Trusted Extensions of Interactive Theorem Provers : Workshop Summary

A fundamental strength of interactive theorem provers (ITPs) is the high degree of trust one can place in formalizations carried out in them. ITPs are usually also extensible, both at the logic level and at the implementation level. There is consequently a substantial body of existing and ongoing research into the extension of ITPs while preserving trust. In order to survey existing and new work in this area, we organized the Trusted Extension of Interactive Theorem Provers (TEITP) workshop. As a result of the workshop we have been able to get an overview of the approaches taken by most of the major ITPs. In this document we summarize the meeting and provide some background information for readers unfamiliar with the area.

[1]  John Harrison,et al.  Towards Self-verification of HOL Light , 2006, IJCAR.

[2]  Natarajan Shankar,et al.  An Integration of Model Checking with Automated Proof Checking , 1995, CAV.

[3]  Robert L. Constable,et al.  The semantics of reflected proof , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[4]  Tobias Nipkow,et al.  Proof Terms for Simply Typed Higher Order Logic , 2000, TPHOLs.

[5]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[6]  Rob Arthan On Formal Specification of a Proof Tool , 1991, VDM Europe.

[7]  Robert S. Boyer,et al.  Metafunctions: Proving Them Correct and Using Them Efficiently as New Proof Procedures. , 1979 .

[8]  Sascha Böhme,et al.  Fast LCF-Style Proof Reconstruction for Z3 , 2010, ITP.

[9]  Samuel Boutin,et al.  Using Reflection to Build Efficient and Certified Decision Procedures , 1997, TACS.

[10]  Robert S. Boyer,et al.  Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic , 1988 .

[11]  Benjamin Grégoire,et al.  Extending Coq with Imperative Features and Its Application to SAT Verification , 2010, ITP.

[12]  Robert Pollack,et al.  How to Believe a Machine-Checked Proof , 1997 .

[13]  Georges Gonthier A computer-checked proof of the Four Colour Theorem , 2005 .

[14]  Richard Boulton,et al.  Efficiency in a fully-expansive theorem prover , 1993 .

[15]  Ulf Norell,et al.  A Brief Overview of Agda - A Functional Language with Dependent Types , 2009, TPHOLs.

[16]  Sandip Ray,et al.  The Right Tools for the Job: Correctness of Cone of Influence Reduction Proved Using ACL2 and HOL4 , 2011, Journal of Automated Reasoning.

[17]  Tobias Nipkow,et al.  Proof Synthesis and Reflection for Linear Arithmetic , 2008, Journal of Automated Reasoning.

[18]  Joe Hurd,et al.  Composable Packages for Higher Order Logic Theories , 2012, VERIFY@IJCAR.