# 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
Instances details

Since: base-2.1

Instance details

#### Methods

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

Since: base-2.1

Instance details

#### Methods

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

Since: base-2.1

Instance details

#### Methods

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

Since: base-4.9.0.0

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#### Methods

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

Since: base-4.9.0.0

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#### Methods

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

Since: base-4.12.0.0

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#### Methods

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

Since: base-4.8.0.0

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#### Methods

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

Since: base-4.8.0.0

Instance details

#### Methods

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

Since: base-4.8.0.0

Instance details

#### Methods

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

Since: base-4.8.0.0

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#### Methods

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

Since: base-4.8.0.0

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#### Methods

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

Since: base-4.8.0.0

Instance details

Defined in Data.Functor.Identity

#### Methods

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

Since: base-4.9.0.0

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Defined in Data.Semigroup

#### Methods

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

Since: base-4.9.0.0

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Defined in Data.Semigroup

#### Methods

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

#### Methods

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

Since: base-4.9.0.0

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Defined in Data.Semigroup

#### Methods

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

Since: base-4.3.0.0

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#### Methods

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

Since: base-2.1

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

Since: base-2.1

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

Since: base-4.9.0.0

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#### Methods

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

Since: base-4.8.0.0

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#### Methods

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

Since: base-4.12.0.0

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#### Methods

mfix :: (a -> Ap f a) -> Ap f a Source

MonadFix ((->) r :: Type -> Type)

Since: base-2.1

Instance details

#### Methods

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

Since: base-4.9.0.0

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#### Methods

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

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Product

#### Methods

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

Since: base-4.9.0.0

Instance details

#### 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`.

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.

© The University of Glasgow and others