{-# LANGUAGE CPP                        #-}
{-# LANGUAGE DeriveGeneric              #-}
{-# LANGUAGE EmptyDataDecls             #-}
{-# LANGUAGE FlexibleContexts           #-}
{-# LANGUAGE DeriveTraversable          #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE ScopedTypeVariables        #-}
{-# LANGUAGE TypeFamilies               #-}
-- This module uses GND
{-# LANGUAGE Trustworthy #-}

-----------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2008-2016 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  portable
--
----------------------------------------------------------------------------
module Data.Bifunctor.Biap
 ( Biap(..)
 ) where

import Control.Applicative
import Control.Monad
import qualified Control.Monad.Fail as Fail (MonadFail)
import Data.Biapplicative
import Data.Bifoldable
import Data.Bitraversable
import Data.Functor.Classes
import qualified Data.Semigroup as S
import GHC.Generics

-- | Pointwise lifting of a class over two arguments, using
-- 'Biapplicative'.
--
-- Classes that can be lifted include 'Monoid', 'Num' and
-- 'Bounded'. Each method of those classes can be defined as lifting
-- themselves over each argument of 'Biapplicative'.
--
-- @
-- mempty        = bipure mempty          mempty
-- minBound      = bipure minBound        minBound
-- maxBound      = bipure maxBound        maxBound
-- fromInteger n = bipure (fromInteger n) (fromInteger n)
--
-- negate = bimap negate negate
--
-- (+)  = biliftA2 (+)  (+)
-- (<>) = biliftA2 (<>) (<>)
-- @
--
-- 'Biap' is to 'Biapplicative' as 'Data.Monoid.Ap' is to
-- 'Applicative'.
--
-- 'Biap' can be used with @DerivingVia@ to derive a numeric instance
-- for pairs:
--
-- @
-- newtype Numpair a = Np (a, a)
--  deriving (S.Semigroup, Monoid, Num, Bounded)
--  via Biap (,) a a
-- @
--
newtype Biap bi a b = Biap { forall (bi :: * -> * -> *) a b. Biap bi a b -> bi a b
getBiap :: bi a b }
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forall (bi :: * -> * -> *) a.
Alternative (bi a) =>
Applicative (Biap bi a)
forall (bi :: * -> * -> *) a a. Alternative (bi a) => Biap bi a a
forall (bi :: * -> * -> *) a a.
Alternative (bi a) =>
Biap bi a a -> Biap bi a [a]
forall (bi :: * -> * -> *) a a.
Alternative (bi a) =>
Biap bi a a -> Biap bi a a -> Biap bi a a
$cempty :: forall (bi :: * -> * -> *) a a. Alternative (bi a) => Biap bi a a
empty :: forall a. Biap bi a a
$c<|> :: forall (bi :: * -> * -> *) a a.
Alternative (bi a) =>
Biap bi a a -> Biap bi a a -> Biap bi a a
<|> :: forall a. Biap bi a a -> Biap bi a a -> Biap bi a a
$csome :: forall (bi :: * -> * -> *) a a.
Alternative (bi a) =>
Biap bi a a -> Biap bi a [a]
some :: forall a. Biap bi a a -> Biap bi a [a]
$cmany :: forall (bi :: * -> * -> *) a a.
Alternative (bi a) =>
Biap bi a a -> Biap bi a [a]
many :: forall a. Biap bi a a -> Biap bi a [a]
Alternative
          , Functor (Biap bi a)
Functor (Biap bi a) =>
(forall a. a -> Biap bi a a)
-> (forall a b. Biap bi a (a -> b) -> Biap bi a a -> Biap bi a b)
-> (forall a b c.
    (a -> b -> c) -> Biap bi a a -> Biap bi a b -> Biap bi a c)
-> (forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b)
-> (forall a b. Biap bi a a -> Biap bi a b -> Biap bi a a)
-> Applicative (Biap bi a)
forall a. a -> Biap bi a a
forall a b. Biap bi a a -> Biap bi a b -> Biap bi a a
forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b
forall a b. Biap bi a (a -> b) -> Biap bi a a -> Biap bi a b
forall a b c.
