Safe Haskell	Safe
Language	Haskell2010

Monad.Trans

Contents

MonadTrans
Free monad transformer

Synopsis

class MonadTrans (t :: (* -> *) -> * -> *) where
data FreeF (f :: * -> *) a b
- = Pure a
- | Free (f b)
liftF :: (Functor f, MonadFree f m) => f a -> 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)
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
newtype FreeT (f :: * -> *) (m :: * -> *) a = FreeT {
- runFreeT :: m (FreeF f a (FreeT f 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 :: (Monad 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)
retractT :: (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a
class Monad m => MonadFree (f :: * -> *) (m :: * -> *) | m -> f where

MonadTrans

class MonadTrans (t :: (* -> *) -> * -> *) where #

The class of monad transformers. Instances should satisfy the following laws, which state that lift is a monad transformation:

```
lift . return = return
```
```
lift (m >>= f) = lift m >>= (lift . f)
```

Minimal complete definition

lift

Methods

lift :: Monad m => m a -> t m a #

Lift a computation from the argument monad to the constructed monad.

Instances

MonadTrans MaybeT
Instance details Defined in Control.Monad.Trans.Maybe Methods lift :: Monad m => m a -> MaybeT m a #
MonadTrans Free	This is not a true monad transformer. It is only a monad transformer "up to `retract`".
Instance details Defined in Control.Monad.Free Methods lift :: Monad m => m a -> Free m a #
MonadTrans Yoneda
Instance details Defined in Data.Functor.Yoneda Methods lift :: Monad m => m a -> Yoneda m a #
MonadTrans ListT
Instance details Defined in List.Transformer Methods lift :: Monad m => m a -> ListT m a #
MonadTrans LogicT
Instance details Defined in Control.Monad.Logic Methods lift :: Monad m => m a -> LogicT m a #
MonadTrans (IdentityT :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Trans.Identity Methods lift :: Monad m => m a -> IdentityT m a #
MonadTrans (ExceptT e)
Instance details Defined in Control.Monad.Trans.Except Methods lift :: Monad m => m a -> ExceptT e m a #
MonadTrans (FreeT f)
Instance details Defined in Control.Monad.Trans.Free Methods lift :: Monad m => m a -> FreeT f m a #
Alternative f => MonadTrans (CofreeT f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods lift :: Monad m => m a -> CofreeT f m a #
MonadTrans (ErrorT e)
Instance details Defined in Control.Monad.Trans.Error Methods lift :: Monad m => m a -> ErrorT e m a #
MonadTrans (StateT s)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods lift :: Monad m => m a -> StateT s m a #
MonadTrans (StateT s)
Instance details Defined in Control.Monad.Trans.State.Strict Methods lift :: Monad m => m a -> StateT s m a #
MonadTrans (WriterT w)
Instance details Defined in Control.Monad.Trans.Writer.CPS.Internal Methods lift :: Monad m => m a -> WriterT w m a #
MonadTrans (ReaderT r :: (* -> ) -> -> *)
Instance details Defined in Control.Monad.Trans.Reader Methods lift :: Monad m => m a -> ReaderT r m a #
MonadTrans (ParsecT e s)
Instance details Defined in Text.Megaparsec.Internal Methods lift :: Monad m => m a -> ParsecT e s m a #
MonadTrans (ContT r)
Instance details Defined in Control.Monad.Trans.Cont Methods lift :: Monad m => m a -> ContT r m a #

Free monad transformer

data FreeF (f :: * -> *) a b #

The base functor for a free monad.

Constructors

Pure a
Free (f b)

Instances

Traversable f => Bitraversable (FreeF f)
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) #
Foldable f => Bifoldable (FreeF f)
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)
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 #
Eq1 f => Eq2 (FreeF f)
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)
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)
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)
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 #
Generic1 (FreeF f a :: * -> *)
Instance details Defined in Control.Monad.Trans.Free Associated Types type Rep1 (FreeF f a) :: k -> * # Methods from1 :: FreeF f a a0 -> Rep1 (FreeF f a) a0 # to1 :: Rep1 (FreeF f a) a0 -> FreeF f a a0 #
Functor f => Functor (FreeF f a)
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 #
Foldable f => Foldable (FreeF f a)
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 # 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 #
Traversable f => Traversable (FreeF f a)
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) #
(Eq1 f, Eq a) => Eq1 (FreeF f a)
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)
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)
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)
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 #
(Eq a, Eq (f b)) => Eq (FreeF f a b)
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)
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 #
(Read a, Read (f b)) => Read (FreeF f a b)
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)
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 #
Generic (FreeF f a b)
Instance details Defined in Control.Monad.Trans.Free Associated Types type Rep (FreeF f a b) :: * -> * # Methods from :: FreeF f a b -> Rep (FreeF f a b) x # to :: Rep (FreeF f a b) x -> FreeF f a b #
type Rep1 (FreeF f a :: * -> *)
Instance details Defined in Control.Monad.Trans.Free type Rep1 (FreeF f a :: * -> *) = D1 (MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.1-9P5wnlKdQjU2MUQcy2f6zg" 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)
Instance details Defined in Control.Monad.Trans.Free type Rep (FreeF f a b) = D1 (MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.1-9P5wnlKdQjU2MUQcy2f6zg" 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))))

liftF :: (Functor f, MonadFree f m) => f a -> m a #

A version of lift that can be used with just a Functor for f.

type Free (f :: * -> *) = FreeT f Identity #

The "free monad" for a functor f.

