free-4.12.4: 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
```

Instances

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