88 lines
2.2 KiB
Markdown
88 lines
2.2 KiB
Markdown
---
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id: 594810f028c0303b75339ad5
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title: Y combinator
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challengeType: 5
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forumTopicId: 302345
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dashedName: y-combinator
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---
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# --description--
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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").
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# --instructions--
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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:**
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<ul>
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<li><a href="https://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
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</ul>
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# --hints--
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Y should return a function.
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```js
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assert.equal(typeof Y((f) => (n) => n), 'function');
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```
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factorial(1) should return 1.
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```js
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assert.equal(factorial(1), 1);
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```
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factorial(2) should return 2.
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```js
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assert.equal(factorial(2), 2);
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```
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factorial(3) should return 6.
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```js
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assert.equal(factorial(3), 6);
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```
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factorial(4) should return 24.
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```js
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assert.equal(factorial(4), 24);
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```
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factorial(10) should return 3628800.
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```js
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assert.equal(factorial(10), 3628800);
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```
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# --seed--
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## --after-user-code--
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```js
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var factorial = Y(f => n => (n > 1 ? n * f(n - 1) : 1));
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```
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## --seed-contents--
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```js
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function Y(f) {
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return function() {
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};
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}
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var factorial = Y(function(f) {
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return function (n) {
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return n > 1 ? n * f(n - 1) : 1;
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};
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});
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```
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# --solutions--
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```js
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var Y = f => (x => x(x))(y => f(x => y(y)(x)));
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```
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