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Automating Induction with an SMT Solver [chapter]

K. Rustan M. Leino
2012 Lecture Notes in Computer Science  
Sometimes an alternative to proof assistants, satisfiability modulo theories (SMT) solvers bring the hope of a higher degree of automation.  ...  hypothesis, and finally passes the proof obligation to an SMT solver.  ...  solver.  ... 
doi:10.1007/978-3-642-27940-9_21 fatcat:jghhbkqa7reknhxopc37vr5a7i

Induction for SMT Solvers [chapter]

Andrew Reynolds, Viktor Kuncak
2015 Lecture Notes in Computer Science  
In addition its overall effectiveness, it has an advantage of accepting SMT-LIB input and being integrated with other SMT solving techniques of CVC4.  ...  We present a set of techniques that introduce inductive reasoning into SMT solving algorithms that is sound with respect to the interpretation of structures in SMT-LIB standard.  ...  Acknowledgments We thank Ravichandhran Madhavan for an initial version of the Leon benchmarks and Cesare Tinelli for discussions about SMT-LIB semantics.  ... 
doi:10.1007/978-3-662-46081-8_5 fatcat:kd4apjhcijhb5lklpkmukazx44

Software engineering and automated deduction

Willem Visser, Nikolaj Bjørner, Natarajan Shankar
2014 Proceedings of the on Future of Software Engineering - FOSE 2014  
We observe that in the past software engineering problems were solved by merely leveraging advances in automated deduction, especially in SAT and SMT solving, whereas we are now entering a phase where  ...  advances in automated deduction are also driven by software engineering requirements.  ...  This check is performed with the aid of decision procedures, such as those found in SMT solvers.  ... 
doi:10.1145/2593882.2593899 dblp:conf/icse/VisserBS14 fatcat:cdgga6syovar5hr4mfzjyyi4se

Toward SMT-Based Refinement Types in Agda [article]

Gan Shen, Lindsey Kuper
2021 arXiv   pre-print
We propose to integrate Satisfiability Modulo Theories (SMT)-based refinement types into the dependently-typed language Agda in an effort to ease some of the burden of programming with dependent types  ...  Dependent types offer great versatility and power, but developing proofs with them can be tedious and requires considerable human guidance.  ...  rule that uses an off-theshelf SMT solver to automate the proof for us.  ... 
arXiv:2110.05771v1 fatcat:6jwhdwhpafaalbb55gidsblaiq

Extending Sledgehammer with SMT Solvers

Jasmin Christian Blanchette, Sascha Böhme, Lawrence C. Paulson
2013 Journal of automated reasoning  
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.  ...  We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture.  ...  Running the SMT solvers in parallel with the ATPs is consistent with our objective of full automation.  ... 
doi:10.1007/s10817-013-9278-5 fatcat:nn4vl6f5nrc5pk7opli3l3tmtq

ESBMC 5.0: an industrial-strength C model checker

Mikhail R. Gadelha, Felipe R. Monteiro, Jeremy Morse, Lucas C. Cordeiro, Bernd Fischer, Denis A. Nicole
2018 Proceedings of the 33rd ACM/IEEE International Conference on Automated Software Engineering - ASE 2018  
We discuss improvements over previous versions of ESBMC, including the description of new front-and back-ends, IEEE floating-point support, and an improved k-induction algorithm.  ...  We are currently extending the k-induction proof rule to use information from the inductive step, to make bug finding more efficiently [16] .  ...  Results over the SV-COMP 2018 benchmark suite show that ESBMC is the strongest k-induction tool currently available.  ... 
doi:10.1145/3238147.3240481 dblp:conf/kbse/GadelhaMMC0N18 fatcat:qwcyixgprbcmzf6ialvthmxq3a

Extending Sledgehammer with SMT Solvers [chapter]

Jasmin Christian Blanchette, Sascha Böhme, Lawrence C. Paulson
2011 Lecture Notes in Computer Science  
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.  ...  We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture.  ...  Running the SMT solvers in parallel with the ATPs is consistent with our objective of full automation.  ... 
doi:10.1007/978-3-642-22438-6_11 fatcat:gv5vgvpccjdarnzc4x7g32dsny

Automating Induction for Solving Horn Clauses [chapter]

Hiroshi Unno, Sho Torii, Hiroki Sakamoto
2017 Lecture Notes in Computer Science  
To automate inductive proofs, we introduce a novel proof system tailored to Horn constraint solving, and use a PDR-based Horn constraint solver as well as an SMT solver to discharge proof obligations arising  ...  The two main advantages of the proposed method are that (1) it can deal with constraints over any background theories supported by the underlying SMT solver, including nonlinear arithmetic and algebraic  ...  The HipSpec [18] inductive prover and the SMT solver CVC4 extended with induction [46] are reported to have proved 80.  ... 
doi:10.1007/978-3-319-63390-9_30 fatcat:pgt2xnaoevcn7otiddwkcsiwnm

