If I have prefix $f = − ◦ ⟨1, · ◦ ⟨2, floor ◦ ÷ ◦ ⟨1, 2⟩⟩⟩$ and I want to prove that it's in infix form $f(a, b) = a − b⌊ab⌋$ , just how am I to go from here?
And if I have $h(x, y) = x^2−y^2$, how can I generate the prefix form of this function?
I don't think I need a straight up answer, but just what directions I'm supposed to be heading when I want to solve these.
Your prefix form is essentially a tree. If you traverse it from the bottom up, you can build an infix form.
Conversely, given an expression in infix form, you can build a parse tree for it, by parsing it according to the precedence rules, aka working an expression from inside out.