{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ExistentialQuantification #-}
module Data.Fold.M1
( M1(..)
, runM1
) 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.Pointed
import Data.Profunctor.Closed
import Data.Profunctor
import Data.Profunctor.Sieve
import Data.Profunctor.Rep as Profunctor
import Data.Profunctor.Unsafe
import Data.Proxy
import Data.Reflection
import Data.Semigroup.Foldable
import Data.Semigroupoid
import Prelude hiding (id,(.))
import Unsafe.Coerce
data M1 a b = forall m. M1 (m -> b) (a -> m) (m -> m -> m)
instance Scan M1 where
run1 :: a -> M1 a b -> b
run1 a
a (M1 m -> b
k a -> m
h m -> m -> m
_) = m -> b
k (a -> m
h a
a)
prefix1 :: a -> M1 a b -> M1 a b
prefix1 a
a (M1 m -> b
k a -> m
h m -> m -> m
m) = case a -> m
h a
a of
m
x -> (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\m
y -> m -> b
k (m -> m -> m
m m
x m
y)) a -> m
h m -> m -> m
m
postfix1 :: M1 a b -> a -> M1 a b
postfix1 (M1 m -> b
k a -> m
h m -> m -> m
m) a
a = case a -> m
h a
a of
m
y -> (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\m
x -> m -> b
k (m -> m -> m
m m
x m
y)) a -> m
h m -> m -> m
m
interspersing :: a -> M1 a b -> M1 a b
interspersing a
a (M1 m -> b
k a -> m
h m -> m -> m
m) = (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 m -> b
k a -> m
h m -> m -> m
m' where
m' :: m -> m -> m
m' m
x m
y = m
x m -> m -> m
`m` a -> m
h a
a m -> m -> m
`m` m
y
{-# INLINE run1 #-}
{-# INLINE prefix1 #-}
{-# INLINE postfix1 #-}
{-# INLINE interspersing #-}
instance Functor (M1 a) where
fmap :: (a -> b) -> M1 a a -> M1 a b
fmap a -> b
f (M1 m -> a
k a -> m
h m -> m -> m
m) = (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (a -> b
f(a -> b) -> (m -> a) -> m -> b
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.m -> a
k) a -> m
h m -> m -> m
m
{-# INLINE fmap #-}
a
b <$ :: a -> M1 a b -> M1 a a
<$ M1 a b
_ = a -> M1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
b
{-# INLINE (<$) #-}
instance Pointed (M1 a) where
point :: a -> M1 a a
point a
x = (() -> a) -> (a -> ()) -> (() -> () -> ()) -> M1 a a
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\() -> a
x) (\a
_ -> ()) (\() () -> ())
{-# INLINE point #-}
instance Apply (M1 a) where
<.> :: M1 a (a -> b) -> M1 a a -> M1 a b
(<.>) = M1 a (a -> b) -> M1 a a -> M1 a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
(<*>)
{-# INLINE (<.>) #-}
<. :: M1 a a -> M1 a b -> M1 a a
(<.) M1 a a
m = \M1 a b
_ -> M1 a a
m
{-# INLINE (<.) #-}
M1 a a
_ .> :: M1 a a -> M1 a b -> M1 a b
.> M1 a b
m = M1 a b
m
{-# INLINE (.>) #-}
instance Applicative (M1 a) where
pure :: a -> M1 a a
pure a
x = (() -> a) -> (a -> ()) -> (() -> () -> ()) -> M1 a a
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\() -> a
x) (\a
_ -> ()) (\() () -> ())
{-# INLINE pure #-}
M1 m -> a -> b
kf a -> m
hf m -> m -> m
mf <*> :: M1 a (a -> b) -> M1 a a -> M1 a b
<*> M1 m -> a
ka a -> m
ha m -> m -> m
ma = (Pair' m m -> b)
-> (a -> Pair' m m)
-> (Pair' m m -> Pair' m m -> Pair' m m)
-> M1 a b
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1
(\(Pair' m
x m
y) -> m -> a -> b
kf m
x (m -> a
ka m
y))
(\a
a -> m -> m -> Pair' m m
forall a b. a -> b -> Pair' a b
Pair' (a -> m
hf a
a) (a -> m
ha a
a))
(\(Pair' m
x1 m
y1) (Pair' m
x2 m
y2) -> m -> m -> Pair' m m
forall a b. a -> b -> Pair' a b
Pair' (m -> m -> m
mf m
x1 m
x2) (m -> m -> m
ma m
y1 m
y2))
<* :: M1 a a -> M1 a b -> M1 a a
(<*) M1 a a
m = \ M1 a b
_ -> M1 a a
m
{-# INLINE (<*) #-}
M1 a a