Functional Pearl: Theorem Proving for All (Equational Reasoning in Liquid Haskell) [article]

Niki Vazou and Joachim Breitner and Will Kunkel and David Van Horn and Graham Hutton
2018 arXiv   pre-print
Proving that the length of a list is non-negative is thus fully automated by the SMT solver.  ...  Compared to these tools, in Liquid Haskell the proofs are Haskell programs while SMT solvers are used to automate reasoning.  ... 
arXiv:1806.03541v1 fatcat:35pswnmiafgavmck2n2kaitm5m

Theorem proving for all: equational reasoning in liquid Haskell (functional pearl)

Niki Vazou, Joachim Breitner, Rose Kunkel, David Van Horn, Graham Hutton
2018 SIGPLAN notices  
Proving that the length of a list is non-negative is thus fully automated by the SMT solver.  ...  Compared to these tools, in Liquid Haskell the proofs are Haskell programs while SMT solvers are used to automate reasoning.  ... 
doi:10.1145/3299711.3242756 fatcat:4hsqb2r5svg67ky4wcbob2o6ea

Proofs by Deduction [chapter]

2017 Logic and Language Models for Computer Science  
of an automated deduction tool, which is increasingly integrated into application tools.  ...  Proofs and models serve two main purposes: (1) as an upcoming paradigm towards the next generation of automated deduction tools where search relies on (partial) proofs and models; (2) as the actual result  ...  ., a single loop) and a postcondition, we show how to, using a Max-SMT solver, an inductive invariant together with a precondition can be synthesized so that the precondition ensures the validity of the  ... 
doi:10.1142/9789813229211_0003 fatcat:cqpgqtobz5gx3db5bq54gxrd4m

Preface to special issue on satisfiability modulo theories

Alberto Griggio, Philipp Rümmer
2017 Formal methods in system design  
Over the last decade, there has been a consolidation in the way SMT solvers are constructed, with the DPLL(T) architecture having emerged as the standard approach.  ...  These ingredients have made SMT techniques well-suited for use in larger automated reasoning and formal verification efforts. This special issue surveys recent developments in the SMT field.  ...  The articles were selected through an open call for contributions, and a two-step selection process, with authors first submitting only an abstract; the authors of all eight abstracts were then invited  ... 
doi:10.1007/s10703-017-0308-5 fatcat:4uinzqoauza33bfjwixtudwhia

Deduction Beyond Satisfiability (Dagstuhl Seminar 19371)

Carsten Fuhs, Philipp Rümmer, Renate Schmidt, Cesare Tinelli, Michael Wagner
2020 Dagstuhl Reports  
Research in automated deduction has traditionally focused on solving decision problems, which are problems with a binary answer.  ...  Research in automated deduction is traditionally focused on the problem of determining the satisfiability of formulas or, more generally, on solving logical problems with yes/no answers.  ...  Participants SMT solvers to reason about firewalls Ruzica Piskac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Inductive Inference with Recursion Analysis in Separation  ... 
doi:10.4230/dagrep.9.9.23 dblp:journals/dagstuhl-reports/FuhsRST19 fatcat:j6moci5zgvgjzgpsqblemwsrlm

Language and Proofs for Higher-Order SMT (Work in Progress)

Haniel Barbosa, Jasmin Christian Blanchette, Simon Cruanes, Daniel El Ouraoui, Pascal Fontaine
2017 Electronic Proceedings in Theoretical Computer Science  
In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs.  ...  Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories.  ...  Between the initial version of this document and the current one, the SMT-LIB extension has been greatly influenced by discussions with Clark Barrett and Cesare Tinelli (the SMT-LIB managers, together  ... 
doi:10.4204/eptcs.262.3 fatcat:dp6jtuq2hne25acty36jcv7h5y

Automating Theorem Proving with SMT [chapter]

K. Rustan M. Leino
2013 Lecture Notes in Computer Science  
The power and automation offered by modern satisfiability-modulotheories (SMT) solvers is changing the landscape for mechanized formal theorem proving.  ...  For instance, the SMT-based program verifier Dafny supports a number of proof features traditionally found only in interactive proof assistants, like inductive, co-inductive, and declarative proofs.  ...  Acknowledgments I am grateful to Maria Christakis, Sophia Drossopoulou, Peter Müller, and David Pichardie for comments on an earlier draft of this paper.  ... 
doi:10.1007/978-3-642-39634-2_2 fatcat:n56eavdz75f6ldiadspg5d36jy
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