System Description: An Infrastructure for Combining Domain Knowledge with Automated Theorem Provers
Article No.: 24, Pages 1 - 10
Abstract
Computer science has seen much progress in the area of automated verification in the last decades. Yet, there are many domains where abstract strategies for verifying standard properties are well-understood by domain experts, but still not automated to a satisfactory degree. One example for such a domain are type soundness proofs. Being able to express domain-specific verification strategies using domain-specific terminology and concepts can help to narrow down this gap toward more automated verification.
We present the requirements, design, and implementation of a configurable verification infrastructure that allows for expressing domain knowledge about proofs and for interfacing with existing automated theorem provers and solvers to verify individual proof steps. As an application scenario for our infrastructure, we present the development of a standard type soundness proof for a typed subset of SQL.
References
[1]
2014. Isabelle documentation. http://isabelle.in.tum.de/documentation.html.
[2]
Jasmin Christian Blanchette. 2012. Automatic proofs and refutations for higher-order logic. Ph.D. Dissertation. Technical University Munich.
[3]
Jasmin C. Blanchette and Lawrence C.Paulson. 2016. Hammering Away - A User's Guide to Sledgehammer for Isabelle/HOL. Technical Report. http://isabelle.in.tum.de/dist/doc/sledgehammer.pdf
[4]
Leonardo De Moura and Nikolaj Bjørner. 2008. Z3: An Efficient SMT Solver. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS). Springer, 337--340.
[5]
David Delahaye. 2000. A Tactic Language for the System Coq. In Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR). 85--95.
[6]
Cop development team. 2014. The Coq proof assistant reference manual.
[7]
Sylvia Grewe, Sebastian Erdweg, Michael Raulf, and Mira Mezini. 2016. Exploration of language specifications by compilation to first-order logic. In Proceedings of International Symposium on Principles and Practice of Declarative Programming (PPDP). 104--117.
[8]
Gudmund Grov, Aleks Kissinger, and Yuhui Lin. 2013. A Graphical Language for Proof Strategies. In Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR). 324--339.
[9]
Gudmund Grov and Vytautas Tumas. 2016. Tactics for the Dafny Program Verifier. In Tools and Algorithms for the Construction and Analysis of Systems (TACAS). 36--53.
[10]
Paul Hudak. 1996. Building Domain-Specific Embedded Languages. ACM Comput. Surv. 28, 4es (1996), 196.
[11]
Laura Kovács and Andrei Voronkov. 2013. First-Order Theorem Proving and Vampire. In Proceedings of International Conference on Computer Aided Verification (CAV). Springer, 1--35.
[12]
K. Rustan M. Leino. 2010. Dafny: An Automatic Program Verifier for Functional Correctness. In Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR). 348--370.
[13]
Daniel Matichuk, Toby C. Murray, and Makarius Wenzel. 2016. Eisbach: A Proof Method Language for Isabelle. J. Autom. Reasoning 56, 3 (2016), 261--282.
[14]
Tobias Nipkow, Lawrence C. Paulson, and Markus Wenzel. 2002. Isabelle/HOL: A Proof Assistant for Higher-order Logic. Springer-Verlag, Berlin, Heidelberg.
[15]
Martin Odersky, Lex Spoon, and Bill Venners. 2011. Programming in Scala: A Comprehensive Step-by-Step Guide, 2Nd Edition (2nd ed.). Artima Incorporation, USA.
[16]
Benjamin C. Pierce. 2002. Types and programming languages. MIT press.
[17]
Julian Richardson and Alan Bundy. 1999. Proof planning methods as schemas. J. Symbolic Computation 11 (1999), 1--000.
[18]
Philipp Rümmer. 2008. A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic. In Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR). Springer, 274--289.
[19]
Stephan Schulz. 2013. System Description: E 1.8. In Proceedings of Logic for Programming, Artificial Intelligence, and Reasoning (LPAR) (LNCS), Vol. 8312. Springer, 735--743.
[20]
Geoff Sutcliffe. 2010. The TPTP World - Infrastructure for Automated Reasoning. In Proceedings of the 16th International Conference on Logic for Programming Artificial Intelligence and Reasoning. Springer-Verlag, 1--12.
[21]
Geoff Sutcliffe. 2017. The TPTP Problem Library and Associated Infrastructure. From CNF to TH0, TPTP v6.4.0. Journal of Automated Reasoning 59, 4 (2017), 483--502.
[22]
Markus Wenzel. 2002. Isabelle, Isar - a versatile environment for human readable formal proof documents. Ph.D. Dissertation. Technical University Munich, Germany.
[23]
Beta Ziliani, Derek Dreyer, Neelakantan R. Krishnaswami, Aleksandar Nanevski, and Viktor Vafeiadis. 2013. Mtac: a monad for typed tactic programming in Coq. In Proceedings of International Conference on Functional Programming (ICFP). 87--100.
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- System Description: An Infrastructure for Combining Domain Knowledge with Automated Theorem Provers
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September 2018
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- SIGPLAN: ACM Special Interest Group on Programming Languages
- Goethe University: Goethe University Frankfurt
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Association for Computing Machinery
New York, NY, United States
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Published: 03 September 2018
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PPDP '18
PPDP '18: The 20th International Symposium on Principles and Practice of Declarative Programming
September 3 - 5, 2018
Frankfurt am Main, Germany
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PPDP '18 Paper Acceptance Rate 22 of 39 submissions, 56%;
Overall Acceptance Rate 230 of 486 submissions, 47%
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