dependencies.js

var curry = function(fn) {
    var arity = fn.length;
    var f = function(args) {
        return function () {
            var newArgs = (args || []).concat([].slice.call(arguments, 0));
            if (newArgs.length >= arity) {
                return fn.apply(this, newArgs);
            }
            else {return f(newArgs);}
        };
    };

    return f([]);
};

var compose = function(f, g) {
    return function() {
        return f.call(this, (g.apply(this, arguments)));
    };
};

var Maybe = function Maybe(val) {
    if (!(this instanceof Maybe)) {return new Maybe(val);}
    this.val = val;
};

var Either = function Either(left, right) {
    if (!(this instanceof Either)) {return new Either(left, right);}
    this.left = left;
    this.right = right;
};

Functor.js

(function(global) {

    global.Functor = function(conf) {
        Functor.types[conf.key] = {
            obj: conf.obj,
            fmap: conf.fmap
        };
    };
    
    Functor.types = {};

    global.fmap = curry(function(f, obj) {
        var key = obj.constructor.name; // or even nastier: obj.constructor.toString().match(/function (\w*)/)[1]
        return Functor.types[key].fmap(f, obj);
    });
}(this));

usage.js

// relies on NFEs to lookup correct fmap. not great.

Functor({key: "Array", obj: Array, fmap: function(f, arr){
    return arr.map(function(x){return f(x);});
}});
 
Functor({key: "Function", obj: Function, fmap: function(f, g) {
    return compose(f, g);
}});
 
Functor({key: "Maybe", obj: Maybe, fmap: function(f, maybe) {
    return (maybe.val == null) ? maybe : Maybe(f(maybe.val));
}});
 
Functor({key: "Either", obj: Either, fmap: function(f, either) {
    return (either.right == null) ? Either(f(either.left), null) : Either(either.left, f(either.right));
}});

var plus1 = function(n) {return n + 1;};
var times2 = function(n) {return n * 2;};

console.log(fmap(plus1, [2, 4, 6, 8])); //=> [3, 5, 7, 9]
console.log(fmap(plus1, Maybe(5))); //=> Maybe(6)
console.log(fmap(plus1, Maybe(null))); //=> Maybe(null)
console.log(fmap(plus1, times2)(3)); //=> 7 (=  3 * 2 + 1)
console.log(fmap(plus1, Either(10, 20))); //=> Either(10, 21)
console.log(fmap(plus1, Either(10, null))); //=> Either(11, null)