Data.Bifunctor.Apply

Contents

• Biappliable bifunctors

Description

Synopsis

• class Bifunctor p where
  • bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
  • first :: (a -> b) -> p a c -> p b c
  • second :: (b -> c) -> p a b -> p a c
• class Bifunctor p => Biapply p where
  • (<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d
  • (.>>) :: p a b -> p c d -> p c d
  • (<<.) :: p a b -> p c d -> p a b
• (<<$>>) :: (a -> b) -> a -> b
• (<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
• bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f
• bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h

Biappliable bifunctors

bimap id id ≡ id

first id ≡ id
second id ≡ id

bimap f g ≡ first f . second g

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

bimap f g ≡ first f . second g

first f ≡ bimap f id

second ≡ bimap id

a .> b ≡ const id <$> a <.> b

a <. b ≡ const <$> a <.> b