_ *> :: M1 a a -> M1 a b -> M1 a b
*> M1 a b
m = M1 a b
m
{-# INLINE (*>) #-}
instance Monad (M1 a) where
return :: a -> M1 a a
return = a -> M1 a a
forall (f :: * -> *) a. Applicative f => a -> f a
pure
{-# INLINE return #-}
M1 a a
m >>= :: M1 a a -> (a -> M1 a b) -> M1 a b
>>= a -> M1 a b
f = (Tree1 a -> a -> b)
-> (a -> Tree1 a)
-> (Tree1 a -> Tree1 a -> Tree1 a)
-> M1 a (a -> b)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\Tree1 a
xs a
a -> Tree1 a -> M1 a b -> b
forall a b. Tree1 a -> M1 a b -> b
walk Tree1 a
xs (a -> M1 a b
f a
a)) a -> Tree1 a
forall a. a -> Tree1 a
Tip1 Tree1 a -> Tree1 a -> Tree1 a
forall a. Tree1 a -> Tree1 a -> Tree1 a
Bin1 M1 a (a -> b) -> M1 a a -> M1 a b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> M1 a a
m
{-# INLINE (>>=) #-}
>> :: M1 a a -> M1 a b -> M1 a b
(>>) = M1 a a -> M1 a b -> M1 a b
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
(*>)
{-# INLINE (>>) #-}
instance MonadZip (M1 a) where
mzipWith :: (a -> b -> c) -> M1 a a -> M1 a b -> M1 a c
mzipWith = (a -> b -> c) -> M1 a a -> M1 a b -> M1 a c
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2
{-# INLINE mzipWith #-}
instance Semigroupoid M1 where
o :: M1 j k1 -> M1 i j -> M1 i k1
o = M1 j k1 -> M1 i j -> M1 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 M1 where
id :: M1 a a
id = (a -> a) -> (a -> a) -> (a -> a -> a) -> M1 a a
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 a -> a
forall k (cat :: k -> k -> *) (a :: k). Category cat => cat a a
id a -> a
forall k (cat :: k -> k -> *) (a :: k). Category cat => cat a a
id a -> a -> a
forall a b. a -> b -> a
const
{-# INLINE id #-}
M1 m -> c
k b -> m
h m -> m -> m
m . :: M1 b c -> M1 a b -> M1 a c
. M1 m -> b
k' a -> m
h' m -> m -> m
m' = (Pair' m m -> c)
-> (a -> Pair' m m)
-> (Pair' m m -> Pair' m m -> Pair' m m)
-> M1 a c
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\(Pair' m
b m
_) -> m -> c
k m
b) a -> Pair' m m
h'' Pair' m m -> Pair' m m -> Pair' m m
m'' where
m'' :: Pair' m m -> Pair' m m -> Pair' m m
m'' (Pair' m
a m
b) (Pair' m
c m
d) = m -> m -> Pair' m m
forall a b. a -> b -> Pair' a b
Pair' (m -> m -> m
m m
a m
c) (m -> m -> m
m' m
b m
d)
h'' :: a -> Pair' m m
h'' a
a = m -> m -> Pair' m m
forall a b. a -> b -> Pair' a b
Pair' (b -> m
h (m -> b
k' m
d)) m
d where d :: m
d = a -> m
h' a
a
{-# INLINE (.) #-}
instance Arrow M1 where
arr :: (b -> c) -> M1 b c
arr b -> c
h = (b -> c) -> (b -> b) -> (b -> b -> b) -> M1 b c
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 b -> c
h b -> b
forall k (cat :: k -> k -> *) (a :: k). Category cat => cat a a
id b -> b -> b
forall a b. a -> b -> a
const
{-# INLINE arr #-}
first :: M1 b c -> M1 (b, d) (c, d)
first (M1 m -> c
k b -> m
h m -> m -> m
m) = ((m, d) -> (c, d))
-> ((b, d) -> (m, d))
-> ((m, d) -> (m, d) -> (m, d))
-> M1 (b, d) (c, d)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> c) -> (m, d) -> (c, d)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first m -> c
k) ((b -> m) -> (b, d) -> (m, d)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first b -> m
h) (m, d) -> (m, d) -> (m, d)
m' where
m' :: (m, d) -> (m, d) -> (m, d)
m' (m
a,d
_) (m
c,d
b) = (m -> m -> m
m m
a m
c, d
b)
{-# INLINE first #-}
second :: M1 b c -> M1 (d, b) (d, c)
second (M1 m -> c
k b -> m
h m -> m -> m
m) = ((d, m) -> (d, c))
-> ((d, b) -> (d, m))
-> ((d, m) -> (d, m) -> (d, m))
-> M1 (d, b) (d, c)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> c) -> (d, m) -> (d, c)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second m -> c
