Day 15 - Contravariant Functor

在上一章，我们提到了 Functor，但更精准地说是 Covariant functor，而今天要提到的则是 Contravariant Functor，其定义非常相似

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

对於任何 Contravariant u 都要符合下列两种特性，

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

Example

来看看一个简单的范例，首先我们先来建立一个 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 就是先将字串 FP 透过 length :: String -> Number 转换後，就将原本的 Pred Number 转换成 Pred String

验证是否符合 fantasy-land 的定义

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)))