free-4.5: Monads for free

PortabilityMPTCs, fundeps
Stabilityprovisional
MaintainerEdward Kmett <ekmett@gmail.com>
Safe HaskellNone

Control.Monad.Trans.Free

Contents

Description

The free monad transformer

Synopsis

The base functor

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) 

The free monad transformer

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, MonadError e m) => MonadError e (FreeT f m) 
(Functor f, MonadReader r m) => MonadReader r (FreeT f m) 
(Functor f, MonadState s m) => MonadState s (FreeT f m) 
(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) 
(Functor f, MonadCont m) => MonadCont (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) 

The free monad

type Free f = FreeT f IdentitySource

The "free monad" for a functor f.

free :: FreeF f a (Free f a) -> Free f aSource

runFree :: Free f a -> FreeF f a (Free f a)Source

Operations

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

Operations of free monad

retract :: Monad f => Free f a -> f aSource

retract is the left inverse of liftF

 retract . liftF = id

iter :: Functor f => (f a -> a) -> Free f a -> aSource

Tear down a Free Monad using iteration.

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

Like iter for monadic values.

Free Monads With Class

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 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 (FT 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)