module Control.Comonad.Cofree
( Cofree(..)
, ComonadCofree(..)
, section
, coiter
, unfold
, _extract
, _unwrap
, telescoped
) where
import Control.Applicative
import Control.Comonad
import Control.Comonad.Trans.Class
import Control.Comonad.Cofree.Class
import Control.Comonad.Env.Class
import Control.Comonad.Store.Class as Class
import Control.Comonad.Traced.Class
import Control.Category
import Data.Functor.Bind
import Data.Functor.Extend
import Data.Distributive
import Data.Foldable
import Data.Semigroup
import Data.Traversable
import Data.Semigroup.Foldable
import Data.Semigroup.Traversable
import Prelude hiding (id,(.))
#ifdef GHC_TYPEABLE
import Data.Data
#endif
infixr 5 :<
data Cofree f a = a :< f (Cofree f a)
coiter :: Functor f => (a -> f a) -> a -> Cofree f a
coiter psi a = a :< (coiter psi <$> psi a)
unfold :: Functor f => (b -> (a, f b)) -> b -> Cofree f a
unfold f c = case f c of
(x, d) -> x :< fmap (unfold f) d
instance Functor f => ComonadCofree f (Cofree f) where
unwrap (_ :< as) = as
instance Distributive f => Distributive (Cofree f) where
distribute w = fmap extract w :< fmap distribute (collect unwrap w)
instance Functor f => Functor (Cofree f) where
fmap f (a :< as) = f a :< fmap (fmap f) as
b <$ (_ :< as) = b :< fmap (b <$) as
instance Functor f => Extend (Cofree f) where
extended = extend
duplicated = duplicate
instance Functor f => Comonad (Cofree f) where
extend f w = f w :< fmap (extend f) (unwrap w)
duplicate w = w :< fmap duplicate (unwrap w)
extract (a :< _) = a
instance ComonadTrans Cofree where
lower (_ :< as) = fmap extract as
instance Alternative f => Monad (Cofree f) where
return x = x :< empty
(a :< m) >>= k = case k a of
b :< n -> b :< (n <|> fmap (>>= k) m)
section :: Comonad f => f a -> Cofree f a
section as = extract as :< extend section as
instance Apply f => Apply (Cofree f) where
(f :< fs) <.> (a :< as) = f a :< ((<.>) <$> fs <.> as)
(f :< fs) <. (_ :< as) = f :< ((<. ) <$> fs <.> as)
(_ :< fs) .> (a :< as) = a :< (( .>) <$> fs <.> as)
instance ComonadApply f => ComonadApply (Cofree f) where
(f :< fs) <@> (a :< as) = f a :< ((<@>) <$> fs <@> as)
(f :< fs) <@ (_ :< as) = f :< ((<@ ) <$> fs <@> as)
(_ :< fs) @> (a :< as) = a :< (( @>) <$> fs <@> as)
instance Applicative f => Applicative (Cofree f) where
pure a = as where as = a :< pure as
(f :< fs) <*> (a :< as) = f a :< ((<*>) <$> fs <*> as)
(f :< fs) <* (_ :< as) = f :< ((<* ) <$> fs <*> as)
(_ :< fs) *> (a :< as) = a :< (( *>) <$> fs <*> as)
instance (Show (f (Cofree f a)), Show a) => Show (Cofree f a) where
showsPrec d (a :< as) = showParen (d > 5) $
showsPrec 6 a . showString " :< " . showsPrec 5 as
instance (Read (f (Cofree f a)), Read a) => Read (Cofree f a) where
readsPrec d r = readParen (d > 5)
(\r' -> [(u :< v,w) |
(u, s) <- readsPrec 6 r',
(":<", t) <- lex s,
(v, w) <- readsPrec 5 t]) r
instance (Eq (f (Cofree f a)), Eq a) => Eq (Cofree f a) where
a :< as == b :< bs = a == b && as == bs
instance (Ord (f (Cofree f a)), Ord a) => Ord (Cofree f a) where
compare (a :< as) (b :< bs) = case compare a b of
LT -> LT
EQ -> compare as bs
GT -> GT
instance Foldable f => Foldable (Cofree f) where
foldMap f = go where
go (a :< as) = f a `mappend` foldMap go as
instance Foldable1 f => Foldable1 (Cofree f) where
foldMap1 f = go where
go (a :< as) = f a <> foldMap1 go as
instance Traversable f => Traversable (Cofree f) where
traverse f = go where
go (a :< as) = (:<) <$> f a <*> traverse go as
instance Traversable1 f => Traversable1 (Cofree f) where
traverse1 f = go where
go (a :< as) = (:<) <$> f a <.> traverse1 go as
#ifdef GHC_TYPEABLE
instance (Typeable1 f) => Typeable1 (Cofree f) where
typeOf1 dfa = mkTyConApp cofreeTyCon [typeOf1 (f dfa)]
where
f :: Cofree f a -> f a
f = undefined
instance (Typeable1 f, Typeable a) => Typeable (Cofree f a) where
typeOf = typeOfDefault
cofreeTyCon :: TyCon
#if __GLASGOW_HASKELL__ < 704
cofreeTyCon = mkTyCon "Control.Comonad.Cofree.Cofree"
#else
cofreeTyCon = mkTyCon3 "free" "Control.Comonad.Cofree" "Cofree"
#endif
instance
( Typeable1 f
, Data (f (Cofree f a))
, Data a
) => Data (Cofree f a) where
gfoldl f z (a :< as) = z (:<) `f` a `f` as
toConstr _ = cofreeConstr
gunfold k z c = case constrIndex c of
1 -> k (k (z (:<)))
_ -> error "gunfold"
dataTypeOf _ = cofreeDataType
dataCast1 f = gcast1 f
cofreeConstr :: Constr
cofreeConstr = mkConstr cofreeDataType ":<" [] Infix
cofreeDataType :: DataType
cofreeDataType = mkDataType "Control.Comonad.Cofree.Cofree" [cofreeConstr]
#endif
instance ComonadEnv e w => ComonadEnv e (Cofree w) where
ask = ask . lower
instance ComonadStore s w => ComonadStore s (Cofree w) where
pos (_ :< as) = Class.pos as
peek s (_ :< as) = extract (Class.peek s as)
instance ComonadTraced m w => ComonadTraced m (Cofree w) where
trace m = trace m . lower
_extract :: Functor f => (a -> f a) -> Cofree g a -> f (Cofree g a)
_extract f (a :< as) = (:< as) <$> f a
_unwrap :: Functor f => (g (Cofree g a) -> f (g (Cofree g a))) -> Cofree g a -> f (Cofree g a)
_unwrap f (a :< as) = (a :<) <$> f as
telescoped :: (Functor f, Functor g) =>
[(Cofree g a -> f (Cofree g a)) -> g (Cofree g a) -> f (g (Cofree g a))] ->
(a -> f a) -> Cofree g a -> f (Cofree g a)
telescoped = Prelude.foldr (\l r -> _unwrap . l . r) _extract