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curriculum/challenges/english/10-coding-interview-prep/rosetta-code/y-combinator.md

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+---
+title: Y combinator
+id: 594810f028c0303b75339ad5
+challengeType: 5
+forumTopicId: 302345
+---
+
+## Description
+<section id='description'>
+
+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.
+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>.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+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.
+<strong>See also:</strong>
+<ul>
+  <li><a href="https://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
+</ul>
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: Y should return a function.
+    testString: assert.equal(typeof Y(f => n => n), 'function');
+  - text: factorial(1) should return 1.
+    testString: assert.equal(factorial(1), 1);
+  - text: factorial(2) should return 2.
+    testString: assert.equal(factorial(2), 2);
+  - text: factorial(3) should return 6.
+    testString: assert.equal(factorial(3), 6);
+  - text: factorial(4) should return 24.
+    testString: assert.equal(factorial(4), 24);
+  - text: factorial(10) should return 3628800.
+    testString: assert.equal(factorial(10), 3628800);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function Y(f) {
+  return function() {
+
+  };
+}
+
+var factorial = Y(function(f) {
+  return function (n) {
+    return n > 1 ? n * f(n - 1) : 1;
+  };
+});
+```
+
+</div>
+
+
+### After Test
+<div id='js-teardown'>
+
+```js
+var factorial = Y(f => n => (n > 1 ? n * f(n - 1) : 1));
+```
+
+</div>
+
+</section>
+
+## Solution
+<section id='solution'>
+
+
+```js
+var Y = f => (x => x(x))(y => f(x => y(y)(x)));
+
+```
+
+</section>