Copyright	(C) 2008-2013 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	MPTCs, fundeps
Safe Haskell	Safe
Language	Haskell2010

Control.Monad.Trans.Free

Contents

The base functor
The free monad transformer
The free monad
Operations
Operations of free monad
Free Monads With Class

Description

The free monad transformer

Synopsis

data FreeF f a b
- = Pure a
- | Free (f b)
newtype FreeT f m a = FreeT {
- runFreeT :: m (FreeF f a (FreeT f m a))
}
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 :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a
iterTM :: (Functor 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, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b
foldFreeT :: (MonadTrans t, Monad (t m), Monad m) => (forall n x. Monad n => f x -> t n x) -> FreeT f m a -> t m a
transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b
joinFreeT :: (Monad m, Traversable f) => FreeT f m a -> m (Free f a)
cutoff :: (Functor f, 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, Functor 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 :: Functor f => (f a -> a) -> Free f a -> a
iterM :: (Functor 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

data FreeF f a b Source #

The base functor for a free monad.

Constructors

Pure a
Free (f b)

Instances

Instances details

Generic1 (FreeF f a :: Type -> Type) Source #
Instance details Defined in Control.Monad.Trans.Free Associated Types type Rep1 (FreeF f a) :: k -> Type # Methods from1 :: forall (a0 :: k). FreeF f a a0 -> Rep1 (FreeF f a) a0 # to1 :: forall (a0 :: k). Rep1 (FreeF f a) a0 -> FreeF f a a0 #
Foldable f => Bifoldable (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods bifold :: Monoid m => FreeF f m m -> m # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> FreeF f a b -> m # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> FreeF f a b -> c # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> FreeF f a b -> c #
Functor f => Bifunctor (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d # first :: (a -> b) -> FreeF f a c -> FreeF f b c # second :: (b -> c) -> FreeF f a b -> FreeF f a c #
Traversable f => Bitraversable (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> FreeF f a b -> f0 (FreeF f c d) #
Eq1 f => Eq2 (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> FreeF f a c -> FreeF f b d -> Bool #
Ord1 f => Ord2 (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> FreeF f a c -> FreeF f b d -> Ordering #
Read1 f => Read2 (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (FreeF f a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [FreeF f a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (FreeF f a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [FreeF f a b] #
Show1 f => Show2 (FreeF f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> FreeF f a b -> ShowS # liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [FreeF f a b] -> ShowS #
Foldable f => Foldable (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods fold :: Monoid m => FreeF f a m -> m # foldMap :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> FreeF f a a0 -> m # foldr :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> FreeF f a a0 -> b # foldl :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> FreeF f a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> FreeF f a a0 -> a0 # toList :: FreeF f a a0 -> [a0] # null :: FreeF f a a0 -> Bool # length :: FreeF f a a0 -> Int # elem :: Eq a0 => a0 -> FreeF f a a0 -> Bool # maximum :: Ord a0 => FreeF f a a0 -> a0 # minimum :: Ord a0 => FreeF f a a0 -> a0 # sum :: Num a0 => FreeF f a a0 -> a0 # product :: Num a0 => FreeF f a a0 -> a0 #
(Eq1 f, Eq a) => Eq1 (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftEq :: (a0 -> b -> Bool) -> FreeF f a a0 -> FreeF f a b -> Bool #
(Ord1 f, Ord a) => Ord1 (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftCompare :: (a0 -> b -> Ordering) -> FreeF f a a0 -> FreeF f a b -> Ordering #
(Read1 f, Read a) => Read1 (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (FreeF f a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [FreeF f a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (FreeF f a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [FreeF f a a0] #
(Show1 f, Show a) => Show1 (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> FreeF f a a0 -> ShowS # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [FreeF f a a0] -> ShowS #
Traversable f => Traversable (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
Functor f => Functor (FreeF f a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods fmap :: (a0 -> b) -> FreeF f a a0 -> FreeF f a b # (<$) :: a0 -> FreeF f a b -> FreeF f a a0 #
(Typeable f, Typeable b, Data a, Data (f b)) => Data (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> FreeF f a b -> c (FreeF f a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (FreeF f a b) # toConstr :: FreeF f a b -> Constr # dataTypeOf :: FreeF f a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (FreeF f a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (FreeF f a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> FreeF f a b -> FreeF f a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> FreeF f a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> FreeF f a b -> r # gmapQ :: (forall d. Data d => d -> u) -> FreeF f a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> FreeF f a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> FreeF f a b -> m (FreeF f a b) #
Generic (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Associated Types type Rep (FreeF f a b) :: Type -> Type # Methods from :: FreeF f a b -> Rep (FreeF f a b) x # to :: Rep (FreeF f a b) x -> FreeF f a b #
(Read a, Read (f b)) => Read (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Methods readsPrec :: Int -> ReadS (FreeF f a b) # readList :: ReadS [FreeF f a b] # readPrec :: ReadPrec (FreeF f a b) # readListPrec :: ReadPrec [FreeF f a b] #
(Show a, Show (f b)) => Show (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Methods showsPrec :: Int -> FreeF f a b -> ShowS # show :: FreeF f a b -> String # showList :: [FreeF f a b] -> ShowS #
(Eq a, Eq (f b)) => Eq (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Methods (==) :: FreeF f a b -> FreeF f a b -> Bool # (/=) :: FreeF f a b -> FreeF f a b -> Bool #
(Ord a, Ord (f b)) => Ord (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free Methods compare :: FreeF f a b -> FreeF f a b -> Ordering # (<) :: FreeF f a b -> FreeF f a b -> Bool # (<=) :: FreeF f a b -> FreeF f a b -> Bool # (>) :: FreeF f a b -> FreeF f a b -> Bool # (>=) :: FreeF f a b -> FreeF f a b -> Bool # max :: FreeF f a b -> FreeF f a b -> FreeF f a b # min :: FreeF f a b -> FreeF f a b -> FreeF f a b #
type Rep1 (FreeF f a :: Type -> Type) Source #
Instance details Defined in Control.Monad.Trans.Free type Rep1 (FreeF f a :: Type -> Type) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.2-8qBzyCSUwFNB6VzdtqY2wi" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
type Rep (FreeF f a b) Source #
Instance details Defined in Control.Monad.Trans.Free type Rep (FreeF f a b) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.2-8qBzyCSUwFNB6VzdtqY2wi" 'False) (C1 ('MetaCons "Pure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Free" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f b))))

