Control.Monad.Free.Class

free-4.12.4: Monads for free

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
- 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 #

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 #
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 #
(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)`.