> cloning the entire structure for every applied function sounds like it will be slow? is that not what you will have to do in practice?

In short, no - as an example, when an element is added to an immutable map, a big part of the newly produced map is structurally shared with the old one (check out [0].)

As for the ordering, you could have a list of geometry -> geometry functions. You could then take the initial geometry and apply the list of functions in order, or a permutation of it, or drop some functions, or apply some others multiple times, and so on.

But anyway, it's just an idea - thinking in terms of atomic geometry transformations instead of alternations may or may not be easier in more complex scenarios, I don't know :)

[0] http://hypirion.com/musings/understanding-persistent-vector-...