{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Rank2Types #-}
#if __GLASGOW_HASKELL__ >= 707
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE Safe #-}
#else
{-# LANGUAGE Trustworthy #-}
#endif
#include "free-common.h"
module Control.Comonad.Trans.Cofree
( CofreeT(..)
, Cofree, cofree, runCofree
, CofreeF(..)
, ComonadCofree(..)
, headF
, tailF
, transCofreeT
, coiterT
) 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.Hoist.Class
import Control.Category
import Data.Bifunctor
import Data.Bifoldable
import Data.Bitraversable
import Data.Foldable
import Data.Functor.Classes
import Data.Functor.Identity
import Data.Traversable
import Control.Monad (liftM)
import Control.Monad.Trans
import Control.Monad.Zip
import Prelude hiding (id,(.))
import Data.Data
#if __GLASGOW_HASKELL__ >= 707
import GHC.Generics hiding (Infix, Prefix)
#endif
#if !(MIN_VERSION_base(4,8,0))
import Data.Monoid
#endif
infixr 5 :<
data CofreeF f a b = a :< f b
deriving (CofreeF f a b -> CofreeF f a b -> Bool
(CofreeF f a b -> CofreeF f a b -> Bool)
-> (CofreeF f a b -> CofreeF f a b -> Bool) -> Eq (CofreeF f a b)
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
forall (f :: * -> *) a b.
(Eq a, Eq (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
/= :: CofreeF f a b -> CofreeF f a b -> Bool
$c/= :: forall (f :: * -> *) a b.
(Eq a, Eq (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
== :: CofreeF f a b -> CofreeF f a b -> Bool
$c== :: forall (f :: * -> *) a b.
(Eq a, Eq (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
Eq,Eq (CofreeF f a b)
Eq (CofreeF f a b)
-> (CofreeF f a b -> CofreeF f a b -> Ordering)
-> (CofreeF f a b -> CofreeF f a b -> Bool)
-> (CofreeF f a b -> CofreeF f a b -> Bool)
-> (CofreeF f a b -> CofreeF f a b -> Bool)
-> (CofreeF f a b -> CofreeF f a b -> Bool)
-> (CofreeF f a b -> CofreeF f a b -> CofreeF f a b)
-> (CofreeF f a b -> CofreeF f a b -> CofreeF f a b)
-> Ord (CofreeF f a b)
CofreeF f a b -> CofreeF f a b -> Bool
CofreeF f a b -> CofreeF f a b -> Ordering
CofreeF f a b -> CofreeF f a b -> CofreeF f a b
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
forall (f :: * -> *) a b. (Ord a, Ord (f b)) => Eq (CofreeF f a b)
forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Ordering
forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> CofreeF f a b
min :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b
$cmin :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> CofreeF f a b
max :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b
$cmax :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> CofreeF f a b
>= :: CofreeF f a b -> CofreeF f a b -> Bool
$c>= :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
> :: CofreeF f a b -> CofreeF f a b -> Bool
$c> :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
<= :: CofreeF f a b -> CofreeF f a b -> Bool
$c<= :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
< :: CofreeF f a b -> CofreeF f a b -> Bool
$c< :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Bool
compare :: CofreeF f a b -> CofreeF f a b -> Ordering
$ccompare :: forall (f :: * -> *) a b.
(Ord a, Ord (f b)) =>
CofreeF f a b -> CofreeF f a b -> Ordering
$cp1Ord :: forall (f :: * -> *) a b. (Ord a, Ord (f b)) => Eq (CofreeF f a b)
Ord,Int -> CofreeF f a b -> ShowS
[CofreeF f a b] -> ShowS
CofreeF f a b -> String
(Int -> CofreeF f a b -> ShowS)
-> (CofreeF f a b -> String)
-> ([CofreeF f a b] -> ShowS)
-> Show (CofreeF f a b)
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
Int -> CofreeF f a b -> ShowS
forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
[CofreeF f a b] -> ShowS
forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
CofreeF f a b -> String
showList :: [CofreeF f a b] -> ShowS
$cshowList :: forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
[CofreeF f a b] -> ShowS
show :: CofreeF f a b -> String
$cshow :: forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
CofreeF f a b -> String
showsPrec :: Int -> CofreeF f a b -> ShowS
$cshowsPrec :: forall (f :: * -> *) a b.
(Show a, Show (f b)) =>
Int -> CofreeF f a b -> ShowS
Show,ReadPrec [CofreeF f a b]
ReadPrec (CofreeF f a b)
Int -> ReadS (CofreeF f a b)
ReadS [CofreeF f a b]
(Int -> ReadS (CofreeF f a b))
-> ReadS [CofreeF f a b]
-> ReadPrec (CofreeF f a b)
-> ReadPrec [CofreeF f a b]
-> Read (CofreeF f a b)
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadPrec [CofreeF f a b]
forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadPrec (CofreeF f a b)
forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
Int -> ReadS (CofreeF f a b)
forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadS [CofreeF f a b]
readListPrec :: ReadPrec [CofreeF f a b]
$creadListPrec :: forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadPrec [CofreeF f a b]
readPrec :: ReadPrec (CofreeF f a b)
$creadPrec :: forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadPrec (CofreeF f a b)
readList :: ReadS [CofreeF f a b]
$creadList :: forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
ReadS [CofreeF f a b]
readsPrec :: Int -> ReadS (CofreeF f a b)
$creadsPrec :: forall (f :: * -> *) a b.
(Read a, Read (f b)) =>
Int -> ReadS (CofreeF f a b)
Read
#if __GLASGOW_HASKELL__ >= 707
,Typeable, (forall x. CofreeF f a b -> Rep (CofreeF f a b) x)
-> (forall x. Rep (CofreeF f a b) x -> CofreeF f a b)
-> Generic (CofreeF f a b)
forall x. Rep (CofreeF f a b) x -> CofreeF f a b
forall x. CofreeF f a b -> Rep (CofreeF f a b) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall (f :: * -> *) a b x. Rep (CofreeF f a b) x -> CofreeF f a b
forall (f :: * -> *) a b x. CofreeF f a b -> Rep (CofreeF f a b) x
$cto :: forall (f :: * -> *) a b x. Rep (CofreeF f a b) x -> CofreeF f a b
$cfrom :: forall (f :: * -> *) a b x. CofreeF f a b -> Rep (CofreeF f a b) x
Generic, (forall a. CofreeF f a a -> Rep1 (CofreeF f a) a)
-> (forall a. Rep1 (CofreeF f a) a -> CofreeF f a a)
-> Generic1 (CofreeF f a)
forall a. Rep1 (CofreeF f a) a -> CofreeF f a a
forall a. CofreeF f a a -> Rep1 (CofreeF f a) a
forall k (f :: k -> *).
