Control.MonadPlus.Free

left-distributive MonadPlus for free.

Documentation

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

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

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

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

(Monad (Free f), Functor f) => MonadFree f (Free f)

(Monad (Free f), Functor f) => MonadFree f (Free f)

(Monad (F f), Functor f) => MonadFree f (F f)

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

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

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

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

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

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

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

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

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

data Free f a

The Free MonadPlus for a Functor f.

Formally

A MonadPlus n is a free MonadPlus for f if every monadplus homomorphism from n to another MonadPlus m is equivalent to a natural transformation from f to m.

We model this internally as if left-distribution holds.

Constructors

Pure a

Free (f (Free f a))

Plus [Free f a]

Instances

MonadTrans Free

This is not a true monad transformer. It is only a monad transformer "up to retract".

(Monad (Free m), Functor m, MonadPlus m, MonadError e m) => MonadError e (Free m)

(Monad (Free m), Functor m, MonadPlus m, MonadReader e m) => MonadReader e (Free m)

(Monad (Free m), Functor m, MonadState s m) => MonadState s (Free m)

(Monoid e, Monad (Free m), Functor m, MonadPlus m, MonadWriter e m) => MonadWriter e (Free m)

(Monad (Free f), Functor f) => MonadFree f (Free f)

Functor f => Monad (Free f)

Functor f => Functor (Free f)

Typeable1 f => Typeable1 (Free f)

(Monad (Free f), Functor f) => MonadPlus (Free f)

(Functor (Free f), Functor f) => Applicative (Free f)

Foldable f => Foldable (Free f)

(Functor (Free f), Foldable (Free f), Traversable f) => Traversable (Free f)

(Applicative (Free f), Functor f) => Alternative (Free f)

(Monad (Free m), Functor m, MonadPlus m, MonadCont m) => MonadCont (Free m)

(Functor (Free f), Functor f) => Apply (Free f)

(Apply (Free f), Functor f) => Bind (Free f)

(Eq (f (Free f a)), Eq a) => Eq (Free f a)

(Typeable (Free f a), Typeable1 f, Typeable a, Data a, Data (f (Free f a))) => Data (Free f a)

(Eq (Free f a), Ord (f (Free f a)), Ord a) => Ord (Free f a)

(Read (f (Free f a)), Read a) => Read (Free f a)

(Show (f (Free f a)), Show a) => Show (Free f a)

Functor f => Monoid (Free f a)

Functor f => Semigroup (Free f a)

retract :: MonadPlus f => Free f a -> f a

retract is the left inverse of lift and liftF

 retract . lift = id
 retract . liftF = id

liftF :: Functor f => f a -> Free f a

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

iter :: Functor f => (f a -> a) -> ([a] -> a) -> Free f a -> a

Tear down a Free Monad using iteration.

hoistFree :: Functor g => (forall a. f a -> g a) -> Free f b -> Free g b

Lift a natural transformation from f to g into a natural transformation from FreeT f to FreeT g.