Generics.Regular.Functions.Fold

Summary: Generic folding and unfolding.

Generic folding

type family Alg f r :: *

type Algebra a r = Alg (PF a) r

class Fold f where

The class fold explains how to convert an algebra Alg into a function from functor to result.

Methods

alg :: Alg f r -> f r -> r

Instances

Fold U

Fold I

Fold (K a)

Fold f => Fold (S s f)

Fold f => Fold (C c f)

Fold g => Fold (:*: I g)

Fold g => Fold (:*: (K a) g)

(Fold f, Fold g) => Fold (:+: f g)

fold :: (Regular a, Fold (PF a), Functor (PF a)) => Algebra a r -> a -> r

Fold with convenient algebras.

Generic unfolding

type family CoAlg f s :: *

type CoAlgebra a s = s -> CoAlg (PF a) s

class Unfold f where

The class unfold explains how to convert a coalgebra CoAlg and a seed into a representation.

Methods

coalg :: (s -> a) -> CoAlg f s -> f a

Instances

Unfold U

Unfold I

Unfold (K a)

Unfold f => Unfold (S s f)

Unfold f => Unfold (C c f)

(Unfold f, Unfold g) => Unfold (:*: f g)

(Unfold f, Unfold g) => Unfold (:+: f g)

unfold :: (Unfold (PF a), Regular a) => CoAlgebra a s -> s -> a

Construction of algebras

(&) :: a -> b -> (a, b)

For constructing algebras it is helpful to use this pairing combinator.