{-# LANGUAGE CPP #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE Rank2Types #-}
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707
{-# LANGUAGE DeriveDataTypeable #-}
#endif
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ <= 707
{-# LANGUAGE KindSignatures #-}
#endif
#if __GLASGOW_HASKELL__ >= 702 && __GLASGOW_HASKELL__ < 710
{-# LANGUAGE Trustworthy #-}
#endif
module Data.Functor.Contravariant.Day
( Day(..)
, day
, runDay
, assoc, disassoc
, swapped
, intro1, intro2
, day1, day2
, diag
, trans1, trans2
) where
#if __GLASGOW_HASKELL__ < 710
import Control.Applicative
#endif
import Data.Functor.Contravariant
import Data.Functor.Contravariant.Rep
import Data.Proxy
import Data.Tuple (swap)
#ifdef __GLASGOW_HASKELL__
import Data.Typeable
#endif
data Day f g a = forall b c. Day (f b) (g c) (a -> (b, c))
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 707
deriving Typeable
#endif
day :: f a -> g b -> Day f g (a, b)
day :: f a -> g b -> Day f g (a, b)
day f a
fa g b
gb = f a -> g b -> ((a, b) -> (a, b)) -> Day f g (a, b)
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f a
fa g b
gb (a, b) -> (a, b)
forall a. a -> a
id
#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ < 707
instance (Typeable1 f, Typeable1 g) => Typeable1 (Day f g) where
typeOf1 tfga = mkTyConApp dayTyCon [typeOf1 (fa tfga), typeOf1 (ga tfga)]
where fa :: t f (g :: * -> *) a -> f a
fa = undefined
ga :: t (f :: * -> *) g a -> g a
ga = undefined
dayTyCon :: TyCon
#if MIN_VERSION_base(4,4,0)
dayTyCon = mkTyCon3 "contravariant" "Data.Functor.Contravariant.Day" "Day"
#else
dayTyCon = mkTyCon "Data.Functor.Contravariant.Day.Day"
#endif
#endif
instance Contravariant (Day f g) where
contramap :: (a -> b) -> Day f g b -> Day f g a
contramap a -> b
f (Day f b
fb g c
gc b -> (b, c)
abc) = f b -> g c -> (a -> (b, c)) -> Day f g a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f b
fb g c
gc (b -> (b, c)
abc (b -> (b, c)) -> (a -> b) -> a -> (b, c)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> b
f)
instance (Representable f, Representable g) => Representable (Day f g) where
type Rep (Day f g) = (Rep f, Rep g)
tabulate :: (a -> Rep (Day f g)) -> Day f g a
tabulate a -> Rep (Day f g)
a2fg = f (Rep f, Rep g)
-> g (Rep f, Rep g)
-> (a -> ((Rep f, Rep g), (Rep f, Rep g)))
-> Day f g a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day (((Rep f, Rep g) -> Rep f) -> f (Rep f, Rep g)
forall (f :: * -> *) a. Representable f => (a -> Rep f) -> f a
tabulate (Rep f, Rep g) -> Rep f
forall a b. (a, b) -> a
fst) (((Rep f, Rep g) -> Rep g) -> g (Rep f, Rep g)
forall (f :: * -> *) a. Representable f => (a -> Rep f) -> f a
tabulate (Rep f, Rep g) -> Rep g
forall a b. (a, b) -> b
snd) ((a -> ((Rep f, Rep g), (Rep f, Rep g))) -> Day f g a)
-> (a -> ((Rep f, Rep g), (Rep f, Rep g))) -> Day f g a
forall a b. (a -> b) -> a -> b
$ \a
a -> let b :: Rep (Day f g)
b = a -> Rep (Day f g)
a2fg a
a in ((Rep f, Rep g)
Rep (Day f g)
b,(Rep f, Rep g)
Rep (Day f g)
b)
index :: Day f g a -> a -> Rep (Day f g)
index (Day f b
fb g c
gc a -> (b, c)
abc) a
a = case a -> (b, c)
abc a
a of
(b
b, c
c) -> (f b -> b -> Rep f
forall (f :: * -> *) a. Representable f => f a -> a -> Rep f
index f b
fb b
b, g c -> c -> Rep g
forall (f :: * -> *) a. Representable f => f a -> a -> Rep f
index g c
gc c
c)
{-# INLINE index #-}
contramapWithRep :: (b -> Either a (Rep (Day f g))) -> Day f g a -> Day f g b
contramapWithRep b -> Either a (Rep (Day f g))
d2eafg (Day f b
fb g c
gc a -> (b, c)
abc) = f (Either b (Rep f))
-> g (Either c (Rep g))
-> (b -> (Either b (Rep f), Either c (Rep g)))
-> Day f g b
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day ((Either b (Rep f) -> Either b (Rep f))
-> f b -> f (Either b (Rep f))
forall (f :: * -> *) b a.
