Portability | non-portable (rank-2 polymorphism) |
---|---|

Stability | provisional |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | None |

"Free Monads for Less"

This is based on the "Free Monads for Less" series of articles:

http://comonad.com/reader/2011/free-monads-for-less/ http://comonad.com/reader/2011/free-monads-for-less-2/

- newtype F f a = F {
- runF :: forall r. (a -> r) -> (f r -> r) -> r

- improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f a
- fromF :: MonadFree f m => F f a -> m a
- iterM :: (Monad m, Functor f) => (f (m a) -> m a) -> F f a -> m a
- toF :: Functor f => Free f a -> F f a
- retract :: Monad m => F m a -> m a
- class Monad m => MonadFree f m | m -> f where
- wrap :: f (m a) -> m a

- liftF :: (Functor f, MonadFree f m) => f a -> m a

# Documentation

The Church-encoded free monad for a functor `f`

.

It is *asymptotically* more efficient to use (`>>=`

) for `F`

than it is to (`>>=`

) with `Free`

.

MonadTrans F | |

Functor f => MonadFree f (F f) | |

MonadReader e m => MonadReader e (F m) | |

MonadWriter w m => MonadWriter w (F m) | |

MonadState s m => MonadState s (F m) | |

Monad (F f) | |

Functor (F f) | |

MonadPlus f => MonadPlus (F f) | |

Applicative (F f) | |

Alternative f => Alternative (F f) | |

Apply (F f) | |

Bind (F f) | |

MonadCont m => MonadCont (F m) |

improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f aSource

Improve the asymptotic performance of code that builds a free monad with only binds and returns by using `F`

behind the scenes.

This is based on the "Free Monads for Less" series of articles by Edward Kmett:

http://comonad.com/reader/2011/free-monads-for-less/ http://comonad.com/reader/2011/free-monads-for-less-2/

and "Asymptotic Improvement of Computations over Free Monads" by Janis Voightländer:

iterM :: (Monad m, Functor f) => (f (m a) -> m a) -> F f a -> m aSource

Like iter for monadic values.

class Monad m => MonadFree f m | m -> f whereSource

Monads provide substitution (`fmap`

) and renormalization (`join`

):

m`>>=`

f =`join`

(`fmap`

f m)

A free `Monad`

is one that does no work during the normalization step beyond simply grafting the two monadic values together.

`[]`

is not a free `Monad`

(in this sense) because

smashes the lists flat.
`join`

[[a]]

On the other hand, consider:

data Tree a = Bin (Tree a) (Tree a) | Tip a

instance`Monad`

Tree where`return`

= Tip Tip a`>>=`

f = f a Bin l r`>>=`

f = Bin (l`>>=`

f) (r`>>=`

f)

This `Monad`

is the free `Monad`

of Pair:

data Pair a = Pair a a

And we could make an instance of `MonadFree`

for it directly:

instance`MonadFree`

Pair Tree where`wrap`

(Pair l r) = Bin l r

Or we could choose to program with

instead of `Free`

Pair`Tree`

and thereby avoid having to define our own `Monad`

instance.

Moreover, Control.Monad.Free.Church provides a `MonadFree`

instance that can improve the *asymptotic* complexity of code that
constructs free monads by effectively reassociating the use of
(`>>=`

). You may also want to take a look at the `kan-extensions`

package (http://hackage.haskell.org/package/kan-extensions).

See `Free`

for a more formal definition of the free `Monad`

for a `Functor`

.

(Functor f, MonadFree f m) => MonadFree f (ListT m) | |

(Functor f, MonadFree f m) => MonadFree f (IdentityT m) | |

(Functor f, MonadFree f m) => MonadFree f (MaybeT m) | |

Functor f => MonadFree f (Free f) | |

Functor f => MonadFree f (Free f) | |

Functor f => MonadFree f (F f) | |

(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) | |

(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) | |

(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) | |

(Functor f, MonadFree f m) => MonadFree f (ContT r m) | |

(Functor f, MonadFree f m) => MonadFree f (StateT s m) | |

(Functor f, MonadFree f m) => MonadFree f (StateT s m) | |

(Functor f, MonadFree f m) => MonadFree f (ReaderT e m) | |

(Functor f, Monad m) => MonadFree f (FreeT f m) | |

(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) | |

(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) |