88 lines
2.2 KiB
Markdown
88 lines
2.2 KiB
Markdown
|
---
|
||
|
|
id: 594810f028c0303b75339ad5
|
||
|
|
title: Y combinator
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302345
|
||
|
|
dashedName: y-combinator
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
In strict [functional programming](https://en.wikipedia.org/wiki/Functional programming "wp: functional programming") and the [lambda calculus](https://en.wikipedia.org/wiki/lambda calculus "wp: lambda calculus"), functions (lambda expressions) don't have state and are only allowed to refer to arguments of enclosing functions. This rules out the usual definition of a recursive function wherein a function is associated with the state of a variable and this variable's state is used in the body of the function. The [Y combinator](https://mvanier.livejournal.com/2897.html) is itself a stateless function that, when applied to another stateless function, returns a recursive version of the function. The Y combinator is the simplest of the class of such functions, called [fixed-point combinators](https://en.wikipedia.org/wiki/Fixed-point combinator "wp: fixed-point combinator").
|
||
|
|
|
||
|
|
# --instructions--
|
||
|
|
|
||
|
|
Define the stateless Y combinator function and use it to compute [factorial](https://en.wikipedia.org/wiki/Factorial "wp: factorial"). The `factorial(N)` function is already given to you. **See also:**
|
||
|
|
|
||
|
|
<ul>
|
||
|
|
<li><a href="https://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
|
||
|
|
</ul>
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
Y should return a function.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(typeof Y((f) => (n) => n), 'function');
|
||
|
|
```
|
||
|
|
|
||
|
|
factorial(1) should return 1.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(factorial(1), 1);
|
||
|
|
```
|
||
|
|
|
||
|
|
factorial(2) should return 2.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(factorial(2), 2);
|
||
|
|
```
|
||
|
|
|
||
|
|
factorial(3) should return 6.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(factorial(3), 6);
|
||
|
|
```
|
||
|
|
|
||
|
|
factorial(4) should return 24.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(factorial(4), 24);
|
||
|
|
```
|
||
|
|
|
||
|
|
factorial(10) should return 3628800.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.equal(factorial(10), 3628800);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --after-user-code--
|
||
|
|
|
||
|
|
```js
|
||
|
|
var factorial = Y(f => n => (n > 1 ? n * f(n - 1) : 1));
|
||
|
|
```
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function Y(f) {
|
||
|
|
return function() {
|
||
|
|
|
||
|
|
};
|
||
|
|
}
|
||
|
|
|
||
|
|
var factorial = Y(function(f) {
|
||
|
|
return function (n) {
|
||
|
|
return n > 1 ? n * f(n - 1) : 1;
|
||
|
|
};
|
||
|
|
});
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
var Y = f => (x => x(x))(y => f(x => y(y)(x)));
|
||
|
|
```
|