ghc-internal-9.1001.0: Basic libraries

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 :: Type -> Type) 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.

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
 Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> NonEmpty a) -> NonEmpty a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Data.Functor.Identity Methodsmfix :: (a -> Identity a) -> Identity a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> First a) -> First a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Last a) -> Last a Source # Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Down a) -> Down a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Dual a) -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Product a) -> Product a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Sum a) -> Sum a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Par1 a) -> Par1 a Source # Source # If the function passed to mfix inspects its argument, the resulting action will throw a FixIOException.Since: ghc-internal-2.17.0.0 Instance detailsDefined in GHC.Internal.TH.Syntax Methodsmfix :: (a -> Q a) -> Q a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> IO a) -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Maybe a) -> Maybe a Source # Source # Since: base-4.15 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Solo a) -> Solo a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> [a]) -> [a] Source # MonadFix (ST s) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.ST.Lazy.Imp Methodsmfix :: (a -> ST s a) -> ST s a Source # Source # Since: base-4.3.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Either e a) -> Either e a Source # MonadFix (ST s) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> ST s a) -> ST s a Source # Monoid a => MonadFix ((,) a) Source # Since: base-4.21 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a0 -> (a, a0)) -> (a, a0) Source # MonadFix f => MonadFix (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Ap f a) -> Ap f a Source # MonadFix f => MonadFix (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Alt f a) -> Alt f a Source # MonadFix f => MonadFix (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> Rec1 f a) -> Rec1 f a Source # (MonadFix f, MonadFix g) => MonadFix (f :*: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> (f :*: g) a) -> (f :*: g) a Source # MonadFix ((->) r) Source # Since: base-2.1 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (a -> r -> a) -> r -> a Source # MonadFix f => MonadFix (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Internal.Control.Monad.Fix Methodsmfix :: (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.

When f is strict, this means that because, by the definition of strictness, f ⊥ = ⊥ and such the least defined fixed point of any strict function is ⊥.

#### Examples

Expand

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,

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

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


Using fix, we can implement versions of repeat as fix . (:) and cycle as fix . (++)

>>> take 10 \$ fix (0:)
[0,0,0,0,0,0,0,0,0,0]

>>> map (fix (\rec n -> if n < 2 then n else rec (n - 1) + rec (n - 2))) [1..10]
[1,1,2,3,5,8,13,21,34,55]


#### Implementation Details

Expand

The current implementation of fix uses structural sharing

fix f = let x = f x in x

A more straightforward but non-sharing version would look like

fix f = f (fix f)