Leveraging the Information Contained in Theory Presentations

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. …