{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ExistentialQuantification #-}
module Data.Fold.R1
( R1(..)
) where
import Control.Applicative
import Control.Arrow
import Control.Category
import Control.Lens
import Control.Monad.Fix
import Control.Monad.Reader.Class
import Control.Monad.Zip
import Data.Distributive
import Data.Fold.Class
import Data.Fold.Internal
import Data.Functor.Apply
import Data.Functor.Rep as Functor
import Data.List.NonEmpty as NonEmpty
import Data.Pointed
import Data.Profunctor.Closed
import Data.Profunctor
import Data.Profunctor.Rep as Profunctor
import Data.Profunctor.Sieve
import Data.Profunctor.Unsafe
import Data.Semigroupoid
import Prelude hiding (id,(.))
import Unsafe.Coerce
data R1 a b = forall c. R1 (c -> b) (a -> c -> c) (a -> c)
instance Scan R1 where
run1 :: a -> R1 a b -> b
run1 a
a (R1 c -> b
k a -> c -> c
_ a -> c
z) = c -> b
k (a -> c
z a
a)
prefix1 :: a -> R1 a b -> R1 a b
prefix1 a
a (R1 c -> b
k a -> c -> c
h a -> c
z) = (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\c
c -> c -> b
k (a -> c -> c
h a
a c
c)) a -> c -> c
h a -> c
z
postfix1 :: R1 a b -> a -> R1 a b
postfix1 (R1 c -> b
k a -> c -> c
h a -> c
z) a
a = (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 c -> b
k a -> c -> c
h (\a
c -> a -> c -> c
h a
c (a -> c
z a
a))
interspersing :: a -> R1 a b -> R1 a b
interspersing a
a (R1 c -> b
k a -> c -> c
h a -> c
z) = (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 c -> b
k (\a
b c
x -> a -> c -> c
h a
b (a -> c -> c
h a
a c
x)) a -> c
z
{-# INLINE run1 #-}
{-# INLINE prefix1 #-}
{-# INLINE postfix1 #-}
{-# INLINE interspersing #-}
instance Functor (R1 a) where
fmap :: (a -> b) -> R1 a a -> R1 a b
fmap a -> b
f (R1 c -> a
k a -> c -> c
h a -> c
z) = (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (a -> b
f(a -> b) -> (c -> a) -> c -> b
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.c -> a
k) a -> c -> c
h a -> c
z
{-# INLINE fmap #-}
a
b <$ :: a -> R1 a b -> R1 a a
<$ R1 a b
_ = a -> R1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
b
{-# INLINE (<$) #-}
instance Pointed (R1 a) where
point :: a -> R1 a a
point a
x = (() -> a) -> (a -> () -> ()) -> (a -> ()) -> R1 a a
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\() -> a
x) (\a
_ () -> ()) (\a
_ -> ())
{-# INLINE point #-}
instance Apply (R1 a) where
<.> :: R1 a (a -> b) -> R1 a a -> R1 a b
(<.>) = R1 a (a -> b) -> R1 a a -> R1 a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>)
{-# INLINE (<.>) #-}
<. :: R1 a a -> R1 a b -> R1 a a
(<.) R1 a a
m = \R1 a b
_ -> R1 a a
m
{-# INLINE (<.) #-}
R1 a a
_ .> :: R1 a a -> R1 a b -> R1 a b
.> R1 a b
m = R1 a b
m
{-# INLINE (.>) #-}
instance Applicative (R1 a) where
pure :: a -> R1 a a
pure a
x = (() -> a) -> (a -> () -> ()) -> (a -> ()) -> R1 a a
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\() -> a
x) (\a
_ () -> ()) (\a
_ -> ())
{-# INLINE pure #-}
R1 c -> a -> b
kf a -> c -> c
hf a -> c
zf <*> :: R1 a (a -> b) -> R1 a a -> R1 a b
<*> R1 c -> a
ka a -> c -> c
ha a -> c
za = (Pair' c c -> b)
-> (a -> Pair' c c -> Pair' c c) -> (a -> Pair' c c) -> R1 a b
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1
(\(Pair' c
x c
y) -> c -> a -> b
kf c
x (c -> a
ka c
y))
(\a
a ~(Pair' c
x c
y) -> c -> c -> Pair' c c
forall a b. a -> b -> Pair' a b
Pair' (a -> c -> c
hf a
a c
x) (a -> c -> c
ha a
a c
y))
(\a
a -> c -> c -> Pair' c c
forall a b. a -> b -> Pair' a b
Pair' (a -> c
