base-4.9.0.0: Basic libraries

Copyright(c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2002
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

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 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 (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 (Alt (TYPE Lifted) f) 

Methods

mfix :: (a -> Alt (TYPE Lifted) f a) -> Alt (TYPE Lifted) f a

(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

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.