2021/03/09 by William DeMeo, DeMeo, William · 1 citation
Computer Science · #68V20 (Primary) 03C05 (Secondary) #Advanced Algebra and Logic #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2103.05581
openalex publication_date 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Agda Universal Algebra Library (UALib) is a library of types and programs (theorems and proofs) we developed to formalize the foundations of universal algebra in dependent type theory using the Agda programming language and proof assistant. The UALib includes a substantial collection of definitions, theorems, and proofs from general algebra and equational logic, including many examples that exhibit the power of inductive and dependent types for representing and reasoning about relations, algebraic structures, and equational theories. In this paper we discuss the logical foundations on which the library is built, and describe the types defined in the first 13 modules of the library. Special attention is given to aspects of the library that seem most interesting or challenging from a type theory or mathematical foundations perspective.