PxTP-2011

First Workshop on Proof eXchange for Theorem Proving

Affiliated with the 23rd International Conference on Automated Deduction
(CADE 23)

August 1st, 2011

Wrocław


Click here to access the Workshop web page on HAL at INRIA.


Background

The goal of this new workshop is to bring together researchers working on proof production from automated theorem provers with potential consumers of proofs. Machine-checkable proofs have been proposed for applications like proof-carrying code and certified compilation, as well as for exchanging knowledge between different automated reasoning systems. For example, interactive theorem provers can import results from otherwise untrusted high-performance solvers, by means of proofs the solvers produce. In such situations, one automated reasoning tool can make use of the results of another, without having to trust that the second tool is sound. It is only necessary to be able to reconstruct a proof that the first tool will accept, in order to import the result without increasing the size of the trusted computing base.

This simple idea of proof exchange for theorem proving becomes quite complicated under the real-world constraints of highly complex and heterogeneous proof producers and proof consumers. For example, even the issue of a standard proof format for a single class of solvers, like SMT solvers, is quite difficult to address, as different solvers use different inference systems. It may be quite challenging, from an engineering and possibly also theoretical point of view, to fit these into a single standard format. Emerging work from several groups proposes standard meta-languages or parametrized formats to achieve flexibility while retaining a universal proof language.


Topics

Topics of interest for this workshop include all aspects of proof exchange among automated reasoning tools. More specifically, some suggested topics are:


Program committee


Submissions

Submitted papers must fall into one of the following two categories

Submissions will be refereed by the program committee, which will select a balanced program of high-quality contributions.

Submissions should be in standard-conforming Postscript or PDF.

To submit a paper, go to the EasyChair PxTP page and follow the instructions there.

You can view the full call for papers.

Final versions

Final versions should be prepared in LaTeX using the easychair.cls class file.


Important dates:


Proceedings

Download here the full PxTP-2011 proceedings.


Program

08:55 - 09:00 Welcome
Session 1: Chair: Stephan Schulz
09:00 - 10:00 Jasmin Blanchette
Invited Talk: Proof Search and Proof Reconstruction in Sledgehammer
Slides
Abstract: Sledgehammer is a popular tool included with the Isabelle/HOL interactive theorem prover that discharges interactive goals using resolution provers (E, SPASS, Vampire) and SMT solvers (CVC3, Yices, Z3). The main difficulty with proof search is to encode type information efficiently, including polymorphism. For SMT solvers, we monomorphize the problem and map the resulting ground types to SMT-LIB sorts. For resolution provers, we experimented with a menagerie of type encodings and selected the most appropriate encoding for each prover, sacrificing soundness for efficiency in some cases. For proof reconstruction, several schemes are supported: (1) SMT solvers can be trusted and used as oracles; (2) Z3 proofs are replayed step by step and can be stored as certificates to speed up replay; (3) from resolution proofs, Sledgehammer extracts the used lemmas and attempts to re-find the proofs in Isabelle; (4) experimentally, we also implemented structured Isabelle proof construction from resolution proofs. This last scheme is the most promising, and we are currently working on improving the readability of the proofs and add support for SMT proofs.
Joint with PSATTT'11
10:00 - 10:30 Coffee
Session 2: Chair: Tjark Weber
10:30 - 11:00 Frédéric Besson, Pierre-Emmanuel Cornilleau and David Pichardie
A Nelson-Oppen based Proof System using Theory Specific Proof Systems
Joint with PSATTT'11
11:00 - 11:30 Geoff Sutcliffe, Cynthia Chang, Deborah Mcguinness, Tim Lebo, Li Ding and Paulo Pinheiro Da Silva
Combining Proofs to form Different Proofs
Joint with PSATTT'11
11:30 - 12:00 Piotr Rudnicki and Josef Urban
Escape to ATP for Mizar
12:00 - 12:30 Stephan Merz and Hernán Vanzetto
Towards certification of TLA+ proof obligations with SMT solvers
Session 3: Chair: Piotr Rudnicki
14.00 - 15.00 John Harrison
Invited Talk: Heterogeneous Theorem Proving, Certification, and Integrated Automation
Slides
Abstract: Theorem provers are being used for an increasing variety of applications in both formal verification and the formalization of mathematics. However, as these applications grow more complex and diverse, it is increasingly difficult to use a single tool for the entire process. Formal verification activities at Intel use a diverse range of tools and methods: for instance some arithmetic proofs use a combination of symbolic simulation and inductive theorem proving, while some protocol proofs use a combination of model checking and ad-hoc state abstraction programs. A similar situation arises in pure mathematics, with the Flyspeck project to formalize the proof of the Kepler conjecture requiring the formalization of results reached by linear and nonlinear optimization software and ad-hoc graph enumeration software, and with some parts of the formal proof done in different theorem provers.
It is thus very desirable to have a principled way of connecting all these tools and methods. Combining them by hand or by ad-oc programs gives rise to two problems: transcription errors at the interfaces between systems, and the increasing difficulty of trusting a large heterogeneous collection of tools. At the very least, one would hope to be able to transfer results in a meaningful way even between systems with different (and perhaps ill-specified) logical foundations. More ambitiously, one would wish to be able to transfer proofs or other "certificates" between such tools, so that logical soundness can be maintained by a complete and rigorous check on all results obtained, perhaps via a general interactive theorem prover that ties all the results together, or a separate and very simple "proof checker". Recent years have seen an increasing number of examples where external tools are used to generate relatively simple certificates that can be checked by other tools. We will survey some interesting examples where this process seems easy and successful and those where it seems difficult, and examine alternative approaches. Finally, even assuming that an interactive theorem prover is equipped with a panoply of classic decision procedures and mathematical solvers, there are still deep challenges in integrating the inferences that these tools can do in isolation, and we will examine some of the challenges and opportunities here.

Joint with PSATTT'11
15.00 - 15.30 Mickael Armand, Germain Faure, Benjamin Grégoire, Chantal Keller and Laurent Thery
Verifying SAT and SMT in Coq for a fully automated decision procedure
Joint with PSATTT'11
15.30 - 16.00 Coffee
Session 4: Chair: Geoff Sutcliffe
16.00 - 16.30 Sascha Böhme and Tjark Weber
Designing Proof Formats: A User's Perspective
16.30 - 17.00 Frédéric Besson, Pascal Fontaine and Laurent Théry
A Flexible Proof Format for SMT: a Proposal
17:00 - 17:30 David Deharbe, Pascal Fontaine and Bruno Woltzenlogel Paleo
Quantifier Inference Rules for SMT proofs
17:30 - 18:00 Discussion: Proofs for SMT
19:30 Informal Workshop Diner
Joint with PSATTT'11