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Adding Decision Procedures to SMT Solvers Using Axioms with Triggers

Claire Dross, Sylvain Conchon, Johannes Kanig, Andrei Paskevich
2015 Journal of automated reasoning  
Adding a theory to that list requires delving into the implementation details of a given SMT solver, and is done mainly by the developers of the solver itself.  ...  Triggers are annotations that suggest instances which are more likely to be useful in proof search.  ...  Acknowledgements We would like to thank the anonymous reviewers for their careful reading of our article, as well as their helpful comments which greatly contributed to the quality of this paper.  ... 
doi:10.1007/s10817-015-9352-2 fatcat:ghddutkfh5aopavvsevnjc7hr4

AltGr-Ergo, a Graphical User Interface for the SMT Solver Alt-Ergo

Sylvain Conchon, Mohamed Iguernlala, Alain Mebsout
2017 Electronic Proceedings in Theoretical Computer Science  
To this end, we have designed AltGr-Ergo, an interactive graphical interface for the SMT solver Alt-Ergo which allows users and tool developers to help the solver finish some proofs.  ...  Due to undecidability and complexity of first-order logic, SMT solvers may not terminate on some problems or require a very long time.  ...  These instances are added to the SAT's context and reasoning continues. Decision procedures component provides a combination of decision algorithms for a collection of built-in theories.  ... 
doi:10.4204/eptcs.239.1 fatcat:geugtjdbdjeojgvnyt5koei4du

Computing with an SMT Solver [chapter]

Nada Amin, K. Rustan M. Leino, Tiark Rompf
2014 Lecture Notes in Computer Science  
Satisfiability modulo theories (SMT) solvers that support quantifier instantiations via matching triggers can be programmed to give practical support for user-defined theories.  ...  By design, such avoidance limits the extent to which the SMT solver is able to apply the definitions of user-defined functions.  ...  Acknowledgments We thank Nik Swamy for useful comments on an earlier draft of this paper.  ... 
doi:10.1007/978-3-319-09099-3_2 fatcat:veoirjvmjffq7d3ihtoa77xxua

Deciding Local Theory Extensions via E-matching [chapter]

Kshitij Bansal, Andrew Reynolds, Tim King, Clark Barrett, Thomas Wies
2015 Lecture Notes in Computer Science  
In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms  ...  Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software.  ...  We would like to thank the anonymous reviewers for their insightful comments and suggestions.  ... 
doi:10.1007/978-3-319-21668-3_6 fatcat:3p365liwjfakviyqss4sfrxcfi

A Three-Tier Strategy for Reasoning About Floating-Point Numbers in SMT [chapter]

Sylvain Conchon, Mohamed Iguernlala, Kailiang Ji, Guillaume Melquiond, Clément Fumex
2017 Lecture Notes in Computer Science  
For these lemmas to be used effectively, we extend the instantiation mechanism of SMT solvers to tightly cooperate with the third layer, the NRA engine of SMT solvers, which provides interval information  ...  The results show that our approach is promising and compete with existing techniques implemented in state-of-the-art SMT solvers.  ...  About the third technique, only few SMT solvers support RIA (with ceiling and floor functions) and providing an efficient and complete decision procedure for it is still an active domain of research.  ... 
doi:10.1007/978-3-319-63390-9_22 fatcat:tewo6v5crfcxpg32fcsydpb7ve

Programming with triggers

Michał Moskal
2009 Proceedings of the 7th International Workshop on Satisfiability Modulo Theories - SMT '09  
We also describe features required from the SMT solver in deductive software verification scenarios.  ...  We give a case study for a Satisfiability Modulo Theories (SMT) solver usage in functional verification of a real world operating system.  ...  with Z3, and Lieven Desmet for his contributions to the early versions of the axiom profiler.  ... 
doi:10.1145/1670412.1670416 fatcat:gmufxmikcrhgdmn5x6sejb2mrq

Yices 2.2 [chapter]

Bruno Dutertre
2014 Lecture Notes in Computer Science  
Yices is an SMT solver developed by SRI International. The first version of Yices was released in 2006 and has been continuously updated since then.  ...  In 2007, we started a complete re-implementation of the solver to improve performance and increase modularity and flexibility. We describe the latest release of Yices, namely, Yices 2.2.  ...  Yices 1 introduced an innovative Simplex-based decision procedure designed to efficiently integrate with a SAT solver [5] , included a congruence-closure algorithm inspired by Simplify's E-graph [6]  ... 
doi:10.1007/978-3-319-08867-9_49 fatcat:zdfnd2kftve3ll3fsdgjqr4wjm

Deductive Verification of Floating-Point Java Programs in KeY [article]