zf a
a) (a -> c
za a
a))
<* :: R1 a a -> R1 a b -> R1 a a
(<*) R1 a a
m = \ R1 a b
_ -> R1 a a
m
{-# INLINE (<*) #-}
R1 a a
_ *> :: R1 a a -> R1 a b -> R1 a b
*> R1 a b
m = R1 a b
m
{-# INLINE (*>) #-}
instance Monad (R1 a) where
return :: a -> R1 a a
return = a -> R1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure
{-# INLINE return #-}
R1 a a
m >>= :: R1 a a -> (a -> R1 a b) -> R1 a b
>>= a -> R1 a b
f = (List1 a -> a -> b)
-> (a -> List1 a -> List1 a) -> (a -> List1 a) -> R1 a (a -> b)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\List1 a
xs a
a -> List1 a -> R1 a b -> b
forall a b. List1 a -> R1 a b -> b
walk List1 a
xs (a -> R1 a b
f a
a)) a -> List1 a -> List1 a
forall a. a -> List1 a -> List1 a
Cons1 a -> List1 a
forall a. a -> List1 a
Last R1 a (a -> b) -> R1 a a -> R1 a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> R1 a a
m
{-# INLINE (>>=) #-}
>> :: R1 a a -> R1 a b -> R1 a b
(>>) = R1 a a -> R1 a b -> R1 a b
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
(*>)
{-# INLINE (>>) #-}
instance MonadZip (R1 a) where
mzipWith :: (a -> b -> c) -> R1 a a -> R1 a b -> R1 a c
mzipWith = (a -> b -> c) -> R1 a a -> R1 a b -> R1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
{-# INLINE mzipWith #-}
instance Semigroupoid R1 where
o :: R1 j k1 -> R1 i j -> R1 i k1
o = R1 j k1 -> R1 i j -> R1 i k1
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
(.)
{-# INLINE o #-}
instance Category R1 where
id :: R1 a a
id = (a -> a) -> R1 a a
forall (a :: * -> * -> *) b c. Arrow a => (b -> c) -> a b c
arr a -> a
forall k (cat :: k -> k -> *) (a :: k). Category cat => cat a a
id
{-# INLINE id #-}
R1 c -> c
k b -> c -> c
h b -> c
z . :: R1 b c -> R1 a b -> R1 a c
. R1 c -> b
k' a -> c -> c
h' a -> c
z' = (Pair' c c -> c)
-> (a -> Pair' c c -> Pair' c c) -> (a -> Pair' c c) -> R1 a c
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\(Pair' c
b c
_) -> c -> c
k c
b) a -> Pair' c c -> Pair' c c
h'' a -> Pair' c c
z'' where
z'' :: a -> Pair' c c
z'' a
a = c -> c -> Pair' c c
forall a b. a -> b -> Pair' a b
Pair' (b -> c
z (c -> b
k' c
b)) c
b where b :: c
b = a -> c
z' a
a
h'' :: a -> Pair' c c -> Pair' c c
h'' a
a (Pair' c
c c
d) = c -> c -> Pair' c c
forall a b. a -> b -> Pair' a b
Pair' (b -> c -> c
h (c -> b
k' c
d') c
c) c
d' where d' :: c
d' = a -> c -> c
h' a
a c
d
{-# INLINE (.) #-}
instance Arrow R1 where
arr :: (b -> c) -> R1 b c
arr b -> c
h = (b -> c) -> (b -> b -> b) -> (b -> b) -> R1 b c
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 b -> c
h b -> b -> b
forall a b. a -> b -> a
const b -> b
forall k (cat :: k -> k -> *) (a :: k). Category cat => cat a a
id
{-# INLINE arr #-}
first :: R1 b c -> R1 (b, d) (c, d)
first (R1 c -> c
k b -> c -> c
h b -> c
z) = ((c, d) -> (c, d))
-> ((b, d) -> (c, d) -> (c, d))
-> ((b, d) -> (c, d))
-> R1 (b, d) (c, d)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> c) -> (c, d) -> (c, d)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first c -> c
k) (b, d) -> (c, d) -> (c, d)
h' ((b -> c) -> (b, d) -> (c, d)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first b -> c
z) where
h' :: (b, d) -> (c, d) -> (c, d)
h' (b
a,d
_) (c
c,d
b) = (b -> c -> c
h b
a c
c, d
b)
{-# INLINE first #-}
second :: R1 b c -> R1 (d, b) (d, c)
second (R1 c -> c
k b -> c -> c
h b -> c
z) = ((d, c) -> (d, c))
-> ((d, b) -> (d, c) -> (d, c))
-> ((d, b) -> (d, c))