k) ((b -> m) -> (d, b) -> (d, m)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second b -> m
h) (d, m) -> (d, m) -> (d, m)
m' where
m' :: (d, m) -> (d, m) -> (d, m)
m' (d
_,m
b) (d
a,m
c) = (d
a, m -> m -> m
m m
b m
c)
{-# INLINE second #-}
M1 m -> c
k b -> m
h m -> m -> m
m *** :: M1 b c -> M1 b' c' -> M1 (b, b') (c, c')
*** M1 m -> c'
k' b' -> m
h' m -> m -> m
m' = ((m, m) -> (c, c'))
-> ((b, b') -> (m, m))
-> ((m, m) -> (m, m) -> (m, m))
-> M1 (b, b') (c, c')
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (m -> c
k (m -> c) -> (m -> c') -> (m, m) -> (c, c')
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** m -> c'
k') (b -> m
h (b -> m) -> (b' -> m) -> (b, b') -> (m, m)
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** b' -> m
h') (m, m) -> (m, m) -> (m, m)
m'' where
m'' :: (m, m) -> (m, m) -> (m, m)
m'' (m
a,m
b) (m
c,m
d) = (m -> m -> m
m m
a m
c, m -> m -> m
m' m
b m
d)
{-# INLINE (***) #-}
M1 m -> c
k b -> m
h m -> m -> m
m &&& :: M1 b c -> M1 b c' -> M1 b (c, c')
&&& M1 m -> c'
k' b -> m
h' m -> m -> m
m' = ((m, m) -> (c, c'))
-> (b -> (m, m)) -> ((m, m) -> (m, m) -> (m, m)) -> M1 b (c, c')
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (m -> c
k (m -> c) -> (m -> c') -> (m, m) -> (c, c')
forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
*** m -> c'
k') (b -> m
h (b -> m) -> (b -> m) -> b -> (m, m)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& b -> m
h') (m, m) -> (m, m) -> (m, m)
m'' where
m'' :: (m, m) -> (m, m) -> (m, m)
m'' (m
a,m
b) (m
c,m
d) = (m -> m -> m
m m
a m
c, m -> m -> m
m' m
b m
d)
{-# INLINE (&&&) #-}
instance Profunctor M1 where
dimap :: (a -> b) -> (c -> d) -> M1 b c -> M1 a d
dimap a -> b
f c -> d
g (M1 m -> c
k b -> m
h m -> m -> m
m) = (m -> d) -> (a -> m) -> (m -> m -> m) -> M1 a d
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (c -> d
g(c -> d) -> (m -> c) -> m -> d
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.m -> c
k) (b -> m
h(b -> m) -> (a -> b) -> a -> m
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) m -> m -> m
m
{-# INLINE dimap #-}
lmap :: (a -> b) -> M1 b c -> M1 a c
lmap a -> b
f (M1 m -> c
k b -> m
h m -> m -> m
m) = (m -> c) -> (a -> m) -> (m -> m -> m) -> M1 a c
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 m -> c
k (b -> m
h(b -> m) -> (a -> b) -> a -> m
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) m -> m -> m
m
{-# INLINE lmap #-}
rmap :: (b -> c) -> M1 a b -> M1 a c
rmap b -> c
g (M1 m -> b
k a -> m
h m -> m -> m
m) = (m -> c) -> (a -> m) -> (m -> m -> m) -> M1 a c
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (b -> c
g(b -> c) -> (m -> b) -> m -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
.m -> b
k) a -> m
h m -> m -> m
m
{-# INLINE rmap #-}
( #. ) q b c
_ = M1 a b -> M1 a c
forall a b. a -> b
unsafeCoerce
{-# INLINE (#.) #-}
M1 b c
x .# :: M1 b c -> q a b -> M1 a c
.# q a b
_ = M1 b c -> M1 a c
forall a b. a -> b
unsafeCoerce M1 b c
x
{-# INLINE (.#) #-}
instance Strong M1 where
first' :: M1 a b -> M1 (a, c) (b, c)
first' = M1 a b -> M1 (a, c) (b, c)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first
{-# INLINE first' #-}
second' :: M1 a b -> M1 (c, a) (c, b)
second' = M1 a b -> M1 (c, a) (c, b)
forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second
{-# INLINE second' #-}
instance Choice M1 where
left' :: M1 a b -> M1 (Either a c) (Either b c)
left' (M1 m -> b
