title: Expressing Y in term of SKI-Combinators in JavaScript
body: <p>I was fiddling with combinators in JavaScript and was being proud of (hopefully) getting S to work when I stumbled upon Wikipedia saying: &quot;The Y combinator can be expressed in the SKI-calculus as: Y = S (K (S I I)) (S (S (K S) K) (K (S I I)))&quot;, so I had to try that:</p>
  <pre><code>var I = function (x) {
              return x;
          };
      
  var K = function (x) {
          return function(){
              return x;}
          };
  
  var S = function (x) {
             return function (y) {
                 return function (z) {
                     return x(z)(y(z));
                 }
             }
         };
  
  var Y = S (K(S(I)(I))) (S(S(K(S))(K)) (K(S(I)(I))));
  
  Y;    //evals to:
  //function (z) {return x(z)(y(z));}
  
  //And this (lifted from Crockford's Site):
  var factorial = Y(function (fac) {
      return function (n) {
          return n &lt;= 2 ? n : n * fac(n - 1);
      };
  });    //fails:
  //RangeError: Maximum call stack size exceeded
  </code></pre>
  <p>What am I doing wrong? Am I not translating that expression correctly? Is there something wrong with how I'm going about this? Does it even make sense? Most of what's to be read about stuff like this just makes my brain want to explode, so the point of this exercise for me was mainly to see if I understood the notation (and would thus be able to translate it to JavaScript).</p>
  <p>Oh, and, by the way: what got me reading &amp; fiddling again was that what prototype.js implements as Prototype.K is actually the I combinator. Has anyone noticed?</p>