(a -> b -> c) -> Biap bi a a -> Biap bi a b -> Biap bi a c
forall (f :: * -> *).
Functor f =>
(forall a. a -> f a)
-> (forall a b. f (a -> b) -> f a -> f b)
-> (forall a b c. (a -> b -> c) -> f a -> f b -> f c)
-> (forall a b. f a -> f b -> f b)
-> (forall a b. f a -> f b -> f a)
-> Applicative f
forall (bi :: * -> * -> *) a.
Applicative (bi a) =>
Functor (Biap bi a)
forall (bi :: * -> * -> *) a a.
Applicative (bi a) =>
a -> Biap bi a a
forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a a
forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a b
forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a (a -> b) -> Biap bi a a -> Biap bi a b
forall (bi :: * -> * -> *) a a b c.
Applicative (bi a) =>
(a -> b -> c) -> Biap bi a a -> Biap bi a b -> Biap bi a c
$cpure :: forall (bi :: * -> * -> *) a a.
Applicative (bi a) =>
a -> Biap bi a a
pure :: forall a. a -> Biap bi a a
$c<*> :: forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a (a -> b) -> Biap bi a a -> Biap bi a b
<*> :: forall a b. Biap bi a (a -> b) -> Biap bi a a -> Biap bi a b
$cliftA2 :: forall (bi :: * -> * -> *) a a b c.
Applicative (bi a) =>
(a -> b -> c) -> Biap bi a a -> Biap bi a b -> Biap bi a c
liftA2 :: forall a b c.
(a -> b -> c) -> Biap bi a a -> Biap bi a b -> Biap bi a c
$c*> :: forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a b
*> :: forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b
$c<* :: forall (bi :: * -> * -> *) a a b.
Applicative (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a a
<* :: forall a b. Biap bi a a -> Biap bi a b -> Biap bi a a
Applicative
          , (forall x. Biap bi a b -> Rep (Biap bi a b) x)
-> (forall x. Rep (Biap bi a b) x -> Biap bi a b)
-> Generic (Biap bi a b)
forall x. Rep (Biap bi a b) x -> Biap bi a b
forall x. Biap bi a b -> Rep (Biap bi a b) x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
forall (bi :: * -> * -> *) a b x.
Rep (Biap bi a b) x -> Biap bi a b
forall (bi :: * -> * -> *) a b x.
Biap bi a b -> Rep (Biap bi a b) x
$cfrom :: forall (bi :: * -> * -> *) a b x.
Biap bi a b -> Rep (Biap bi a b) x
from :: forall x. Biap bi a b -> Rep (Biap bi a b) x
$cto :: forall (bi :: * -> * -> *) a b x.
Rep (Biap bi a b) x -> Biap bi a b
to :: forall x. Rep (Biap bi a b) x -> Biap bi a b
Generic
          , (forall a. Biap bi a a -> Rep1 (Biap bi a) a)
-> (forall a. Rep1 (Biap bi a) a -> Biap bi a a)
-> Generic1 (Biap bi a)
forall a. Rep1 (Biap bi a) a -> Biap bi a a
forall a. Biap bi a a -> Rep1 (Biap bi 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 (bi :: * -> * -> *) a a. Rep1 (Biap bi a) a -> Biap bi a a
forall (bi :: * -> * -> *) a a. Biap bi a a -> Rep1 (Biap bi a) a
$cfrom1 :: forall (bi :: * -> * -> *) a a. Biap bi a a -> Rep1 (Biap bi a) a
from1 :: forall a. Biap bi a a -> Rep1 (Biap bi a) a
$cto1 :: forall (bi :: * -> * -> *) a a. Rep1 (Biap bi a) a -> Biap bi a a
to1 :: forall a. Rep1 (Biap bi a) a -> Biap bi a a
Generic1
          , Applicative (Biap bi a)
Applicative (Biap bi a) =>
(forall a b. Biap bi a a -> (a -> Biap bi a b) -> Biap bi a b)
-> (forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b)
-> (forall a. a -> Biap bi a a)
-> Monad (Biap bi a)
forall a. a -> Biap bi a a
forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b
forall a b. Biap bi a a -> (a -> Biap bi a b) -> Biap bi a b
forall (m :: * -> *).
