Control.Monad.Trans.Free

Every functor f gives rise to a corresponding free monad: Free f.

A free monad over a functor resembles a "list" of that functor:

• pure behaves like [] by not using the functor at all
• wrap behaves like (:) by prepending another layer of the functor

The Free monad

data FreeF f r x

Constructors

Pure r

Wrap (f x)

type Free f = FreeT f Identity

The Free type is isomorphic to:

data Free f r = Pure r | Wrap (f (Free f r))

... except that if you want to pattern match against those constructors, you must first use runFree to unwrap the value first.

Similarly, you don't use the raw constructors to build a value of type Free. You instead use the smart constructors pure (from Control.Applicative) and wrap.

wrap :: Monad m => f (FreeT f m r) -> FreeT f m r

runFree :: Free f r -> FreeF f r (Free f r)

The FreeT monad transformer

data FreeT f m r

A free monad transformer alternates nesting the base functor f and the base monad m.

• f - The functor that generates the free monad
• m - The base monad
• r - The type of the return value

This type commonly arises in coroutine/iteratee libraries under various names.

Constructors

FreeT

Fields

• runFreeT :: m (FreeF f r (FreeT f m r))

Instances

MonadTrans (FreeT f)

Methods

lift :: Monad m => m a -> FreeT f m a

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

Methods

(>>=) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b

(>>) :: FreeT f m a -> FreeT f m b -> FreeT f m b

return :: a -> FreeT f m a

fail :: String -> FreeT f m a

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

Methods

fmap :: (a -> b) -> FreeT f m a -> FreeT f m b

(<$) :: a -> FreeT f m b -> FreeT f m a

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

Methods

pure :: a -> FreeT f m a

(<*>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b

(*>) :: FreeT f m a -> FreeT f m b -> FreeT f m b

(<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a