{-# OPTIONS_GHC -Wunused-imports #-}

module Agda.Utils.Tuple
  ( (-*-)
  , mapFst
  , mapSnd
  , (/\)
  , fst3
  , snd3
  , thd3
  , swap
  , uncurry3
  , uncurry4
  , mapPairM
  , mapFstM
  , mapSndM
  , Pair(..)
  ) where

import Control.Arrow   ( (&&&) )
import Control.DeepSeq ( NFData )

import Data.Bifunctor  ( bimap, first, second )
import Data.Tuple      ( swap )

import GHC.Generics    ( Generic )

infix 2 -*-
infix 3 /\ -- backslashes at EOL interact badly with CPP...

-- | Bifunctoriality for pairs.
(-*-) :: (a -> c) -> (b -> d) -> (a,b) -> (c,d)
-*- :: forall a c b d. (a -> c) -> (b -> d) -> (a, b) -> (c, d)
(-*-) = (a -> c) -> (b -> d) -> (a, b) -> (c, d)
forall a c b d. (a -> c) -> (b -> d) -> (a, b) -> (c, d)
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap

-- | @mapFst f = f -*- id@
mapFst :: (a -> c) -> (a,b) -> (c,b)
mapFst :: forall a c b. (a -> c) -> (a, b) -> (c, b)
mapFst = (a -> c) -> (a, b) -> (c, b)
forall a c b. (a -> c) -> (a, b) -> (c, b)
forall (p :: * -> * -> *) a b c.
Bifunctor p =>
(a -> b) -> p a c -> p b c
first

-- | @mapSnd g = id -*- g@
mapSnd :: (b -> d) -> (a,b) -> (a,d)
mapSnd :: forall b d a. (b -> d) -> (a, b) -> (a, d)
mapSnd = (b -> d) -> (a, b) -> (a, d)
forall b d a. (b -> d) -> (a, b) -> (a, d)
forall (p :: * -> * -> *) b c a.
Bifunctor p =>
(b -> c) -> p a b -> p a c
second

-- | Lifted pairing.
(/\) :: (a -> b) -> (a -> c) -> a -> (b,c)
/\ :: forall a b c. (a -> b) -> (a -> c) -> a -> (b, c)
(/\) = (a -> b) -> (a -> c) -> a -> (b, c)
forall a b c. (a -> b) -> (a -> c) -> a -> (b, c)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
(&&&)

-- * Triple (stolen from Data.Tuple.HT)

{-# INLINE fst3 #-}
fst3 :: (a,b,c) -> a
fst3 :: forall a b c. (a, b, c) -> a
fst3 ~(a
x,b
_,c
_) = a
x

{-# INLINE snd3 #-}
snd3 :: (a,b,c) -> b
snd3 :: forall a b c. (a, b, c) -> b
snd3 ~(a
_,b
x,c
_) = b
x

{-# INLINE thd3 #-}
thd3 :: (a,b,c) -> c
thd3 :: forall a b c. (a, b, c) -> c
thd3 ~(a
_,b
_,c
x) = c
x

{-# INLINE uncurry3 #-}
uncurry3 :: (a -> b -> c -> d) -> (a,b,c) -> d
uncurry3 :: forall a b c d. (a -> b -> c -> d) -> (a, b, c) -> d
uncurry3 a -> b -> c -> d
f ~(a
x,b
y,c
z) = a -> b -> c -> d
f a
x b
y c
z

{-# INLINE uncurry4 #-}
uncurry4 :: (a -> b -> c -> d -> e) -> (a,b,c,d) -> e
uncurry4 :: forall a b c d e. (a -> b -> c -> d -> e) -> (a, b, c, d) -> e
uncurry4 a -> b -> c -> d -> e
f ~(a
w,b
x,c
y,d
z) = a -> b -> c -> d -> e
f a
w b
x c
y d
z

-- | Monadic version of '-*-'.
mapPairM :: (Applicative m) => (a -> m c) -> (b -> m d) -> (a,b) -> m (c,d)
mapPairM :: forall (m :: * -> *) a c b d.
Applicative m =>
(a -> m c) -> (b -> m d) -> (a, b) -> m (c, d)
mapPairM a -> m c
f b -> m d
g ~(a
a,b
b) = (,) (c -> d -> (c, d)) -> m c -> m (d -> (c, d))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m c
f a
a m (d -> (c, d)) -> m d -> m (c, d)
forall a b. m (a -> b) -> m a -> m b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> b -> m d
g b
b