Applicative m =>
(forall a b. m a -> (a -> m b) -> m b)
-> (forall a b. m a -> m b -> m b)
-> (forall a. a -> m a)
-> Monad m
forall (bi :: * -> * -> *) a.
Monad (bi a) =>
Applicative (Biap bi a)
forall (bi :: * -> * -> *) a a. Monad (bi a) => a -> Biap bi a a
forall (bi :: * -> * -> *) a a b.
Monad (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a b
forall (bi :: * -> * -> *) a a b.
Monad (bi a) =>
Biap bi a a -> (a -> Biap bi a b) -> Biap bi a b
$c>>= :: forall (bi :: * -> * -> *) a a b.
Monad (bi a) =>
Biap bi a a -> (a -> Biap bi a b) -> Biap bi a b
>>= :: forall a b. Biap bi a a -> (a -> Biap bi a b) -> Biap bi a b
$c>> :: forall (bi :: * -> * -> *) a a b.
Monad (bi a) =>
Biap bi a a -> Biap bi a b -> Biap bi a b
>> :: forall a b. Biap bi a a -> Biap bi a b -> Biap bi a b
$creturn :: forall (bi :: * -> * -> *) a a. Monad (bi a) => a -> Biap bi a a
return :: forall a. a -> Biap bi a a
Monad
          , Monad (Biap bi a)
Monad (Biap bi a) =>
(forall a. String -> Biap bi a a) -> MonadFail (Biap bi a)
forall a. String -> Biap bi a a
forall (m :: * -> *).
Monad m =>
(forall a. String -> m a) -> MonadFail m
forall (bi :: * -> * -> *) a. MonadFail (bi a) => Monad (Biap bi a)
forall (bi :: * -> * -> *) a a.
MonadFail (bi a) =>
String -> Biap bi a a
$cfail :: forall (bi :: * -> * -> *) a a.
MonadFail (bi a) =>
String -> Biap bi a a
fail :: forall a. String -> Biap bi a a
Fail.MonadFail
          , Monad (Biap bi a)
Alternative (Biap bi a)
(Alternative (Biap bi a), Monad (Biap bi a)) =>
(forall a. Biap bi a a)
-> (forall a. Biap bi a a -> Biap bi a a -> Biap bi a a)
-> MonadPlus (Biap bi a)
forall a. Biap bi a a
forall a. Biap bi a a -> Biap bi a a -> Biap bi a a
forall (m :: * -> *).
(Alternative m, Monad m) =>
(forall a. m a) -> (forall a. m a -> m a -> m a) -> MonadPlus m
forall (bi :: * -> * -> *) a. MonadPlus (bi a) => Monad (Biap bi a)
forall (bi :: * -> * -> *) a.
MonadPlus (bi a) =>
Alternative (Biap bi a)
forall (bi :: * -> * -> *) a a. MonadPlus (bi a) => Biap bi a a
forall (bi :: * -> * -> *) a a.
MonadPlus (bi a) =>
Biap bi a a -> Biap bi a a -> Biap bi a a
$cmzero :: forall (bi :: * -> * -> *) a a. MonadPlus (bi a) => Biap bi a a
mzero :: forall a. Biap bi a a
$cmplus :: forall (bi :: * -> * -> *) a a.
MonadPlus (bi a) =>
Biap bi a a -> Biap bi a a -> Biap bi a a
mplus :: forall a. Biap bi a a -> Biap bi a a -> Biap bi a a
MonadPlus
          , (forall a. Eq a => Eq (Biap bi a a)) =>
(forall a b.