The free monad transformer

newtype FreeT f m a Source #

The "free monad transformer" for a functor f

Constructors

FreeT
Fields runFreeT :: m (FreeF f a (FreeT f m a))

Instances

Instances details

(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 #
(Functor f, MonadError e m) => MonadError e (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods throwError :: e -> FreeT f m a # catchError :: FreeT f m a -> (e -> FreeT f m a) -> FreeT f m a #
(Functor f, MonadReader r m) => MonadReader r (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods ask :: FreeT f m r # local :: (r -> r) -> FreeT f m a -> FreeT f m a # reader :: (r -> a) -> FreeT f m a #
(Functor f, MonadState s m) => MonadState s (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods get :: FreeT f m s # put :: s -> FreeT f m () # state :: (s -> (a, s)) -> FreeT f m a #
(Functor f, MonadWriter w m) => MonadWriter w (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods writer :: (a, w) -> FreeT f m a # tell :: w -> FreeT f m () # listen :: FreeT f m a -> FreeT f m (a, w) # pass :: FreeT f m (a, w -> w) -> FreeT f m a #
(Functor f, MonadBase b m) => MonadBase b (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftBase :: b α -> FreeT f m α Source #
Functor f => MonadTrans (FreeT f) Source #
Instance details Defined in Control.Monad.Trans.Free Methods lift :: Monad m => m a -> FreeT f m a #
(Functor f, MonadFail m) => MonadFail (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods fail :: String -> FreeT f m a #
(Functor f, MonadIO m) => MonadIO (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftIO :: IO a -> FreeT f m a #
(Foldable m, Foldable f) => Foldable (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods fold :: Monoid m0 => FreeT f m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> FreeT f m a -> m0 # foldr :: (a -> b -> b) -> b -> FreeT f m a -> b # foldr' :: (a -> b -> b) -> b -> FreeT f m a -> b # foldl :: (b -> a -> b) -> b -> FreeT f m a -> b # foldl' :: (b -> a -> b) -> b -> FreeT f m a -> b # foldr1 :: (a -> a -> a) -> FreeT f m a -> a # foldl1 :: (a -> a -> a) -> FreeT f m a -> a # toList :: FreeT f m a -> [a] # null :: FreeT f m a -> Bool # length :: FreeT f m a -> Int # elem :: Eq a => a -> FreeT f m a -> Bool # maximum :: Ord a => FreeT f m a -> a # minimum :: Ord a => FreeT f m a -> a # sum :: Num a => FreeT f m a -> a # product :: Num a => FreeT f m a -> a #
(Eq1 f, Eq1 m) => Eq1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftEq :: (a -> b -> Bool) -> FreeT f m a -> FreeT f m b -> Bool #
(Ord1 f, Ord1 m) => Ord1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftCompare :: (a -> b -> Ordering) -> FreeT f m a -> FreeT f m b -> Ordering #
(Read1 f, Read1 m) => Read1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (FreeT f m a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [FreeT f m a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (FreeT f m a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [FreeT f m a] #
(Show1 f, Show1 m) => Show1 (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> FreeT f m a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [FreeT f m a] -> ShowS #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
(Functor f, MonadPlus m) => Alternative (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods empty :: FreeT f m a # (<\|>) :: FreeT f m a -> FreeT f m a -> FreeT f m a # some :: FreeT f m a -> FreeT f m [a] # many :: FreeT f m a -> FreeT f m [a] #
(Functor f, Monad m) => Applicative (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods pure :: a -> FreeT f m a # (<>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b # liftA2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c # (>) :: FreeT f m a -> FreeT f m b -> FreeT f m b # (<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a #
(Functor f, Functor m) => Functor (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free 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) => Monad (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free 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 #
(Functor f, MonadPlus m) => MonadPlus (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods mzero :: FreeT f m a # mplus :: FreeT f m a -> FreeT f m a -> FreeT f m a #
