Data.Functor.Foldable.Mod

Module containing the main typeclasses and recursion schemes on them.

zygo : Recursive f t => (f b -> b) -> (f (b, a) -> a) -> t -> a

Zygomorphism (see here for a neat example)

prepro : Recursive f t => Corecursive f t => (f t -> f t) -> (f a -> a) -> t -> a

Prepromorphism. Fold a structure while applying a natural transformation at each step.

postpro : Recursive f t => Corecursive f t => (f t -> f t) -> (a -> f a) -> a -> t

Postpromorphism. Unfold a structure, applying a natural transformation along the way.

para : Recursive f t => Corecursive f t => (f (t, a) -> a) -> t -> a

Paramorphism

mutu : Recursive f t => (f (a, a) -> a) -> (f (a, a) -> a) -> t -> a

Mutumorphism

hylo : Functor f => (f b -> b) -> (a -> f a) -> a -> b

Hylomorphism; equivalent to a catamorphism and an anamorphism taken together.

histo : Recursive f t => (f (Cofree f a) -> a) -> t -> a

Histomorphism

ghylo : Functor f => Comonad w => Monad m => (k : f (w b9) -> w (f b9)) -> (l : m (f c) -> f (m c)) -> (f' : f (w b) -> b) -> (g' : a -> f (m a)) -> a -> b

Generalized hylomorphism

k

A distributive law on f

l

A distributive law on l

f'

A (f . w)-algebra

g'

A (f . m)-coalgebra

gcata : Recursive f t => Comonad w => (k : f (w b) -> w (f b)) -> (g : f (w a) -> a) -> t -> a

Generalized catamorphism

k

A distributive law

g

A (f . w)-algebra

gana : Corecursive f t => Monad m => (k : m (f b) -> f (m b)) -> (g : a -> f (m a)) -> a -> t

Generalized Anamorphism

k

A distributive law

g

A (f . m)-coalgebra

futu : Corecursive f t => (a -> f (Free f a)) -> a -> t

Futumorphism

distHisto : Functor f => f (Cofree f a) -> Cofree f (f a)

Distributive law for histomorphisms

distFutu : Functor f => Free f (f a) -> f (Free f a)

Distributive law for futumorphisms.

distCata : Functor f => f (Identity a) -> Identity (f a)

Distributive law for catamorphisms

distAna : Functor f => Identity (f a) -> f (Identity a)

Distributive law for anamorphisms.

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

Catamorphism interweaving two data types.

chrono : Functor f => (f (Cofree f b) -> b) -> (a -> f (Free f a)) -> a -> b

Chronomorphism

cata : Recursive f t => (f a -> a) -> t -> a

Catamorphism. Folds a structure. (see here)

ana : Corecursive f t => (a -> f a) -> a -> t

Anamorphism, meant to build up a structure recursively.

interface Recursive 

Recursive types correspond to catamorphisms.

project : Recursive f t => t -> f t

interface Corecursive 

Interface for corecursive data types. Corecursive types correspond to
anamorphisms.

embed : Corecursive f t => f t -> t

interface Base 

This is an interface which does nothing interesting, but it functions as a
way of saying "f is a base functor with underlying type t"