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/Haskell 8

Control.Monad.Fix

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

Description

Monadic fixpoints.

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

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 []	Since: 2.1
Methods mfix :: (a -> [a]) -> [a] Source
MonadFix Maybe	Since: 2.1
Methods mfix :: (a -> Maybe a) -> Maybe a Source
MonadFix IO	Since: 2.1
Methods mfix :: (a -> IO a) -> IO a Source
MonadFix Par1	Since: 4.9.0.0
Methods mfix :: (a -> Par1 a) -> Par1 a Source
MonadFix Last	Since: 4.8.0.0
Methods mfix :: (a -> Last a) -> Last a Source
MonadFix First	Since: 4.8.0.0
Methods mfix :: (a -> First a) -> First a Source
MonadFix Product	Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a Source
MonadFix Sum	Since: 4.8.0.0
Methods mfix :: (a -> Sum a) -> Sum a Source
MonadFix Dual	Since: 4.8.0.0
Methods mfix :: (a -> Dual a) -> Dual a Source
MonadFix Identity	Since: 4.8.0.0
Methods mfix :: (a -> Identity a) -> Identity a Source
MonadFix NonEmpty	Since: 4.9.0.0
Methods mfix :: (a -> NonEmpty a) -> NonEmpty a Source
MonadFix Option	Since: 4.9.0.0
Methods mfix :: (a -> Option a) -> Option a Source
MonadFix Last	Since: 4.9.0.0
Methods mfix :: (a -> Last a) -> Last a Source
MonadFix First	Since: 4.9.0.0
Methods mfix :: (a -> First a) -> First a Source
MonadFix Max	Since: 4.9.0.0
Methods mfix :: (a -> Max a) -> Max a Source
MonadFix Min	Since: 4.9.0.0
Methods mfix :: (a -> Min a) -> Min a Source
MonadFix (Either e)	Since: 4.3.0.0
Methods mfix :: (a -> Either e a) -> Either e a Source
MonadFix (ST s)	Since: 2.1
Methods mfix :: (a -> ST s a) -> ST s a Source
MonadFix (ST s)	Since: 2.1
Methods mfix :: (a -> ST s a) -> ST s a Source
MonadFix f => MonadFix (Rec1 * f)	Since: 4.9.0.0
Methods mfix :: (a -> Rec1 * f a) -> Rec1 * f a Source
MonadFix f => MonadFix (Alt * f)	Since: 4.8.0.0
Methods mfix :: (a -> Alt * f a) -> Alt * f a Source
MonadFix ((->) LiftedRep LiftedRep r)	Since: 2.1
Methods mfix :: (a -> (LiftedRep -> LiftedRep) r a) -> (LiftedRep -> LiftedRep) r a Source
(MonadFix f, MonadFix g) => MonadFix ((::) f g)	Since: 4.9.0.0
Methods mfix :: (a -> (* :: f) g a) -> ( :*: f) g a Source
(MonadFix f, MonadFix g) => MonadFix (Product * f g)	Since: 4.9.0.0
Methods mfix :: (a -> Product * f g a) -> Product * f g a Source
MonadFix f => MonadFix (M1 * i c f)	Since: 4.9.0.0
Methods mfix :: (a -> M1 * i c f a) -> M1 * i c f 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.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Control-Monad-Fix.html