What is applicative functor:

the ability to apply functors to each other.

For example we have tow functors: Container(2), Container(3)

// We can't do this because the numbers are bottled up.
add(Container.of(), Container.of()); // NaN

We cannot just add two functors!

Instead we should do:

const map = (fn, m) => m.map(fn);
const containerOfAdd2 = map(add(), Container.of()); // Container(5)

or

Container.of().chain(two => Container.of().map(add(two)));

Previous solution should work. but there are better way to do it:

1. ap

Container.prototype.ap = function (otherContainer) {
return otherContainer.map(this.$value);
};

As you can see, 'ap' takes a fuctor then applya map to it.

We can see ap:

Container.of().map(add).ap(Container.of()); // Container(5)

Or, we add lift 'add(2)' into Container, then apply Container(3):

Container.of(add()).ap(Container.of()); // Container(5)

Because 'add' is partially  applied in add(2), when doing '.ap(Container.of(3))', we give the rest input '3' to it.

Now, we can define applicative functor in programming language:

An applicative functor is a pointed functor with an ap method

Note the dependence on pointed.

Laws behind:

F.of(x).map(f) === F.of(f).ap(F.of(x))

Main idea is: lift 'f' (function) into Functor, then 'ap' (apply) another Functor with the value (x).

Some example:

Maybe.of(add).ap(Maybe.of()).ap(Maybe.of()) // Just(5)
Task.of(add).ap(Task.of()).ap(Task.of()) // Task(5)

Equals:

Maybe.of(add()).ap(Maybe.of()) // Just(5)
Task.of(add()).ap(Task.of()) // Task(5)

More examples:

// Http.get :: String -> Task Error HTML

const renderPage = curry((destinations, events) => { /* render page */ });

Task.of(renderPage).ap(Http.get('/destinations')).ap(Http.get('/events'));
// Task("<div>some page with dest and events</div>")
// $ :: String -> IO DOM
const $ = selector => new IO(() => document.querySelector(selector)); // getVal :: String -> IO String
const getVal = compose(map(prop('value')), $); // signIn :: String -> String -> Bool -> User
const signIn = curry((username, password, rememberMe) => { /* signing in */ }); IO.of(signIn).ap(getVal('#email')).ap(getVal('#password')).ap(IO.of(false));
// IO({ id: 3, email: 'gg@allin.com' })

----

const R = require('ramda');

class Container {
static of(x) {
return new Container(x);
} constructor(x) {
this.$value = x;
} map (fn) {
return Container.of(fn(this.$value));
} ap (functor) {
return functor.map(this.$value);
} join() {
return this.$value;
} chain(fn) {
return this.map(fn).join();
} inspect() {
return `Container(${this.$value})`;
}
} class Maybe {
get isNothing() {
return this.$value === null || this.$value === undefined;
} get isJust() {
return !this.isNothing;
} constructor(x) {
this.$value = x;
} inspect() {
return this.isNothing ? 'Nothing' : `Just(${this.$value})`;
} // ----- Pointed Maybe
static of(x) {
return new Maybe(x);
} // ----- Functor Maybe
map(fn) {
return this.isNothing ? this : Maybe.of(fn(this.$value));
} // ----- Applicative Maybe
ap(f) {
return this.isNothing ? this : f.map(this.$value);
} // ----- Monad Maybe
chain(fn) {
return this.map(fn).join();
} join() {
return this.isNothing ? this : this.$value;
} // ----- Traversable Maybe
sequence(of) {
this.traverse(of, identity);
} traverse(of, fn) {
return this.isNothing ? of(this) : fn(this.$value).map(Maybe.of);
}
} const add = a => b => a + b;
const map = (fn, m) => m.map(fn);
const notWorking = add(Container.of(2), Container.of(3));
const containerOfAdd2 = map(add(3), Container.of(2));
console.log(containerOfAdd2); // Contianer(5) const works = Container.of(2).chain(v => Container.of(3).map(add(v)));
console.log(works); // Contianer(5) const ap = Container.of(2).map(add).ap(Container.of(3));
console.log(ap) const ap2 = Container.of(add(2)).ap(Container.of(3));
console.log(Maybe.of(add).ap(Maybe.of(2)).ap(Maybe.of(3)))
console.log(Maybe.of(add(2)).ap(Maybe.of(3)))

  

[Functional Programming] Working with two functors(Applicative Functors)-- Part1 --.ap的更多相关文章

  1. [Functional Programming] Working with two functors(Applicative Functors)-- Part2 --liftAN

    Let's examine a pointfree way to write these applicative calls. Since we know map is equal to of/ap, ...

