2020/06/05 by Jacques Carette, Carette, Jacques, William M. Farmer +3
Computer Science · #Advanced Database Systems and Queries #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2006.09292
openalex publication_date 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of which was started as Universal Algebra. Various constructions (homomorphism, term algebras, products, etc) and their properties are both universal and constructive. Thus they are ripe for being automated. Unfortunately, current practice still requires library builders to write these by hand. We first highlight specific redundancies in libraries of existing systems. Then we describe a framework for generating these derived concepts from theory definitions. We demonstrate the usefulness of this framework on a test library of 227 theories.