 (a -> b -> Bool) -> Biap bi a a -> Biap bi a b -> Bool)
-> Eq1 (Biap bi a)
forall a. Eq a => Eq (Biap bi a a)
forall a b. (a -> b -> Bool) -> Biap bi a a -> Biap bi a b -> Bool
forall (f :: * -> *).
(forall a. Eq a => Eq (f a)) =>
(forall a b. (a -> b -> Bool) -> f a -> f b -> Bool) -> Eq1 f
forall (bi :: * -> * -> *) a a.
(Eq1 (bi a), Eq a) =>
Eq (Biap bi a a)
forall (bi :: * -> * -> *) a a b.
Eq1 (bi a) =>
(a -> b -> Bool) -> Biap bi a a -> Biap bi a b -> Bool
$cliftEq :: forall (bi :: * -> * -> *) a a b.
Eq1 (bi a) =>
(a -> b -> Bool) -> Biap bi a a -> Biap bi a b -> Bool
liftEq :: forall a b. (a -> b -> Bool) -> Biap bi a a -> Biap bi a b -> Bool
Eq1
          , Eq1 (Biap bi a)
(Eq1 (Biap bi a), forall a. Ord a => Ord (Biap bi a a)) =>
(forall a b.
 (a -> b -> Ordering) -> Biap bi a a -> Biap bi a b -> Ordering)
-> Ord1 (Biap bi a)
forall a. Ord a => Ord (Biap bi a a)
forall a b.
(a -> b -> Ordering) -> Biap bi a a -> Biap bi a b -> Ordering
forall (f :: * -> *).
(Eq1 f, forall a. Ord a => Ord (f a)) =>
(forall a b. (a -> b -> Ordering) -> f a -> f b -> Ordering)
-> Ord1 f
forall (bi :: * -> * -> *) a. Ord1 (bi a) => Eq1 (Biap bi a)
forall (bi :: * -> * -> *) a a.
(Ord1 (bi a), Ord a) =>
Ord (Biap bi a a)
forall (bi :: * -> * -> *) a a b.
Ord1 (bi a) =>
(a -> b -> Ordering) -> Biap bi a a -> Biap bi a b -> Ordering
$cliftCompare :: forall (bi :: * -> * -> *) a a b.
Ord1 (bi a) =>
(a -> b -> Ordering) -> Biap bi a a -> Biap bi a b -> Ordering
liftCompare :: forall a b.
(a -> b -> Ordering) -> Biap bi a a -> Biap bi a b -> Ordering
Ord1
          , (forall a. Functor (Biap bi a)) =>
(forall a b c d.
 (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d)
-> (forall a b c. (a -> b) -> Biap bi a c -> Biap bi b c)
-> (forall b c a. (b -> c) -> Biap bi a b -> Biap bi a c)
-> Bifunctor (Biap bi)
forall a. Functor (Biap bi a)
forall a b c. (a -> b) -> Biap bi a c -> Biap bi b c
forall b c a. (b -> c) -> Biap bi a b -> Biap bi a c
forall a b c d. (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
forall (bi :: * -> * -> *) a. Bifunctor bi => Functor (Biap bi a)
forall (bi :: * -> * -> *) a b c.
Bifunctor bi =>
(a -> b) -> Biap bi a c -> Biap bi b c
forall (bi :: * -> * -> *) b c a.
Bifunctor bi =>
(b -> c) -> Biap bi a b -> Biap bi a c
forall (bi :: * -> * -> *) a b c d.
Bifunctor bi =>
(a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
forall (p :: * -> * -> *).
(forall a. Functor (p a)) =>
(forall a b c d. (a -> b) -> (c -> d) -> p a c -> p b d)
-> (forall a b c. (a -> b) -> p a c -> p b c)
-> (forall b c a. (b -> c) -> p a b -> p a c)
-> Bifunctor p
$cbimap :: forall (bi :: * -> * -> *) a b c d.
Bifunctor bi =>
(a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
bimap :: forall a b c d. (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
$cfirst :: forall (bi :: * -> * -> *) a b c.
