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POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal

The field of p-adic numbers Qp and the ring of p-adic integers Zp are essential constructions of modern number theory. Hensel’s lemma, described by Gouvêa as the “most important algebraic property of the p-adic numbers”, shows the existence of roots of polynomials over Zp provided an initial seed point. The theorem can be proved for the p-adics with significantly weaker hypotheses than for general rings. We construct Qp and Zp in the Lean proof assistant, with various associated algebraic properties, and formally prove a strong form of Hensel’s lemma. The proof lies at the intersection of algebraic and analytic reasoning and demonstrates how the Lean mathematical library handles such a heterogeneous topic.

Mon 14 Jan

CPP-2019
16:00 - 17:30: CPP 2019 - Research Papers: Formalization of Mathematics and Computer Algebra at Sala XII
Chair(s): Georges GonthierInria
CPP-201916:00 - 16:30
Research paper
Robert Y. LewisVrije Universiteit Amsterdam
DOI
CPP-201916:30 - 17:00
Research paper
Wenda LiUniversity of Cambridge, Lawrence PaulsonUniversity of Cambridge
DOI
CPP-201917:00 - 17:30
Research paper
DOI