-> R1 (d, b) (d, c)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> c) -> (d, c) -> (d, c)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second c -> c
k) (d, b) -> (d, c) -> (d, c)
h' ((b -> c) -> (d, b) -> (d, c)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second b -> c
z) where
h' :: (d, b) -> (d, c) -> (d, c)
h' (d
_,b
b) (d
a,c
c) = (d
a, b -> c -> c
h b
b c
c)
{-# INLINE second #-}
R1 c -> c
k b -> c -> c
h b -> c
z *** :: R1 b c -> R1 b' c' -> R1 (b, b') (c, c')
*** R1 c -> c'
k' b' -> c -> c
h' b' -> c
z' = ((c, c) -> (c, c'))
-> ((b, b') -> (c, c) -> (c, c))
-> ((b, b') -> (c, c))
-> R1 (b, b') (c, c')
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (c -> c
k (c -> c) -> (c -> c') -> (c, c) -> (c, c')
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** c -> c'
k') (b, b') -> (c, c) -> (c, c)
h'' (b -> c
z (b -> c) -> (b' -> c) -> (b, b') -> (c, c)
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** b' -> c
z') where
h'' :: (b, b') -> (c, c) -> (c, c)
h'' (b
a,b'
b) (c
c,c
d) = (b -> c -> c
h b
a c
c, b' -> c -> c
h' b'
b c
d)
{-# INLINE (***) #-}
R1 c -> c
k b -> c -> c
h b -> c
z &&& :: R1 b c -> R1 b c' -> R1 b (c, c')
&&& R1 c -> c'
k' b -> c -> c
h' b -> c
z' = ((c, c) -> (c, c'))
-> (b -> (c, c) -> (c, c)) -> (b -> (c, c)) -> R1 b (c, c')
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (c -> c
k (c -> c) -> (c -> c') -> (c, c) -> (c, c')
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** c -> c'
k') b -> (c, c) -> (c, c)
h'' (b -> c
z (b -> c) -> (b -> c) -> b -> (c, c)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& b -> c
z') where
h'' :: b -> (c, c) -> (c, c)
h'' b
a (c
c,c
d) = (b -> c -> c
h b
a c
c, b -> c -> c
h' b
a c
d)
{-# INLINE (&&&) #-}
instance Profunctor R1 where
dimap :: (a -> b) -> (c -> d) -> R1 b c -> R1 a d
dimap a -> b
f c -> d
g (R1 c -> c
k b -> c -> c
h b -> c
z) = (c -> d) -> (a -> c -> c) -> (a -> c) -> R1 a d
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (c -> d
g(c -> d) -> (c -> c) -> c -> d
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.c -> c
k) (b -> c -> c
h(b -> c -> c) -> (a -> b) -> a -> c -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.a -> b
f) (b -> c
z(b -> c) -> (a -> b) -> a -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.a -> b
f)
{-# INLINE dimap #-}
lmap :: (a -> b) -> R1 b c -> R1 a c
lmap a -> b
f (R1 c -> c
k b -> c -> c
h b -> c
z) = (c -> c) -> (a -> c -> c) -> (a -> c) -> R1 a c
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 c -> c
k (b -> c -> c
h(b -> c -> c) -> (a -> b) -> a -> c -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.a -> b
f) (b -> c
z(b -> c) -> (a -> b) -> a -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.a -> b
f)
{-# INLINE lmap #-}
rmap :: (b -> c) -> R1 a b -> R1 a c
rmap b -> c
g (R1 c -> b
k a -> c -> c
h a -> c
z) = (c -> c) -> (a -> c -> c) -> (a -> c) -> R1 a c
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (b -> c
g(b -> c) -> (c -> b) -> c -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.c -> b
k) a -> c -> c
h a -> c
z
{-# INLINE rmap #-}
( #. ) q b c
_ = R1 a b -> R1 a c
forall a b. a -> b
unsafeCoerce
{-# INLINE (#.) #-}
R1 b c
x .# :: R1 b c -> q a b -> R1 a c
.# q a b
_ = R1 b c -> R1 a c
forall a b. a -> b
unsafeCoerce R1 b c
x
{-# INLINE (.#) #-}
instance Strong R1 where
first' :: R1 a b -> R1 (a, c) (b, c)
first' = R1 a b -> R1 (a, c) (b, c)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first