Bifunctor bi =>
(a -> b) -> Biap bi a c -> Biap bi b c
first :: forall a b c. (a -> b) -> Biap bi a c -> Biap bi b c
$csecond :: forall (bi :: * -> * -> *) b c a.
Bifunctor bi =>
(b -> c) -> Biap bi a b -> Biap bi a c
second :: forall b c a. (b -> c) -> Biap bi a b -> Biap bi a c
Bifunctor
          , Bifunctor (Biap bi)
Bifunctor (Biap bi) =>
(forall a b. a -> b -> Biap bi a b)
-> (forall a b c d.
    Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d)
-> (forall a b c d e f.
    (a -> b -> c)
    -> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f)
-> (forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi c d)
-> (forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi a b)
-> Biapplicative (Biap bi)
forall a b. a -> b -> Biap bi a b
forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi a b
forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi c d
forall a b c d.
Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d
forall a b c d e f.
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
forall (p :: * -> * -> *).
Bifunctor p =>
(forall a b. a -> b -> p a b)
-> (forall a b c d. p (a -> b) (c -> d) -> p a c -> p b d)
-> (forall a b c d e f.
    (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f)
-> (forall a b c d. p a b -> p c d -> p c d)
-> (forall a b c d. p a b -> p c d -> p a b)
-> Biapplicative p
forall (bi :: * -> * -> *). Biapplicative bi => Bifunctor (Biap bi)
forall (bi :: * -> * -> *) a b.
Biapplicative bi =>
a -> b -> Biap bi a b
forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi a b -> Biap bi c d -> Biap bi a b
forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi a b -> Biap bi c d -> Biap bi c d
forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d
forall (bi :: * -> * -> *) a b c d e f.
Biapplicative bi =>
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
$cbipure :: forall (bi :: * -> * -> *) a b.
Biapplicative bi =>
a -> b -> Biap bi a b
bipure :: forall a b. a -> b -> Biap bi a b
$c<<*>> :: forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d
<<*>> :: forall a b c d.
Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d
$cbiliftA2 :: forall (bi :: * -> * -> *) a b c d e f.
Biapplicative bi =>
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
biliftA2 :: forall a b c d e f.
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
$c*>> :: forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi a b -> Biap bi c d -> Biap bi c d
*>> :: forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi c d
$c<<* :: forall (bi :: * -> * -> *) a b c d.
Biapplicative bi =>
Biap bi a b -> Biap bi c d -> Biap bi a b
<<* :: forall a b c d. Biap bi a b -> Biap bi c d -> Biap bi a b
Biapplicative
          , (forall m. Monoid m => Biap bi m m -> m)
-> (forall m a b.
    Monoid m =>
    (a -> m) -> (b -> m) -> Biap bi a b -> m)
-> (forall a c b.
    (a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c)
-> (forall c a b.
    (c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c)
-> Bifoldable (Biap bi)
forall m. Monoid m => Biap bi m m -> m
forall m a b. Monoid m => (a -> m) -> (b -> m) -> Biap bi a b -> m
forall c a b.
(c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c
forall a c b.
(a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c
forall (bi :: * -> * -> *) m.
(Bifoldable bi, Monoid m) =>
Biap bi m m -> m
forall (bi :: * -> * -> *) m a b.
(Bifoldable bi, Monoid m) =>
(a -> m) -> (b -> m) -> Biap bi a b -> m
forall (bi :: * -> * -> *) c a b.
Bifoldable bi =>
(c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c
forall (bi :: * -> * -> *) a c b.
Bifoldable bi =>
(a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c
forall (p :: * -> * -> *).
(forall m. Monoid m => p m m -> m)
-> (forall m a b. Monoid m => (a -> m) -> (b -> m) -> p a b -> m)
-> (forall a c b.
    (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c)
-> (forall c a b.
    (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c)
-> Bifoldable p
$cbifold :: forall (bi :: * -> * -> *) m.
