{-# LANGUAGE Safe #-}{-# LANGUAGE CPP #-}------------------------------------------------------------------------------- |-- Module : Data.Bifunctor-- Copyright : (C) 2008-2014 Edward Kmett,-- License : BSD-style (see the file LICENSE)---- Maintainer : libraries@haskell.org-- Stability : provisional-- Portability : portable---- @since 4.8.0.0----------------------------------------------------------------------------moduleData.Bifunctor(Bifunctor (..))whereimportControl.Applicative (Const (..))-- | Formally, the class 'Bifunctor' represents a bifunctor-- from @Hask@ -> @Hask@.---- Intuitively it is a bifunctor where both the first and second-- arguments are covariant.---- You can define a 'Bifunctor' by either defining 'bimap' or by-- defining both 'first' and 'second'.---- If you supply 'bimap', you should ensure that:---- @'bimap' 'id' 'id' ≡ 'id'@---- If you supply 'first' and 'second', ensure:---- @-- 'first' 'id' ≡ 'id'-- 'second' 'id' ≡ 'id'-- @---- If you supply both, you should also ensure:---- @'bimap' f g ≡ 'first' f '.' 'second' g@---- These ensure by parametricity:---- @-- 'bimap' (f '.' g) (h '.' i) ≡ 'bimap' f h '.' 'bimap' g i-- 'first' (f '.' g) ≡ 'first' f '.' 'first' g-- 'second' (f '.' g) ≡ 'second' f '.' 'second' g-- @---- @since 4.8.0.0classBifunctor p where{-# MINIMAL bimap | first, second #-}-- | Map over both arguments at the same time.---- @'bimap' f g ≡ 'first' f '.' 'second' g@bimap ::(a ->b )->(c ->d )->p a c ->p b d bimap f g =first f . second g -- | Map covariantly over the first argument.---- @'first' f ≡ 'bimap' f 'id'@first ::(a ->b )->p a c ->p b c first f =bimap f id -- | Map covariantly over the second argument.---- @'second' ≡ 'bimap' 'id'@second ::(b ->c )->p a b ->p a c second =bimap id instanceBifunctor (,)wherebimap f g ~(a ,b )=(f a ,g b )instanceBifunctor ((,,)x1 )wherebimap f g ~(x1 ,a ,b )=(x1 ,f a ,g b )instanceBifunctor ((,,,)x1 x2 )wherebimap f g ~(x1 ,x2 ,a ,b )=(x1 ,x2 ,f a ,g b )instanceBifunctor ((,,,,)x1 x2 x3 )wherebimap f g ~(x1 ,x2 ,x3 ,a ,b )=(x1 ,x2 ,x3 ,f a ,g b )instanceBifunctor ((,,,,,)x1 x2 x3 x4 )wherebimap f g ~(x1 ,x2 ,x3 ,x4 ,a ,b )=(x1 ,x2 ,x3 ,x4 ,f a ,g b )instanceBifunctor ((,,,,,,)x1 x2 x3 x4 x5 )wherebimap f g ~(x1 ,x2 ,x3 ,x4 ,x5 ,a ,b )=(x1 ,x2 ,x3 ,x4 ,x5 ,f a ,g b )instanceBifunctor Either wherebimap f _(Left a )=Left (f a )bimap_g (Right b )=Right (g b )instanceBifunctor Const wherebimap f _(Const a )=Const (f a )