k a -> m
h m -> m -> m
m) = (Either m c -> Either b c)
-> (Either a c -> Either m c)
-> (Either m c -> Either m c -> Either m c)
-> M1 (Either a c) (Either b c)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> Identity b) -> Either m c -> Identity (Either b c)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((m -> Identity b) -> Either m c -> Identity (Either b c))
-> (m -> b) -> Either m c -> Either b c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ m -> b
k) ((a -> Identity m) -> Either a c -> Identity (Either m c)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((a -> Identity m) -> Either a c -> Identity (Either m c))
-> (a -> m) -> Either a c -> Either m c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ a -> m
h) Either m c -> Either m c -> Either m c
step where
step :: Either m c -> Either m c -> Either m c
step (Left m
x) (Left m
y) = m -> Either m c
forall a b. a -> Either a b
Left (m -> m -> m
m m
x m
y)
step (Right c
c) Either m c
_ = c -> Either m c
forall a b. b -> Either a b
Right c
c
step Either m c
_ (Right c
c) = c -> Either m c
forall a b. b -> Either a b
Right c
c
{-# INLINE left' #-}
right' :: M1 a b -> M1 (Either c a) (Either c b)
right' (M1 m -> b
k a -> m
h m -> m -> m
m) = (Either c m -> Either c b)
-> (Either c a -> Either c m)
-> (Either c m -> Either c m -> Either c m)
-> M1 (Either c a) (Either c b)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> Identity b) -> Either c m -> Identity (Either c b)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((m -> Identity b) -> Either c m -> Identity (Either c b))
-> (m -> b) -> Either c m -> Either c b
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ m -> b
k) ((a -> Identity m) -> Either c a -> Identity (Either c m)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((a -> Identity m) -> Either c a -> Identity (Either c m))
-> (a -> m) -> Either c a -> Either c m
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ a -> m
h) Either c m -> Either c m -> Either c m
step where
step :: Either c m -> Either c m -> Either c m
step (Right m
x) (Right m
y) = m -> Either c m
forall a b. b -> Either a b
Right (m -> m -> m
m m
x m
y)
step (Left c
c) Either c m
_ = c -> Either c m
forall a b. a -> Either a b
Left c
c
step Either c m
_ (Left c
c) = c -> Either c m
forall a b. a -> Either a b
Left c
c
{-# INLINE right' #-}
instance ArrowChoice M1 where
left :: M1 b c -> M1 (Either b d) (Either c d)
left (M1 m -> c
k b -> m
h m -> m -> m
m) = (Either m d -> Either c d)
-> (Either b d -> Either m d)
-> (Either m d -> Either m d -> Either m d)
-> M1 (Either b d) (Either c d)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> Identity c) -> Either m d -> Identity (Either c d)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((m -> Identity c) -> Either m d -> Identity (Either c d))
-> (m -> c) -> Either m d -> Either c d
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ m -> c
k) ((b -> Identity m) -> Either b d -> Identity (Either m d)
forall a c b. Prism (Either a c) (Either b c) a b
_Left ((b -> Identity m) -> Either b d -> Identity (Either m d))
-> (b -> m) -> Either b d -> Either m d
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ b -> m
h) Either m d -> Either m d -> Either m d
step where
step :: Either m d -> Either m d -> Either m d
step (Left m
x) (Left m
y) = m -> Either m d
forall a b. a -> Either a b
Left (m -> m -> m
m m
x m
y)
step (Right d
c) Either m d
_ = d -> Either m d