(Bifoldable bi, Monoid m) =>
Biap bi m m -> m
bifold :: forall m. Monoid m => Biap bi m m -> m
$cbifoldMap :: forall (bi :: * -> * -> *) m a b.
(Bifoldable bi, Monoid m) =>
(a -> m) -> (b -> m) -> Biap bi a b -> m
bifoldMap :: forall m a b. Monoid m => (a -> m) -> (b -> m) -> Biap bi a b -> m
$cbifoldr :: forall (bi :: * -> * -> *) a c b.
Bifoldable bi =>
(a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c
bifoldr :: forall a c b.
(a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c
$cbifoldl :: forall (bi :: * -> * -> *) c a b.
Bifoldable bi =>
(c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c
bifoldl :: forall c a b.
(c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c
Bifoldable
          , (forall a. Eq a => Eq1 (Biap bi a)) =>
(forall a b c d.
 (a -> b -> Bool)
 -> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool)
-> Eq2 (Biap bi)
forall a. Eq a => Eq1 (Biap bi a)
forall a b c d.
(a -> b -> Bool)
-> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool
forall (bi :: * -> * -> *) a. (Eq2 bi, Eq a) => Eq1 (Biap bi a)
forall (bi :: * -> * -> *) a b c d.
Eq2 bi =>
(a -> b -> Bool)
-> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool
forall (f :: * -> * -> *).
(forall a. Eq a => Eq1 (f a)) =>
(forall a b c d.
 (a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool)
-> Eq2 f
$cliftEq2 :: forall (bi :: * -> * -> *) a b c d.
Eq2 bi =>
(a -> b -> Bool)
-> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool
liftEq2 :: forall a b c d.
(a -> b -> Bool)
-> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool
Eq2
          , Eq2 (Biap bi)
(Eq2 (Biap bi), forall a. Ord a => Ord1 (Biap bi a)) =>
(forall a b c d.
 (a -> b -> Ordering)
 -> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering)
-> Ord2 (Biap bi)
forall a. Ord a => Ord1 (Biap bi a)
forall a b c d.
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering
forall (bi :: * -> * -> *). Ord2 bi => Eq2 (Biap bi)
forall (bi :: * -> * -> *) a. (Ord2 bi, Ord a) => Ord1 (Biap bi a)
forall (bi :: * -> * -> *) a b c d.
Ord2 bi =>
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering
forall (f :: * -> * -> *).
(Eq2 f, forall a. Ord a => Ord1 (f a)) =>
(forall a b c d.
 (a -> b -> Ordering)
 -> (c -> d -> Ordering) -> f a c -> f b d -> Ordering)
-> Ord2 f
$cliftCompare2 :: forall (bi :: * -> * -> *) a b c d.
Ord2 bi =>
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering
liftCompare2 :: forall a b c d.
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering
Ord2
          )

instance Bitraversable bi => Bitraversable (Biap bi) where
 bitraverse :: forall (f :: * -> *) a c b d.
Applicative f =>
(a -> f c) -> (b -> f d) -> Biap bi a b -> f (Biap bi c d)
bitraverse a -> f c
f b -> f d
g (Biap bi a b
as) = bi c d -> Biap bi c d
forall (bi :: * -> * -> *) a b. bi a b -> Biap bi a b
Biap (bi c d -> Biap bi c d) -> f (bi c d) -> f (Biap bi c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f c) -> (b -> f d) -> bi a b -> f (bi c d)
forall (f :: * -> *) a c b d.
Applicative f =>
(a -> f c) -> (b -> f d) -> bi a b -> f (bi c d)
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 c
f b -> f d
g bi a b
as

instance (Biapplicative bi, S.Semigroup a, S.Semigroup b) => S.Semigroup (Biap bi a b) where
  <> :: Biap bi a b -> Biap bi a b -> Biap bi a b
(<>) = (a -> a -> a)
-> (b -> b -> b) -> Biap bi a b -> Biap bi a b -> Biap bi a b
forall a b c d e f.
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
forall (p :: * -> * -> *) a b c d e f.
