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Paul Khuong's personal blog. Some Lisp, some optimisation, mathematical or computer.
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Paul Khuong
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Paul Khuong: some Lisp Paul Khuong: some Lisp Blog Archives RSS Fixing the hashing in "Hashing modulo α-equivalence" Dec 29th, 2022 | Comments Per Vognsen sent me a link to Maziarz et al’s Hashing Modulo Alpha-Equivalence because its Lemma 6.6 claims to solve a thorny problem we have both encountered several times. Essentially, the lemma says that computing the natural recursive combination of hash values over \(2^b\) bits for two distinct trees (ADT instances) \(a\) and \(b\) yields a collision probability at most \(\frac{|a| + |b|}{2^b}\) if we use a random hash function (sure), and Section 6.2 claims without proof that the result can be safely extended to the unspecified “seeded” hash function they use. That’s a minor result, and the paper’s most interesting contribution (to me) is an algorithmically efficient alternative to the locally nameless representation : rather than representing bindings with simple binders and complex references, as in de Bruijn i...
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