(forall (a :: k). f a -> Rep1 f a)
-> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f
forall (f :: * -> *) a a. Rep1 (CofreeF f a) a -> CofreeF f a a
forall (f :: * -> *) a a. CofreeF f a a -> Rep1 (CofreeF f a) a
$cto1 :: forall (f :: * -> *) a a. Rep1 (CofreeF f a) a -> CofreeF f a a
$cfrom1 :: forall (f :: * -> *) a a. CofreeF f a a -> Rep1 (CofreeF f a) a
Generic1
#endif
)
#ifdef LIFTED_FUNCTOR_CLASSES
instance Show1 f => Show2 (CofreeF f) where
liftShowsPrec2 :: (Int -> a -> ShowS)
-> ([a] -> ShowS)
-> (Int -> b -> ShowS)
-> ([b] -> ShowS)
-> Int
-> CofreeF f a b
-> ShowS
liftShowsPrec2 Int -> a -> ShowS
spa [a] -> ShowS
_sla Int -> b -> ShowS
spb [b] -> ShowS
slb Int
d (a
a :< f b
fb) =
Bool -> ShowS -> ShowS
showParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
5) (ShowS -> ShowS) -> ShowS -> ShowS
forall a b. (a -> b) -> a -> b
$
Int -> a -> ShowS
spa Int
6 a
a ShowS -> ShowS -> ShowS
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. String -> ShowS
showString String
" :< " ShowS -> ShowS -> ShowS
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> f b -> ShowS
forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
liftShowsPrec Int -> b -> ShowS
spb [b] -> ShowS
slb Int
6 f b
fb
instance (Show1 f, Show a) => Show1 (CofreeF f a) where
liftShowsPrec :: (Int -> a -> ShowS)
-> ([a] -> ShowS) -> Int -> CofreeF f a a -> ShowS
liftShowsPrec = (Int -> a -> ShowS)
-> ([a] -> ShowS)
-> (Int -> a -> ShowS)
-> ([a] -> ShowS)
-> Int
-> CofreeF f a a
-> ShowS
forall (f :: * -> * -> *) a b.
Show2 f =>
(Int -> a -> ShowS)
-> ([a] -> ShowS)
-> (Int -> b -> ShowS)
-> ([b] -> ShowS)
-> Int
-> f a b
-> ShowS
liftShowsPrec2 Int -> a -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec [a] -> ShowS
forall a. Show a => [a] -> ShowS
showList
#else
instance (Functor f, Show1 f, Show a) => Show1 (CofreeF f a) where
showsPrec1 d (a :< fb) = showParen (d > 5) $
showsPrec 6 a . showString " :< " . showsPrec1 6 fb
#endif
#ifdef LIFTED_FUNCTOR_CLASSES
instance Read1 f => Read2 (CofreeF f) where
liftReadsPrec2 :: (Int -> ReadS a)
-> ReadS [a]
-> (Int -> ReadS b)
-> ReadS [b]
-> Int
-> ReadS (CofreeF f a b)
liftReadsPrec2 Int -> ReadS a
rpa ReadS [a]
_rla Int -> ReadS b
rpb ReadS [b]
rlb Int
d =
Bool -> ReadS (CofreeF f a b) -> ReadS (CofreeF f a b)
forall a. Bool -> ReadS a -> ReadS a
readParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
5) (ReadS (CofreeF f a b) -> ReadS (CofreeF f a b))
-> ReadS (CofreeF f a b) -> ReadS (CofreeF f a b)
forall a b. (a -> b) -> a -> b
$
(\String
r' -> [ (a
u a -> f b -> CofreeF f a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< f b
v, String
w)
| (a
u, String
s) <- Int -> ReadS a
rpa Int
6 String
r'
, (String
":<", String
t) <- ReadS String
lex String
s
, (f b
v, String
w) <- (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (f b)
forall (f :: * -> *) a.
Read1 f =>
(Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
liftReadsPrec Int -> ReadS b
rpb ReadS [b]
rlb Int
6 String
t
])
instance (Read1 f, Read a) => Read1 (CofreeF f a) where
liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (CofreeF f a a)
liftReadsPrec = (Int -> ReadS a)
-> ReadS [a]
-> (Int -> ReadS a)
-> ReadS [a]
-> Int
-> ReadS (CofreeF f a a)
forall (f :: * -> * -> *) a b.
Read2 f =>
(Int -> ReadS a)
-> ReadS [a]
-> (Int -> ReadS b)
-> ReadS [b]
-> Int
-> ReadS (f a b)
liftReadsPrec2 Int -> ReadS a
forall a. Read a => Int -> ReadS a
readsPrec ReadS [a]
forall a. Read a => ReadS [a]
readList
#else
instance (Read1 f, Read a) => Read1 (CofreeF f a) where
readsPrec1 d =
readParen (d > 5) $
(\r' -> [ (u :< v,w)
| (u, s) <- readsPrec 6 r'
, (":<", t) <- lex s
, (v, w) <- readsPrec1 6 t
])
#endif
#ifdef LIFTED_FUNCTOR_CLASSES
instance Eq1 f => Eq2 (CofreeF f) where
liftEq2 :: (a -> b -> Bool)
-> (c -> d -> Bool) -> CofreeF f a c -> CofreeF f b d -> Bool
liftEq2 a -> b -> Bool
eqa c -> d -> Bool
eqfb (a
a :< f c
fb) (b
a' :< f d
fb') = a -> b -> Bool
eqa a
a b
a' Bool -> Bool -> Bool
&& (c -> d -> Bool) -> f c -> f d -> Bool
forall (f :: * -> *) a b.
