Control.Monad.Trans.Free

The free monad transformer

Documentation

data FreeF f a b

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

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

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, the kan-extensions package provides MonadFree instances that can improve the asymptotic complexity of code that constructors free monads by effectively reassociating the use of (>>=).

See Free for a more formal definition of the free Monad for a Functor.

Methods

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

Add a layer.

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)

(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, Monad m) => f a -> FreeT f m a

FreeT is a functor from the category of functors to the category of monads.

This provides the mapping.

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

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 b

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