Representable f =>
(b -> Either a (Rep f)) -> f a -> f b
contramapWithRep Either b (Rep f) -> Either b (Rep f)
forall a. a -> a
id f b
fb) ((Either c (Rep g) -> Either c (Rep g))
-> g c -> g (Either c (Rep g))
forall (f :: * -> *) b a.
Representable f =>
(b -> Either a (Rep f)) -> f a -> f b
contramapWithRep Either c (Rep g) -> Either c (Rep g)
forall a. a -> a
id g c
gc) ((b -> (Either b (Rep f), Either c (Rep g))) -> Day f g b)
-> (b -> (Either b (Rep f), Either c (Rep g))) -> Day f g b
forall a b. (a -> b) -> a -> b
$ \b
d -> case b -> Either a (Rep (Day f g))
d2eafg b
d of
Left a
a -> case a -> (b, c)
abc a
a of
(b
b, c
c) -> (b -> Either b (Rep f)
forall a b. a -> Either a b
Left b
b, c -> Either c (Rep g)
forall a b. a -> Either a b
Left c
c)
Right (vf, vg) -> (Rep f -> Either b (Rep f)
forall a b. b -> Either a b
Right Rep f
vf, Rep g -> Either c (Rep g)
forall a b. b -> Either a b
Right Rep g
vg)
{-# INLINE tabulate #-}
runDay :: (Contravariant f, Contravariant g) => Day f g a -> (f a, g a)
runDay :: Day f g a -> (f a, g a)
runDay (Day f b
fb g c
gc a -> (b, c)
abc) =
( (a -> b) -> f b -> f a
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap ((b, c) -> b
forall a b. (a, b) -> a
fst ((b, c) -> b) -> (a -> (b, c)) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, c)
abc) f b
fb
, (a -> c) -> g c -> g a
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap ((b, c) -> c
forall a b. (a, b) -> b
snd ((b, c) -> c) -> (a -> (b, c)) -> a -> c
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, c)
abc) g c
gc
)
assoc :: Day f (Day g h) a -> Day (Day f g) h a
assoc :: Day f (Day g h) a -> Day (Day f g) h a
assoc (Day f b
fb (Day g b
gd h c
he c -> (b, c)
cde) a -> (b, c)
abc) = Day f g (b, b) -> h c -> (a -> ((b, b), c)) -> Day (Day f g) h a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day (f b -> g b -> ((b, b) -> (b, b)) -> Day f g (b, b)
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f b
fb g b
gd (b, b) -> (b, b)
forall a. a -> a
id) h c
he ((a -> ((b, b), c)) -> Day (Day f g) h a)
-> (a -> ((b, b), c)) -> Day (Day f g) h a
forall a b. (a -> b) -> a -> b
$ \a
a ->
case c -> (b, c)
cde (c -> (b, c)) -> (b, c) -> (b, (b, c))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> (b, c)
abc a
a of
(b
b, (b
d, c
e)) -> ((b
b, b
d), c
e)
disassoc :: Day (Day f g) h a -> Day f (Day g h) a
disassoc :: Day (Day f g) h a -> Day f (Day g h) a
disassoc (Day (Day f b
fd g c
ge b -> (b, c)
bde) h c
hc a -> (b, c)
abc) = f b -> Day g h (c, c) -> (a -> (b, (c, c))) -> Day f (Day g h) a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f b
fd (g c -> h c -> ((c, c) -> (c, c)) -> Day g h (c, c)
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day g c
ge h c
hc (c, c) -> (c, c)
forall a. a -> a
id) ((a -> (b, (c, c))) -> Day f (Day g h) a)
-> (a -> (b, (c, c))) -> Day f (Day g h) a
forall a b. (a -> b) -> a -> b
$ \a
a ->
