| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Data.Functor.Foldable.Exotic
Contents
Description
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.
- cataM :: (Recursive t, Traversable (Base t), Monad m) => (Base t a -> m a) -> t -> m a
- anaM :: (Corecursive t, Traversable (Base t), Monad m) => (a -> m (Base t a)) -> a -> m t
- hyloM :: (Functor f, Monad m, Traversable f) => (f b -> m b) -> (a -> m (f a)) -> a -> m b
- dendro :: (Recursive t', Functor f) => ((f a -> a) -> Trans b b) -> (f a -> a) -> (Base t' b -> b) -> t' -> b
- scolio :: (Functor f, Functor g) => ((f b -> b) -> Trans b b) -> ((a -> f a) -> Lens' a a) -> (g b -> b) -> (a -> g a) -> (f b -> b) -> (a -> f a) -> a -> b
- chema :: (Corecursive t', Functor f) => ((a -> f a) -> Lens' b b) -> (a -> f a) -> (b -> Base t' b) -> b -> t'
- dicata :: Recursive a => (Base a (b, a) -> b) -> (Base a (b, a) -> a) -> a -> b
- micro :: Corecursive a => (b -> Either a (Base a b)) -> b -> a
- mutu :: Recursive t => (Base t (b, a) -> b) -> (Base t (b, a) -> a) -> t -> a
- type Trans s a = forall f. Functor f => (f a -> a) -> f s -> s
- finish :: Eq a => (a -> a) -> a -> a
Monadic recursion schemes
cataM :: (Recursive t, Traversable (Base t), Monad m) => (Base t a -> m a) -> t -> m a Source #
A monadic catamorphism
anaM :: (Corecursive t, Traversable (Base t), Monad m) => (a -> m (Base t a)) -> a -> m t Source #
A monadic anamorphism
hyloM :: (Functor f, Monad m, Traversable f) => (f b -> m b) -> (a -> m (f a)) -> a -> m b Source #
A monadic hylomorphism
Recursion schemes for interdependent data types
Arguments
| :: (Recursive t', Functor f) | |
| => ((f a -> a) -> Trans b b) | A pseudoprism parametric in an \(F \)-algebra that allows |
| -> (f a -> a) | A |
| -> (Base t' b -> b) | A |
| -> t' | |
| -> b |
A dendromorphism entangles two catamorphisms
Arguments
| :: (Functor f, Functor g) | |
| => ((f b -> b) -> Trans b b) | A pseudoprism parametric in an \( F \)-algebra that allows |
| -> ((a -> f a) -> Lens' a a) | A lens parametric in an \( F \)-coalgebra that allows |
| -> (g b -> b) | A |
| -> (a -> g a) | A |
| -> (f b -> b) | An |
| -> (a -> f a) | An |
| -> a | |
| -> b |
Entangle two hylomorphisms.
Arguments
| :: (Corecursive t', Functor f) | |
| => ((a -> f a) -> Lens' b b) | A lens parametric in an \( F \)-coalgebra that allows |
| -> (a -> f a) | A |
| -> (b -> Base t' b) | A |
| -> b | |
| -> t' |
Exotic recursion schemes
dicata :: Recursive a => (Base a (b, a) -> b) -> (Base a (b, a) -> a) -> a -> b Source #
Catamorphism collapsing along two data types simultaneously. Basically a fancy zygomorphism.
micro :: Corecursive a => (b -> Either a (Base a b)) -> b -> a Source #
A micromorphism is an Elgot algebra specialized to unfolding.
Data type for transformations
type Trans s a = forall f. Functor f => (f a -> a) -> f s -> s Source #
A map of \( F \)-algebras (pseudoprism)