# W3cubDocs

#### 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.

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.

Since: 2.1

#### Methods

mfix :: (a -> [a]) -> [a] Source

Since: 2.1

#### Methods

mfix :: (a -> Maybe a) -> Maybe a Source

Since: 2.1

#### Methods

mfix :: (a -> IO a) -> IO a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Par1 a) -> Par1 a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Last a) -> Last a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> First a) -> First a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Product a) -> Product a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Sum a) -> Sum a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Dual a) -> Dual a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Identity a) -> Identity a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> NonEmpty a) -> NonEmpty a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Option a) -> Option a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Last a) -> Last a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> First a) -> First a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Max a) -> Max a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Min a) -> Min a Source

Since: 4.3.0.0

#### Methods

mfix :: (a -> Either e a) -> Either e a Source

Since: 2.1

#### Methods

mfix :: (a -> ST s a) -> ST s a Source

Since: 2.1

#### Methods

mfix :: (a -> ST s a) -> ST s a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Rec1 * f a) -> Rec1 * f a Source

Since: 4.8.0.0

#### Methods

mfix :: (a -> Alt * f a) -> Alt * f a Source

Since: 2.1

#### Methods

mfix :: (a -> (LiftedRep -> LiftedRep) r a) -> (LiftedRep -> LiftedRep) r a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> (* :*: f) g a) -> (* :*: f) g a Source

Since: 4.9.0.0

#### Methods

mfix :: (a -> Product * f g a) -> Product * f g a Source

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`.

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