{-# INLINE first' #-}
second' :: R1 a b -> R1 (c, a) (c, b)
second' = R1 a b -> R1 (c, a) (c, b)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second
{-# INLINE second' #-}
instance Choice R1 where
left' :: R1 a b -> R1 (Either a c) (Either b c)
left' (R1 c -> b
k a -> c -> c
h a -> c
z) = (Either c c -> Either b c)
-> (Either a c -> Either c c -> Either c c)
-> (Either a c -> Either c c)
-> R1 (Either a c) (Either b c)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> Identity b) -> Either c c -> Identity (Either b c)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((c -> Identity b) -> Either c c -> Identity (Either b c))
-> (c -> b) -> Either c c -> Either b c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ c -> b
k) Either a c -> Either c c -> Either c c
step ((a -> Identity c) -> Either a c -> Identity (Either c c)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((a -> Identity c) -> Either a c -> Identity (Either c c))
-> (a -> c) -> Either a c -> Either c c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ a -> c
z) where
step :: Either a c -> Either c c -> Either c c
step (Left a
x) (Left c
y) = c -> Either c c
forall a b. a -> Either a b
Left (a -> c -> c
h a
x c
y)
step (Right c
c) Either c c
_ = c -> Either c c
forall a b. b -> Either a b
Right c
c
step Either a c
_ (Right c
c) = c -> Either c c
forall a b. b -> Either a b
Right c
c
{-# INLINE left' #-}
right' :: R1 a b -> R1 (Either c a) (Either c b)
right' (R1 c -> b
k a -> c -> c
h a -> c
z) = (Either c c -> Either c b)
-> (Either c a -> Either c c -> Either c c)
-> (Either c a -> Either c c)
-> R1 (Either c a) (Either c b)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> Identity b) -> Either c c -> Identity (Either c b)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((c -> Identity b) -> Either c c -> Identity (Either c b))
-> (c -> b) -> Either c c -> Either c b
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ c -> b
k) Either c a -> Either c c -> Either c c
step ((a -> Identity c) -> Either c a -> Identity (Either c c)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((a -> Identity c) -> Either c a -> Identity (Either c c))
-> (a -> c) -> Either c a -> Either c c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ a -> c
z) where
step :: Either c a -> Either c c -> Either c c
step (Right a
x) (Right c
y) = c -> Either c c
forall a b. b -> Either a b
Right (a -> c -> c
h a
x c
y)
step (Left c
c) Either c c
_ = c -> Either c c
forall a b. a -> Either a b
Left c
c
step Either c a
_ (Left c
c) = c -> Either c c
forall a b. a -> Either a b
Left c
c
{-# INLINE right' #-}
instance ArrowChoice R1 where
left :: R1 b c -> R1 (Either b d) (Either c d)
left (R1 c -> c
k b -> c -> c
h b -> c
z) = (Either c d -> Either c d)
-> (Either b d -> Either c d -> Either c d)
-> (Either b d -> Either c d)
-> R1 (Either b d) (Either c d)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> Identity c) -> Either c d -> Identity (Either c d)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((c -> Identity c) -> Either c d -> Identity (Either c d))
-> (c -> c) -> Either c d -> Either c d
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ c -> c
k) Either b d -> Either c d -> Either c d
step ((b -> Identity c) -> Either b d -> Identity (Either c d)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((b -> Identity c) -> Either b d -> Identity (Either c d))
-> (b -> c) -> Either b d -> Either c d
