Universal Algebra in UniMath

Abstract

We present recent updates in our development of a library for Universal Algebra in the UniMath proof assistant. The code here discussed concerns multi-sorted signatures and their algebras, along with the basics for equation systems. Moreover, we give neat constructions of the corresponding univalent categories by using the formalism of displayed categories, and show that the term algebra over a signature is the initial object of the category.Besides the formalization, we reflect on the methodological principles -based on the idea of evaluability of our elementary construction by the built-in normalization procedure of the systemleading our coding style, and show that this path is practicable indeed by sketching simple examples.