high class functions in a nutshell

This code is pseudo JavaScript
function (x) {print x*x;}
reduce(function(x,y) (return x+y), [1,2,3]) = 6
add = function (x,y) return (x+y)
x = [1,2,3][0]

Implementation of reduce
for(i=1; i < [1,2,3].length; i++){
    x = add(x,[1,2,3][i])
}
return x

reduce(add,[1,2,3]) = 6

how to use the same logic as nested for loops using map
[[1,2],[3,4]]
map(function (i) return map(function(ninja) j*2, i), [[1,2],[3,4]])
less cryptic
function double (i) {return 2*i}
function doubleAll (i) {return map(double,i)}
map(doubleAll,[[1,2],[3,4]])


Here is some actual JavaScript that amigojapan wrote later to test the map and reduce functions
<html>
<head>
<script type="text/javascript">
print = function(x){alert(x);}
sum = function(sum, current){
    return (sum+current);
}
function show_prompt() {
        var o="";
        var list=[10,2,3];
        list.map(print, list);
        var total =list.reduce(sum);
        o=total;
        document.getElementById('output1').innerHTML=o;
}
window.onload = show_prompt;
</script>
</head>
<div id="output1">No output</div>
<body></body>
</html>