(Functor f, MonadCatch m) => MonadCatch (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods catch :: (HasCallStack, Exception e) => FreeT f m a -> (e -> FreeT f m a) -> FreeT f m a #
(Functor f, MonadThrow m) => MonadThrow (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods throwM :: (HasCallStack, Exception e) => e -> FreeT f m a #
(Functor f, MonadCont m) => MonadCont (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods callCC :: ((a -> FreeT f m b) -> FreeT f m a) -> FreeT f m a #
(Functor f, Monad m) => Apply (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods (<.>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b Source # (.>) :: FreeT f m a -> FreeT f m b -> FreeT f m b Source # (<.) :: FreeT f m a -> FreeT f m b -> FreeT f m a Source # liftF2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c Source #
(Functor f, Monad m) => Bind (FreeT f m) Source #
Instance details Defined in Control.Monad.Trans.Free Methods (>>-) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b Source # join :: FreeT f m (FreeT f m a) -> FreeT f m a Source #
(Read1 f, Read1 m, Read a) => Read (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods readsPrec :: Int -> ReadS (FreeT f m a) # readList :: ReadS [FreeT f m a] # readPrec :: ReadPrec (FreeT f m a) # readListPrec :: ReadPrec [FreeT f m a] #
(Show1 f, Show1 m, Show a) => Show (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods showsPrec :: Int -> FreeT f m a -> ShowS # show :: FreeT f m a -> String # showList :: [FreeT f m a] -> ShowS #
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods (==) :: FreeT f m a -> FreeT f m a -> Bool # (/=) :: FreeT f m a -> FreeT f m a -> Bool #
(Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a) Source #
Instance details Defined in Control.Monad.Trans.Free Methods compare :: FreeT f m a -> FreeT f m a -> Ordering # (<) :: FreeT f m a -> FreeT f m a -> Bool # (<=) :: FreeT f m a -> FreeT f m a -> Bool # (>) :: FreeT f m a -> FreeT f m a -> Bool # (>=) :: FreeT f m a -> FreeT f m a -> Bool # max :: FreeT f m a -> FreeT f m a -> FreeT f m a # min :: FreeT f m a -> FreeT f m a -> FreeT f m a #

The free monad

type Free f = FreeT f Identity Source #

The "free monad" for a functor f.

free :: FreeF f a (Free f a) -> Free f a Source #

Pushes a layer into a free monad value.

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

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

hoistFreeT :: (Functor m, Functor 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 FreeT f m to FreeT f n

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

foldFreeT :: (MonadTrans t, Monad (t m), Monad m) => (forall n x. Monad n => f x -> t n x) -> FreeT f m a -> t m a Source #

The very definition of a free monad transformer is that given a natural transformation you get a monad transformer homomorphism.

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

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

joinFreeT :: (Monad m, Traversable f) => FreeT f m a -> m (Free f a) Source #

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

cutoff :: (Functor f, 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 retract . cutoff n is always terminating, provided each of the steps in the iteration is terminating.

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              ≡ m
partialIterT (n+1) phi . return ≡ return
partialIterT (n+1) phi . lift   ≡ lift
partialIterT (n+1) phi . wrap   ≡ join . lift . phi

intersperseT :: (Monad m, Functor f) => f a -> FreeT f m b -> FreeT f m b Source #

intersperseT f m inserts a layer f between every two layers in m.

intersperseT f . return ≡ return
intersperseT f . lift   ≡ lift
intersperseT f . wrap   ≡ wrap . fmap (iterTM (wrap . (<$ f) . wrap))

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

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

retract is the left inverse of liftF

retract . liftF = id

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

Tear down a FreeF Monad using iteration.

iterM :: (Functor 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 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

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 #