Copyright	(C) 2008-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable (fundeps, MPTCs)
Safe Haskell	Safe
Language	Haskell2010

Control.Monad.Free.Class

Description

Monads for free.

Synopsis

class Monad m => MonadFree f m | m -> f where
- wrap :: f (m a) -> m a
liftF :: ( Functor f, MonadFree f m) => f a -> m a
wrapT :: ( Functor f, MonadFree f m, MonadTrans t, Monad (t m)) => f (t m a) -> t m a

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

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

Instances

Instances details

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