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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  
SMT solvers.  ...  This paper presents a technique for translating common comprehension expressions ( sum , count , product , min , and max ) into verification conditions that can be tackled by two off-the-shelf first-order  ...  We present a technique for translating common comprehension expressions into verification conditions that can be tackled by a first-order Satisfiability Modulo Theories (SMT) solver.  ... 
doi:10.1145/1529282.1529411 dblp:conf/sac/LeinoM09 fatcat:glo7hapbhfbxzltbs3r4slfe7a

Symbolic Computation and Satisfiability Checking : Report of Dagstuhl Seminar 15471

Erika Ábrahám, Pascal Fontaine, Thomas Sturm, Dongming Wang, Dongming Wang, Erika Ábrahám, Pascal Fontaine, Thomas Sturm
2016 Dagstuhl Reports  
The seminar focused on satisfiability checking for combinations of first-order logic and subclasses thereof with arithmetic theories in a very liberal sense, also covering quantifiers and parameters.  ...  Nowadays, SMT-LIB is supported by all the main SMT solvers. It is used as the interface language of many tools (e.g. verification platforms) with their SMT solver backends.  ...  The aim of this initiative was at first to collect a library of benchmarks.  ... 
doi:10.18154/rwth-2017-01217 fatcat:5aaxyhouqrdcfhhvek76vkdwjm

Encoding TLA + into unsorted and many-sorted first-order logic

Stephan Merz, Hernán Vanzetto
2018 Science of Computer Programming  
theorem provers and smt solvers for the TLA + Proof System.  ...  We present an encoding of a non-temporal fragment of TLA + into (unsorted) first-order logic and many-sorted first-order logic, the input languages of first-order automated theorem provers.  ...  , which provides automated proof methods based on first-order reasoning and rewriting; Zenon, a tableau prover for first-order logic with equality that includes extensions for reasoning about sets and  ... 
doi:10.1016/j.scico.2017.09.004 fatcat:fvibuppmabaaxe6jebvjddkq24

Encoding TLA $$^{+}$$ + into Many-Sorted First-Order Logic [chapter]

Stephan Merz, Hernán Vanzetto
2016 Lecture Notes in Computer Science  
solvers.  ...  solvers for the TLA + Proof System.  ...  , which provides automated proof methods based on first-order reasoning and rewriting; Zenon, a tableau prover for first-order logic with equality that includes extensions for reasoning about sets and  ... 
doi:10.1007/978-3-319-33600-8_3 fatcat:ljkokz3bjnelfc4ow5fx2arz4a

SMT Solvers for Validation of B and Event-B Models [chapter]

Sebastian Krings, Michael Leuschel
2016 Lecture Notes in Computer Science  
We apply the combined solver to B and Event-B predicates, featuring higher-order datatypes and constructs like set comprehensions.  ...  We present an integration of the constraint solving kernel of the ProB model checker with the SMT solver Z3.  ...  For SMT solvers in general they suggest the ppTrans approach. Here, set theory and arithmetic are broken down into first-order formulas using uninterpreted functions for membership, etc.  ... 
doi:10.1007/978-3-319-33693-0_23 fatcat:dfaq5ffi2nfxlljytxrcblg7kq

Encoding TLA+ set theory into many-sorted first-order logic [article]

Stephan Merz, Hernán Vanzetto
2015 arXiv   pre-print
We present an encoding of Zermelo-Fraenkel set theory into many-sorted first-order logic, the input language of state-of-the-art SMT solvers.  ...  This translation is the main component of a back-end prover based on SMT solvers in the TLA+ Proof System.  ...  proof methods based on first-order reasoning and rewriting; Zenon [5] , a tableau prover for first-order logic with equality that includes extensions for reasoning about sets and functions; and a backend  ... 
arXiv:1508.03838v1 fatcat:7dlr77t36fddxjuydwd2y3mpee

SMT Solvers for Rodin [chapter]

David Déharbe, Pascal Fontaine, Yoann Guyot, Laurent Voisin
2012 Lecture Notes in Computer Science  
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  ...  Adding SMT solvers to Atelier B provers reduces to one fourth the number of sequents that need to be proved interactively.  ...  Since SMT solvers handle first-order logic, this approach does not make it possible to reason about sets of sets. The second approach removes this restriction.  ... 
doi:10.1007/978-3-642-30885-7_14 fatcat:3kgqrvnz25fwfm6aawewk73yby

Integrating SMT solvers in Rodin

David Déharbe, Pascal Fontaine, Yoann Guyot, Laurent Voisin
2014 Science of Computer Programming  
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  ...  On this domain, adding SMT solvers to Atelier B provers reduces significantly the number of sequents that need to be proved interactively.  ...  Since SMT solvers handle first-order logic, this approach does not make it possible to reason about sets of sets. The second approach removes this restriction.  ... 
doi:10.1016/j.scico.2014.04.012 fatcat:iki2utjgpbdytdl2mt6ee44sym

