base-4.3.1.0: Basic libraries

Portability | portable
Stability | experimental
Maintainer | libraries@haskell.org

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

- class Monad m => MonadFix m where
  - mfix :: (a -> m a) -> m a
- fix :: (a -> a) -> a

# 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` (`Control.Monad.liftM` h . f) = `Control.Monad.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.

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 [] |
MonadFix IO |
MonadFix Maybe |
MonadFix ((->) r) |
MonadFix (Either e) |
MonadFix (ST s) |
MonadFix (ST s) |

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`.