Prologue.Data.Bifunctor

Documentation

mapFirst :: Bifunctor p => (a -> b) -> p a c -> p b c

mapSecond :: Bifunctor p => (b -> c) -> p a b -> p a c

class Bifunctor (p :: Type -> Type -> Type) where

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.

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: base-4.8.0.0

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d

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

Instances

Bifunctor Either

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d

first :: (a -> b) -> Either a c -> Either b c

second :: (b -> c) -> Either a b -> Either a c

Bifunctor (,)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)

first :: (a -> b) -> (a, c) -> (b, c)

second :: (b -> c) -> (a, b) -> (a, c)

Bifunctor Arg

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d

first :: (a -> b) -> Arg a c -> Arg b c

second :: (b -> c) -> Arg a b -> Arg a c

Bifunctor ListF

Defined in Data.Functor.Foldable

Methods

bimap :: (a -> b) -> (c -> d) -> ListF a c -> ListF b d

first :: (a -> b) -> ListF a c -> ListF b c

second :: (b -> c) -> ListF a b -> ListF a c

Bifunctor NonEmptyF

Defined in Data.Functor.Base

Methods

bimap :: (a -> b) -> (c -> d) -> NonEmptyF a c -> NonEmptyF b d

first :: (a -> b) -> NonEmptyF a c -> NonEmptyF b c

second :: (b -> c) -> NonEmptyF a b -> NonEmptyF a c

Bifunctor ((,,) x1)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d)

first :: (a -> b) -> (x1, a, c) -> (x1, b, c)

second :: (b -> c) -> (x1, a, b) -> (x1, a, c)

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d

first :: (a -> b) -> Const a c -> Const b c

second :: (b -> c) -> Const a b -> Const a c

Functor f => Bifunctor (FreeF f)

Defined in Control.Monad.Trans.Free

Methods

bimap :: (a -> b) -> (c -> d) -> FreeF f a c -> FreeF f b d

first :: (a -> b) -> FreeF f a c -> FreeF f b c

second :: (b -> c) -> FreeF f a b -> FreeF f a c

Functor f => Bifunctor (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d

first :: (a -> b) -> CofreeF f a c -> CofreeF f b c

second :: (b -> c) -> CofreeF f a b -> CofreeF f a c

Bifunctor (Tagged :: Type -> Type -> Type)

Defined in Data.Tagged

Methods

bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d

first :: (a -> b) -> Tagged a c -> Tagged b c

second :: (b -> c) -> Tagged a b -> Tagged a c

Bifunctor (K1 i :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d

first :: (a -> b) -> K1 i a c -> K1 i b c

second :: (b -> c) -> K1 i a b -> K1 i a c

Bifunctor ((,,,) x1 x2)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d)

first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c)

second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c)

Bifunctor ((,,,,) x1 x2 x3)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d)

first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c)

second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c)

Bifunctor p => Bifunctor (WrappedBifunctor p)

Defined in Data.Bifunctor.Wrapped

Methods

bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d

first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c

second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c

Functor g => Bifunctor (Joker g :: Type -> Type -> Type)

Defined in Data.Bifunctor.Joker

Methods

bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d

first :: (a -> b) -> Joker g a c -> Joker g b c

second :: (b -> c) -> Joker g a b -> Joker g a c

Bifunctor p => Bifunctor (Flip p)

Defined in Data.Bifunctor.Flip

Methods

bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d

first :: (a -> b) -> Flip p a c -> Flip p b c

second :: (b -> c) -> Flip p a b -> Flip p a c

Functor f => Bifunctor (Clown f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Clown

Methods

bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d

first :: (a -> b) -> Clown f a c -> Clown f b c

second :: (b -> c) -> Clown f a b -> Clown f a c

Bifunctor ((,,,,,) x1 x2 x3 x4)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c)

(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q)

Defined in Data.Bifunctor.Sum

Methods

bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d

first :: (a -> b) -> Sum p q a c -> Sum p q b c

second :: (b -> c) -> Sum p q a b -> Sum p q a c

(Bifunctor f, Bifunctor g) => Bifunctor (Product f g)

Defined in Data.Bifunctor.Product

Methods

bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d

first :: (a -> b) -> Product f g a c -> Product f g b c

second :: (b -> c) -> Product f g a b -> Product f g a c

Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d)

first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c)

second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c)

(Functor f, Bifunctor p) => Bifunctor (Tannen f p)

Defined in Data.Bifunctor.Tannen

Methods

bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d

first :: (a -> b) -> Tannen f p a c -> Tannen f p b c

second :: (b -> c) -> Tannen f p a b -> Tannen f p a c

(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g)

Defined in Data.Bifunctor.Biff

Methods

bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d

first :: (a -> b) -> Biff p f g a c -> Biff p f g b c

second :: (b -> c) -> Biff p f g a b -> Biff p f g a c

deriveBitraversable :: Name -> Q [Dec]

Generates a Bitraversable instance declaration for the given data type or data family instance.

deriveBifoldable :: Name -> Q [Dec]

Generates a Bifoldable instance declaration for the given data type or data family instance.

deriveBifunctor :: Name -> Q [Dec]

Generates a Bifunctor instance declaration for the given data type or data family instance.