forall a b. b -> Either a b
Right d
c
step Either m d
_ (Right d
c) = d -> Either m d
forall a b. b -> Either a b
Right d
c
{-# INLINE left #-}
right :: M1 b c -> M1 (Either d b) (Either d c)
right (M1 m -> c
k b -> m
h m -> m -> m
m) = (Either d m -> Either d c)
-> (Either d b -> Either d m)
-> (Either d m -> Either d m -> Either d m)
-> M1 (Either d b) (Either d c)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 ((m -> Identity c) -> Either d m -> Identity (Either d c)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((m -> Identity c) -> Either d m -> Identity (Either d c))
-> (m -> c) -> Either d m -> Either d c
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ m -> c
k) ((b -> Identity m) -> Either d b -> Identity (Either d m)
forall c a b. Prism (Either c a) (Either c b) a b
_Right ((b -> Identity m) -> Either d b -> Identity (Either d m))
-> (b -> m) -> Either d b -> Either d m
forall s t a b. ASetter s t a b -> (a -> b) -> s -> t
%~ b -> m
h) Either d m -> Either d m -> Either d m
step where
step :: Either d m -> Either d m -> Either d m
step (Right m
x) (Right m
y) = m -> Either d m
forall a b. b -> Either a b
Right (m -> m -> m
m m
x m
y)
step (Left d
c) Either d m
_ = d -> Either d m
forall a b. a -> Either a b
Left d
c
step Either d m
_ (Left d
c) = d -> Either d m
forall a b. a -> Either a b
Left d
c
{-# INLINE right #-}
walk :: Tree1 a -> M1 a b -> b
walk :: Tree1 a -> M1 a b -> b
walk Tree1 a
xs0 (M1 m -> b
k a -> m
h m -> m -> m
m) = m -> b
k (Tree1 a -> m
go Tree1 a
xs0) where
go :: Tree1 a -> m
go (Tip1 a
a) = a -> m
h a
a
go (Bin1 Tree1 a
xs Tree1 a
ys) = m -> m -> m
m (Tree1 a -> m
go Tree1 a
xs) (Tree1 a -> m
go Tree1 a
ys)
{-# INLINE walk #-}
runM1 :: Foldable1 f => f a -> M1 a b -> b
runM1 :: f a -> M1 a b -> b
runM1 f a
p (M1 m -> b
k a -> m
h (m -> m -> m
m :: m -> m -> m)) = (m -> m -> m)
-> (forall s. Reifies s (m -> m -> m) => Proxy s -> b) -> b
forall a r. a -> (forall s. Reifies s a => Proxy s -> r) -> r
reify m -> m -> m
m ((forall s. Reifies s (m -> m -> m) => Proxy s -> b) -> b)
-> (forall s. Reifies s (m -> m -> m) => Proxy s -> b) -> b
forall a b. (a -> b) -> a -> b
$ \ (Proxy s
_ :: Proxy s) -> m -> b
k (m -> b) -> m -> b
forall a b. (a -> b) -> a -> b
$ S m s -> m
forall a s. S a s -> a
runS ((a -> S m s) -> f a -> S m s
forall (t :: * -> *) m a.
(Foldable1 t, Semigroup m) =>
(a -> m) -> t a -> m
foldMap1 (m -> S m s
forall a s. a -> S a s
S (m -> S m s) -> (a -> m) -> a -> S m s
forall (p :: * -> * -> *) a b c (q :: * -> * -> *).
(Profunctor p, Coercible c b) =>
q b c -> p a b -> p a c
#. a -> m
h) f a
p :: S m s)
instance Closed M1 where
closed :: M1 a b -> M1 (x -> a) (x -> b)
closed (M1 m -> b
k a -> m
h m -> m -> m
m) = ((x -> m) -> x -> b)
-> ((x -> a) -> x -> m)
-> ((x -> m) -> (x -> m) -> x -> m)
-> M1 (x -> a) (x -> b)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\x -> m
f x
x -> m -> b
k (x -> m
f x
x)) ((a -> m) -> (x -> a) -> x -> m
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> m
h) ((m -> m -> m) -> (x -> m) -> (x -> m) -> x -> m
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 m -> m -> m
m)
instance Distributive (M1 a) where
distribute :: f (M1 a a) -> M1 a (f a)
distribute f (M1 a a)
fm = (Tree1 a -> f a)
-> (a -> Tree1 a) -> (Tree1 a -> Tree1 a -> Tree1 a) -> M1 a (f a)
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (\Tree1 a
t -> let g :: FreeSemigroup a
g = Tree1 a -> FreeSemigroup a
forall (f :: * -> *) a.
