free-4.2: Monads for free

Portability | MPTCs, fundeps
Stability | provisional
Maintainer | Edward Kmett <ekmett@gmail.com>
Safe Haskell | None

Control.Monad.Trans.Free

Description

The free monad transformer

Synopsis

- data FreeF f a b
  - = Pure a
  - | Free (f b)
- newtype FreeT f m a = FreeT {
  - runFreeT :: m (FreeF f a (FreeT f 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
- iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a
- hoistFreeT :: (Monad m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b
- transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b

# Documentation

data FreeF f a b Source

The base functor for a free monad.

Constructors

Pure a |
Free (f b) |

Instances

Typeable1 f => Typeable2 (FreeF f) |
Traversable f => Bitraversable (FreeF f) |
Functor f => Bifunctor (FreeF f) |
Foldable f => Bifoldable (FreeF f) |
Functor f => Functor (FreeF f a) |
Foldable f => Foldable (FreeF f a) |
Traversable f => Traversable (FreeF f a) |
(Eq a, Eq (f b)) => Eq (FreeF f a b) |
(Typeable1 f, Typeable a, Typeable b, Data a, Data (f b), Data b) => Data (FreeF f a b) |
(Ord a, Ord (f b)) => Ord (FreeF f a b) |
(Read a, Read (f b)) => Read (FreeF f a b) |
(Show a, Show (f b)) => Show (FreeF f a b) |

newtype FreeT f m a Source

The "free monad transformer" for a functor `f`.

Constructors

FreeT |

Fields

runFreeT :: m (FreeF f a (FreeT f m a))

Instances

(Functor f, Monad m) => MonadFree f (FreeT f m) |
MonadTrans (FreeT f) |
(Functor f, Monad m) => Monad (FreeT f m) |
(Functor f, Monad m) => Functor (FreeT f m) |
(Typeable1 f, Typeable1 w) => Typeable1 (FreeT f w) |
(Functor f, MonadPlus m) => MonadPlus (FreeT f m) |
(Functor f, Monad m) => Applicative (FreeT f m) |
(Foldable m, Foldable f) => Foldable (FreeT f m) |
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m) |
(Functor f, MonadPlus m) => Alternative (FreeT f m) |
(Functor f, MonadIO m) => MonadIO (FreeT f m) |
Eq (m (FreeF f a (FreeT f m a))) => Eq (FreeT f m a) |
(Typeable1 f, Typeable1 w, Typeable a, Data (w (FreeF f a (FreeT f w a))), Data a) => Data (FreeT f w a) |
Ord (m (FreeF f a (FreeT f m a))) => Ord (FreeT f m a) |
Read (m (FreeF f a (FreeT f m a))) => Read (FreeT f m a) |
Show (m (FreeF f a (FreeT f m a))) => Show (FreeT f m a) |

class Monad m => MonadFree f m | m -> f where Source

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 ``join` [[a]]` smashes the lists flat.

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 ``Free` Pair` instead of `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`.

Methods

wrap :: f (m a) -> m aSource

Add a layer.

     wrap (fmap f x) ≡ wrap (fmap return x) >>= f

Instances

(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) |
Monad m => MonadFree Identity (IterT m) |
(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) |

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

A version of lift that can be used with just a Functor for f.

iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m aSource

Tear down a free monad transformer using iteration.

hoistFreeT :: (Monad m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n bSource

Lift a monad homomorphism from `m` to `n` into a monad homomorphism from ``FreeT` f m` to ``FreeT` f n`

    hoistFreeT :: (Monad m, Functor f) => (m ~> n) -> FreeT f m ~> FreeT f n

transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m bSource

Lift a natural transformation from `f` to `g` into a monad homomorphism from ``FreeT` f m` to ``FreeT` g n`