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I present a simple algorithm for enumerating the trees generated by a ContextFree Grammar (CFG). The algorithm uses a pairing function to form a bijectionbetween CFG derivations and natural numbers, so that trees can be uniquelydecoded from counting. This provides a general way to number expressions innatural logical languages, and potentially can be extended to othercombinatorial problems. I also show how this algorithm may be generalized tomore general forms of derivation, including analogs of Lempel-Ziv coding ontrees.

How to enumerate trees from a context-free grammar