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ b -> c
z) where
step :: Either b d -> Either c d -> Either c d
step (Left b
x) (Left c
y) = c -> Either c d
forall a b. a -> Either a b
Left (b -> c -> c
h b
x c
y)
step (Right d
c) Either c d
_ = d -> Either c d
forall a b. b -> Either a b
Right d
c
step Either b d
_ (Right d
c) = d -> Either c d
forall a b. b -> Either a b
Right d
c
{-# INLINE left #-}
right :: R1 b c -> R1 (Either d b) (Either d c)
right (R1 c -> c
k b -> c -> c
h b -> c
z) = (Either d c -> Either d c)
-> (Either d b -> Either d c -> Either d c)
-> (Either d b -> Either d c)
-> R1 (Either d b) (Either d c)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 ((c -> Identity c) -> Either d c -> Identity (Either d c)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((c -> Identity c) -> Either d c -> Identity (Either d c))
-> (c -> c) -> Either d c -> Either d c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ c -> c
k) Either d b -> Either d c -> Either d c
step ((b -> Identity c) -> Either d b -> Identity (Either d c)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((b -> Identity c) -> Either d b -> Identity (Either d c))
-> (b -> c) -> Either d b -> Either d c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ b -> c
z) where
step :: Either d b -> Either d c -> Either d c
step (Right b
x) (Right c
y) = c -> Either d c
forall a b. b -> Either a b
Right (b -> c -> c
h b
x c
y)
step (Left d
c) Either d c
_ = d -> Either d c
forall a b. a -> Either a b
Left d
c
step Either d b
_ (Left d
c) = d -> Either d c
forall a b. a -> Either a b
Left d
c
{-# INLINE right #-}
walk :: List1 a -> R1 a b -> b
walk :: List1 a -> R1 a b -> b
walk List1 a
xs0 (R1 c -> b
k a -> c -> c
h a -> c
z) = c -> b
k (List1 a -> c
go List1 a
xs0) where
go :: List1 a -> c
go (Last a
a) = a -> c
z a
a
go (Cons1 a
a List1 a
as) = a -> c -> c
h a
a (List1 a -> c
go List1 a
as)
{-# INLINE walk #-}
instance Closed R1 where
closed :: R1 a b -> R1 (x -> a) (x -> b)
closed (R1 c -> b
k a -> c -> c
h a -> c
z) = ((x -> c) -> x -> b)
-> ((x -> a) -> (x -> c) -> x -> c)
-> ((x -> a) -> x -> c)
-> R1 (x -> a) (x -> b)
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (\x -> c
f x
x -> c -> b
k (x -> c
f x
x)) ((a -> c -> c) -> (x -> a) -> (x -> c) -> x -> c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 a -> c -> c
h) ((a -> c) -> (x -> a) -> x -> c
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> c
z)
instance Cosieve R1 NonEmpty where
cosieve :: R1 a b -> NonEmpty a -> b
cosieve (R1 c -> b
k a -> c -> c
h a -> c
z) NonEmpty a
l = c -> b
k ((a -> c -> c) -> (a -> c) -> NonEmpty a -> c
forall a c. (a -> c -> c) -> (a -> c) -> NonEmpty a -> c
cata a -> c -> c
h a -> c
z NonEmpty a
l)
cata :: (a -> c -> c) -> (a -> c) -> NonEmpty a -> c
cata :: (a -> c -> c) -> (a -> c) -> NonEmpty a -> c
cata a -> c -> c
f0 a -> c
z0 (a
a0 :| [a]
as0) = (a -> c -> c) -> (a -> c) -> a -> [a] -> c
forall t t. (t -> t -> t) -> (t -> t) -> t -> [t] -> t
go a -> c -> c
f0 a -> c
z0 a
a0 [a]
as0 where
go :: (t -> t -> t) -> (t -> t) -> t -> [t] -> t
go t -> t -> t
_ t -> t
z t
a [] = t -> t
z t
a
go t -> t -> t
f t -> t
z t
a (t
b:[t]
bs) = t -> t -> t
f t
a ((t -> t -> t) -> (t -> t) -> t -> [t] -> t
go t -> t -> t
f t -> t
z t
b [t]
bs)
instance Costrong R1 where
unfirst :: R1 (a, d) (b, d) -> R1 a b
unfirst = R1 (a, d) (b, d) -> R1 a b
forall (p :: * -> * -> *) a d b.
