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|
{-# LANGUAGE CPP
, FlexibleContexts
, FlexibleInstances
, UndecidableInstances
, MultiParamTypeClasses #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Comonad.Cofree
-- Copyright : (C) 2008-2011 Edward Kmett,
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : Edward Kmett <ekmett@gmail.com>
-- Stability : provisional
-- Portability : MPTCs, fundeps
--
-- Cofree comonads
--
----------------------------------------------------------------------------
module Control.Comonad.Cofree
( Cofree(..)
, section
, unwrap
, coiter
, unfold
-- * Lenses into cofree comonads
, extractLens
, unwrapLens
, telescope
) 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.Trans.Store
import Control.Comonad.Traced.Class
import Control.Category
import Data.Lens.Common
import Data.Functor.Bind
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 <$) as
instance Functor f => Extend (Cofree f) where
extend f w = f w :< fmap (extend f) (unwrap w)
duplicate w = w :< fmap duplicate (unwrap w)
instance Functor f => Comonad (Cofree f) where
extract (a :< _) = a
instance ComonadTrans Cofree where
lower (_ :< as) = fmap extract as
-- | lower . section = id
section :: Comonad f => f a -> Cofree f a
section as = extract as :< extend section as
instance Apply f => Apply (Cofree f) where
(f :< fs) <.> (a :< as) = f a :< ((<.>) <$> fs <.> as)
(f :< fs) <. (_ :< as) = f :< ((<. ) <$> fs <.> as)
(_ :< fs) .> (a :< as) = a :< (( .>) <$> fs <.> as)
instance 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 (a :< as) = f a `mappend` foldMap (foldMap f) as
instance Foldable1 f => Foldable1 (Cofree f) where
foldMap1 f (a :< as) = f a <> foldMap1 (foldMap1 f) as
instance Traversable f => Traversable (Cofree f) where
traverse f (a :< as) = (:<) <$> f a <*> traverse (traverse f) as
instance Traversable1 f => Traversable1 (Cofree f) where
traverse1 f (a :< as) = (:<) <$> f a <.> traverse1 (traverse1 f) 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
{-# NOINLINE cofreeTyCon #-}
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
{-# NOINLINE cofreeConstr #-}
cofreeDataType :: DataType
cofreeDataType = mkDataType "Control.Comonad.Cofree.Cofree" [cofreeConstr]
{-# NOINLINE cofreeDataType #-}
#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
extractLens :: Lens (Cofree f a) a
extractLens = Lens $ \(a :< as) -> store (:< as) a
unwrapLens :: Lens (Cofree f a) (f (Cofree f a))
unwrapLens = Lens $ \(a :< as) -> store (a :<) as
-- |
-- We'd prefer the following non-Haskell 98 type to make parametricity clearer,
-- but this suffices
--
-- > telescope :: (forall b. [Lens (f b) b]) -> Lens (Cofree f a) a
telescope :: [Lens (f (Cofree f a)) (Cofree f a)] -> Lens (Cofree f a) a
telescope [] = extractLens
telescope (l:ls) = telescope ls . l . unwrapLens
|
