90 lines
2.6 KiB
Markdown
90 lines
2.6 KiB
Markdown
---
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title: Y combinator
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id: 594810f028c0303b75339ad5
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challengeType: 5
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forumTopicId: 302345
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---
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## Description
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<section id='description'>
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In strict <a href="https://en.wikipedia.org/wiki/Functional programming" title="wp: functional programming" target="_blank">functional programming</a> and the <a href="https://en.wikipedia.org/wiki/lambda calculus" title="wp: lambda calculus" target="_blank">lambda calculus</a>, 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.
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The <a href="https://mvanier.livejournal.com/2897.html" target="_blank">Y combinator</a> 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 <a href="https://en.wikipedia.org/wiki/Fixed-point combinator" title="wp: fixed-point combinator" target="_blank">fixed-point combinators</a>.
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</section>
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## Instructions
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<section id='instructions'>
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Define the stateless Y combinator function and use it to compute <a href="https://en.wikipedia.org/wiki/Factorial" title="wp: factorial" target="_blank">factorial</a>. The <code>factorial(N)</code> function is already given to you.
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<strong>See also:</strong>
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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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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: Y should return a function.
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testString: assert.equal(typeof Y(f => n => n), 'function');
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- text: factorial(1) should return 1.
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testString: assert.equal(factorial(1), 1);
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- text: factorial(2) should return 2.
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testString: assert.equal(factorial(2), 2);
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- text: factorial(3) should return 6.
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testString: assert.equal(factorial(3), 6);
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- text: factorial(4) should return 24.
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testString: assert.equal(factorial(4), 24);
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- text: factorial(10) should return 3628800.
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testString: assert.equal(factorial(10), 3628800);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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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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</div>
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### After Test
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<div id='js-teardown'>
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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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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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