Data.Bifunctor.Apply

Biappliable bifunctors

class Bifunctor p where

Minimal definition either bimap or first and second

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

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

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

Map covariantly over the first argument.

first f ≡ bimap f id

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

Map covariantly over the second argument.

second ≡ bimap id

Instances

Bifunctor Either

Bifunctor (,)

Bifunctor Const

Bifunctor Arg

Bifunctor ((,,) x)

Bifunctor p => Bifunctor (WrappedBifunctor p)

Functor g => Bifunctor (Joker g)

Bifunctor p => Bifunctor (Flip p)

Functor f => Bifunctor (Clown f)

Bifunctor (Tagged *)

Bifunctor ((,,,) x y)

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

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

Bifunctor ((,,,,) x y z)

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

Bifunctor ((,,,,,) x y z w)

Bifunctor ((,,,,,,) x y z w v)

class Bifunctor p => Biapply p where

Minimal complete definition

(<<.>>)

Methods

(<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d infixl 4

(.>>) :: p a b -> p c d -> p c d infixl 4

a .> b ≡ const id <$> a <.> b

(<<.) :: p a b -> p c d -> p a b infixl 4

a <. b ≡ const <$> a <.> b

Instances

Biapply (,)

Biapply Const

Biapply Arg

Semigroup x => Biapply ((,,) x)

Biapply p => Biapply (WrappedBifunctor p)

Apply g => Biapply (Joker g)

Biapply p => Biapply (Flip p)

Apply f => Biapply (Clown f)

Biapply (Tagged *)

(Semigroup x, Semigroup y) => Biapply ((,,,) x y)

(Apply f, Biapply p) => Biapply (Tannen f p)

(Biapply p, Biapply q) => Biapply (Product p q)

(Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z)

(Biapply p, Apply f, Apply g) => Biapply (Biff p f g)

(<<$>>) :: (a -> b) -> a -> b infixl 4

(<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d infixl 4

bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f

Lift binary functions

bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h

Lift ternary functions