Eq1 f =>
(a -> b -> Bool) -> f a -> f b -> Bool
liftEq c -> d -> Bool
eqfb f c
fb f d
fb'
instance (Eq1 f, Eq a) => Eq1 (CofreeF f a) where
liftEq :: (a -> b -> Bool) -> CofreeF f a a -> CofreeF f a b -> Bool
liftEq = (a -> a -> Bool)
-> (a -> b -> Bool) -> CofreeF f a a -> CofreeF f a b -> Bool
forall (f :: * -> * -> *) a b c d.
Eq2 f =>
(a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool
liftEq2 a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==)
#else
instance (Eq1 f, Eq a) => Eq1 (CofreeF f a) where
eq1 (a :< fb) (a' :< fb') = a == a' && eq1 fb fb'
#endif
#ifdef LIFTED_FUNCTOR_CLASSES
instance Ord1 f => Ord2 (CofreeF f) where
liftCompare2 :: (a -> b -> Ordering)
-> (c -> d -> Ordering)
-> CofreeF f a c
-> CofreeF f b d
-> Ordering
liftCompare2 a -> b -> Ordering
cmpa c -> d -> Ordering
cmpfb (a
a :< f c
fb) (b
a' :< f d
fb') =
case a -> b -> Ordering
cmpa a
a b
a' of
Ordering
LT -> Ordering
LT
Ordering
EQ -> (c -> d -> Ordering) -> f c -> f d -> Ordering
forall (f :: * -> *) a b.
Ord1 f =>
(a -> b -> Ordering) -> f a -> f b -> Ordering
liftCompare c -> d -> Ordering
cmpfb f c
fb f d
fb'
Ordering
GT -> Ordering
GT
instance (Ord1 f, Ord a) => Ord1 (CofreeF f a) where
liftCompare :: (a -> b -> Ordering) -> CofreeF f a a -> CofreeF f a b -> Ordering
liftCompare = (a -> a -> Ordering)
-> (a -> b -> Ordering)
-> CofreeF f a a
-> CofreeF f a b
-> Ordering
forall (f :: * -> * -> *) a b c d.
Ord2 f =>
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> f a c -> f b d -> Ordering
liftCompare2 a -> a -> Ordering
forall a. Ord a => a -> a -> Ordering
compare
#else
instance (Ord1 f, Ord a) => Ord1 (CofreeF f a) where
compare1 (a :< fb) (a' :< fb') =
case compare a a' of
LT -> LT
EQ -> compare1 fb fb'
GT -> GT
#endif
headF :: CofreeF f a b -> a
headF :: CofreeF f a b -> a
headF (a
a :< f b
_) = a
a
tailF :: CofreeF f a b -> f b
tailF :: CofreeF f a b -> f b
tailF (a
_ :< f b
as) = f b
as
instance Functor f => Functor (CofreeF f a) where
fmap :: (a -> b) -> CofreeF f a a -> CofreeF f a b
fmap a -> b
f (a
a :< f a
as) = a
a a -> f b -> CofreeF f a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f f a
as
instance Foldable f => Foldable (CofreeF f a) where
foldMap :: (a -> m) -> CofreeF f a a -> m
foldMap a -> m
f (a
_ :< f a
as) = (a -> m) -> f a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f f a
as
instance Traversable f => Traversable (CofreeF f a) where
traverse :: (a -> f b) -> CofreeF f a a -> f (CofreeF f a b)
traverse a -> f b
f (a
a :< f a
as) = (a
a a -> f b -> CofreeF f a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:<) (f b -> CofreeF f a b) -> f (f b) -> f (CofreeF f a b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse a -> f b
f f a
as
instance Functor f => Bifunctor (CofreeF f) where
bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d
bimap a -> b
f c -> d
g (a
a :< f c
as) = a -> b
f a
a b -> f d -> CofreeF f b d
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< (c -> d) -> f c -> f d
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap c -> d
g f c
as
instance Foldable f => Bifoldable (CofreeF f) where
bifoldMap :: (a -> m) -> (b -> m) -> CofreeF f a b -> m
bifoldMap a -> m
f b -> m
g (a
a :< f b
as) = a -> m
f a
a m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` (b -> m) -> f b -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap b -> m
g f b
as
instance Traversable f => Bitraversable (CofreeF f) where
bitraverse :: (a -> f c) -> (b -> f d) -> CofreeF f a b -> f (CofreeF f c d)
bitraverse a -> f c
f b -> f d
g (a
a :< f b
as) = c -> f d -> CofreeF f c d
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
(:<) (c -> f d -> CofreeF f c d) -> f c -> f (f d -> CofreeF f c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f c
f a
a f (f d -> CofreeF f c d) -> f (f d) -> f (CofreeF f c d)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (b -> f d) -> f b -> f (f d)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse b -> f d
g f b
as
transCofreeF :: (forall x. f x -> g x) -> CofreeF f a b -> CofreeF g a b
transCofreeF :: (forall x. f x -> g x) -> CofreeF f a b -> CofreeF g a b
transCofreeF forall x. f x -> g x
t (a
a :< f b
fb) = a
a a -> g b -> CofreeF g a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< f b -> g b
forall x. f x -> g x
t f b
fb
{-# INLINE transCofreeF #-}
newtype CofreeT f w a = CofreeT { CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT :: w (CofreeF f a (CofreeT f w a)) }
#if __GLASGOW_HASKELL__ >= 707
deriving Typeable
#endif
type Cofree f = CofreeT f Identity
cofree :: CofreeF f a (Cofree f a) -> Cofree f a
cofree :: CofreeF f a (Cofree f a) -> Cofree f a
cofree = Identity (CofreeF f a (Cofree f a)) -> Cofree f a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (Identity (CofreeF f a (Cofree f a)) -> Cofree f a)
-> (CofreeF f a (Cofree f a)
-> Identity (CofreeF f a (Cofree f a)))
-> CofreeF f a (Cofree f a)
-> Cofree f a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeF f a (Cofree f a) -> Identity (CofreeF f a (Cofree f a))
forall a. a -> Identity a
Identity
{-# INLINE cofree #-}
runCofree :: Cofree f a -> CofreeF f a (Cofree f a)
runCofree :: Cofree f a -> CofreeF f a (Cofree f a)
