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TypeClass brings (semi-)principled type classes to Elixir

README

Quick Start
Type Classes
Escape Hatches
Example
- TypeClass
- Haskell

Quick Start

def deps do
  [{:type_class, "~> 1.1"}]
end

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 Enumerable 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/2 macro to handle generating all of the modules, submodules, and protocols.

definst/3 (and definst/2) is very similar to defimpl/3, 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/2 (more on that later).

Hierarchical

Type classes can be hierarchical. The extend/2 macro allows defining another class that your class depends on existing. A common and similar example from Haskell is how the monad instance must also be an applicative, which in turn must be a functor. definst/3 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 dependent 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/3 will property test a small batch of examples on every data type 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/2 and definst/3 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/2.

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 typed holes. Elixir is dynamically typed, so this one doesn't apply to us.

Escape Hatches

In the cases that you really need to override the prop checker, you have two options:

`@force_type_class true`

This will force the prop checker to pass for all data types for the class. This is generally a bad idea (see section on principled classes above), but may be nessesary for some extreme edge cases.

Using this option will trigger a compile time warning. See defclass/2 on how to use.

`@force_type_instance true`

This will force the prop checker to pass for a particular instance.

This is sometimes needed, since TypeClass's property checker may not be able to accurately validate all data types correctly for all possible cases, especially when only subsets of built-in types are valid. (For example, a class that can only be deifned on 2-tuples).

Forcing a type instance in this way is like telling the checker "trust me this is correct", and should only be used as a last resort. If at all possible, try to use custom_generator/2 first.

Using this option will trigger a compile time warning. See definst/3 on how to use.

`custom_generator/2`

If you need to specify a certain type of data that conforms to the type class, you can specify it with custom_generator/2 inside of the definst/3.

For example, Tuples should only have instances for 2-tuples for certain classes, so we can restrict the prop test data to 2-tuples rather than n-tuples.

The generator must conform to the standard unary generator format.

definst AwesomeClass, for: Tuple do
  custom_generator(a) do
    {:always_two, a}
  end

  # the rest as normal
  def awesome_level(_), do: 9000
end

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 _ = []

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