Whether you're in a hybrid functional/OO language like F# or OCaml, or in a purely functional language like Haskell where side-effects are relegated to the IO monad, it's mostly the case that a ton of the work required to manage a GUI is much more like a "side effect" than like a purely functional algorithm.
That said, there has been some really solid research put into functional GUIs. There are even some (mostly) functional toolkits such as Fudgets or FranTk.
