Control.Monad.Free.Class

Monads 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, 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 a

Add a layer.

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

wrap :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a

Add a layer.

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

Instances

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

Methods

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

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

Methods

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

Applicative f => MonadFree f (Free f)

Methods

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

Functor f => MonadFree f (Free f)

Methods

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

Functor f => MonadFree f (F f)

Methods

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

Monad m => MonadFree Identity (IterT m)

Methods

wrap :: Identity (IterT m a) -> IterT m a

(Functor f, MonadFree f m) => MonadFree f (ExceptT e m)

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

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

Methods

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

MonadFree f (FT f m)

Methods

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

(Functor f, MonadFree f m) => MonadFree f (ContT * r m)

Methods

wrap :: f (ContT * r m a) -> ContT * r m a

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

Methods

wrap :: f (ReaderT * e m a) -> ReaderT * e m a

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

Methods

wrap :: f (RWST r w s m a) -> RWST r w s m a

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

Methods

wrap :: f (RWST r w s m a) -> RWST r w s m a

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

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

wrapT :: (Functor f, MonadFree f m, MonadTrans t, Monad (t m)) => f (t m a) -> t m a

A version of wrap for monad transformers over a free monad.

Note: that this is the default implementation for wrap for MonadFree f (t m).