Integrating SMT with Theorem Proving for Analog/Mixed-Signal Circuit Verification [chapter]

Yan Peng, Mark Greenstreet
2015 Lecture Notes in Computer Science  
SMT (satisfiability modulo theory) solvers eliminate much of the tedium associated with detailed proofs by providing automatic reasoning about propositional formulas including equalities and inequalities  ...  A theorem prover complements the SMT solver by providing a proof structuring and proof by induction.  ...  Acknowledgements We thank Leo Moura, David Rager, Jijie Wei, and Ge Yu for helpful discussions about this research.  ... 
doi:10.1007/978-3-319-17524-9_22 fatcat:qp5dgklxmzb2ln3hnfmhmsb5ze

Building Better Bit-Blasting for Floating-Point Problems [chapter]

Martin Brain, Florian Schanda, Youcheng Sun
2019 Lecture Notes in Computer Science  
This paper presents SymFPU, a library of encodings that can be included in solvers.  ...  So there is a pressing need for SMT solvers to be able to reason about floating-point variables.  ...  To reason about contemporary software, we must be able to efficiently reason about floating-point. To derive proofs, counter-examples, test cases or attack vectors we need bit-accurate results.  ... 
doi:10.1007/978-3-030-17462-0_5 fatcat:j3xvahui2fgltobml66nwuttaa

A Survey on String Constraint Solving [article]

Roberto Amadini
2021 arXiv   pre-print
This paper reports a comprehensive survey on string constraint solving by exploring the large number of approaches that have been proposed over the last decades to solve string constraints.  ...  The authors claimed that CVC4 was the first solver able to reason about a language of mixed constraints including strings together with integers, reals, arrays, and algebraic datatypes.  ...  An interesting paper about automata-based approaches is [82] , where Hooimeijer et al. study a comprehensive set of algorithms and data structures for automata operations in order to give a fair comparison  ... 
arXiv:2002.02376v8 fatcat:why6oeufmrbozbl22jlf7yivea

Beaver: Engineering an Efficient SMT Solver for Bit-Vector Arithmetic [chapter]

Susmit Jha, Rhishikesh Limaye, Sanjit A. Seshia
2009 Lecture Notes in Computer Science  
We present the key ideas in the design and implementation of Beaver, an SMT solver for quantifier-free finite-precision bit-vector logic (QF BV).  ...  We present an experimental analysis of the effectiveness of Beaver's techniques on both hardware and software benchmarks with a selection of back-end SAT solvers.  ...  Of the many first-order theories for which SMT solvers are available, one of the most useful is the theory of finite-precision bit-vector arithmetic, abbreviated as QF BV [14] .  ... 
doi:10.1007/978-3-642-02658-4_53 fatcat:26gzopw5wjbppl7vg47zfad55i

Automating Separation Logic Using SMT [chapter]

Ruzica Piskac, Thomas Wies, Damien Zufferey
2013 Lecture Notes in Computer Science  
Our approach provides a simple method of integrating separation logic into existing verification tools that provide SMT backends, and an elegant way of combining SL fragments with other decidable first-order  ...  In this paper, we present a reduction of decidable SL fragments to a decidable first-order theory that fits well into the satisfiability modulo theories (SMT) framework.  ...  Our reduction enables the seamless integration of an SL prover into an SMT solver, which has promising applications in program verification.  ... 
doi:10.1007/978-3-642-39799-8_54 fatcat:kb6sfaasmrdu5cvfgor4g6jmle

The Axiom Profiler: Understanding and Debugging SMT Quantifier Instantiations [chapter]

Nils Becker, Peter Müller, Alexander J. Summers
2019 Lecture Notes in Computer Science  
SMT solvers typically reason about universal quantifiers via E-matching: syntactic matching patterns for each quantifier prescribe shapes of ground terms whose presence in the SMT run will trigger quantifier  ...  The effectiveness and performance of the SMT solver depend crucially on well-chosen patterns.  ...  We thank Nikolaj Bjørner for his assistance with Z3, and Micha l Moskal for generous advice and feedback on earlier versions of the tool.  ... 
doi:10.1007/978-3-030-17462-0_6 fatcat:rcn6w3yf2zgf7df4ugi54ecjze

Harnessing SMT Solvers for TLA+ Proofs

Stephan Merz, Hernán Vanzetto
2012 Electronic Communications of the EASST  
We recently developed a backend that relies on a typing discipline to encode (untyped) TLA+ formulas into multi-sorted first-order logic for SMT solvers.  ...  We also present a number of techniques based on rewriting in order to simplify the resulting formulas.  ...  Acknowledgements: Damien Doligez, Leslie Lamport, and Tom Rodeheffer provided useful feedback on the SMT backends.  ... 
doi:10.14279/tuj.eceasst.53.766 dblp:journals/eceasst/MerzV12 fatcat:oltyc4u2w5cyfnakasp6vncp5m
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