data-fix-0.2.1: Fixpoint data types

Data.Fix

Description

Fix-point type. It allows to define generic recursion 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 FieldsunFix :: f (Fix f)
Instances

# Simple recursion

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

cata :: Functor f => (f a -> a) -> Fix f -> a Source #

Catamorphism or generic function fold.

ana :: Functor f => (a -> f a) -> a -> Fix f Source #

Anamorphism or generic function unfold.

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

Hylomorphism is anamorphism followed by catamorphism.

(~>) :: Functor f => (a -> f a) -> (f b -> b) -> a -> b Source #

Infix version of hylo.

Type f should be a Traversable.

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