Copyright	(c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2002
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Monad.Fix

Description

Monadic fixpoints.

For a detailed discussion, see Levent Erkok's thesis, Value Recursion in Monadic Computations, Oregon Graduate Institute, 2002.

Synopsis

Documentation

class Monad m => MonadFix m where #

Monads having fixed points with a 'knot-tying' semantics. Instances of MonadFix should satisfy the following laws:

purity: mfix (return . h) = return (fix h)
left shrinking (or tightening): mfix (\x -> a >>= \y -> f x y) = a >>= \y -> mfix (\x -> f x y)
sliding: mfix (liftM h . f) = liftM h (mfix (f . h)), for strict h.
nesting: mfix (\x -> mfix (\y -> f x y)) = mfix (\x -> f x x)

This class is used in the translation of the recursive do notation supported by GHC and Hugs.

Minimal complete definition

mfix

Methods

mfix :: (a -> m a) -> m a #

The fixed point of a monadic computation. mfix f executes the action f only once, with the eventual output fed back as the input. Hence f should not be strict, for then mfix f would diverge.

Instances

MonadFix [] #
Methods mfix :: (a -> [a]) -> [a] #
MonadFix Maybe #
Methods mfix :: (a -> Maybe a) -> Maybe a #
MonadFix IO #
Methods mfix :: (a -> IO a) -> IO a #
MonadFix Par1 #
Methods mfix :: (a -> Par1 a) -> Par1 a #
MonadFix Last #
Methods mfix :: (a -> Last a) -> Last a #
MonadFix First #
Methods mfix :: (a -> First a) -> First a #
MonadFix Product #
Methods mfix :: (a -> Product a) -> Product a #
MonadFix Sum #
Methods mfix :: (a -> Sum a) -> Sum a #
MonadFix Dual #
Methods mfix :: (a -> Dual a) -> Dual a #
MonadFix NonEmpty #
Methods mfix :: (a -> NonEmpty a) -> NonEmpty a #
MonadFix Option #
Methods mfix :: (a -> Option a) -> Option a #
MonadFix Last #
Methods mfix :: (a -> Last a) -> Last a #
MonadFix First #
Methods mfix :: (a -> First a) -> First a #
MonadFix Max #
Methods mfix :: (a -> Max a) -> Max a #
MonadFix Min #
Methods mfix :: (a -> Min a) -> Min a #
MonadFix Identity #
Methods mfix :: (a -> Identity a) -> Identity a #
MonadFix ((->) r) #
Methods mfix :: (a -> r -> a) -> r -> a #
MonadFix (Either e) #
Methods mfix :: (a -> Either e a) -> Either e a #
MonadFix f => MonadFix (Rec1 f) #
Methods mfix :: (a -> Rec1 f a) -> Rec1 f a #
MonadFix (ST s) #
Methods mfix :: (a -> ST s a) -> ST s a #
MonadFix (ST s) #
Methods mfix :: (a -> ST s a) -> ST s a #
(MonadFix f, MonadFix g) => MonadFix ((:*:) f g) #
Methods mfix :: (a -> (f :: g) a) -> (f :: g) a #
MonadFix f => MonadFix (Alt * f) #
Methods mfix :: (a -> Alt * f a) -> Alt * f a #
MonadFix f => MonadFix (M1 i c f) #
Methods mfix :: (a -> M1 i c f a) -> M1 i c f a #
(MonadFix f, MonadFix g) => MonadFix (Product * f g) #
Methods mfix :: (a -> Product * f g a) -> Product * f g a #

fix :: (a -> a) -> a #

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.