free-5.1.10: Monads for free
Copyright (C) 2008-2014 Edward Kmett
License BSD-style (see the file LICENSE)
Maintainer Edward Kmett <ekmett@gmail.com>
Stability provisional
Portability non-portable (rank-2 polymorphism, MTPCs)
Safe Haskell Safe
Language Haskell2010

Control.Monad.Trans.Free.Church

Description

Church-encoded free monad transformer.

Synopsis

The free monad transformer

newtype FT f m a Source #

The "free monad transformer" for a functor f

Constructors

FT

Fields

  • runFT :: forall r. (a -> m r) -> ( forall x. (x -> m r) -> f x -> m r) -> m r

Instances

Instances details
( Functor f, Functor m, MonadWriter w m) => MonadWriter w ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

writer :: (a, w) -> FT f m a Source #

tell :: w -> FT f m () Source #

listen :: FT f m a -> FT f m (a, w) Source #

pass :: FT f m (a, w -> w) -> FT f m a Source #

MonadState s m => MonadState s ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

get :: FT f m s Source #

put :: s -> FT f m () Source #

state :: (s -> (a, s)) -> FT f m a Source #

MonadReader r m => MonadReader r ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

ask :: FT f m r Source #

local :: (r -> r) -> FT f m a -> FT f m a Source #

reader :: (r -> a) -> FT f m a Source #

( Functor f, MonadError e m) => MonadError e ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

throwError :: e -> FT f m a Source #

catchError :: FT f m a -> (e -> FT f m a) -> FT 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 #

MonadTrans ( FT f) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

lift :: Monad m => m a -> FT f m a Source #

Monad ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

(>>=) :: FT f m a -> (a -> FT f m b) -> FT f m b Source #

(>>) :: FT f m a -> FT f m b -> FT f m b Source #

return :: a -> FT f m a Source #

Functor ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

fmap :: (a -> b) -> FT f m a -> FT f m b Source #

(<$) :: a -> FT f m b -> FT f m a Source #

MonadFail m => MonadFail ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Applicative ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

pure :: a -> FT f m a Source #

(<*>) :: FT f m (a -> b) -> FT f m a -> FT f m b Source #

liftA2 :: (a -> b -> c) -> FT f m a -> FT f m b -> FT f m c Source #

(*>) :: FT f m a -> FT f m b -> FT f m b Source #

(<*) :: FT f m a -> FT f m b -> FT f m a Source #

( Foldable f, Foldable m, Monad m) => Foldable ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

fold :: Monoid m0 => FT f m m0 -> m0 Source #

foldMap :: Monoid m0 => (a -> m0) -> FT f m a -> m0 Source #

foldMap' :: Monoid m0 => (a -> m0) -> FT f m a -> m0 Source #

foldr :: (a -> b -> b) -> b -> FT f m a -> b Source #

foldr' :: (a -> b -> b) -> b -> FT f m a -> b Source #

foldl :: (b -> a -> b) -> b -> FT f m a -> b Source #

foldl' :: (b -> a -> b) -> b -> FT f m a -> b Source #

foldr1 :: (a -> a -> a) -> FT f m a -> a Source #

foldl1 :: (a -> a -> a) -> FT f m a -> a Source #

toList :: FT f m a -> [a] Source #

null :: FT f m a -> Bool Source #

length :: FT f m a -> Int Source #

elem :: Eq a => a -> FT f m a -> Bool Source #

maximum :: Ord a => FT f m a -> a Source #

minimum :: Ord a => FT f m a -> a Source #

sum :: Num a => FT f m a -> a Source #

product :: Num a => FT f m a -> a Source #

( Monad m, Traversable m, Traversable f) => Traversable ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

traverse :: Applicative f0 => (a -> f0 b) -> FT f m a -> f0 ( FT f m b) Source #

sequenceA :: Applicative f0 => FT f m (f0 a) -> f0 ( FT f m a) Source #

mapM :: Monad m0 => (a -> m0 b) -> FT f m a -> m0 ( FT f m b) Source #

sequence :: Monad m0 => FT f m (m0 a) -> m0 ( FT f m a) Source #

( Functor f, Monad m, Eq1 f, Eq1 m) => Eq1 ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

liftEq :: (a -> b -> Bool ) -> FT f m a -> FT f m b -> Bool Source #

( Functor f, Monad m, Ord1 f, Ord1 m) => Ord1 ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

liftCompare :: (a -> b -> Ordering ) -> FT f m a -> FT f m b -> Ordering Source #

MonadIO m => MonadIO ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

liftIO :: IO a -> FT f m a Source #

Alternative m => Alternative ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

