Thanks everybody for their help!

I solved the problem (almost) but only for my specific f(x,y), which
is enough for me for now. Paul Mooser's hint about accumulating state
was the key I needed. By introducing another accumulator I got my
color compositing to blend correctly from front to back.

The reason I say I almost solved the problem, is that because I'm
keeping track of an extra accumulator, the problem that I actually
solved was:

Given: f(x,y), a0
Find: g(x,y), h(x), and b0 such that, for any list of numbers v

 (reduce f a0 v) = (h (reduce g b0 (reverse v)))

-Patrick
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