runCofree = Identity (CofreeF f a (Cofree f a)) -> CofreeF f a (Cofree f a)
forall a. Identity a -> a
runIdentity (Identity (CofreeF f a (Cofree f a)) -> CofreeF f a (Cofree f a))
-> (Cofree f a -> Identity (CofreeF f a (Cofree f a)))
-> Cofree f a
-> CofreeF f a (Cofree f a)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Cofree f a -> Identity (CofreeF f a (Cofree f a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
{-# INLINE runCofree #-}
instance (Functor f, Functor w) => Functor (CofreeT f w) where
fmap :: (a -> b) -> CofreeT f w a -> CofreeT f w b
fmap a -> b
f = w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b)
-> (CofreeT f w a -> w (CofreeF f b (CofreeT f w b)))
-> CofreeT f w a
-> CofreeT f w b
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (CofreeF f a (CofreeT f w a) -> CofreeF f b (CofreeT f w b))
-> w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f b (CofreeT f w b))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((a -> b)
-> (CofreeT f w a -> CofreeT f w b)
-> CofreeF f a (CofreeT f w a)
-> CofreeF f b (CofreeT f w b)
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> b
f ((a -> b) -> CofreeT f w a -> CofreeT f w b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f)) (w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f b (CofreeT f w b)))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> w (CofreeF f b (CofreeT f w b))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance (Functor f, Comonad w) => Comonad (CofreeT f w) where
extract :: CofreeT f w a -> a
extract = CofreeF f a (CofreeT f w a) -> a
forall (f :: * -> *) a b. CofreeF f a b -> a
headF (CofreeF f a (CofreeT f w a) -> a)
-> (CofreeT f w a -> CofreeF f a (CofreeT f w a))
-> CofreeT f w a
-> a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. w (CofreeF f a (CofreeT f w a)) -> CofreeF f a (CofreeT f w a)
forall (w :: * -> *) a. Comonad w => w a -> a
extract (w (CofreeF f a (CofreeT f w a)) -> CofreeF f a (CofreeT f w a))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> CofreeF f a (CofreeT f w a)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
extend :: (CofreeT f w a -> b) -> CofreeT f w a -> CofreeT f w b
extend CofreeT f w a -> b
f = w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b)
-> (CofreeT f w a -> w (CofreeF f b (CofreeT f w b)))
-> CofreeT f w a
-> CofreeT f w b
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (w (CofreeF f a (CofreeT f w a)) -> CofreeF f b (CofreeT f w b))
-> w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f b (CofreeT f w b))
forall (w :: * -> *) a b. Comonad w => (w a -> b) -> w a -> w b
extend (\w (CofreeF f a (CofreeT f w a))
w -> CofreeT f w a -> b
f (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT w (CofreeF f a (CofreeT f w a))
w) b -> f (CofreeT f w b) -> CofreeF f b (CofreeT f w b)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< ((CofreeT f w a -> b) -> CofreeT f w a -> CofreeT f w b
forall (w :: * -> *) a b. Comonad w => (w a -> b) -> w a -> w b
extend CofreeT f w a -> b
f (CofreeT f w a -> CofreeT f w b)
-> f (CofreeT f w a) -> f (CofreeT f w b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> CofreeF f a (CofreeT f w a) -> f (CofreeT f w a)
forall (f :: * -> *) a b. CofreeF f a b -> f b
tailF (w (CofreeF f a (CofreeT f w a)) -> CofreeF f a (CofreeT f w a)
forall (w :: * -> *) a. Comonad w => w a -> a
extract w (CofreeF f a (CofreeT f w a))
w))) (w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f b (CofreeT f w b)))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> w (CofreeF f b (CofreeT f w b))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance (Foldable f, Foldable w) => Foldable (CofreeT f w) where
foldMap :: (a -> m) -> CofreeT f w a -> m
foldMap a -> m
f = (CofreeF f a (CofreeT f w a) -> m)
-> w (CofreeF f a (CofreeT f w a)) -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap ((a -> m)
-> (CofreeT f w a -> m) -> CofreeF f a (CofreeT f w a) -> m
forall (p :: * -> * -> *) m a b.
(Bifoldable p, Monoid m) =>
(a -> m) -> (b -> m) -> p a b -> m
bifoldMap a -> m
f ((a -> m) -> CofreeT f w a -> m
forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
foldMap a -> m
f)) (w (CofreeF f a (CofreeT f w a)) -> m)
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> m
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance (Traversable f, Traversable w) => Traversable (CofreeT f w) where
traverse :: (a -> f b) -> CofreeT f w a -> f (CofreeT f w b)
traverse a -> f b
f = (w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b)
-> f (w (CofreeF f b (CofreeT f w b))) -> f (CofreeT f w b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (f (w (CofreeF f b (CofreeT f w b))) -> f (CofreeT f w b))
-> (CofreeT f w a -> f (w (CofreeF f b (CofreeT f w b))))
-> CofreeT f w a
-> f (CofreeT f w b)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (CofreeF f a (CofreeT f w a) -> f (CofreeF f b (CofreeT f w b)))
-> w (CofreeF f a (CofreeT f w a))
-> f (w (CofreeF f b (CofreeT f w b)))
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse ((a -> f b)
-> (CofreeT f w a -> f (CofreeT f w b))
-> CofreeF f a (CofreeT f w a)
-> f (CofreeF f b (CofreeT f w b))
forall (t :: * -> * -> *) (f :: * -> *) a c b d.
