Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
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) -> UnsafePrism b b) -> (f a -> a) -> (Base t' b -> b) -> t' -> b
- symplecto :: (Functor f, Functor g) => ((f b -> b) -> UnsafePrism 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
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
:: (Recursive t', Functor f) | |
=> ((f a -> a) -> UnsafePrism b b) | A prism parametric in an F-algebra that allows |
-> (f a -> a) | A (Base t)-algebra |
-> (Base t' b -> b) | A (Base t')-algebra |
-> t' | |
-> b |
A dendromorphism entangles two catamorphisms
:: (Functor f, Functor g) | |
=> ((f b -> b) -> UnsafePrism b b) | A prism 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 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.
:: (Corecursive t', Functor f) | |
=> ((a -> f a) -> Lens' b b) | A lens parametric in an F-coalgebra that allows |
-> (a -> f a) | A (Base t)-coalgebra |
-> (b -> Base t' b) | A (Base t')-coalgebra |
-> 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.