Biapplicative p =>
(a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
biliftA2 a -> a -> a
forall a. Semigroup a => a -> a -> a
(S.<>) b -> b -> b
forall a. Semigroup a => a -> a -> a
(S.<>)

instance (Biapplicative bi, Monoid a, Monoid b) => Monoid (Biap bi a b) where
  mempty :: Biap bi a b
mempty = a -> b -> Biap bi a b
forall a b. a -> b -> Biap bi a b
forall (p :: * -> * -> *) a b. Biapplicative p => a -> b -> p a b
bipure a
forall a. Monoid a => a
mempty b
forall a. Monoid a => a
mempty
#if !(MIN_VERSION_base(4,11,0))
  mappend = biliftA2 mappend mappend
#endif

instance (Biapplicative bi, Bounded a, Bounded b) => Bounded (Biap bi a b) where
  minBound :: Biap bi a b
minBound = a -> b -> Biap bi a b
forall a b. a -> b -> Biap bi a b
forall (p :: * -> * -> *) a b. Biapplicative p => a -> b -> p a b
bipure a
forall a. Bounded a => a
minBound b
forall a. Bounded a => a
minBound
  maxBound :: Biap bi a b
maxBound = a -> b -> Biap bi a b
forall a b. a -> b -> Biap bi a b
forall (p :: * -> * -> *) a b. Biapplicative p => a -> b -> p a b
bipure a
forall a. Bounded a => a
maxBound b
forall a. Bounded a => a
maxBound

instance (Biapplicative bi, Num a, Num b) => Num (Biap bi a b) where
  + :: Biap bi a b -> Biap bi a b -> Biap bi a b
(+) = (a -> a -> a)
-> (b -> b -> b) -> Biap bi a b -> Biap bi a b -> Biap bi a b
forall a b c d e f.
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
forall (p :: * -> * -> *) a b c d e f.
Biapplicative p =>
(a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
biliftA2 a -> a -> a
forall a. Num a => a -> a -> a
(+) b -> b -> b
forall a. Num a => a -> a -> a
(+)
  * :: Biap bi a b -> Biap bi a b -> Biap bi a b
(*) = (a -> a -> a)
-> (b -> b -> b) -> Biap bi a b -> Biap bi a b -> Biap bi a b
forall a b c d e f.
(a -> b -> c)
-> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f
forall (p :: * -> * -> *) a b c d e f.
Biapplicative p =>
(a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
biliftA2 a -> a -> a
forall a. Num a => a -> a -> a
(*) b -> b -> b
forall a. Num a => a -> a -> a
(*)

  negate :: Biap bi a b -> Biap bi a b
negate = (a -> a) -> (b -> b) -> Biap bi a b -> Biap bi a b
forall a b c d. (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> a
forall a. Num a => a -> a
negate b -> b
forall a. Num a => a -> a
negate
  abs :: Biap bi a b -> Biap bi a b
abs    = (a -> a) -> (b -> b) -> Biap bi a b -> Biap bi a b
forall a b c d. (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> a
forall a. Num a => a -> a
abs    b -> b
forall a. Num a => a -> a
abs
  signum :: Biap bi a b -> Biap bi a b
signum = (a -> a) -> (b -> b) -> Biap bi a b -> Biap bi a b
forall a b c d. (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d
forall (p :: * -> * -> *) a b c d.
Bifunctor p =>
(a -> b) -> (c -> d) -> p a c -> p b d
bimap a -> a
forall a. Num a => a -> a
signum b -> b
forall a. Num a => a -> a
signum

  fromInteger :: Integer -> Biap bi a b
fromInteger Integer
n = a -> b -> Biap bi a b
forall a b. a -> b -> Biap bi a b
forall (p :: * -> * -> *) a b. Biapplicative p => a -> b -> p a b
bipure (Integer -> a
forall a. Num a => Integer -> a
fromInteger Integer
n) (Integer -> b
forall a. Num a => Integer -> a
fromInteger Integer
n)