-- | Monadic 'mapFst'.
mapFstM :: Functor m => (a -> m c) -> (a,b) -> m (c,b)
mapFstM :: forall (m :: * -> *) a c b.
Functor m =>
(a -> m c) -> (a, b) -> m (c, b)
mapFstM a -> m c
f ~(a
a,b
b) = (,b
b) (c -> (c, b)) -> m c -> m (c, b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> m c
f a
a

-- | Monadic 'mapSnd'.
mapSndM :: Functor m => (b -> m d) -> (a,b) -> m (a,d)
mapSndM :: forall (m :: * -> *) b d a.
Functor m =>
(b -> m d) -> (a, b) -> m (a, d)
mapSndM b -> m d
f ~(a
a,b
b) = (a
a,) (d -> (a, d)) -> m d -> m (a, d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> b -> m d
f b
b

data Pair a = Pair a a
  deriving (Int -> Pair a -> ShowS
[Pair a] -> ShowS
Pair a -> String
(Int -> Pair a -> ShowS)
-> (Pair a -> String) -> ([Pair a] -> ShowS) -> Show (Pair a)
forall a. Show a => Int -> Pair a -> ShowS
forall a. Show a => [Pair a] -> ShowS
forall a. Show a => Pair a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> Pair a -> ShowS
showsPrec :: Int -> Pair a -> ShowS
$cshow :: forall a. Show a => Pair a -> String
show :: Pair a -> String
$cshowList :: forall a. Show a => [Pair a] -> ShowS
showList :: [Pair a] -> ShowS
Show, Pair a -> Pair a -> Bool
(Pair a -> Pair a -> Bool)
-> (Pair a -> Pair a -> Bool) -> Eq (Pair a)
forall a. Eq a => Pair a -> Pair a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall a. Eq a => Pair a -> Pair a -> Bool
== :: Pair a -> Pair a -> Bool
$c/= :: forall a. Eq a => Pair a -> Pair a -> Bool
/= :: Pair a -> Pair a -> Bool
Eq, (forall x. Pair a -> Rep (Pair a) x)
-> (forall x. Rep (Pair a) x -> Pair a) -> Generic (Pair a)
forall x. Rep (Pair a) x -> Pair a
forall x. Pair a -> Rep (Pair a) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall a x. Rep (Pair a) x -> Pair a
forall a x. Pair a -> Rep (Pair a) x
$cfrom :: forall a x. Pair a -> Rep (Pair a) x
from :: forall x. Pair a -> Rep (Pair a) x
$cto :: forall a x. Rep (Pair a) x -> Pair a
to :: forall x. Rep (Pair a) x -> Pair a
Generic, (forall a b. (a -> b) -> Pair a -> Pair b)
-> (forall a b. a -> Pair b -> Pair a) -> Functor Pair
forall a b. a -> Pair b -> Pair a
forall a b. (a -> b) -> Pair a -> Pair b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
$cfmap :: forall a b. (a -> b) -> Pair a -> Pair b
fmap :: forall a b. (a -> b) -> Pair a -> Pair b
$c<$ :: forall a b. a -> Pair b -> Pair a
<$ :: forall a b. a -> Pair b -> Pair a
Functor, (forall m. Monoid m => Pair m -> m)
-> (forall m a. Monoid m => (a -> m) -> Pair a -> m)
-> (forall m a. Monoid m => (a -> m) -> Pair a -> m)
-> (forall a b. (a -> b -> b) -> b -> Pair a -> b)
-> (forall a b. (a -> b -> b) -> b -> Pair a -> b)
-> (forall b a. (b -> a -> b) -> b -> Pair a -> b)
-> (forall b a. (b -> a -> b) -> b -> Pair a -> b)
-> (forall a. (a -> a -> a) -> Pair a -> a)
-> (forall a. (a -> a -> a) -> Pair a -> a)
-> (forall a. Pair a -> [a])
-> (forall a. Pair a -> Bool)
-> (forall a. Pair a -> Int)
-> (forall a. Eq a => a -> Pair a -> Bool)
-> (forall a. Ord a => Pair a -> a)
-> (forall a. Ord a => Pair a -> a)
-> (forall a. Num a => Pair a -> a)
-> (forall a. Num a => Pair a -> a)
-> Foldable Pair
forall a. Eq a => a -> Pair a -> Bool
forall a. Num a => Pair a -> a
forall a. Ord a => Pair a -> a
forall m. Monoid m => Pair m -> m
forall a. Pair a -> Bool
forall a. Pair a -> Int
forall a. Pair a -> [a]
forall a. (a -> a -> a) -> Pair a -> a
forall m a. Monoid m => (a -> m) -> Pair a -> m
forall b a. (b -> a -> b) -> b -> Pair a -> b
