Functional UI programming

I started using Scala recently to develop a movie player as a side project, with the goal of using functional constructs whenever possible. I found myself using imperative-style programming when interacting with the UI framework. This got me thinking, is there a functional state-less way to develop UIs? A bit of Googling revealed the following:

• A StackOverflow post that talks about this problem and references functional reactive programming (FRP). 
• The Haskell people have developed UI frameworks around FRP.
• For the rest of us non-Haskell people, there is Flapjax, an FRP model built on top of JavaScript for the web.
• The spreadsheet is an example of a FRP model where cells are re-evaluated when dependent values change.
• Clojure creater Rich Hickey recommends sticking with state-ful programming but keeping it to a minimal.