(Bitraversable t, Applicative f) =>
(a -> f c) -> (b -> f d) -> t a b -> f (t c d)
bitraverse a -> f b
f ((a -> f b) -> CofreeT f w a -> f (CofreeT f w b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
traverse a -> f b
f)) (w (CofreeF f a (CofreeT f w a))
-> f (w (CofreeF f b (CofreeT f w b))))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> f (w (CofreeF f b (CofreeT f w b)))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance ComonadTrans (CofreeT f) where
lower :: CofreeT f w a -> w a
lower = (CofreeF f a (CofreeT f w a) -> a)
-> w (CofreeF f a (CofreeT f w a)) -> w a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap CofreeF f a (CofreeT f w a) -> a
forall (f :: * -> *) a b. CofreeF f a b -> a
headF (w (CofreeF f a (CofreeT f w a)) -> w a)
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> w a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance (Functor f, Comonad w) => ComonadCofree f (CofreeT f w) where
unwrap :: CofreeT f w a -> f (CofreeT f w a)
unwrap = CofreeF f a (CofreeT f w a) -> f (CofreeT f w a)
forall (f :: * -> *) a b. CofreeF f a b -> f b
tailF (CofreeF f a (CofreeT f w a) -> f (CofreeT f w a))
-> (CofreeT f w a -> CofreeF f a (CofreeT f w a))
-> CofreeT f w a
-> f (CofreeT f w a)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. w (CofreeF f a (CofreeT f w a)) -> CofreeF f a (CofreeT f w a)
forall (w :: * -> *) a. Comonad w => w a -> a
extract (w (CofreeF f a (CofreeT f w a)) -> CofreeF f a (CofreeT f w a))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> CofreeF f a (CofreeT f w a)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance (Functor f, ComonadEnv e w) => ComonadEnv e (CofreeT f w) where
ask :: CofreeT f w a -> e
ask = w a -> e
forall e (w :: * -> *) a. ComonadEnv e w => w a -> e
ask (w a -> e) -> (CofreeT f w a -> w a) -> CofreeT f w a -> e
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w a
forall (t :: (* -> *) -> * -> *) (w :: * -> *) a.
(ComonadTrans t, Comonad w) =>
t w a -> w a
lower
{-# INLINE ask #-}
instance Functor f => ComonadHoist (CofreeT f) where
cohoist :: (forall x. w x -> v x) -> CofreeT f w a -> CofreeT f v a
cohoist forall x. w x -> v x
g = v (CofreeF f a (CofreeT f v a)) -> CofreeT f v a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (v (CofreeF f a (CofreeT f v a)) -> CofreeT f v a)
-> (CofreeT f w a -> v (CofreeF f a (CofreeT f v a)))
-> CofreeT f w a
-> CofreeT f v a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (CofreeF f a (CofreeT f w a) -> CofreeF f a (CofreeT f v a))
-> v (CofreeF f a (CofreeT f w a))
-> v (CofreeF f a (CofreeT f v a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((CofreeT f w a -> CofreeT f v a)
-> CofreeF f a (CofreeT f w a) -> CofreeF f a (CofreeT f v a)
forall (p :: * -> * -> *) b c a.
Bifunctor p =>
(b -> c) -> p a b -> p a c
second ((forall x. w x -> v x) -> CofreeT f w a -> CofreeT f v a
forall (t :: (* -> *) -> * -> *) (w :: * -> *) (v :: * -> *) a.
(ComonadHoist t, Comonad w, Comonad v) =>
(forall x. w x -> v x) -> t w a -> t v a
cohoist forall x. w x -> v x
g)) (v (CofreeF f a (CofreeT f w a))
-> v (CofreeF f a (CofreeT f v a)))
-> (CofreeT f w a -> v (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> v (CofreeF f a (CofreeT f v a))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. w (CofreeF f a (CofreeT f w a)) -> v (CofreeF f a (CofreeT f w a))
forall x. w x -> v x
g (w (CofreeF f a (CofreeT f w a))
-> v (CofreeF f a (CofreeT f w a)))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> v (CofreeF f a (CofreeT f w a))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
instance Show (w (CofreeF f a (CofreeT f w a))) => Show (CofreeT f w a) where
showsPrec :: Int -> CofreeT f w a -> ShowS
showsPrec Int
d (CofreeT w (CofreeF f a (CofreeT f w a))
w) = Bool -> ShowS -> ShowS
showParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (ShowS -> ShowS) -> ShowS -> ShowS
forall a b. (a -> b) -> a -> b
$
String -> ShowS
showString String
"CofreeT " ShowS -> ShowS -> ShowS
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Int -> w (CofreeF f a (CofreeT f w a)) -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec Int
11 w (CofreeF f a (CofreeT f w a))
w
instance Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a) where
readsPrec :: Int -> ReadS (CofreeT f w a)
readsPrec Int
d = Bool -> ReadS (CofreeT f w a) -> ReadS (CofreeT f w a)
forall a. Bool -> ReadS a -> ReadS a
readParen (Int
d Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
10) (ReadS (CofreeT f w a) -> ReadS (CofreeT f w a))
-> ReadS (CofreeT f w a) -> ReadS (CofreeT f w a)
forall a b. (a -> b) -> a -> b
$ \String
r ->
[(w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT w (CofreeF f a (CofreeT f w a))
w, String
t) | (String
"CofreeT", String
s) <- ReadS String
lex String
r, (w (CofreeF f a (CofreeT f w a))
w, String
t) <- Int -> ReadS (w (CofreeF f a (CofreeT f w a)))
forall a. Read a => Int -> ReadS a
readsPrec Int
11 String
s]
instance Eq (w (CofreeF f a (CofreeT f w a))) => Eq (CofreeT f w a) where
CofreeT w (CofreeF f a (CofreeT f w a))
a == :: CofreeT f w a -> CofreeT f w a -> Bool
== CofreeT w (CofreeF f a (CofreeT f w a))
b = w (CofreeF f a (CofreeT f w a))
a w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f a (CofreeT f w a)) -> Bool
forall a. Eq a => a -> a -> Bool
