base-4.11.0.0: Basic libraries

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

Description

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

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120


This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120


Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix' argument, hence the recursion is reintroduced.