Uniquely parsing Polish notation?

Another end-of-chapter exercise in IFL2 very briefly introduces Polish notation for propositional logic, and invites you to construe a few Polish wffs, and (going in the other direction) to render some standard wffs into prefix Polish. So far, so easy!

Then — at the moment! — I cheerfully add, “Show that Polish notation, although bracket-free, introduces no structural ambiguities (i.e. every Polish wff can be parsed in only one way).”

But now I find, when I come to write up the answers to the exercises, that my first draft attempt at explaining uniqueness isn’t super user-friendly. Before I try to massage it something better, any pointers to a particularly nice explanation already out there which is likely to be immediately grasped by just-beginning philosophy students of why the prefix notation is unambiguous?

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