A Machine-Checked Proof of Birkhoff's Variety Theorem in Martin-Löf Type Theory

Document Type

Conference Proceeding

Publication Date

8-1-2022

Abstract

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 a significant theorem in the field.

Identifier

85137091182 (Scopus)

ISBN

[9783959772549]

Publication Title

Leibniz International Proceedings in Informatics Lipics

External Full Text Location

https://doi.org/10.4230/LIPIcs.TYPES.2021.4

ISSN

18688969

Volume

239

Grant

771005

Fund Ref

Engineering Research Centers

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