Haskell语言学习笔记（60）Biapplicative _学习笔记

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Biapplicative

class Bifunctor p => Biapplicative p where bipure :: a -> b -> p a b(< < *> > ) :: p (a -> b) (c -> d) -> p a c -> p b d(*> > ) :: p a b -> p c d -> p c d a *> > b = bimap (const id) (const id) < < $> > a < < *> > b(< < *) :: p a b -> p c d -> p a b a < < * b = bimap const const < < $> > a < < *> > b(< < $> > ) :: (a -> b) -> a -> b (< < $> > ) = id

【Haskell语言学习笔记（60）Biapplicative】Biapplicative 是个类型类。主要用于在二元数据结构上应用 Applicative。
(,) 是个 Biapplicative

instance Biapplicative (,) where bipure = (,) (f, g) < < *> > (a, b) = (f a, g b)

Const 是个 Biapplicative

instance Biapplicative Const where bipure a _ = Const a Const f < < *> > Const x = Const (f x)

应用 Biapplicative

Prelude Data.Biapplicative> ((+2),(*3)) < < *> > (3,4) (5,12) Prelude Data.Biapplicative Control.Applicative> Const (+2) < < *> > Const 3 Const 5 Prelude Data.Biapplicative> bimap (+) (*) < < $> > (2,3) < < *> > (3,4) (5,12) Prelude Data.Biapplicative Control.Applicative> bimap (+) (*) < < $> > Const 2 < < *> > Const 3 Const 5

(< < **> > ), biliftA2, biliftA3

(< < **> > ) :: Biapplicative p => p a c -> p (a -> b) (c -> d) -> p b d (< < **> > ) = biliftA2 (flip id) (flip id)biliftA2 :: Biapplicative w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f biliftA2 f g a b = bimap f g < < $> > a < < *> > bbiliftA3 :: Biapplicative w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h biliftA3 f g a b c = bimap f g < < $> > a < < *> > b < < *> > c

Prelude Data.Biapplicative> (2,3) < < **> > ((2^), (3*)) (4,9) Prelude Data.Biapplicative> biliftA2 (+) (*) (2,3) (4,5) (6,15) Prelude Data.Biapplicative Control.Applicative> biliftA2 (+) (*) (Const 2) (Const 3) Const 5