Control.Monad.Trans.Fraxl.Free

The base functor

data FreeF f m a where

The base functor for a free monad.

Constructors

Pure :: a -> FreeF f m a

Free :: f b -> FastTCQueue (Kleisli (FreeT f m)) b a -> FreeF f m a

Instances

(Applicative f, Monad m) => Functor (FreeF f m)

The free monad transformer

newtype FreeT f m a

The "free monad transformer" for an applicative functor f

Constructors

FreeT

Fields

runFreeT :: m (FreeF f m a)

Instances

(Applicative f, Monad m) => MonadFree f (FreeT f m)

(Applicative f, MonadError e m) => MonadError e (FreeT f m)

(Applicative f, MonadReader r m) => MonadReader r (FreeT f m)

(Applicative f, MonadState s m) => MonadState s (FreeT f m)

(Applicative f, MonadWriter w m) => MonadWriter w (FreeT f m)

Monad m => MonadFraxl f (FreerT f m)

(Monad m, (∈) (* -> *) f r) => MonadFraxl f (Fraxl r m)

MonadTrans (FreeT f)

(Applicative f, Monad m) => Monad (FreeT f m)

(Applicative f, Monad m) => Functor (FreeT f m)

(Applicative f, Monad m) => Applicative (FreeT f m)

(Applicative f, MonadPlus m) => Alternative (FreeT f m)

(Applicative f, MonadPlus m) => MonadPlus (FreeT f m)

(Applicative f, MonadThrow m) => MonadThrow (FreeT f m)

(Applicative f, MonadCatch m) => MonadCatch (FreeT f m)

(Applicative f, MonadIO m) => MonadIO (FreeT f m)

(Applicative f, MonadCont m) => MonadCont (FreeT f m)

The free monad

type Free f = FreeT f Identity

The "free monad" for an applicative functor f.

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

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

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

Lift a monad homomorphism from m to n into a monad homomorphism from FreeT f m to FreeT f n

hoistFreeT :: (Monad m, Functor f) => (m ~> n) -> FreeT f m ~> FreeT f n

transFreeT :: (Applicative f, Monad m) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b

Lift a natural transformation from f to g into a monad homomorphism from FreeT f m to FreeT g m

joinFreeT :: forall m f a. (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.

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

retract :: Monad f => Free f a -> f a

retract is the left inverse of liftF

retract . liftF = id

iter :: Applicative f => (f a -> a) -> Free f a -> a

Tear down a Free Monad using iteration.

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 (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

Add a layer.

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

Instances

(Functor f, MonadFree f m) => MonadFree f (MaybeT m)

(Functor f, MonadFree f m) => MonadFree f (ListT m)

(Functor f, MonadFree f m) => MonadFree f (IdentityT m)

(Applicative f, Monad m) => MonadFree f (FreeT f m)

(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m)

(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m)

(Functor f, MonadFree f m) => MonadFree f (StateT s m)

(Functor f, MonadFree f m) => MonadFree f (StateT s m)

(Functor f, MonadFree f m) => MonadFree f (ReaderT e m)

(Functor f, MonadFree f m) => MonadFree f (ExceptT e m)

(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m)

(Functor f, MonadFree f m) => MonadFree f (ContT r m)

(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m)

(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m)