1.0.0 🎉

Happy New Year, and happy 1.0.0! TypeClass adds the ability to write (semi-)principled type classes in Elixir. This is used as the backbone for Witchcraft, the algebra library porting much of Haskell's Prelude to Elixir.

Type Classes

Type classes are not unlike protocols. They are essentially a mechanism for ad hoc polymorphism. However, doing extensive work with protocols can be cumbersome in Elixir. Even the standard library uses the confusingly named Enumerator protocol to support the Enum module. TypeClass attempts to hide many of the details to give you a single module interface.

Condensed Style

To this end, TypeClass provides the defclass macro to handle generating all of the modules, submodules, and protocols.

definstance is very similar to defimpl, except that you don't need to pass it the actual protocol; you only pass it just the "top" class module. It will also automatically run a number of checks at compile time to help keep everything running as per the definition in defclass (more on that later)

Hierarchical

Type classes can be hierarchical. The extend macro allows defining another class that your class depends on existing. A common example from Haskell and similar is how the monad instance must also be an applicative, which in turn must be a functor. definstance will check that the type you are implementing already has an implementation of the parent classes. Specifying multiple parents is totally okay, as this is superclassing, not subclassing like in an object oriented system.

Principled

Type classes have the ability to be abused. For instance, in languages such as Haskell, a programmer can define an instance of Monad a that is not actually a monad. This can lead to confusing and unexpected behaviour. After all the purpose of protocols and type classes is so that we abstract some invariant behaviour over many data types.

At the core, type classes are about the properties that enable its functions to work correctly. To emphasize that: properties are the most important part of a type class. Strictly speaking, for the compiler to enforce properties at compile time, it needs to have a lot of type-level information (ideally dependant types, GADTs, or very advanced static analysis). Elixir is dynamically typed, and has almost no type information at compile time.

TypeClass meets this challenge halfway: property testing. definst will property test a small batch of examples on every data typed that the class is defined for at compile time. By default, it skips this check in production, runs a minimal set of cases in development, and runs a larger suite in the test environment. Property testing lets TypeClass check hundreds of specific examples very quickly, so while it doesn't give you a guarantee that your instance is correct, it does give you a high level of confidence.

John De Goes defines principled type classes as:

Haskell-style. A baked-in notion of type classes in the overall style of Haskell, Purescript, Idris, etc.

defclass and definst get us 99% of the way here. It's not as lightweight as in Haskell &c, but it's close (and much more succinct than what is available in Kernel)

Lawful. First-class laws for type classes, which are enforced by the compiler.

As mentioned above, we meet laws/properties halfway with compile-time property tests.

Hierarchical. A compiler-verified requirement that a subclass of a type class must have at least one more law than that type class.

TypeClass requires at least one property per class. You can build type class hierarchies with extend.

Globally Unambiguous. Type class resolution that produces an error if there exists more than one instances which satisfies the constraints at the point where the compiler must choose an instance.

Elixir is dynamically typed, and so we cannot constrain functions at compile time. However, the point is well taken: rather than creating a renamed variant of a type so that you can have multiple instances (ex. Monoid can be integer addition or multiplication), extend the TypeClass and give it the additional properties that you're interested in for each case (ex. AdditiveMonoid and MultiplicativeMonoid extend Monoid).

Abstractable. The ability to abstract over type classes themselves.

De Goes is referring here to abstracting over type holes. Elixir is dynamically typed, so this one doesn't apply to us.

Example

TypeClass

defclass Algebra.Monoid do
  extend Algebra.Semigroup

  where do
    def empty(sample)
  end

  properties do
    def left_identity(data) do
      a = generate(data)
      Semigroup.concat(Monoid.empty(a), a) == a
    end

    def right_identity(data) do
      a = generate(data)
      Semigroup.concat(a, Monoid.empty(a)) == a
    end
  end
end

Haskell

The rough equivalent in Haskell

module Algebra.Monoid where

class (Setoid a, Semigroup a) => Monoid a where
  identity :: a -> a

  -- Not actually needed in this case
  -- Just here to illustrate including functions for minimal definitions
  append_id :: a -> a
  append_id a = identity a `append` a

instance Monoid [a] where
  identity _ = []