forall a b. (a -> b -> b) -> b -> Pair a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
$cfold :: forall m. Monoid m => Pair m -> m
fold :: forall m. Monoid m => Pair m -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> Pair a -> m
foldMap :: forall m a. Monoid m => (a -> m) -> Pair a -> m
$cfoldMap' :: forall m a. Monoid m => (a -> m) -> Pair a -> m
foldMap' :: forall m a. Monoid m => (a -> m) -> Pair a -> m
$cfoldr :: forall a b. (a -> b -> b) -> b -> Pair a -> b
foldr :: forall a b. (a -> b -> b) -> b -> Pair a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> Pair a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> Pair a -> b
$cfoldl :: forall b a. (b -> a -> b) -> b -> Pair a -> b
foldl :: forall b a. (b -> a -> b) -> b -> Pair a -> b
$cfoldl' :: forall b a. (b -> a -> b) -> b -> Pair a -> b
foldl' :: forall b a. (b -> a -> b) -> b -> Pair a -> b
$cfoldr1 :: forall a. (a -> a -> a) -> Pair a -> a
foldr1 :: forall a. (a -> a -> a) -> Pair a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> Pair a -> a
foldl1 :: forall a. (a -> a -> a) -> Pair a -> a
$ctoList :: forall a. Pair a -> [a]
toList :: forall a. Pair a -> [a]
$cnull :: forall a. Pair a -> Bool
null :: forall a. Pair a -> Bool
$clength :: forall a. Pair a -> Int
length :: forall a. Pair a -> Int
$celem :: forall a. Eq a => a -> Pair a -> Bool
elem :: forall a. Eq a => a -> Pair a -> Bool
$cmaximum :: forall a. Ord a => Pair a -> a
maximum :: forall a. Ord a => Pair a -> a
$cminimum :: forall a. Ord a => Pair a -> a
minimum :: forall a. Ord a => Pair a -> a
$csum :: forall a. Num a => Pair a -> a
sum :: forall a. Num a => Pair a -> a
$cproduct :: forall a. Num a => Pair a -> a
product :: forall a. Num a => Pair a -> a
Foldable, Functor Pair
Foldable Pair
(Functor Pair, Foldable Pair) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> Pair a -> f (Pair b))
-> (forall (f :: * -> *) a.
    Applicative f =>
    Pair (f a) -> f (Pair a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> Pair a -> m (Pair b))
-> (forall (m :: * -> *) a. Monad m => Pair (m a) -> m (Pair a))
-> Traversable Pair
forall (t :: * -> *).
(Functor t, Foldable t) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a. Monad m => Pair (m a) -> m (Pair a)
forall (f :: * -> *) a. Applicative f => Pair (f a) -> f (Pair a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Pair a -> m (Pair b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Pair a -> f (Pair b)
$ctraverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Pair a -> f (Pair b)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> Pair a -> f (Pair b)
$csequenceA :: forall (f :: * -> *) a. Applicative f => Pair (f a) -> f (Pair a)
sequenceA :: forall (f :: * -> *) a. Applicative f => Pair (f a) -> f (Pair a)
$cmapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Pair a -> m (Pair b)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b) -> Pair a -> m (Pair b)
$csequence :: forall (m :: * -> *) a. Monad m => Pair (m a) -> m (Pair a)
sequence :: forall (m :: * -> *) a. Monad m => Pair (m a) -> m (Pair a)
Traversable)

instance Applicative Pair where
  pure :: forall a. a -> Pair a
pure a
a                  = a -> a -> Pair a
forall a. a -> a -> Pair a
Pair a
a a
a
  Pair a -> b
f a -> b
f' <*> :: forall a b. Pair (a -> b) -> Pair a -> Pair b
<*> Pair a
a a
a' = b -> b -> Pair b
forall a. a -> a -> Pair a
Pair (a -> b
f a
a) (a -> b
f' a
a')

instance NFData a => NFData (Pair a)