== w (CofreeF f a (CofreeT f w a))
b
instance Ord (w (CofreeF f a (CofreeT f w a))) => Ord (CofreeT f w a) where
compare :: CofreeT f w a -> CofreeT f w a -> Ordering
compare (CofreeT w (CofreeF f a (CofreeT f w a))
a) (CofreeT w (CofreeF f a (CofreeT f w a))
b) = w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f a (CofreeT f w a)) -> Ordering
forall a. Ord a => a -> a -> Ordering
compare w (CofreeF f a (CofreeT f w a))
a w (CofreeF f a (CofreeT f w a))
b
instance (Alternative f, Monad w) => Monad (CofreeT f w) where
#if __GLASGOW_HASKELL__ < 710
return = CofreeT . return . (:< empty)
{-# INLINE return #-}
#endif
CofreeT w (CofreeF f a (CofreeT f w a))
cx >>= :: CofreeT f w a -> (a -> CofreeT f w b) -> CofreeT f w b
>>= a -> CofreeT f w b
f = w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b)
-> w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall a b. (a -> b) -> a -> b
$ do
a
a :< f (CofreeT f w a)
m <- w (CofreeF f a (CofreeT f w a))
cx
b
b :< f (CofreeT f w b)
n <- CofreeT f w b -> w (CofreeF f b (CofreeT f w b))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT (CofreeT f w b -> w (CofreeF f b (CofreeT f w b)))
-> CofreeT f w b -> w (CofreeF f b (CofreeT f w b))
forall a b. (a -> b) -> a -> b
$ a -> CofreeT f w b
f a
a
CofreeF f b (CofreeT f w b) -> w (CofreeF f b (CofreeT f w b))
forall (m :: * -> *) a. Monad m => a -> m a
return (CofreeF f b (CofreeT f w b) -> w (CofreeF f b (CofreeT f w b)))
-> CofreeF f b (CofreeT f w b) -> w (CofreeF f b (CofreeT f w b))
forall a b. (a -> b) -> a -> b
$ b
b b -> f (CofreeT f w b) -> CofreeF f b (CofreeT f w b)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< (f (CofreeT f w b)
n f (CofreeT f w b) -> f (CofreeT f w b) -> f (CofreeT f w b)
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> (CofreeT f w a -> CofreeT f w b)
-> f (CofreeT f w a) -> f (CofreeT f w b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (CofreeT f w a -> (a -> CofreeT f w b) -> CofreeT f w b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> CofreeT f w b
f) f (CofreeT f w a)
m)
instance (Alternative f, Applicative w) => Applicative (CofreeT f w) where
pure :: a -> CofreeT f w a
pure = w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> (a -> w (CofreeF f a (CofreeT f w a))) -> a -> CofreeT f w a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeF f a (CofreeT f w a) -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) a. Applicative f => a -> f a
pure (CofreeF f a (CofreeT f w a) -> w (CofreeF f a (CofreeT f w a)))
-> (a -> CofreeF f a (CofreeT f w a))
-> a
-> w (CofreeF f a (CofreeT f w a))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> f (CofreeT f w a) -> CofreeF f a (CofreeT f w a)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< f (CofreeT f w a)
forall (f :: * -> *) a. Alternative f => f a
empty)
{-# INLINE pure #-}
CofreeT f w (a -> b)
wf <*> :: CofreeT f w (a -> b) -> CofreeT f w a -> CofreeT f w b
<*> CofreeT f w a
wa = w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b)
-> w (CofreeF f b (CofreeT f w b)) -> CofreeT f w b
forall a b. (a -> b) -> a -> b
$ CofreeF f (a -> b) (CofreeT f w (a -> b))
-> CofreeF f a (CofreeT f w a) -> CofreeF f b (CofreeT f w b)
forall (f :: * -> *) a a.
Alternative f =>
CofreeF f (a -> a) (CofreeT f w (a -> a))
-> CofreeF f a (CofreeT f w a) -> CofreeF f a (CofreeT f w a)
go (CofreeF f (a -> b) (CofreeT f w (a -> b))
-> CofreeF f a (CofreeT f w a) -> CofreeF f b (CofreeT f w b))
-> w (CofreeF f (a -> b) (CofreeT f w (a -> b)))
-> w (CofreeF f a (CofreeT f w a) -> CofreeF f b (CofreeT f w b))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> CofreeT f w (a -> b)
-> w (CofreeF f (a -> b) (CofreeT f w (a -> b)))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT CofreeT f w (a -> b)
wf w (CofreeF f a (CofreeT f w a) -> CofreeF f b (CofreeT f w b))
-> w (CofreeF f a (CofreeT f w a))
-> w (CofreeF f b (CofreeT f w b))
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT CofreeT f w a
wa where
go :: CofreeF f (a -> a) (CofreeT f w (a -> a))
-> CofreeF f a (CofreeT f w a) -> CofreeF f a (CofreeT f w a)
go (a -> a
f :< f (CofreeT f w (a -> a))
t) CofreeF f a (CofreeT f w a)
a = case (a -> a)
-> (CofreeT f w a -> CofreeT f w a)
-> CofreeF f a (CofreeT f w a)
-> CofreeF f a (CofreeT f w a)
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> a
f ((a -> a) -> CofreeT f w a -> CofreeT f w a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> a
f) CofreeF f a (CofreeT f w a)
a of
a
b :< f (CofreeT f w a)
n -> a
b a -> f (CofreeT f w a) -> CofreeF f a (CofreeT f w a)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< (f (CofreeT f w a)
n f (CofreeT f w a) -> f (CofreeT f w a) -> f (CofreeT f w a)
forall (f :: * -> *) a. Alternative f => f a -> f a -> f a
<|> (CofreeT f w (a -> a) -> CofreeT f w a)
-> f (CofreeT f w (a -> a)) -> f (CofreeT f w a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (CofreeT f w (a -> a) -> CofreeT f w a -> CofreeT f w a
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> CofreeT f w a
wa) f (CofreeT f w (a -> a))
t)
{-# INLINE (<*>) #-}
instance Alternative f => MonadTrans (CofreeT f) where
lift :: m a -> CofreeT f m a
lift = m (CofreeF f a (CofreeT f m a)) -> CofreeT f m a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (m (CofreeF f a (CofreeT f m a)) -> CofreeT f m a)
