Data/Bifunctor.hs

    {-# 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
    ----------------------------------------------------------------------------
    module Data.Bifunctor
      ( Bifunctor(..)
      ) where

    import Control.Applicative  ( Const(..) )
    import GHC.Generics ( K1(..) )

    -- | 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 4.8.0.0
    class Bifunctor 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

    -- | @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)