Data.Algebra.Internal

Documentation

type family Signature c :: * -> *

The signature datatype for the class c.

class Traversable f => AlgebraSignature f where

Associated Types

type Class f :: * -> Constraint

The class for which f is the signature.

Methods

evaluate :: Class f b => f b -> b

Translate the operations of the signature to method calls of the class.

class Algebra f a where

Methods

algebra :: AlgebraSignature f => f a -> a

An algebra f a -> a corresponds to an instance of a of the class Class f. In some cases, for example for tuple types, you can give an algebra generically for every signature:

instance (Class f m, Class f n) => Algebra f (m, n) where
  algebra fmn = (evaluate (fmap fst fmn), evaluate (fmap snd fmn))

Instances

Algebra f ()

Class f b => Algebra f (STM b)

Class f b => Algebra f (Maybe b)

Class f b => Algebra f (IO b)

(Monoid m, Class f b) => Algebra f (Const m b)

Class f b => Algebra f (Either a b)

Class f b => Algebra f (a -> b)

(Class f m, Class f n) => Algebra f (m, n)

algebraA :: (Applicative g, Class f b, AlgebraSignature f) => f (g b) -> g b

If you just want to applicatively lift existing instances, you can use this default implementation of algebra.