Safe Haskell | Safe |
---|---|
Language | Haskell2010 |
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 :: (Functor 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
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 :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a Source #
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 Source #
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 :: (Functor m, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b Source #
Lift a monad homomorphism from m
to n
into a monad homomorphism from
to FreeT
f mFreeT
f n
hoistFreeT
:: (Functor
m,Applicative
f) => (m ~> n) ->FreeT
f m ~>FreeT
f n
transFreeT :: (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b Source #
joinFreeT :: (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a) Source #
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) 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 ≡ mpartialIterT
(n+1) phi.
return
≡return
partialIterT
(n+1) phi.
lift
≡lift
partialIterT
(n+1) phi.
wrap
≡join
.lift
. phi
intersperseT :: (Monad m, Applicative m, Applicative f) => f a -> FreeT f m b -> FreeT f m b Source #
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
iter :: Applicative f => (f a -> a) -> Free f a -> a Source #
iterM :: (Applicative 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
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, 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