# W3cubDocs

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

#### Description

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

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.

#### 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

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`.

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