{-# LANGUAGE CPP #-} {-# LANGUAGE QuantifiedConstraints #-} {-# LANGUAGE Safe #-} ----------------------------------------------------------------------------- -- | -- 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 ---------------------------------------------------------------------------- module Data.Bifunctor ( Bifunctor(..) ) where import Control.Applicative ( Const(..) ) import GHC.Generics ( K1(..) ) -- $setup -- >>> import Prelude -- >>> import Data.Char (toUpper) -- | A bifunctor is a type constructor that takes -- two type arguments and is a functor in /both/ arguments. That -- is, unlike with 'Functor', a type constructor such as 'Either' -- does not need to be partially applied for a 'Bifunctor' -- instance, and the methods in this class permit mapping -- functions over the 'Left' value or the 'Right' value, -- or both at the same time. -- -- 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'. A partially applied 'Bifunctor' -- must be a 'Functor' and the 'second' method must agree with 'fmap'. -- From this it follows that: -- -- @'second' 'id' = 'id'@ -- -- 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 4.18.0.0 'Functor' is a superclass of 'Bifunctor. -- -- @since 4.8.0.0 class (forall a. Functor (p a)) => Bifunctor p where {-# MINIMAL bimap | first, second #-} -- | Map over both arguments at the same time. -- -- @'bimap' f g ≡ 'first' f '.' 'second' g@ -- -- ==== __Examples__ -- >>> bimap toUpper (+1) ('j', 3) -- ('J',4) -- -- >>> bimap toUpper (+1) (Left 'j') -- Left 'J' -- -- >>> bimap toUpper (+1) (Right 3) -- Right 4 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'@ -- -- ==== __Examples__ -- >>> first toUpper ('j', 3) -- ('J',3) -- -- >>> first toUpper (Left 'j') -- Left 'J' first :: (a -> b) -> p a c -> p b c first f = bimap f id -- | Map covariantly over the second argument. -- -- @'second' ≡ 'bimap' 'id'@ -- -- ==== __Examples__ -- >>> second (+1) ('j', 3) -- ('j',4) -- -- >>> second (+1) (Right 3) -- Right 4 second :: (b -> c) -> p a b -> p a c second = bimap id -- | Class laws for tuples hold only up to laziness. Both -- 'first' 'id' and 'second' 'id' are lazier than 'id' (and 'fmap' 'id'): -- -- >>> first id (undefined :: (Int, Word)) `seq` () -- () -- >>> second id (undefined :: (Int, Word)) `seq` () -- () -- >>> id (undefined :: (Int, Word)) `seq` () -- *** Exception: Prelude.undefined -- -- @since 4.8.0.0 instance Bifunctor (,) where bimap f g ~(a, b) = (f a, g b) -- | @since 4.8.0.0 instance Bifunctor ((,,) x1) where bimap f g ~(x1, a, b) = (x1, f a, g b) -- | @since 4.8.0.0 instance Bifunctor ((,,,) x1 x2) where bimap f g ~(x1, x2, a, b) = (x1, x2, f a, g b) -- | @since 4.8.0.0 instance Bifunctor ((,,,,) x1 x2 x3) where bimap f g ~(x1, x2, x3, a, b) = (x1, x2, x3, f a, g b) -- | @since 4.8.0.0 instance Bifunctor ((,,,,,) x1 x2 x3 x4) where bimap f g ~(x1, x2, x3, x4, a, b) = (x1, x2, x3, x4, f a, g b) -- | @since 4.8.0.0 instance Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) where bimap f g ~(x1, x2, x3, x4, x5, a, b) = (x1, x2, x3, x4, x5, f a, g b) -- | @since 4.8.0.0 instance Bifunctor Either where bimap f _ (Left a) = Left (f a) bimap _ g (Right b) = Right (g b) -- | @since 4.8.0.0 instance Bifunctor Const where bimap f _ (Const a) = Const (f a) -- | @since 4.9.0.0 instance Bifunctor (K1 i) where bimap f _ (K1 c) = K1 (f c)