2026-07-24T10:14:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16773 2024-03-06T10:58:14Z ddc:004 open_access

A Machine-Checked Proof of Birkhoff’s Variety Theorem in Martin-Löf Type Theory DeMeo, William Carette, Jacques Agda constructive mathematics dependent types equational logic formal verification Martin-Löf type theory model theory universal algebra The Agda Universal Algebra Library is a project aimed at formalizing the foundations of universal algebra, equational logic and model theory in dependent type theory using Agda. In this paper we draw from many components of the library to present a self-contained, formal, constructive proof of Birkhoff’s HSP theorem in Martin-Löf dependent type theory. This achieves one of the project’s initial goals: to demonstrate the expressive power of inductive and dependent types for representing and reasoning about general algebraic and relational structures by using them to formalize a significant theorem in the field. Schloss Dagstuhl – Leibniz-Zentrum für Informatik William DeMeo and Jacques Carette 2022 Is Part Of LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TYPES.2021.4 urn:nbn:de:0030-drops-167737 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.4 eng https://creativecommons.org/licenses/by/4.0/legalcode