  2. UCF Local Programming Contest 2016 J题(二分+bfs)

    题目链接如下: https://nanti.jisuanke.com/t/43321 思路: 显然我们要采用二分的方法来寻找答案,给定一个高度如果能确定在这个高度时是否可以安全到达终点,那我们就可以很 ...

  3. Programming | 中/ 英文词频统计(MATLAB实现)

    一.英文词频统计 英文词频统计很简单,只需借助split断句,再统计即可. 完整MATLAB代码: function wordcount %思路:中文词频统计涉及到对"词语"的判断 ...

  4. Coursera Algorithms Programming Assignment 4: 8 Puzzle (100分)

    题目原文:http://coursera.cs.princeton.edu/algs4/assignments/8puzzle.html 题目要求:设计一个程序解决8 puzzle问题以及该问题的推广 ...

  5. Coursera Algorithms Programming Assignment 3: Pattern Recognition (100分)

    题目原文详见http://coursera.cs.princeton.edu/algs4/assignments/collinear.html 程序的主要目的是寻找n个points中的line seg ...

  6. The 2019 Asia Nanchang First Round Online Programming Contest C. Hello 2019(动态dp)

    题意:要找到一个字符串里面存在子序列9102 而不存在8102 输出最小修改次数 思路:对于单次询问 我们可以直接区间dpOn求出最小修改次数 但是对于多次询问 我在大部分题解看到的解释一般是用线段树 ...

  7. Functional Programming 资料收集

    书籍: Functional Programming for Java Developers SICP(Structure and Interpretation of Computer Program ...

  8. Adaptive AUTOSAR 学习笔记 3 - AP 背景、技术及特征(中文翻译)

    本系列学习笔记基于 AUTOSAR Adaptive Platform 官方文档 R20-11 版本.本文从AUTOSAR_EXP_PlatformDesign.pdf开始,一边学习,一边顺带着翻译一 ...

  9. windows下gVim(Vi/vim)基本使用

    Vim 是一个Linux 平台上功能非常强大的编辑器,他是早年的Vi 编辑器的加强版.这个gVim 是windows 版的,并且有了标准的windows 风格的图形界面,所以叫g(graphical) ...

随机推荐

  1. 如果修改GeneXus Android的一些源码文件(FlexibleClient)

    在使用GeneXus开发Android应用的过程中遇到了一个问题,使用tabs控件时发现默认高度过高,和UI设计要求的高度不一致,找了很久发现没有地方设置.后来联系了GeneXus中国厂商,得到了答复 ...

  2. GeneXus手机开发基础配置

    最近使用GeneXus15 U3版本做了几个手机端的项目,感觉还不错,开发速度很快,而且想要的功能也都实现了.其中有一些常用的配置和小技巧和大家分享一下. 基础环境要求 如果想开发Android程序, ...

  3. JAVA中常见异常小结

    1.java.lang.ArithmeticException 算术运算异常,例如除数为0,所以引发了算数异常 2.Java.lang.StringIndexOutOfBoundsException: ...

  4. Java 8中你可能没听过的10个新特性

    lambda表达式,lambda表达式,还是lambda表达式.一提到Java 8就只能听到这个,但这不过是其中的一个新功能而已,Java 8还有许多新的特性——有一些功能强大的新类或者新的用法,还有 ...

  5. 【BZOJ 3160】 3160: 万径人踪灭 (FFT)

    3160: 万径人踪灭 Time Limit: 10 Sec  Memory Limit: 256 MBSubmit: 1440  Solved: 799 Description Input Outp ...

  6. 【BZOJ 3727】 3727: PA2014 Final Zadanie (递推)

    3727: PA2014 Final Zadanie Time Limit: 10 Sec  Memory Limit: 128 MBSubmit: 279  Solved: 121 Descript ...

  7. BZOJ1086 SCOI2005王室联邦

    想学树上莫队结果做了个树分块. 看完题后想到了菊花图的形状认为无解,结果仔细一瞧省会可以在外省尴尬 对于每一颗子树进行深搜,一旦遇到加在一起大小达到B则将它们并为一省,因为他子树搜完以后没有分出块的大 ...

  8. python3-开发进阶Flask的基础(5)

    内容概要: SQLAlchemy flsak-sqlalchemy flask-script flask-migrate Flask的目录结构 一.SQLAlchemy 1.概述 SQLAlchemy ...

  9. python开发_copy(浅拷贝|深拷贝)_博主推荐

    在python中,有着深拷贝和浅拷贝,即copy模块 下面我们就来聊一下: 运行效果: ================================================== 代码部分: ...

  10. [转]Android ListView最佳处理方式,ListView拖动防重复数据显示,单击响应子控件

      Android ListView最佳处理方式,ListView拖动防重复数据显示,单击响应子控件. 1.为了防止拖动ListView时,在列表末尾重复数据显示.需要加入 HashMap<In ...