# How to enumerate trees from a context-free grammar

arXiv: https://arxiv.org/abs/2305.00522 · HTML: https://mlsanity.com/paper/2305.00522/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 23 references that are in the map.
- First posted on arXiv 30 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [The Syntax and Semantics of einsum](https://mlsanity.com/paper/2509.20020/) (2025)

## Abstract (arXiv)

I present a simple algorithm for enumerating the trees generated by a Context Free Grammar (CFG). The algorithm uses a pairing function to form a bijection between CFG derivations and natural numbers, so that trees can be uniquely decoded from counting. This provides a general way to number expressions in natural logical languages, and potentially can be extended to other combinatorial problems. I also show how this algorithm may be generalized to more general forms of derivation, including analogs of Lempel-Ziv coding on trees.