand((A(), B(), C(), D()), 10000);
display(@benchmark foo!($xs);)

end

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  74.210 μs … 231.032 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     75.119 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   79.962 μs ±  13.458 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  █▃  ▄▂▄  ▄▃   ▂▁                                             ▁
  ███▆████▅███▇▇████▆█▅▇▅▇▇▆▇▆▅▅▅▆▅▅▅▅▅▅▅▆▅▅▅▆▅▅▅▅▅▁▅▅▅▅▅▄▄▅▅▅ █
  74.2 μs       Histogram: log(frequency) by time       152 μs <

 Memory estimate: 0 bytes, allocs estimate: 0.

And Unityper.jl:

module UnityperTest

using Unityper, BenchmarkTools

@compactify begin
    @abstract struct AT
        common_field::Int = 0
    end
    struct A <: AT
        a::Bool = true
        b::Int = 10
    end
    struct B <: AT
        a::Int = 1
        b::Float64 = 1.0
        d::Complex = 1 + 1.0im # not isbits
    end
    struct C <: AT
        b::Float64 = 2.0
        d::Bool = false
        e::Float64 = 3.0
        k::Complex{Real} = 1 + 2im # not isbits
    end
    struct D <: AT
        b::Any = :hi # not isbits
    end
end

foo!(xs) = for i in eachindex(xs)
    @inbounds x = xs[i]
    @inbounds xs[i] = @compactified x::AT begin
        A => B()
        B => C()
        C => D()
        D => A()
    end
end

xs = rand((A(), B(), C(), D()), 10000);
display(@benchmark foo!($xs);)

end

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  69.355 μs … 234.343 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     75.388 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   77.753 μs ±  13.757 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

  █▃▄▃▇▆▆▃▄      ▁                                             ▂
  ██████████▇▇█▇▇█████▆▆▆▆▆▆▇▆▅▇▆▆▅▄▆▇▆▆▆▅▇▆▅▆▅▄▅▄▄▅▄▆▅▅▅▅▅▅▅▅ █
  69.4 μs       Histogram: log(frequency) by time       149 μs <

 Memory estimate: 0 bytes, allocs estimate: 0.

Unityper.jl and SumTypes.jl are about equal in this benchmark. SumTypes.jl has some advantages relative to Unityper.jl too, such as:

• SumTypes.jl allows parametric types for much greater container flexibility (Unityper does some memory layout optimizations that won't work with parametric types).
• SumTypes.jl does not require default values for every field of the struct
• SumTypes.jl's @cases macro is more powerful and flexible than Unityper's @compactified.
• SumTypes.jl allows you to hide its variants from the namespace (opt in).

Whereas some advantages of Unityper.jl are:

• A @compactified type from Unityper.jl will often have a smaller memory footprint than a corresponding type from SumTypes.jl
• If we had used D(;common_field=1, b="hi") in our benchmarks, SumTypes.jl could have incurred an allocation whereas Unitypeper.jl would not. This allocation is due to the compiler heuristics involved in ::Union{T, Nothing} fields of structs and may be fixed in future versions of julia.

Custom printing

SumTypes.jl automatically overloads Base.show(::IO, ::YourType) and Base.show(::IO, ::MIME"text/plain", ::YourType) for your type when you create a sum type, but it forwards that call to an internal function SumTypes.show_sumtype. If you wish to customize the printing of a sum type, then you should overload SumTypes.show_sumtype:

julia> SumTypes.show_sumtype(io::IO, x::Fruit2) = @cases x begin
           apple => print(io, "apple")
           orange => print(io, "orange")
           banana => print(io, "banana")
       end

julia> apple
apple

julia> SumTypes.show_sumtype(io::IO, ::MIME"text/plain", x::Fruit2) = @cases x begin
           apple => print(io, "apple!")
           orange => print(io, "orange!")
           banana => print(io, "banana!")
       end

julia> apple
apple!

If you overload Base.show directly inside a package, you might get annoying method deletion warnings during pre-compilation.