| 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 | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| 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 where #
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
, for strictmfix(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 # | Since: base-4.15.0.0 |
Defined in Data.Complex | |
| MonadFix Identity # | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| MonadFix First # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix Last # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix Down # | Since: base-4.12.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix First # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadFix Last # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadFix Max # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadFix Min # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadFix Option # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadFix Dual # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix Product # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix Sum # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix NonEmpty # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix Par1 # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix IO # | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFix Maybe # | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFix Solo # | Since: base-4.15 |
Defined in Control.Monad.Fix | |
| MonadFix [] # | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFix (ST s) # | Since: base-2.1 |
Defined in Control.Monad.ST.Lazy.Imp | |
| MonadFix (Either e) # | Since: base-4.3.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix (ST s) # | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFix f => MonadFix (Ap f) # | Since: base-4.12.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix f => MonadFix (Alt f) # | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix f => MonadFix (Rec1 f) # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| (MonadFix f, MonadFix g) => MonadFix (Product f g) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
| (MonadFix f, MonadFix g) => MonadFix (f :*: g) # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| MonadFix ((->) r) # | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFix f => MonadFix (M1 i c f) # | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
is the least fixed point of the function fix ff,
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 5120
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)) 5120
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.