MonadPlus m => MonadPlus ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

mzero :: FT f m a Source #

mplus :: FT f m a -> FT f m a -> FT f m a Source #

MonadThrow m => MonadThrow ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

throwM :: Exception e => e -> FT f m a Source #

( Functor f, MonadCatch m) => MonadCatch ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

catch :: Exception e => FT f m a -> (e -> FT f m a) -> FT f m a Source #

MonadCont m => MonadCont ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

callCC :: ((a -> FT f m b) -> FT f m a) -> FT f m a Source #

Apply ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

(<.>) :: FT f m (a -> b) -> FT f m a -> FT f m b Source #

(.>) :: FT f m a -> FT f m b -> FT f m b Source #

(<.) :: FT f m a -> FT f m b -> FT f m a Source #

liftF2 :: (a -> b -> c) -> FT f m a -> FT f m b -> FT f m c Source #

Bind ( FT f m) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

Methods

(>>-) :: FT f m a -> (a -> FT f m b) -> FT f m b Source #

join :: FT f m ( FT f m a) -> FT f m a Source #

( Functor f, Monad m, Eq1 f, Eq1 m, Eq a) => Eq ( FT f m a) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

( Functor f, Monad m, Ord1 f, Ord1 m, Ord a) => Ord ( FT f m a) Source #
Instance details

Defined in Control.Monad.Trans.Free.Church

The free monad

type F f = FT f Identity Source #

The "free monad" for a functor f .

free :: ( forall r. (a -> r) -> (f r -> r) -> r) -> F f a Source #

Wrap a Church-encoding of a "free monad" as the free monad for a functor.

runF :: Functor f => F f a -> forall r. (a -> r) -> (f r -> r) -> r Source #

Unwrap the Free monad to obtain it's Church-encoded representation.

Operations

improveT :: ( Functor f, Monad m) => ( forall t. MonadFree f (t m) => t m a) -> FreeT f m a Source #

Improve the asymptotic performance of code that builds a free monad transformer with only binds and returns by using FT behind the scenes.

Similar to improve .

toFT :: Monad m => FreeT f m a -> FT f m a Source #

Generate a Church-encoded free monad transformer from a FreeT monad transformer.

fromFT :: ( Monad m, Functor f) => FT f m a -> FreeT f m a Source #

Convert to a FreeT free monad representation.

iterT :: ( Functor f, Monad m) => (f (m a) -> m a) -> FT f m a -> m a Source #

Tear down a free monad transformer using iteration.

iterTM :: ( Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FT f m a -> t m a Source #

Tear down a free monad transformer using iteration over a transformer.

hoistFT :: ( Monad m, Monad n) => ( forall a. m a -> n a) -> FT f m b -> FT f n b Source #

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

hoistFT :: (Monad m, Monad n, Functor f) => (m ~> n) -> FT f m ~> FT f n

transFT :: ( forall a. f a -> g a) -> FT f m b -> FT g m b Source #

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

joinFT :: ( Monad m, Traversable f) => FT f m a -> m ( F f a) Source #

Pull out and join m layers of FreeT f m a .

cutoff :: ( Functor f, Monad m) => Integer -> FT f m a -> FT 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 'retract . cutoff n' is always terminating, provided each of the steps in the iteration is terminating.

Operations of free monad

improve :: Functor f => ( forall m. MonadFree f m => m a) -> Free f a Source #

Improve the asymptotic performance of code that builds a free monad with only binds and returns by using F behind the scenes.

This is based on the "Free Monads for Less" series of articles by Edward Kmett:

http://comonad.com/reader/2011/free-monads-for-less/ http://comonad.com/reader/2011/free-monads-for-less-2/

and "Asymptotic Improvement of Computations over Free Monads" by Janis Voightländer:

http://www.iai.uni-bonn.de/~jv/mpc08.pdf

fromF :: ( Functor f, MonadFree f m) => F f a -> m a Source #

Convert to another free monad representation.

toF :: Free f a -> F f a Source #

Generate a Church-encoded free monad from a Free monad.

retract :: Monad f => F f a -> f a Source #

retract is the left inverse of liftF

retract . liftF = id

retractT :: ( MonadTrans t, Monad (t m), Monad m) => FT (t m) m a -> t m a Source #

Tear down a free monad transformer using iteration over a transformer.

iter :: Functor f => (f a -> a) -> F f a -> a Source #

Tear down an F Monad using iteration.

iterM :: ( Functor f, Monad m) => (f (m a) -> m a) -> F 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 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 :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a Source #

Instances

Instances details
( Functor f, MonadFree f m) => MonadFree f ( ListT m) Source #
Instance details

Defined in Control.Monad.Free.Class

Methods

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

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 ( Free f) Source #
Instance details

Defined in Control.Monad.Free

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 #

Monad m => MonadFree Identity ( IterT m) Source #
Instance details

Defined in Control.Monad.Trans.Iter

( Functor f, MonadFree f m, Error e) => MonadFree f ( ErrorT e m) Source #
Instance details

Defined in Control.Monad.Free.Class

Methods

wrap :: f ( ErrorT e m a) -> ErrorT e 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

( 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 ( 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) => 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 #

( Applicative f, Applicative m, 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 #

( 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 #

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 ( 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 #

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.