-> (m a -> m (CofreeF f a (CofreeT f m a))) -> m a -> CofreeT f m a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (a -> CofreeF f a (CofreeT f m a))
-> m a -> m (CofreeF f a (CofreeT f m a))
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (a -> f (CofreeT f m a) -> CofreeF f a (CofreeT f m a)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< f (CofreeT f m a)
forall (f :: * -> *) a. Alternative f => f a
empty)
instance (Alternative f, MonadZip f, MonadZip m) => MonadZip (CofreeT f m) where
mzip :: CofreeT f m a -> CofreeT f m b -> CofreeT f m (a, b)
mzip (CofreeT m (CofreeF f a (CofreeT f m a))
ma) (CofreeT m (CofreeF f b (CofreeT f m b))
mb) = m (CofreeF f (a, b) (CofreeT f m (a, b))) -> CofreeT f m (a, b)
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (m (CofreeF f (a, b) (CofreeT f m (a, b))) -> CofreeT f m (a, b))
-> m (CofreeF f (a, b) (CofreeT f m (a, b))) -> CofreeT f m (a, b)
forall a b. (a -> b) -> a -> b
$ do
(a
a :< f (CofreeT f m a)
fa, b
b :< f (CofreeT f m b)
fb) <- m (CofreeF f a (CofreeT f m a))
-> m (CofreeF f b (CofreeT f m b))
-> m (CofreeF f a (CofreeT f m a), CofreeF f b (CofreeT f m b))
forall (m :: * -> *) a b. MonadZip m => m a -> m b -> m (a, b)
mzip m (CofreeF f a (CofreeT f m a))
ma m (CofreeF f b (CofreeT f m b))
mb
CofreeF f (a, b) (CofreeT f m (a, b))
-> m (CofreeF f (a, b) (CofreeT f m (a, b)))
forall (m :: * -> *) a. Monad m => a -> m a
return (CofreeF f (a, b) (CofreeT f m (a, b))
-> m (CofreeF f (a, b) (CofreeT f m (a, b))))
-> CofreeF f (a, b) (CofreeT f m (a, b))
-> m (CofreeF f (a, b) (CofreeT f m (a, b)))
forall a b. (a -> b) -> a -> b
$ (a
a, b
b) (a, b)
-> f (CofreeT f m (a, b)) -> CofreeF f (a, b) (CofreeT f m (a, b))
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< ((CofreeT f m a -> CofreeT f m b -> CofreeT f m (a, b))
-> (CofreeT f m a, CofreeT f m b) -> CofreeT f m (a, b)
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry CofreeT f m a -> CofreeT f m b -> CofreeT f m (a, b)
forall (m :: * -> *) a b. MonadZip m => m a -> m b -> m (a, b)
mzip ((CofreeT f m a, CofreeT f m b) -> CofreeT f m (a, b))
-> f (CofreeT f m a, CofreeT f m b) -> f (CofreeT f m (a, b))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (CofreeT f m a)
-> f (CofreeT f m b) -> f (CofreeT f m a, CofreeT f m b)
forall (m :: * -> *) a b. MonadZip m => m a -> m b -> m (a, b)
mzip f (CofreeT f m a)
fa f (CofreeT f m b)
fb)
transCofreeT :: (Functor g, Comonad w) => (forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a
transCofreeT :: (forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a
transCofreeT forall x. f x -> g x
t = w (CofreeF g a (CofreeT g w a)) -> CofreeT g w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF g a (CofreeT g w a)) -> CofreeT g w a)
-> (CofreeT f w a -> w (CofreeF g a (CofreeT g w a)))
-> CofreeT f w a
-> CofreeT g w a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (CofreeF f a (CofreeT f w a) -> CofreeF g a (CofreeT g w a))
-> w (CofreeF f a (CofreeT f w a))
-> w (CofreeF g a (CofreeT g w a))
forall (w :: * -> *) a b. Comonad w => (a -> b) -> w a -> w b
liftW ((CofreeT f w a -> CofreeT g w a)
-> CofreeF g a (CofreeT f w a) -> CofreeF g a (CofreeT g w a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a
forall (g :: * -> *) (w :: * -> *) (f :: * -> *) a.
(Functor g, Comonad w) =>
(forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a
transCofreeT forall x. f x -> g x
t) (CofreeF g a (CofreeT f w a) -> CofreeF g a (CofreeT g w a))
-> (CofreeF f a (CofreeT f w a) -> CofreeF g a (CofreeT f w a))
-> CofreeF f a (CofreeT f w a)
-> CofreeF g a (CofreeT g w a)
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (forall x. f x -> g x)
-> CofreeF f a (CofreeT f w a) -> CofreeF g a (CofreeT f w a)
forall (f :: * -> *) (g :: * -> *) a b.
(forall x. f x -> g x) -> CofreeF f a b -> CofreeF g a b
transCofreeF forall x. f x -> g x
t) (w (CofreeF f a (CofreeT f w a))
-> w (CofreeF g a (CofreeT g w a)))
-> (CofreeT f w a -> w (CofreeF f a (CofreeT f w a)))
-> CofreeT f w a
-> w (CofreeF g a (CofreeT g w a))
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
forall (f :: * -> *) (w :: * -> *) a.
CofreeT f w a -> w (CofreeF f a (CofreeT f w a))
runCofreeT
coiterT :: (Functor f, Comonad w) => (w a -> f (w a)) -> w a -> CofreeT f w a
coiterT :: (w a -> f (w a)) -> w a -> CofreeT f w a
coiterT w a -> f (w a)
psi = w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> (w a -> w (CofreeF f a (CofreeT f w a))) -> w a -> CofreeT f w a
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. (w a -> CofreeF f a (CofreeT f w a))
-> w a -> w (CofreeF f a (CofreeT f w a))
forall (w :: * -> *) a b. Comonad w => (w a -> b) -> w a -> w b
extend (\w a
w -> w a -> a
forall (w :: * -> *) a. Comonad w => w a -> a
extract w a
w a -> f (CofreeT f w a) -> CofreeF f a (CofreeT f w a)
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
:< (w a -> CofreeT f w a) -> f (w a) -> f (CofreeT f w a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((w a -> f (w a)) -> w a -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
(Functor f, Comonad w) =>
(w a -> f (w a)) -> w a -> CofreeT f w a
coiterT w a -> f (w a)
psi) (w a -> f (w a)
psi w a
w))
#if __GLASGOW_HASKELL__ < 707
instance Typeable1 f => Typeable2 (CofreeF f) where
typeOf2 t = mkTyConApp cofreeFTyCon [typeOf1 (f t)] where