Rosa Abbasi Boroujeni, Jonas Schiffl, Eva Darulova, Mattias Ulbrich, Wolfgang Ahrendt
2021 arXiv   pre-print
Our support in the KeY verifier handles arithmetic via floating-point decision procedures inside SMT solvers and transcendental functions via axiomatization.  ...  This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and 'Not a Number' (NaN).  ...  The authors would like to thank Daniel Eddeland, who together with co-author W. Ahrendt performed prestudies which impacted the current work.  ... 
arXiv:2101.08733v1 fatcat:gbpg7i5v2fanje46m7nfj52rli

Deductive Verification of Floating-Point Java Programs in KeY [chapter]

Rosa Abbasi, Jonas Schiffl, Eva Darulova, Mattias Ulbrich, Wolfgang Ahrendt
2021 Lecture Notes in Computer Science  
Our support in the KeY verifier handles arithmetic via floating-point decision procedures inside SMT solvers and transcendental functions via axiomatization.  ...  This is unfortunate, as floating-point arithmetic is particularly unintuitive to reason about due to rounding as well as the presence of the special values infinity and 'Not a Number' (NaN).  ...  The authors would like to thank Daniel Eddeland, who together with co-author W. Ahrendt performed prestudies which impacted the current work.  ... 
doi:10.1007/978-3-030-72013-1_13 fatcat:shfgyytxprfyhhpgchgpr3zyxu

SMT Solvers for Rodin [chapter]

David Déharbe, Pascal Fontaine, Yoann Guyot, Laurent Voisin
2012 Lecture Notes in Computer Science  
Adding SMT solvers to Atelier B provers reduces to one fourth the number of sequents that need to be proved interactively.  ...  We here investigate the use of SMT (Satisfiability Modulo Theories) solvers in addition to the traditional tools, and detail the techniques used for the cooperation between the Rodin platform and SMT solvers  ...  Acknowledgement: we would like to thank the anonymous reviewers for their remarks.  ... 
doi:10.1007/978-3-642-30885-7_14 fatcat:3kgqrvnz25fwfm6aawewk73yby

Reasoning about comprehensions with first-order SMT solvers

K. Rustan M. Leino, Rosemary Monahan
2009 Proceedings of the 2009 ACM symposium on Applied Computing - SAC '09  
programs and, furthermore, that can be used automatically by the SMT solver.  ...  Since a firstorder SMT solver does not directly support the bound variables that occur in comprehension expressions, the challenge is to provide a sound axiomatisation that is strong enough to prove interesting  ...  Also, using Simplify as the SMT solver, we have not experienced any problems with the fragile trigger of the distribution axiom.  ... 
doi:10.1145/1529282.1529411 dblp:conf/sac/LeinoM09 fatcat:glo7hapbhfbxzltbs3r4slfe7a

Extending Sledgehammer with SMT Solvers [chapter]

Jasmin Christian Blanchette, Sascha Böhme, Lawrence C. Paulson
2011 Lecture Notes in Computer Science  
We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture.  ...  The ATPs and SMT solvers nicely complement each other, and Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs' reach.  ...  Michał Moskal provided expert help on Z3 triggers.  ... 
doi:10.1007/978-3-642-22438-6_11 fatcat:gv5vgvpccjdarnzc4x7g32dsny

Extending Sledgehammer with SMT Solvers

Jasmin Christian Blanchette, Sascha Böhme, Lawrence C. Paulson
2013 Journal of automated reasoning  
We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture.  ...  The ATPs and SMT solvers nicely complement each other, and Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs' reach.  ...  Michał Moskal provided expert help on Z3 triggers.  ... 
doi:10.1007/s10817-013-9278-5 fatcat:nn4vl6f5nrc5pk7opli3l3tmtq

A Polymorphic Intermediate Verification Language: Design and Logical Encoding [chapter]

K. Rustan M. Leino, Philipp Rümmer
2010 Lecture Notes in Computer Science  
The paper gives two encodings of types and formulae in simply typed logic such that SMT solvers and other theorem provers can be used to discharge verification conditions.  ...  While such intermediate languages traditionally only offer rather simple type systems, this paper argues that it is both advantageous and feasible to integrate richer type systems with features like (higher-ranked  ...  We thank Stephan Tobies and Shuvendu Lahiri for providing us with Boogie files from VCC and HAVOC for use as benchmarks.  ... 
doi:10.1007/978-3-642-12002-2_26 fatcat:5ghnjvv3vze3lmiebfa5pwl4ye

Identifying Overly Restrictive Matching Patterns in SMT-based Program Verifiers (extended version) [article]

Alexandra Bugariu, Arshavir Ter-Gabrielyan, Peter Müller
2021 arXiv   pre-print
We designed a novel algorithm to synthesize missing triggering terms required to complete a proof.  ...  Tool developers can use this information to refine their matching patterns and prevent similar verification errors, or to fix a detected unsoundness.  ...  We are also grateful to Felix Wolf for providing us the Gobra benchmarks, and to Evgenii Kotelnikov for his detailed explanations about Vampire.  ... 
arXiv:2105.04385v3 fatcat:j2z7cz5n7fgc5k2z3cgovzoxsa
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