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 Source

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 Source

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] Source
MonadFix Maybe
Methods mfix :: (a -> Maybe a) -> Maybe a Source
MonadFix IO
Methods mfix :: (a -> IO a) -> IO a Source
MonadFix Last
Methods mfix :: (a -> Last a) -> Last a Source
MonadFix First
Methods mfix :: (a -> First a) -> First a Source
MonadFix Product
Methods mfix :: (a -> Product a) -> Product a Source
MonadFix Sum
Methods mfix :: (a -> Sum a) -> Sum a Source
MonadFix Dual
Methods mfix :: (a -> Dual a) -> Dual a Source
MonadFix NonEmpty
Methods mfix :: (a -> NonEmpty a) -> NonEmpty a Source
MonadFix Option
Methods mfix :: (a -> Option a) -> Option a Source
MonadFix Last
Methods mfix :: (a -> Last a) -> Last a Source
MonadFix First
Methods mfix :: (a -> First a) -> First a Source
MonadFix Max
Methods mfix :: (a -> Max a) -> Max a Source
MonadFix Min
Methods mfix :: (a -> Min a) -> Min a Source
MonadFix Identity
Methods mfix :: (a -> Identity a) -> Identity a Source
MonadFix ((->) r)
Methods mfix :: (a -> r -> a) -> r -> a Source
MonadFix (Either e)
Methods mfix :: (a -> Either e a) -> Either e a Source
MonadFix (ST s)
Methods mfix :: (a -> ST s a) -> ST s a Source
MonadFix (ST s)
Methods mfix :: (a -> ST s a) -> ST s a Source
MonadFix f => MonadFix (Alt (TYPE Lifted) f)
Methods mfix :: (a -> Alt (TYPE Lifted) f a) -> Alt (TYPE Lifted) f a Source
(MonadFix f, MonadFix g) => MonadFix (Product (TYPE Lifted) f g)
Methods mfix :: (a -> Product (TYPE Lifted) f g a) -> Product (TYPE Lifted) f g a Source

fix :: (a -> a) -> a Source

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