Array_shift.js

function shift(arr, i) {
    var cut = arr.length - i;
    return arr.slice(cut).concat(arr.slice(0, cut));
}

var arr = [1,2,3,4,5];
shift(arr, 1); //[5, 1, 2, 3, 4]
shift(arr, 3); //[3, 4, 5, 1, 2]

cart.js

function cartWith(fn, a, b) {
    var copyA = a.slice(0);
    var copyB = b.slice(0);
    var result = [];
    while (copyA.length) {
        result.push.apply(result, (copyB.map(fn.bind(this, copyA.shift()))));
    }
    return result;
}
function sum(a, b) {
    return a + b;
}
function makeVariadic(fn) {
    return function () {
        var args = Array.prototype.slice.call(arguments, 0);
        var a, result;
        var b = args.pop();
        while (args.length) {
            a = args.pop();
            b = fn(a, b);
        }
        return b;
    };
}

makeVariadic(cartWith.bind(null, sum))(["a", "b"], [1,2,3], ["x", "y"]);

cartWith.js

function cartWith(fn, a, b) {
    var copyA = a.slice(0);
    var copyB = b.slice(0);
    var result = [];
    while (copyA.length) {
        result.push.apply(result, (copyB.map(fn.bind(this, copyA.shift()))));
    }
    return result;
}

function sum(a, b) {
    return a + b;
}

cartWith(sum, ["a", "b"], [1,2,3]);

cartWith(sum, ["a", "b"], cartWith(sum, [1,2,3], ["x", "y"]));

function tuple(a, b) {
    return [a].concat(b);
}

cartWith(tuple, ["a", "b"], cartWith(tuple, [1,2,3], ["x", "y"]));