| Copyright | (c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2002 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Control.Monad.Fix
Description
Monadic fixpoints.
For a detailed discussion, see Levent Erkok's thesis, Value Recursion in Monadic Computations, Oregon Graduate Institute, 2002.
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(fixh)- Left shrinking (or Tightening)
mfix(\x -> a >>= \y -> f x y) = a >>= \y ->mfix(\x -> f x y)- Sliding
mfix(liftMh . f) =liftMh (mfix(f . h))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
Instances
| MonadFix Complex Source # | Since: base-4.15.0.0 |
| MonadFix First Source # | Since: base-4.9.0.0 |
| MonadFix Last Source # | Since: base-4.9.0.0 |
| MonadFix Max Source # | Since: base-4.9.0.0 |
| MonadFix Min Source # | Since: base-4.9.0.0 |
| MonadFix NonEmpty | Since: base-4.9.0.0 |
| MonadFix Identity | Since: base-4.8.0.0 |
| MonadFix First | Since: base-4.8.0.0 |
| MonadFix Last | Since: base-4.8.0.0 |
| MonadFix Down | Since: base-4.12.0.0 |
| MonadFix Dual | Since: base-4.8.0.0 |
| MonadFix Product | Since: base-4.8.0.0 |
| MonadFix Sum | Since: base-4.8.0.0 |
| MonadFix Par1 | Since: base-4.9.0.0 |
| MonadFix IO | Since: base-2.1 |
| MonadFix Maybe | Since: base-2.1 |
| MonadFix Solo | Since: base-4.15 |
| MonadFix [] | Since: base-2.1 |
Defined in GHC.Internal.Control.Monad.Fix | |
| MonadFix (ST s) | Since: base-2.1 |
| MonadFix (Either e) | Since: base-4.3.0.0 |
| MonadFix (ST s) | Since: base-2.1 |
| MonadFix f => MonadFix (Ap f) | Since: base-4.12.0.0 |
| MonadFix f => MonadFix (Alt f) | Since: base-4.8.0.0 |
| MonadFix f => MonadFix (Rec1 f) | Since: base-4.9.0.0 |
| (MonadFix f, MonadFix g) => MonadFix (Product f g) Source # | Since: base-4.9.0.0 |
| (MonadFix f, MonadFix g) => MonadFix (f :*: g) | Since: base-4.9.0.0 |
| MonadFix ((->) r) | Since: base-2.1 |
Defined in GHC.Internal.Control.Monad.Fix | |
| MonadFix f => MonadFix (M1 i c f) | Since: base-4.9.0.0 |
fix ff,
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
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 5120
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)) 5120
Using fix, we can implement versions of repeat as fix . (:)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]