(MuRef1 f, Bifoldable1 (DeRef1 f)) =>
f a -> FreeSemigroup a
foldDeRef1 Tree1 a
t in FreeSemigroup a -> M1 a a -> a
forall (f :: * -> *) a b. Foldable1 f => f a -> M1 a b -> b
runM1 FreeSemigroup a
g (M1 a a -> a) -> f (M1 a a) -> f a
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> f (M1 a a)
fm) a -> Tree1 a
forall a. a -> Tree1 a
Tip1 Tree1 a -> Tree1 a -> Tree1 a
forall a. Tree1 a -> Tree1 a -> Tree1 a
Bin1
{-# INLINE distribute #-}
instance Cosieve M1 FreeSemigroup where
cosieve :: M1 a b -> FreeSemigroup a -> b
cosieve = (FreeSemigroup a -> M1 a b -> b) -> M1 a b -> FreeSemigroup a -> b
forall a b c. (a -> b -> c) -> b -> a -> c
flip FreeSemigroup a -> M1 a b -> b
forall (f :: * -> *) a b. Foldable1 f => f a -> M1 a b -> b
runM1
instance Profunctor.Corepresentable M1 where
type Corep M1 = FreeSemigroup
cotabulate :: (Corep M1 d -> c) -> M1 d c
cotabulate Corep M1 d -> c
f = (Tree1 d -> c)
-> (d -> Tree1 d) -> (Tree1 d -> Tree1 d -> Tree1 d) -> M1 d c
forall a b m. (m -> b) -> (a -> m) -> (m -> m -> m) -> M1 a b
M1 (Corep M1 d -> c
FreeSemigroup d -> c
f (FreeSemigroup d -> c)
-> (Tree1 d -> FreeSemigroup d) -> Tree1 d -> c
forall k (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Tree1 d -> FreeSemigroup d
forall (f :: * -> *) a.
(MuRef1 f, Bifoldable1 (DeRef1 f)) =>
f a -> FreeSemigroup a
foldDeRef1) d -> Tree1 d
forall a. a -> Tree1 a
Tip1 Tree1 d -> Tree1 d -> Tree1 d
forall a. Tree1 a -> Tree1 a -> Tree1 a
Bin1
instance Functor.Representable (M1 a) where
type Rep (M1 a) = FreeSemigroup a
tabulate :: (Rep (M1 a) -> a) -> M1 a a
tabulate = (Rep (M1 a) -> a) -> M1 a a
forall (p :: * -> * -> *) d c.
Corepresentable p =>
(Corep p d -> c) -> p d c
cotabulate
index :: M1 a a -> Rep (M1 a) -> a
index = M1 a a -> Rep (M1 a) -> a
forall (p :: * -> * -> *) (f :: * -> *) a b.
Cosieve p f =>
p a b -> f a -> b
cosieve
instance Costrong M1 where
unfirst :: M1 (a, d) (b, d) -> M1 a b
unfirst = M1 (a, d) (b, d) -> M1 a b
forall (p :: * -> * -> *) a d b.
Corepresentable p =>
p (a, d) (b, d) -> p a b
unfirstCorep
unsecond :: M1 (d, a) (d, b) -> M1 a b
unsecond = M1 (d, a) (d, b) -> M1 a b
forall (p :: * -> * -> *) d a b.
Corepresentable p =>
p (d, a) (d, b) -> p a b
unsecondCorep
instance MonadReader (FreeSemigroup a) (M1 a) where
ask :: M1 a (FreeSemigroup a)
ask = M1 a (FreeSemigroup a)
forall (f :: * -> *). Representable f => f (Rep f)
askRep
local :: (FreeSemigroup a -> FreeSemigroup a) -> M1 a a -> M1 a a
local = (FreeSemigroup a -> FreeSemigroup a) -> M1 a a -> M1 a a
forall (f :: * -> *) a.
Representable f =>
(Rep f -> Rep f) -> f a -> f a
localRep
instance MonadFix (M1 a) where
mfix :: (a -> M1 a a) -> M1 a a
mfix = (a -> M1 a a) -> M1 a a
forall (f :: * -> *) a. Representable f => (a -> f a) -> f a
mfixRep