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    <p>The problem here is that you are using a strictly evaluated programming language. The Y-combinator, pretty much like any other fixed point combinator, will only work properly when your functions are called by need, or 'lazily evaluated'.</p> <p>I know of a way to work around this (<a href="http://utrechthaskellcompiler.wordpress.com/2010/10/18/haskell-to-javascript-backend/">one of my professors looked into it a while ago</a>), but it will make your code completely unreadable.</p> <p>Below I've shown what's going on exactly, hoping you can see why JavaScript can't handle a straightforward implementation of SKI-calculus.</p> <hr> <p>This is what <code>Y</code> looks like after JavaScript evaluated your SKI-expression:</p> <pre><code>var Y = function (q) { return (function(p){return q(p(p))})(function(p){return q(p(p))}); }; </code></pre> <p>Now let's see what happens if you feed it your function <code>function (fac) { ... }</code>. Let's call that function <code>f</code>:</p> <pre><code>var factorial = (function(p){return f(p(p))})(function(p){return f(p(p))}); </code></pre> <p>Since the first anonymous function is applied to an argument, it will be evaluated into this:</p> <pre><code>var factorial = f( (function(p){return f(p(p))})(function(p){return f(p(p))}) ); </code></pre> <p>In a lazily evaluated language, the argument to <code>f</code> would now be left alone, and <code>f</code> itself would be evaluated. However, because JavaScript is a strictly evaluated language (or 'call-by-value'), it wants to know what argument it needs to pass to function <code>f</code> before actually running that function. So let's evaluate that argument, shall we?</p> <pre><code>var factorial = f(f( (function(p){return f(p(p))})(function(p){return f(p(p))}) ) ); </code></pre> <p>I guess now you're starting to see now where things go wrong, and how the Y-combinator actually works. In any case, your JavaScript machine will run out of stack space, because it's trying to build an infinite stack of calls to <code>f</code>.</p>
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    1. POExpressing Y in term of SKI-Combinators in JavaScript
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    1. COThanks for that great & enlightening answer :)
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      1. USTimm Schäffner
 

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