case a -> (b, c)
abc a
a of
(b
b, c
c) -> case b -> (b, c)
bde b
b of
(b
d, c
e) -> (b
d, (c
e, c
c))
swapped :: Day f g a -> Day g f a
swapped :: Day f g a -> Day g f a
swapped (Day f b
fb g c
gc a -> (b, c)
abc) = g c -> f b -> (a -> (c, b)) -> Day g f a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day g c
gc f b
fb ((b, c) -> (c, b)
forall a b. (a, b) -> (b, a)
swap ((b, c) -> (c, b)) -> (a -> (b, c)) -> a -> (c, b)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, c)
abc)
intro1 :: f a -> Day Proxy f a
intro1 :: f a -> Day Proxy f a
intro1 f a
fa = Proxy () -> f a -> (a -> ((), a)) -> Day Proxy f a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day Proxy ()
forall k (t :: k). Proxy t
Proxy f a
fa ((a -> ((), a)) -> Day Proxy f a)
-> (a -> ((), a)) -> Day Proxy f a
forall a b. (a -> b) -> a -> b
$ \a
a -> ((),a
a)
intro2 :: f a -> Day f Proxy a
intro2 :: f a -> Day f Proxy a
intro2 f a
fa = f a -> Proxy () -> (a -> (a, ())) -> Day f Proxy a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f a
fa Proxy ()
forall k (t :: k). Proxy t
Proxy ((a -> (a, ())) -> Day f Proxy a)
-> (a -> (a, ())) -> Day f Proxy a
forall a b. (a -> b) -> a -> b
$ \a
a -> (a
a,())
day1 :: Contravariant f => Day f g a -> f a
day1 :: Day f g a -> f a
day1 (Day f b
fb g c
_ a -> (b, c)
abc) = (a -> b) -> f b -> f a
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap ((b, c) -> b
forall a b. (a, b) -> a
fst ((b, c) -> b) -> (a -> (b, c)) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, c)
abc) f b
fb
day2 :: Contravariant g => Day f g a -> g a
day2 :: Day f g a -> g a
day2 (Day f b
_ g c
gc a -> (b, c)
abc) = (a -> c) -> g c -> g a
forall (f :: * -> *) a b. Contravariant f => (a -> b) -> f b -> f a
contramap ((b, c) -> c
forall a b. (a, b) -> b
snd ((b, c) -> c) -> (a -> (b, c)) -> a -> c
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> (b, c)
abc) g c
gc
diag :: f a -> Day f f a
diag :: f a -> Day f f a
diag f a
fa = f a -> f a -> (a -> (a, a)) -> Day f f a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f a
fa f a
fa ((a -> (a, a)) -> Day f f a) -> (a -> (a, a)) -> Day f f a
forall a b. (a -> b) -> a -> b
$ \a
a -> (a
a,a
a)
trans1 :: (forall x. f x -> g x) -> Day f h a -> Day g h a
trans1 :: (forall x. f x -> g x) -> Day f h a -> Day g h a
trans1 forall x. f x -> g x
fg (Day f b
fb h c
hc a -> (b, c)
abc) = g b -> h c -> (a -> (b, c)) -> Day g h a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day (f b -> g b
forall x. f x -> g x
fg f b
fb) h c
hc a -> (b, c)
abc
trans2 :: (forall x. g x -> h x) -> Day f g a -> Day f h a
trans2 :: (forall x. g x -> h x) -> Day f g a -> Day f h a
trans2 forall x. g x -> h x
gh (Day f b
fb g c
gc a -> (b, c)
abc) = f b -> h c -> (a -> (b, c)) -> Day f h a
forall (f :: * -> *) (g :: * -> *) a b c.
f b -> g c -> (a -> (b, c)) -> Day f g a
Day f b
fb (g c -> h c
forall x. g x -> h x
gh g c
gc) a -> (b, c)
abc