free-4.2: Monads for free

Portability | non-portable (fundeps, MPTCs)
Stability | experimental
Maintainer | Edward Kmett <ekmett@gmail.com>
Safe Haskell | Safe-Inferred

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`.

Methods

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

Add a layer.

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

Instances

(Functor f, MonadFree f m) => MonadFree f (ListT m) |
(Functor f, MonadFree f m) => MonadFree f (IdentityT m) |
(Functor f, MonadFree f m) => MonadFree f (MaybeT m) |
Functor f => MonadFree f (Free f) |
Functor f => MonadFree f (Free f) |
Functor f => MonadFree f (F f) |
Monad m => MonadFree Identity (IterT m) |
(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) |
(Functor f, MonadFree f m) => MonadFree f (ContT r m) |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) |
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m) |
(Functor f, Monad m) => MonadFree f (FreeT f m) |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) |

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

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 aSource

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)`.