Portability | MPTCs, fundeps |
---|---|
Stability | provisional |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Safe Haskell | None |
The free monad transformer
- data FreeF f a b
- newtype FreeT f m a = FreeT {}
- class Monad m => MonadFree f m | m -> f where
- wrap :: f (m a) -> m a
- liftF :: (Functor f, Monad m) => f a -> FreeT f 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
Documentation
The base functor for a free monad.
Typeable1 f => Typeable2 (FreeF f) | |
(Bifunctor (FreeF f), Bifoldable (FreeF f), Traversable f) => Bitraversable (FreeF f) | |
Functor f => Bifunctor (FreeF f) | |
Foldable f => Bifoldable (FreeF f) | |
Functor f => Functor (FreeF f a) | |
Foldable f => Foldable (FreeF f a) | |
(Functor (FreeF f a), Foldable (FreeF f a), Traversable f) => Traversable (FreeF f a) | |
(Eq a, Eq (f b)) => Eq (FreeF f a b) | |
(Typeable (FreeF f a b), Typeable1 f, Typeable a, Typeable b, Data a, Data (f b), Data b) => Data (FreeF f a b) | |
(Eq (FreeF f a b), Ord a, Ord (f b)) => Ord (FreeF f a b) | |
(Read a, Read (f b)) => Read (FreeF f a b) | |
(Show a, Show (f b)) => Show (FreeF f a b) |
The "free monad transformer" for a functor f
.
class Monad m => MonadFree f m | m -> f whereSource
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
instanceMonad
Tree wherereturn
= 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:
instanceMonadFree
Pair Tree wherewrap
(Pair l r) = Bin l r
Or we could choose to program with
instead of Free
PairTree
and thereby avoid having to define our own Monad
instance.
Moreover, the kan-extensions
package provides MonadFree
instances that can
improve the asymptotic complexity of code that constructors free monads by
effectively reassociating the use of (>>=
).
See Free
for a more formal definition of the free Monad
for a Functor
.
liftF :: (Functor f, Monad m) => f a -> FreeT f m aSource
FreeT is a functor from the category of functors to the category of monads.
This provides the mapping.