f :: CofreeF f a b -> f a
f = undefined
instance (Typeable1 f, Typeable1 w) => Typeable1 (CofreeT f w) where
typeOf1 t = mkTyConApp cofreeTTyCon [typeOf1 (f t), typeOf1 (w t)] where
f :: CofreeT f w a -> f a
f = undefined
w :: CofreeT f w a -> w a
w = undefined
cofreeFTyCon, cofreeTTyCon :: TyCon
#if __GLASGOW_HASKELL__ < 704
cofreeTTyCon = mkTyCon "Control.Comonad.Trans.Cofree.CofreeT"
cofreeFTyCon = mkTyCon "Control.Comonad.Trans.Cofree.CofreeF"
#else
cofreeTTyCon = mkTyCon3 "free" "Control.Comonad.Trans.Cofree" "CofreeT"
cofreeFTyCon = mkTyCon3 "free" "Control.Comonad.Trans.Cofree" "CofreeF"
#endif
{-# NOINLINE cofreeTTyCon #-}
{-# NOINLINE cofreeFTyCon #-}
#else
#define Typeable1 Typeable
#endif
instance
( Typeable1 f, Typeable a, Typeable b
, Data a, Data (f b), Data b
) => Data (CofreeF f a b) where
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> CofreeF f a b -> c (CofreeF f a b)
gfoldl forall d b. Data d => c (d -> b) -> d -> c b
f forall g. g -> c g
z (a
a :< f b
as) = (a -> f b -> CofreeF f a b) -> c (a -> f b -> CofreeF f a b)
forall g. g -> c g
z a -> f b -> CofreeF f a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
(:<) c (a -> f b -> CofreeF f a b) -> a -> c (f b -> CofreeF f a b)
forall d b. Data d => c (d -> b) -> d -> c b
`f` a
a c (f b -> CofreeF f a b) -> f b -> c (CofreeF f a b)
forall d b. Data d => c (d -> b) -> d -> c b
`f` f b
as
toConstr :: CofreeF f a b -> Constr
toConstr CofreeF f a b
_ = Constr
cofreeFConstr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (CofreeF f a b)
gunfold forall b r. Data b => c (b -> r) -> c r
k forall r. r -> c r
z Constr
c = case Constr -> Int
constrIndex Constr
c of
Int
1 -> c (f b -> CofreeF f a b) -> c (CofreeF f a b)
forall b r. Data b => c (b -> r) -> c r
k (c (a -> f b -> CofreeF f a b) -> c (f b -> CofreeF f a b)
forall b r. Data b => c (b -> r) -> c r
k ((a -> f b -> CofreeF f a b) -> c (a -> f b -> CofreeF f a b)
forall r. r -> c r
z a -> f b -> CofreeF f a b
forall (f :: * -> *) a b. a -> f b -> CofreeF f a b
(:<)))
Int
_ -> String -> c (CofreeF f a b)
forall a. HasCallStack => String -> a
error String
"gunfold"
dataTypeOf :: CofreeF f a b -> DataType
dataTypeOf CofreeF f a b
_ = DataType
cofreeFDataType
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (CofreeF f a b))
dataCast1 forall d. Data d => c (t d)
f = c (t b) -> Maybe (c (CofreeF f a b))
forall k1 k2 (c :: k1 -> *) (t :: k2 -> k1) (t' :: k2 -> k1)
(a :: k2).
(Typeable t, Typeable t') =>
c (t a) -> Maybe (c (t' a))
gcast1 c (t b)
forall d. Data d => c (t d)
f
instance
( Typeable1 f, Typeable1 w, Typeable a
, Data (w (CofreeF f a (CofreeT f w a)))
, Data a
) => Data (CofreeT f w a) where
gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> CofreeT f w a -> c (CofreeT f w a)
gfoldl forall d b. Data d => c (d -> b) -> d -> c b
f forall g. g -> c g
z (CofreeT w (CofreeF f a (CofreeT f w a))
w) = (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> c (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
forall g. g -> c g
z w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT c (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> w (CofreeF f a (CofreeT f w a)) -> c (CofreeT f w a)
forall d b. Data d => c (d -> b) -> d -> c b
`f` w (CofreeF f a (CofreeT f w a))
w
toConstr :: CofreeT f w a -> Constr
toConstr CofreeT f w a
_ = Constr
cofreeTConstr
gunfold :: (forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (CofreeT f w a)
gunfold forall b r. Data b => c (b -> r) -> c r
k forall r. r -> c r
z Constr
c = case Constr -> Int
constrIndex Constr
c of
Int
1 -> c (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> c (CofreeT f w a)
forall b r. Data b => c (b -> r) -> c r
k ((w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
-> c (w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a)
forall r. r -> c r
z w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
forall (f :: * -> *) (w :: * -> *) a.
w (CofreeF f a (CofreeT f w a)) -> CofreeT f w a
CofreeT)
Int
_ -> String -> c (CofreeT f w a)
forall a. HasCallStack => String -> a
error String
"gunfold"
dataTypeOf :: CofreeT f w a -> DataType
dataTypeOf CofreeT f w a
_ = DataType
cofreeTDataType
dataCast1 :: (forall d. Data d => c (t d)) -> Maybe (c (CofreeT f w a))
dataCast1 forall d. Data d => c (t d)
f = c (t a) -> Maybe (c (CofreeT f w a))
forall k1 k2 (c :: k1 -> *) (t :: k2 -> k1) (t' :: k2 -> k1)
(a :: k2).
(Typeable t, Typeable t') =>
c (t a) -> Maybe (c (t' a))
gcast1 c (t a)
forall d. Data d => c (t d)
f
cofreeFConstr, cofreeTConstr :: Constr
cofreeFConstr :: Constr
cofreeFConstr = DataType -> String -> [String] -> Fixity -> Constr
mkConstr DataType
cofreeFDataType String
":<" [] Fixity
Infix
cofreeTConstr :: Constr
cofreeTConstr = DataType -> String -> [String] -> Fixity -> Constr
mkConstr DataType
cofreeTDataType String
"CofreeT" [] Fixity
Prefix
{-# NOINLINE cofreeFConstr #-}
{-# NOINLINE cofreeTConstr #-}
cofreeFDataType, cofreeTDataType :: DataType
cofreeFDataType :: DataType
cofreeFDataType = String -> [Constr] -> DataType
mkDataType String
"Control.Comonad.Trans.Cofree.CofreeF" [Constr
cofreeFConstr]
cofreeTDataType :: DataType
cofreeTDataType = String -> [Constr] -> DataType
mkDataType String
"Control.Comonad.Trans.Cofree.CofreeT" [Constr
cofreeTConstr]
{-# NOINLINE cofreeFDataType #-}
{-# NOINLINE cofreeTDataType #-}