Hashing Modulo Alpha-equivalence

Maziarz Krzysztof, Ellis Tom, Lawrence Alan, Fitzgibbon Andrew, Jones Simon Peyton. Arxiv 2021

[Paper]    
ARXIV

In many applications one wants to identify identical subtrees of a program syntax tree. This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good efficiency (better than $\mathcal{O}(n^2)$ in expression size). We present a new, asymptotically efficient way to hash modulo alpha-equivalence. A key insight of our method is to use a weak (commutative) hash combiner at exactly one point in the construction, which admits an algorithm with $\mathcal{O}(n(logn{)}^2)$ time complexity. We prove that the use of the commutative combiner nevertheless yields a strong hash with low collision probability. Numerical benchmarks attest to the asymptotic behaviour of the method.

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