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fix(challenges): Y problem

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Kris Koishigawa
2019-03-11 16:27:54 +09:00
committed by mrugesh
parent 723ee2cfa5
commit 12d84e83a8
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curriculum/challenges/english/08-coding-interview-prep/rosetta-code/y-combinator.english.md
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@ -6,31 +6,17 @@ challengeType: 5
## Description
<section id='description'>
<p>
In strict
<a href="https://en.wikipedia.org/wiki/Functional programming" title="wp: functional programming">functional programming</a> and
the <a href="https://en.wikipedia.org/wiki/lambda calculus" title="wp: lambda calculus">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.
</p>
<p>
The <a href="http://mvanier.livejournal.com/2897.html">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">fixed-point combinators</a>.
</p>
Task:
Define the stateless Y combinator function and use it to compute
<a href="https://en.wikipedia.org/wiki/Factorial" title="wp: factorial">factorial</a>.
<code>factorial(N)</code> function is already given to you.
See also <a href="http://vimeo.com/45140590">Jim Weirich: Adventures in Functional Programming</a>.
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="http://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">factorial</a>. The <code>factorial(N)</code> function is already given to you.
<b>See also:</b>
<ul>
<li><a href="http://vimeo.com/45140590" target="_blank">Jim Weirich: Adventures in Functional Programming</a>.</li>
</ul>
</section>
## Tests