| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Control.Monad.Trans.Free.Ap
Description
Given an applicative, the free monad transformer.
Synopsis
- 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 :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a
- iterTM :: (Applicative 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, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b
- transFreeT :: (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b
- joinFreeT :: (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a)
- cutoff :: (Applicative f, Applicative m, 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, Applicative m, Applicative 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 :: Applicative f => (f a -> a) -> Free f a -> a
- iterM :: (Applicative 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.
Instances
The free monad transformer
The "free monad transformer" for an applicative f
Instances
The free monad
Operations
liftF :: (Functor f, MonadFree f m) => f a -> m a #
A version of lift that can be used with just a Functor for f.
iterT :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a #
Given an applicative homomorphism from f (m a) to m a,
tear down a free monad transformer using iteration.
iterTM :: (Applicative f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a #
Given an applicative homomorphism from f (t m a) to t m a,
tear down a free monad transformer using iteration over a transformer.
hoistFreeT :: (Monad m, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b #
transFreeT :: (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b #
joinFreeT :: (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a) #
Pull out and join m layers of FreeT f m a
cutoff :: (Applicative f, Applicative m, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a) #
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):
cutoff0 _ ≡returnNothingcutoff(n+1).return≡return.Justcutoff(n+1).lift≡lift.liftMJustcutoff(n+1).wrap≡wrap.fmap(cutoffn)
Calling retract . cutoff n
partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b #
partialIterT n phi m interprets first n layers of m using phi.
This is sort of the opposite for cutoff
Some examples (n ≥ 0):
partialIterT0 _ m ≡ mpartialIterT(n+1) phi.return≡returnpartialIterT(n+1) phi.lift≡liftpartialIterT(n+1) phi.wrap≡join.lift. phi
intersperseT :: (Monad m, Applicative m, Applicative 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 #
intercalateT f m inserts a layer f between every two layers in
m and then retracts the result.
intercalateTf ≡retractT.intersperseTf
retractT :: (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a #
Tear down a free monad transformer using Monad instance for t m.
Operations of free monad
iter :: Applicative f => (f a -> a) -> Free f a -> a #
iterM :: (Applicative f, Monad m) => (f (m a) -> m a) -> Free f a -> m a #
Like iter for monadic values.
Free Monads With Class
class Monad m => MonadFree f m | m -> f where #
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
Add a layer.
wrap (fmap f x) ≡ wrap (fmap return x) >>= f
default wrap :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a #