free-5.1.1: Monads for free

Copyright (C) 2008-2015 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett experimental non-portable (fundeps, MPTCs) Safe Haskell2010

Control.Monad.Free.Class

Description

Monads for free.

Synopsis

# Documentation

class Monad m => MonadFree f m | m -> f where Source #

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.

Minimal complete definition

Nothing

Methods

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

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 Source #

Add a layer.

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

Instances
 (Functor f, MonadFree f m) => MonadFree f (ListT m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (ListT m a) -> ListT m a Source # (Functor f, MonadFree f m) => MonadFree f (MaybeT m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (MaybeT m a) -> MaybeT m a Source # Applicative f => MonadFree f (Free f) Source # Instance detailsDefined in Control.Monad.Free.Ap Methodswrap :: f (Free f a) -> Free f a Source # Functor f => MonadFree f (Free f) Source # Instance detailsDefined in Control.Monad.Free Methodswrap :: f (Free f a) -> Free f a Source # Functor f => MonadFree f (F f) Source # Instance detailsDefined in Control.Monad.Free.Church Methodswrap :: f (F f a) -> F f a Source # Monad m => MonadFree Identity (IterT m) Source # Instance detailsDefined in Control.Monad.Trans.Iter Methodswrap :: Identity (IterT m a) -> IterT m a Source # (Functor f, MonadFree f m) => MonadFree f (ExceptT e m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (ExceptT e m a) -> ExceptT e m a Source # (Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (ErrorT e m a) -> ErrorT e m a Source # (Functor f, MonadFree f m) => MonadFree f (IdentityT m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (IdentityT m a) -> IdentityT m a Source # (Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (WriterT w m a) -> WriterT w m a Source # (Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (WriterT w m a) -> WriterT w m a Source # (Functor f, MonadFree f m) => MonadFree f (StateT s m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (StateT s m a) -> StateT s m a Source # (Functor f, MonadFree f m) => MonadFree f (StateT s m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (StateT s m a) -> StateT s m a Source # (Applicative f, Applicative m, Monad m) => MonadFree f (FreeT f m) Source # Instance detailsDefined in Control.Monad.Trans.Free.Ap Methodswrap :: f (FreeT f m a) -> FreeT f m a Source # (Functor f, Monad m) => MonadFree f (FreeT f m) Source # Instance detailsDefined in Control.Monad.Trans.Free Methodswrap :: f (FreeT f m a) -> FreeT f m a Source # MonadFree f (FT f m) Source # Instance detailsDefined in Control.Monad.Trans.Free.Church Methodswrap :: f (FT f m a) -> FT f m a Source # (Functor f, MonadFree f m) => MonadFree f (ContT r m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (ContT r m a) -> ContT r m a Source # (Functor f, MonadFree f m) => MonadFree f (ReaderT e m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (ReaderT e m a) -> ReaderT e m a Source # (Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (RWST r w s m a) -> RWST r w s m a Source # (Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source # Instance detailsDefined in Control.Monad.Free.Class Methodswrap :: f (RWST r w s m a) -> RWST r w s m a Source #

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

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 Source #

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).