memoizer_ackermann.js

      var memoizer = function (memo, fundamental) {
        
        var make_query = function(args) {
          var i = 0, query = '';
          for( ; i < args.length - 1 ; i += 1 ) {
            query += args[i] + ',';
          }
          query += args[i]; // i == args.length - 1
          return query;
        };
        
        var shell = function () {
          var args = Array.prototype.slice.apply(arguments);
          var query = make_query(args);
          var result = memo[ query ];
          if ( result === undefined ) {
            result = fundamental.apply(null, [shell].concat(args) );
            memo[ query ] = result;
            document.writeln('<br>caching: ('+query+')='+result);
          }
          return result;
        }; 
        return shell;
      };
      
      //arguments[1] is m, arguments[2] is n
      var ack = memoizer({}, function(shell, m, n) {
        if( m === 0 )          return n + 1;
        if( m === 1 )          return n + 2;                //special case
        if( m === 2 )          return n*2 + 3;              //special case
        if( m === 3 )          return Math.pow(2, n+3) - 3; //special case
        if( m > 0 && n === 0 ) return shell(m-1, 1);
        if( m > 0 && n > 0 )   return shell(m-1, shell(m, n-1) );
        return NaN; //you shouldn't get this.
      });

      document.writeln( ack(4,2) ); //This will just resolve to infinity .........