Control.Monad.Trans.Free

The free monad transformer

Documentation

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 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 (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.