I'm glad to see more people writing about functional programming for JavaScript web applications. I liked a lot of the ideas here, but I don't really see the need for the "component" data type. Why not just regular functions? Also, I don't think that letting each component determine whether or not it needs to redraw is a good idea. I'd rather just let the rendering system handle it by diffing the tree. With immutable data, it's trivial to see if a node has changed and redraw the subtree.

I've been doing experiments with Mithril (provides virtual DOM) and various functional reactive programming libraries (such as Kefir), and I think something like that is the right way to go.