Data.Functor.Foldable.Exotic

Several extensions to Edward Kmett's recursion schemes package. The monadic recursion schemes and exotic recursion schemes should be stable, but the recursion schemes for interdependent data type (and their attendant typeclasses) are experimental.

Classes

class (Functor f, Functor g) => SubHom f g a b where

Class that yields g-algebra homomorphisms between mutually recursive types.

Minimal complete definition

homo

Methods

homo :: (f a -> a) -> (g b -> b) -> g b -> b

Homomorphism of g-algebras parametrized by an f-algebra

Instances

(Functor ErnieF, Functor BertF) => SubHom ErnieF BertF Ernie Bert

Methods

homo :: (ErnieF Ernie -> Ernie) -> (BertF Bert -> Bert) -> BertF Bert -> Bert

(Functor BertF, Functor ErnieF) => SubHom BertF ErnieF Bert Ernie

Methods

homo :: (BertF Bert -> Bert) -> (ErnieF Ernie -> Ernie) -> ErnieF Ernie -> Ernie

class SubType b where

Minimal complete definition

switch

Methods

switch :: b -> b

Resolve nested functions.

Instances

SubType Ernie

Methods

switch :: Ernie -> Ernie

SubType Bert

Methods

switch :: Bert -> Bert

class (Functor f, Functor g) => CoSubHom f g a b where

Class that yields g-coalgebra homomorphisms between mutually recursive types.

Minimal complete definition

homoCo

Methods

homoCo :: (a -> f a) -> (b -> g b) -> b -> g b

Homomorphism of g-coalgebras paramterized by an f-coalgebra

class Dummy t where

We need this class to make type resolution work.

Minimal complete definition

dummy

Methods

dummy :: t

Instances

Dummy Ernie

Methods

dummy :: Ernie

Dummy Bert

Methods

dummy :: Bert

Monadic recursion schemes

cataM :: (Recursive t, Traversable (Base t), Monad m) => (Base t a -> m a) -> t -> m a

A monadic catamorphism

anaM :: (Corecursive t, Traversable (Base t), Monad m) => (a -> m (Base t a)) -> a -> m t

A monadic anamorphism

hyloM :: (Functor f, Monad m, Traversable f) => (f b -> m b) -> (a -> m (f a)) -> a -> m b

A monadic hylomorphism

Recursion schemes for interdependent data types

dendro

Arguments

:: (SubHom (Base t) (Base t') a b, SubType b, Recursive t')

=> t

dummy type

-> (Base t a -> a)

A (Base t)-algebra

-> (Base t' b -> b)

A (Base t')-algebra

-> t'

-> b

A dendromorphism entangles two catamorphisms

dendroTri

Arguments

:: (SubHom (Base t) (Base t') a b, SubType b, Recursive t', SubHom (Base t'') (Base t) c a, SubType a, Recursive t)

=> t

dummy type

-> t''

another dummy type

-> (Base t'' c -> c)

A (Base t'')-algebra

-> (Base t a -> a)

-> (Base t' b -> b)

-> t'

-> b

Entangle three base functors.

symplecto

Arguments

:: (SubHom g f b b, CoSubHom g f a a)

=> (g b -> b)

A g-algebra

-> (a -> g a)

A g-coalgebra

-> (f b -> b)

An f-algebra

-> (a -> f a)

An f-coalgebra

-> a

-> b

Entangle two hylomorphisms. Not the same thing as a symplectomorphism from geometry.

chema

Arguments

:: (CoSubHom (Base t) (Base t') a b, SubType b, Corecursive t')

=> t

dummy type

-> (a -> Base t a)

-> (b -> Base t' b)

-> b

-> t'

Exotic recursion schemes

dicata :: Recursive a => (Base a (b, a) -> b) -> (Base a (b, a) -> a) -> a -> b

Catamorphism collapsing along two data types simultaneously. Basically a fancy zygomorphism.

micro :: Corecursive a => (b -> Either a (Base a b)) -> b -> a

A micromorphism is an Elgot algebra specialized to unfolding.