Observable.scan

scan.js

Rx.Observable.prototype.scan = function (/* [seed], accumulator */) {
    var hasSeed = false, seed, accumulator, source = this;
    if (arguments.length === 2) {
        hasSeed = true;
        seed = arguments[0];
        accumulator = arguments[1];        
    } else {
        accumulator = arguments[0];
    }
    return Rx.Observable.createWithDisposable(function (observer) {
        var hasAccumulation, accumulation, hasValue;
        return source.subscribe (
            function (x) {
                try {
                    if (!hasValue) {
                        hasValue = true;
                    }
 
                    if (hasAccumulation) {
                        accumulation = accumulator(accumulation, x);
                    } else {
                        accumulation = hasSeed ? accumulator(seed, x) : x;
                        hasAccumulation = true;
                    }                    
                } catch (e) {
                    observer.onError(e);
                    return;
                }
 
                observer.onNext(accumulation);
            },
            observer.onError.bind(observer),
            function () {
                if (!hasValue && hasSeed) {
                    observer.onNext(seed);
                }
                observer.onCompleted();
            }
        );
    });
};

usage.js

function add(x, y) { return x + y; }

function createObserver(num) {
    return Rx.Observer.create(
        function (x) {
            console.log('next ' + num + ':' + x);
        },
        function (e) {
            console.log(e.message);   
        },
        function () {
            console.log('completed ' + num);    
        }
    );
}

// Usage
var obs1 = Rx.Observable.empty().scan(add);
var obs2 = Rx.Observable.empty().scan(0, add);

var obs3 = Rx.Observable.range(1, 3).scan(add);
var obs4 = Rx.Observable.range(1, 3).scan(0, add);

obs1.subscribe(createObserver(1));
// => completed 1

obs2.subscribe(createObserver(2));
// => next 2:0 
// => completed 2

obs3.subscribe(createObserver(3));
// => next 3:1 
// => next 3:3 
// => next 3:6 
// => completed 3

obs4.subscribe(createObserver(4));
// => next 4:1 
// => next 4:3 
// => next 4:6 
// => completed 4

This is to conform to Haskell:

scanl (+) 0 [] == [0]

scanl1 (+) [] == []

Or even F#:

Seq.empty<int> |> Seq.scan (+) 0
// => [0]

Interesting. And actually, this makes more sense. If there is a seed, the seed is presumably the identity of the function under its parameter types.