• DOI:10.1145/3453483.3454088
• Corpus ID: 230726720

Hashing modulo alpha-equivalence

@article{Maziarz2021HashingMA,
  title={Hashing modulo alpha-equivalence},
  author={Krzysztof Maziarz and Tom Ellis and Alan Christopher Lawrence and Andrew William Fitzgibbon and Simon L. Peyton Jones},
  journal={Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
  year={2021}
}

• Krzysztof Maziarz, Tom Ellis, +2 authors S. Jones
• Published 6 May 2021
• Computer Science, Mathematics
• Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

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 O(n2) 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 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.