Core Concepts
Formalizing algebras and equations in the UniMath framework for universal algebra.
Abstract
The article presents a library for Universal Algebra in UniMath, focusing on multi-sorted signatures, term algebras, and equation systems. It introduces term algebras without general inductive constructions, enriching UniMath with homotopy W-types. The formalization includes constructions of univalent categories of algebras and equational algebras using displayed categories. The computational relevance is showcased through examples from algebra and propositional logic.
Stats
"UniMath" framework dealing with multi-sorted signatures.
Single sorted ground term algebras are instances of homotopy W-types.
Term algebra over a signature is the initial object of the category of algebras.
Quotes
"We present an implementation of the basics of universal algebra in univalent foundations within the formal environment of UniMath."
"UniMath provides a minimalist implementation of univalent type theory."
"Our formalisation introduces central notions concerning multi-sorted signatures."