Safe Haskell	Safe
Language	Haskell2010

Control.Monad.Free.Ap

Description

"Applicative Effects in Free Monads"

Often times, the (\<*\>) operator can be more efficient than ap. Conventional free monads don't provide any means of modeling this. The free monad can be modified to make use of an underlying applicative. But it does require some laws, or else the (\<*\>) = ap law is broken. When interpreting this free monad with foldFree, the natural transformation must be an applicative homomorphism. An applicative homomorphism hm :: (Applicative f, Applicative g) => f x -> g x will satisfy these laws.

```
hm (pure a) = pure a
```
```
hm (f <*> a) = hm f <*> hm a
```

This is based on the "Applicative Effects in Free Monads" series of articles by Will Fancher

Synopsis

class Monad m => MonadFree (f :: Type -> Type) (m :: Type -> Type) | m -> f where
- wrap :: f (m a) -> m a
data Free (f :: Type -> Type) a
- = Pure a
- | Free (f (Free f a))
retract :: Monad f => Free f a -> f a
liftF :: (Functor f, MonadFree f m) => f a -> m a
iter :: Applicative f => (f a -> a) -> Free f a -> a
iterA :: (Applicative p, Applicative f) => (f (p a) -> p a) -> Free f a -> p a
iterM :: (Monad m, Applicative f) => (f (m a) -> m a) -> Free f a -> m a
hoistFree :: (Applicative f, Applicative g) => (forall a. f a -> g a) -> Free f b -> Free g b
foldFree :: (Applicative f, Monad m) => (forall x. f x -> m x) -> Free f a -> m a
toFreeT :: forall (f :: Type -> Type) (m :: Type -> Type) a. (Applicative f, Monad m) => Free f a -> FreeT f m a
cutoff :: forall (f :: Type -> Type) a. Applicative f => Integer -> Free f a -> Free f (Maybe a)
unfold :: Applicative f => (b -> Either a (f b)) -> b -> Free f a
unfoldM :: (Applicative f, Traversable f, Monad m) => (b -> m (Either a (f b))) -> b -> m (Free f a)
_Pure :: forall (f :: Type -> Type) m a p. (Choice p, Applicative m) => p a (m a) -> p (Free f a) (m (Free f a))
_Free :: forall f m a p. (Choice p, Applicative m) => p (f (Free f a)) (m (f (Free f a))) -> p (Free f a) (m (Free f a))

Documentation

class Monad m => MonadFree (f :: Type -> Type) (m :: Type -> Type) | 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 join [[a]] smashes the lists flat.

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 Free Pair instead of 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.

Minimal complete definition

Nothing

Methods

wrap :: f (m a) -> m a Source #

Add a layer.

wrap (fmap f x) ≡ wrap (fmap return x) >>= f

default wrap :: forall (t :: (Type -> Type) -> Type -> Type) (n :: Type -> Type) a. (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a Source #

Instances

Instances details

Monad m => MonadFree Identity (IterT m) Source #
Instance details Defined in Control.Monad.Trans.Iter Methods wrap :: Identity (IterT m a) -> IterT m a Source #
Functor f => MonadFree f (Free f) Source #
Instance details Defined in Control.Monad.Free Methods wrap :: f (Free f a) -> Free f a Source #
Applicative f => MonadFree f (Free f) Source #
Instance details Defined in Control.Monad.Free.Ap Methods wrap :: f (Free f a) -> Free f a Source #
Functor f => MonadFree f (F f) Source #
Instance details Defined in Control.Monad.Free.Church Methods wrap :: f (F f a) -> F f a Source #
(Functor f, MonadFree f m) => MonadFree f (MaybeT m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (MaybeT m a) -> MaybeT m a Source #
(Functor f, Monad m) => MonadFree f (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods wrap :: f (FreeT f m a) -> FreeT f m a Source #
(Applicative f, Monad m) => MonadFree f (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Ap Methods wrap :: f (FreeT f m a) -> FreeT f m a Source #
MonadFree f (FT f m) Source #
Instance details Defined in Control.Monad.Trans.Free.Church Methods wrap :: f (FT f m a) -> FT f m a Source #
(Functor f, MonadFree f m) => MonadFree f (ExceptT e m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ExceptT e m a) -> ExceptT e m a Source #
(Functor f, MonadFree f m) => MonadFree f (IdentityT m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (IdentityT m a) -> IdentityT m a Source #
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ReaderT e m a) -> ReaderT e m a Source #
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a Source #
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a Source #
(Functor f, MonadFree f m) => MonadFree f (ContT r m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ContT r m a) -> ContT r m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a Source #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source #
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a Source #

data Free (f :: Type -> Type) a Source #

A free monad given an applicative

Constructors

Pure a
Free (f (Free f a))

Instances

Instances details

MonadTrans Free Source #

This is not a true monad transformer. It is only a monad transformer "up to retract".

Instance details