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

Pushes a layer into a free monad value.

runFree :: Free f a -> FreeF f a (Free f a) #

Evaluates the first layer out of a free monad value.

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

retract is the left inverse of liftF

retract . liftF = id

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

Tear down a Free Monad using iteration.

iterM :: (Functor f, Monad m) => (f (m a) -> m a) -> Free f a -> m a #

Like iter for monadic values.

newtype FreeT (f :: * -> *) (m :: * -> *) a #

The "free monad transformer" for a functor f

Constructors

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

Instances

(Functor f, MonadReader r m) => MonadReader r (FreeT f m)
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)
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, Monad m) => MonadFree f (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods wrap :: f (FreeT f m a) -> FreeT f m a #
(Functor f, MonadError e m) => MonadError e (FreeT f m)
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, MonadWriter w m) => MonadWriter w (FreeT f m)
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)
Instance details Defined in Control.Monad.Trans.Free Methods liftBase :: b α -> FreeT f m α #
MonadTrans (FreeT f)
Instance details Defined in Control.Monad.Trans.Free Methods lift :: Monad m => m a -> FreeT f m a #
(Functor f, Monad m) => Monad (FreeT f m)
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 # fail :: String -> FreeT f m a #
(Functor f, Monad m) => Functor (FreeT f m)
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) => MonadFail (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods fail :: String -> FreeT f m a #
(Functor f, Monad m) => Applicative (FreeT f m)
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 #
(Foldable m, Foldable f) => Foldable (FreeT f m)
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 # 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 #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
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)
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, MonadPlus m) => MonadPlus (FreeT f m)
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 #
(Eq1 f, Eq1 m) => Eq1 (FreeT f m)
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)
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)
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)
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 #
(Functor f, MonadIO m) => MonadIO (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods liftIO :: IO a -> FreeT f m a #
(Functor f, MonadThrow m) => MonadThrow (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods throwM :: Exception e => e -> FreeT f m a #
(Functor f, MonadCatch m) => MonadCatch (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods catch :: Exception e => FreeT f m a -> (e -> FreeT f m a) -> FreeT f m a #
(Functor f, Monad m) => Apply (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods (<.>) :: 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 # liftF2 :: (a -> b -> c) -> FreeT f m a -> FreeT f m b -> FreeT f m c #
(Functor f, MonadCont m) => MonadCont (FreeT f m)
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) => Bind (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods (>>-) :: FreeT f m a -> (a -> FreeT f m b) -> FreeT f m b # join :: FreeT f m (FreeT f m a) -> FreeT f m a #
(Functor f, Zoom m n s t) => Zoom (FreeT f m) (FreeT f n) s t
Instance details Defined in Control.Lens.Zoom Methods zoom :: LensLike' (Zoomed (FreeT f m) c) t s -> FreeT f m c -> FreeT f n c #
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a)
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)
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 #
(Read1 f, Read1 m, Read a) => Read (FreeT f m a)
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)
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 #
(Traversable f, Traversable m) => Plated (FreeT f m a)
Instance details Defined in Control.Lens.Plated Methods plate :: Traversal' (FreeT f m a) (FreeT f m a) #
Wrapped (FreeT f m a)
Instance details Defined in Control.Lens.Wrapped Associated Types type Unwrapped (FreeT f m a) :: * # Methods _Wrapped' :: Iso' (FreeT f m a) (Unwrapped (FreeT f m a)) #
t ~ FreeT f' m' a' => Rewrapped (FreeT f m a) t
Instance details Defined in Control.Lens.Wrapped
type Zoomed (FreeT f m)
Instance details Defined in Control.Lens.Zoom type Zoomed (FreeT f m) = FocusingFree f m (Zoomed m)
type Unwrapped (FreeT f m a)
Instance details Defined in Control.Lens.Wrapped type Unwrapped (FreeT f m a) = m (FreeF f a (FreeT f m a))

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

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 #

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

hoistFreeT :: (Monad m, Functor 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

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 #

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 #

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) #

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.

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.

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)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (MaybeT m a) -> MaybeT m a #
(Functor f, MonadFree f m) => MonadFree f (ListT m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ListT m a) -> ListT m a #
(Functor f, MonadFree f m) => MonadFree f (Yoneda m)
Instance details Defined in Data.Functor.Yoneda Methods wrap :: f (Yoneda m a) -> Yoneda m a #
Functor f => MonadFree f (Free f)
Instance details Defined in Control.Monad.Free Methods wrap :: f (Free f a) -> Free f a #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (WriterT w m a) -> WriterT w m a #
(Functor f, MonadFree f m) => MonadFree f (StateT s m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a #
(Functor f, MonadFree f m) => MonadFree f (StateT s m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (StateT s m a) -> StateT s m a #
(Functor f, MonadFree f m) => MonadFree f (IdentityT m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (IdentityT m a) -> IdentityT m a #
(Functor f, MonadFree f m) => MonadFree f (ExceptT e m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ExceptT e m a) -> ExceptT e m a #
(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ErrorT e m a) -> ErrorT e m a #
(Functor f, Monad m) => MonadFree f (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods wrap :: f (FreeT f m a) -> FreeT f m a #
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ReaderT e m a) -> ReaderT e m a #
(Functor f, MonadFree f m) => MonadFree f (ContT r m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (ContT r m a) -> ContT r m a #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a #
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m)
Instance details Defined in Control.Monad.Free.Class Methods wrap :: f (RWST r w s m a) -> RWST r w s m a #