A case study on formalizing algebra in a module system

Authors:
Stefania Dumbrava;Fulya Horozal;Kristina Sojakova
Affiliations:
Jacobs University, Bremen, Germany;Jacobs University, Bremen, Germany;Jacobs University, Bremen, Germany
Venue:
Proceedings of the 1st Workshop on Modules and Libraries for Proof Assistants
Year:
2009

Citing 4
Cited 2

A framework for defining logics

Journal of the ACM (JACM)
Towards an Evolutionary Formal Software-Development Using CASL

WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
Little Theories

CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
An Infrastructure for Intertheory Reasoning

CADE-17 Proceedings of the 17th International Conference on Automated Deduction

Towards MKM in the large: modular representation and scalable software architecture

AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
A scalable module system

Information and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a case study on a modular formal representation of algebra in the recently developed module system for the Twelf implementation of the Edinburgh Logical Framework LF. The module system employs signature morphisms as its main primitive concept, which makes it particularly useful to reason about structural translations between mathematical concepts. The mathematical content is encoded in the usual way using LF's higher order abstract syntax and judgments-as-types paradigm, but using the module system to treat all algebraic structures independently. Signature morphisms are used to give an explicit yet simple representation of modular dependency between the algebraic structures. Our results demonstrate the feasibility of comprehensively formalizing large-scale theorems and proofs and thus promise significant future applications.