在上一章，我們提到了 Functor，但更精準地說是 Covariant functor，而今天要提到的則是 Contravariant Functor，其定義非常相似

contramap :: Contravariant f => f a ~> (b -> a) -> f b
map :: Functor f => f a ~> (a -> b) -> f b

Type Signature

contramap :: Contravariant f => f a ~> (b -> a) -> f b

Law

對於任何 Contravariant u 都要符合下列兩種特性，

• Identity: u.contramap(x => x) === u
• Composition: u.contramap(f).contramap(g) === u.contramap(x => g(f(x)))

Example

來看看一個簡單的範例，首先我們先來建立一個 Contravariant Functors Pred

import * as R from 'ramda';

// contramap :: Pred a ~> (b -> a) -> Pred b
const Pred = run => ({
    run,
    contramap: g => Pred(R.compose(run, g))
})

// Pred Number
const isEven = Pred(num => num % 2 === 0)

const length = x => x.length

const lengthIsEven = isEven.contramap(length)

lengthIsEven.run('FP') // true

可以看到 lengthIsEven 就是先將 字串 FP 透過 length :: String -> Number 轉換後，就將原本的 Pred Number 轉換成 Pred String

驗證是否符合 fantasy-land 的定義

const exclaim = str => str.concat('!')

// Identity
Pred(isEven).contramap(x => x) === Pred(isEven)

// Composition
Pred(isEven).contramap(length).contramap(exclaim) === Pred(isEven).contramap(x => length(exclaim(x)))

小結

今天太忙了，決定明天再進行補充!!!

NEXT: Functor & Contravariant Functor

Reference

1. Contravariant