Corepresentable p =>
p (a, d) (b, d) -> p a b
unfirstCorep
unsecond :: R1 (d, a) (d, b) -> R1 a b
unsecond = R1 (d, a) (d, b) -> R1 a b
forall (p :: * -> * -> *) d a b.
Corepresentable p =>
p (d, a) (d, b) -> p a b
unsecondCorep
instance Profunctor.Corepresentable R1 where
type Corep R1 = NonEmpty
cotabulate :: (Corep R1 d -> c) -> R1 d c
cotabulate Corep R1 d -> c
f = ([d] -> c) -> (d -> [d] -> [d]) -> (d -> [d]) -> R1 d c
forall a b c. (c -> b) -> (a -> c -> c) -> (a -> c) -> R1 a b
R1 (NonEmpty d -> c
Corep R1 d -> c
f (NonEmpty d -> c) -> ([d] -> NonEmpty d) -> [d] -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. [d] -> NonEmpty d
forall a. [a] -> NonEmpty a
NonEmpty.fromList ([d] -> NonEmpty d) -> ([d] -> [d]) -> [d] -> NonEmpty d
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. [d] -> [d]
forall a. [a] -> [a]
Prelude.reverse) (:) d -> [d]
forall (f :: * -> *) a. Applicative f => a -> f a
pure
{-# INLINE cotabulate #-}
instance Distributive (R1 a) where
distribute :: f (R1 a a) -> R1 a (f a)
distribute = f (R1 a a) -> R1 a (f a)
forall (f :: * -> *) (w :: * -> *) a.
(Representable f, Functor w) =>
w (f a) -> f (w a)
distributeRep
instance Functor.Representable (R1 a) where
type Rep (R1 a) = NonEmpty a
tabulate :: (Rep (R1 a) -> a) -> R1 a a
tabulate = (Rep (R1 a) -> a) -> R1 a a
forall (p :: * -> * -> *) d c.
Corepresentable p =>
(Corep p d -> c) -> p d c
cotabulate
index :: R1 a a -> Rep (R1 a) -> a
index = R1 a a -> Rep (R1 a) -> a
forall (p :: * -> * -> *) (f :: * -> *) a b.
Cosieve p f =>
p a b -> f a -> b
cosieve
instance MonadReader (NonEmpty a) (R1 a) where
ask :: R1 a (NonEmpty a)
ask = R1 a (NonEmpty a)
forall (f :: * -> *). Representable f => f (Rep f)
askRep
local :: (NonEmpty a -> NonEmpty a) -> R1 a a -> R1 a a
local = (NonEmpty a -> NonEmpty a) -> R1 a a -> R1 a a
forall (f :: * -> *) a.
Representable f =>
(Rep f -> Rep f) -> f a -> f a
localRep
instance MonadFix (R1 a) where
mfix :: (a -> R1 a a) -> R1 a a
mfix = (a -> R1 a a) -> R1 a a
forall (f :: * -> *) a. Representable f => (a -> f a) -> f a
mfixRep