Download PDFOpen PDF in browser

User-friendly Support for Common Mathematical Concepts in a Lightweight Verifier

16 pagesPublished: May 15, 2012


Machine verification of formal arguments can only increase our confidence in the correctness of those arguments, but the costs of employing machine verification still outweigh the benefits for some common kinds of formal reasoning activities. As a result, usability is becoming increasingly important in the design of formal verification tools. We describe the ``aartifact" lightweight verification system, designed for processing formal arguments involving basic, ubiquitous mathematical concepts. The system is a prototype for investigating potential techniques for improving the usability of formal verification systems. It leverages techniques drawn both from existing work and from our own efforts. In addition to a parser for a familiar concrete syntax and a mechanism for automated syntax lookup, the system integrates (1) a basic logical inference algorithm, (2) a database of propositions governing common mathematical concepts, and (3) a data structure that computes congruence closures of relations found in this database. Together, these components allow the system to better accommodate the expectations of users interested in verifying typical formal arguments involving algebraic manipulations of numbers, sets, vectors, and related operators and predicates. We demonstrate the reasonable performance of this system on typical formal arguments and briefly discuss how the system's design contributes to its usability in two use cases.

Keyphrases: automated theorem proving, formal verification, tool support

In: Markus Aderhold, Serge Autexier and Heiko Mantel (editors). VERIFY-2010. 6th International Verification Workshop, vol 3, pages 94--109

BibTeX entry
  author    = {Andrei Lapets},
  title     = {User-friendly Support for Common Mathematical Concepts in a Lightweight Verifier},
  booktitle = {VERIFY-2010. 6th International Verification Workshop},
  editor    = {Markus Aderhold and Serge Autexier and Heiko Mantel},
  series    = {EPiC Series in Computing},
  volume    = {3},
  pages     = {94--109},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/p79n}}
Download PDFOpen PDF in browser