| Copyright | (C) 2008-2014 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | provisional |
| Portability | non-portable (rank-2 polymorphism, MTPCs) |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Control.Monad.Trans.Free.Church
Contents
Description
Church-encoded free monad transformer.
Synopsis
- newtype FT f m a = FT {
- runFT :: forall r. (a -> m r) -> (forall x. (x -> m r) -> f x -> m r) -> m r
- type F f = FT f Identity
- free :: (forall r. (a -> r) -> (f r -> r) -> r) -> F f a
- runF :: Functor f => F f a -> forall r. (a -> r) -> (f r -> r) -> r
- improveT :: (Functor f, Monad m) => (forall t. MonadFree f (t m) => t m a) -> FreeT f m a
- toFT :: Monad m => FreeT f m a -> FT f m a
- fromFT :: (Monad m, Functor f) => FT f m a -> FreeT f m a
- iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FT f m a -> m a
- iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FT f m a -> t m a
- hoistFT :: (Monad m, Monad n) => (forall a. m a -> n a) -> FT f m b -> FT f n b
- transFT :: (forall a. f a -> g a) -> FT f m b -> FT g m b
- joinFT :: (Monad m, Traversable f) => FT f m a -> m (F f a)
- cutoff :: (Functor f, Monad m) => Integer -> FT f m a -> FT f m (Maybe a)
- improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f a
- fromF :: (Functor f, MonadFree f m) => F f a -> m a
- toF :: Free f a -> F f a
- retract :: Monad f => F f a -> f a
- retractT :: (MonadTrans t, Monad (t m), Monad m) => FT (t m) m a -> t m a
- iter :: Functor f => (f a -> a) -> F f a -> a
- iterM :: (Functor f, Monad m) => (f (m a) -> m a) -> F f a -> m a
- 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
The free monad transformer
The "free monad transformer" for a functor f
Instances
The free monad
free :: (forall r. (a -> r) -> (f r -> r) -> r) -> F f a Source #
Wrap a Church-encoding of a "free monad" as the free monad for a functor.
runF :: Functor f => F f a -> forall r. (a -> r) -> (f r -> r) -> r Source #
Unwrap the FreeF monad to obtain it's Church-encoded representation.
Operations
toFT :: Monad m => FreeT f m a -> FT f m a Source #
Generate a Church-encoded free monad transformer from a FreeT monad
transformer.
fromFT :: (Monad m, Functor f) => FT f m a -> FreeT f m a Source #
Convert to a FreeT free monad representation.
iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FT 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) -> FT f m a -> t m a Source #
Tear down a free monad transformer using iteration over a transformer.
joinFT :: (Monad m, Traversable f) => FT f m a -> m (F f a) Source #
Pull out and join m layers of FreeT f m a
cutoff :: (Functor f, Monad m) => Integer -> FT f m a -> FT 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 'retract . cutoff n' is always terminating, provided each of the steps in the iteration is terminating.
Operations of free monad
improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f a Source #
Improve the asymptotic performance of code that builds a free monad with only binds and returns by using F behind the scenes.
This is based on the "Free Monads for Less" series of articles by Edward Kmett:
http://comonad.com/reader/2011/free-monads-for-less/ http://comonad.com/reader/2011/free-monads-for-less-2/
and "Asymptotic Improvement of Computations over Free Monads" by Janis Voightländer:
fromF :: (Functor f, MonadFree f m) => F f a -> m a Source #
Convert to another free monad representation.
retractT :: (MonadTrans t, Monad (t m), Monad m) => FT (t m) m a -> t m a Source #
Tear down a free monad transformer using iteration over a transformer.
iterM :: (Functor f, Monad m) => (f (m a) -> m a) -> F 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(fmapf 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]]
On the other hand, consider:
data Tree a = Bin (Tree a) (Tree a) | Tip a
instanceMonadTree 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:
instanceMonadFreePair Tree wherewrap(Pair l r) = Bin l r
Or we could choose to program with Free PairTree
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
wrap :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a Source #
Add a layer.
wrap (fmap f x) ≡ wrap (fmap return x) >>= f