Copyright | (C) 2008-2013 Edward Kmett |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | provisional |

Portability | MPTCs, fundeps |

Safe Haskell | Safe |

Language | Haskell2010 |

The free monad transformer

- data FreeF f a b
- newtype FreeT f m a = FreeT {}
- type Free f = FreeT f Identity
- free :: FreeF f a (Free f a) -> Free f a
- runFree :: Free f a -> FreeF f a (Free f a)
- liftF :: (Functor f, MonadFree f m) => f a -> m a
- iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a
- iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a
- hoistFreeT :: (Monad m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b
- transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b
- joinFreeT :: (Monad m, Traversable f) => FreeT f m a -> m (Free f a)
- cutoff :: (Functor f, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a)
- partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b
- intersperseT :: (Monad m, Functor f) => f a -> FreeT f m b -> FreeT f m b
- intercalateT :: (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b
- retractT :: (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a
- retract :: Monad f => Free f a -> f a
- iter :: Functor f => (f a -> a) -> Free f a -> a
- iterM :: (Functor f, Monad m) => (f (m a) -> m a) -> Free f a -> m a
- class Monad m => MonadFree f m | m -> f where
- wrap :: f (m a) -> m a

# The base functor

The base functor for a free monad.

Functor f => Bifunctor (FreeF f) Source | |

Traversable f => Bitraversable (FreeF f) Source | |

Foldable f => Bifoldable (FreeF f) Source | |

Eq1 f => Eq2 (FreeF f) Source | |

Ord1 f => Ord2 (FreeF f) Source | |

Show1 f => Show2 (FreeF f) Source | |

Read1 f => Read2 (FreeF f) Source | |

Functor f => Functor (FreeF f a) Source | |

Foldable f => Foldable (FreeF f a) Source | |

Traversable f => Traversable (FreeF f a) Source | |

(Eq1 f, Eq a) => Eq1 (FreeF f a) Source | |

(Ord1 f, Ord a) => Ord1 (FreeF f a) Source | |

(Show1 f, Show a) => Show1 (FreeF f a) Source | |

(Read1 f, Read a) => Read1 (FreeF f a) Source | |

(Eq a, Eq (f b)) => Eq (FreeF f a b) Source | |

(Ord a, Ord (f b)) => Ord (FreeF f a b) Source | |

(Read a, Read (f b)) => Read (FreeF f a b) Source | |

(Show a, Show (f b)) => Show (FreeF f a b) Source |

# The free monad transformer

The "free monad transformer" for a functor `f`

# The free monad

runFree :: Free f a -> FreeF f a (Free f a) Source

Evaluates the first layer out of a free monad value.

# Operations

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.

iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a Source

Tear down a free monad transformer using iteration.

iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a Source

Tear down a free monad transformer using iteration over a transformer.

joinFreeT :: (Monad m, Traversable f) => FreeT f m a -> m (Free f a) Source

Pull out and join `m`

layers of

.`FreeT`

f m a

cutoff :: (Functor f, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a) Source

Cuts off a tree of computations at a given depth.
If the depth is `0`

or less, no computation nor
monadic effects will take place.

Some examples (`n ≥ 0`

):

`cutoff`

0 _ ≡`return`

`Nothing`

`cutoff`

(n+1)`.`

`return`

≡`return`

`.`

`Just`

`cutoff`

(n+1)`.`

`lift`

≡`lift`

`.`

`liftM`

`Just`

`cutoff`

(n+1)`.`

`wrap`

≡`wrap`

`.`

`fmap`

(`cutoff`

n)

Calling

is always terminating, provided each of the
steps in the iteration is terminating.`retract`

`.`

`cutoff`

n

partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b Source

`partialIterT n phi m`

interprets first `n`

layers of `m`

using `phi`

.
This is sort of the opposite for

.`cutoff`

Some examples (`n ≥ 0`

):

`partialIterT`

0 _ m ≡ m`partialIterT`

(n+1) phi`.`

`return`

≡`return`

`partialIterT`

(n+1) phi`.`

`lift`

≡`lift`

`partialIterT`

(n+1) phi`.`

`wrap`

≡`join`

.`lift`

. phi

intercalateT :: (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b Source

`intercalateT f m`

inserts a layer `f`

between every two layers in
`m`

and then retracts the result.

`intercalateT`

f ≡`retractT`

.`intersperseT`

f

retractT :: (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a Source

Tear down a free monad transformer using Monad instance for `t m`

.

# Operations of free monad

iterM :: (Functor f, Monad m) => (f (m a) -> m a) -> Free f a -> m a Source

Like `iter`

for monadic values.

# Free Monads With Class

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

smashes the lists flat.`join`

[[a]]

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

instead of `Free`

Pair`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`

.

Nothing