Safe Haskell	Safe-Inferred

Data.Fix

Contents

Description

Fix-point type. It allows to define generic recurion schemes.

 Fix f = f (Fix f)

Type f should be a Functor if you want to use simple recursion schemes or Traversable if you want to use monadic recursion schemes. This style allows you to express recursive functions in non-recursive manner. You can imagine that a non-recursive function holds values of the previous iteration.

Little example:

 type List a = Fix (L a) data L a b = Nil | Cons a b instance Functor (L a) where fmap f x = case x of Nil -> Nil Cons a b -> Cons a (f b) length :: List a -> Int length = cata $ \x -> case x of Nil -> 0 Cons _ n -> n + 1 sum :: Num a => List a -> a sum = cata $ \x -> case x of Nil -> 0 Cons a s -> a + s

Synopsis

Documentation

newtype Fix f Source

A fix-point type.

Constructors

Fix
Fields unFix :: f (Fix f)

Instances

Eq (f (Fix f)) => Eq (Fix f)
Ord (f (Fix f)) => Ord (Fix f)
Show (f (Fix f)) => Show (Fix f)

Simple recursion

Type f should be a Functor. They transform non-recursive functions to recursive ones.

cata :: Functor f => (f a -> a) -> Fix f -> aSource

Catamorphism or generic function fold.

ana :: Functor f => (a -> f a) -> a -> Fix fSource

Anamorphism or generic function unfold.

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

Hylomorphism is anamorphism followed by catamorphism.

(~>) :: Functor f => (a -> f a) -> (f b -> b) -> a -> bSource

Infix version of hylo.

Monadic recursion

Type f should be a Traversable.

cataM :: (Applicative m, Monad m, Traversable t) => (t a -> m a) -> Fix t -> m aSource

Monadic catamorphism.

anaM :: (Applicative m, Monad m, Traversable t) => (a -> m (t a)) -> a -> m (Fix t)Source

Monadic anamorphism.

hyloM :: (Applicative m, Monad m, Traversable t) => (t b -> m b) -> (a -> m (t a)) -> a -> m bSource

Monadic hylomorphism.