Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?

Marco B Caminati, Manfred Kerber, Christoph Lange, Colin Rowat

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin’s 2004 survey article on Auction Theory using the Isabelle/HOL system, and we have verified software code that implements combinatorial Vickrey auctions. A fundamental question in this was how to represent some basic concepts: since set theory is available inside Isabelle/HOL, when introducing new definitions there is often the issue of balancing the amount of set-theoretical objects and of objects expressed using entities which are more typical of higher order logic such as functions or lists. Likewise, a user has often to answer the question whether to use a constructive or a non-constructive definition. Such decisions have consequences for the proof development and the usability of the formalization. For instance, sets are usually closer to the representation that economists would use and recognize, while the other objects are closer to the extraction of computational content. We have studied the advantages and disadvantages of these approaches, and their relationship, in the concrete application setting of auction theory. In addition, we present the corresponding Isabelle library of definitions and theorems, most prominently those dealing with relations and quotients.
Original languageUndefined/Unknown
Title of host publicationInternational Conference on Intelligent Computer Mathematics
EditorsJames H Davenport, Stephen M Watt, Alan P Sexton, Petr Sojka, Josef Urban
PublisherSpringer
Pages236-251
Number of pages16
Volume8543
DOIs
Publication statusPublished - 2014

Publication series

NameLNAI
PublisherSpringer

Keywords

  • auctions
  • software verification
  • formal methods
  • theorem proving
  • mechanised reasoning

Cite this