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
Description
The free monad transformer
Synopsis
- data FreeF f a b
- newtype FreeT f m a = FreeT {}
- 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
The base functor for a free monad.
Instances
Generic1 (FreeF f a :: Type -> Type) Source # | |
Foldable f => Bifoldable (FreeF f) Source # | |
Functor f => Bifunctor (FreeF f) Source # | |
Traversable f => Bitraversable (FreeF f) Source # | |
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 # | |
Defined in Control.Monad.Trans.Free | |
Ord1 f => Ord2 (FreeF f) Source # | |
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 # | |
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 # | |
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 # | |
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] 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 | |
(Eq1 f, Eq a) => Eq1 (FreeF f a) Source # | |
Defined in Control.Monad.Trans.Free | |
(Ord1 f, Ord a) => Ord1 (FreeF f a) Source # | |
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 # | |
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 # | |
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 # | |
Defined in Control.Monad.Trans.Free | |
Functor f => Functor (FreeF f a) Source # | |
Generic (FreeF f a b) Source # | |
(Read a, Read (f b)) => Read (FreeF f a b) Source # | |
Defined in Control.Monad.Trans.Free | |
(Show a, Show (f b)) => Show (FreeF f a b) Source # | |
(Eq a, Eq (f b)) => Eq (FreeF f a b) Source # | |
(Ord a, Ord (f b)) => Ord (FreeF f a b) Source # | |
Defined in Control.Monad.Trans.Free | |
type Rep1 (FreeF f a :: Type -> Type) Source # | |
Defined in Control.Monad.Trans.Free type Rep1 (FreeF f a :: Type -> Type) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.1.10-K5jEhJUIDyTG2poEakoEDI" '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 # | |
Defined in Control.Monad.Trans.Free type Rep (FreeF f a b) = D1 ('MetaData "FreeF" "Control.Monad.Trans.Free" "free-5.1.10-K5jEhJUIDyTG2poEakoEDI" '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
The "free monad transformer" for a functor f
Instances
(Functor f, Monad m) => MonadFree f (FreeT f m) Source # | |
(Functor f, MonadError e m) => MonadError e (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, Functor m, MonadReader r m) => MonadReader r (FreeT f m) Source # | |
(Functor f, MonadState s m) => MonadState s (FreeT f m) Source # | |
(Functor f, Functor m, MonadWriter w m) => MonadWriter w (FreeT f m) Source # | |
(Functor f, MonadBase b m) => MonadBase b (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
Functor f => MonadTrans (FreeT f) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, MonadFail m) => MonadFail (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, MonadIO m) => MonadIO (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Foldable m, Foldable f) => Foldable (FreeT f m) Source # | |
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 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 | |
(Eq1 f, Eq1 m) => Eq1 (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Ord1 f, Ord1 m) => Ord1 (FreeT f m) Source # | |
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 # | |
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 # | |
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 # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, MonadPlus m) => Alternative (FreeT f m) Source # | |
(Functor f, Monad m) => Applicative (FreeT f m) Source # | |
(Functor f, Monad m) => Functor (FreeT f m) Source # | |
(Functor f, Monad m) => Monad (FreeT f m) Source # | |
(Functor f, MonadPlus m) => MonadPlus (FreeT f m) Source # | |
(Functor f, MonadCatch m) => MonadCatch (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, MonadThrow m) => MonadThrow (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, MonadCont m) => MonadCont (FreeT f m) Source # | |
Defined in Control.Monad.Trans.Free | |
(Functor f, Monad m) => Apply (FreeT f m) Source # | |
(Functor f, Monad m) => Bind (FreeT f m) Source # | |
(Read1 f, Read1 m, Read a) => Read (FreeT f m a) Source # | |
Defined in Control.Monad.Trans.Free | |
(Show1 f, Show1 m, Show a) => Show (FreeT f m a) Source # | |
(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) Source # | |
(Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a) Source # | |
Defined in Control.Monad.Trans.Free |
The free monad
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
to FreeT
f mFreeT
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 #
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
is always terminating, provided each of the
steps in the iteration is terminating.retract
.
cutoff
n
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 ≡ mpartialIterT
(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
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
smashes the lists flat.join
[[a]]
On the other hand, consider:
data Tree a = Bin (Tree a) (Tree a) | Tip a
instanceMonad
Tree wherereturn
= 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:
instanceMonadFree
Pair Tree wherewrap
(Pair l r) = Bin l r
Or we could choose to program with
instead of Free
PairTree
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
Instances
Monad m => MonadFree Identity (IterT m) Source # | |
Functor f => MonadFree f (Free f) Source # | |
Applicative f => MonadFree f (Free f) Source # | |
Functor f => MonadFree f (F f) Source # | |
(Functor f, MonadFree f m) => MonadFree f (ListT m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (MaybeT m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, Monad m) => MonadFree f (FreeT f m) Source # | |
(Applicative f, Applicative m, Monad m) => MonadFree f (FreeT f m) Source # | |
MonadFree f (FT f m) Source # | |
(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (ExceptT e m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (IdentityT m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (ReaderT e m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m) => MonadFree f (ContT r m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source # | |
Defined in Control.Monad.Free.Class | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) Source # | |
Defined in Control.Monad.Free.Class |