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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.  ...  To show that proof tools rooted in SMT are growing up, this paper presents, using Dafny, a series of examples that illustrate how theorems are expressed and proved.  ...  With unrestricted use of the postcondition of this call, the co-induction hypothesis obtained would trivially prove the theorem itself.  ... 
doi:10.1007/978-3-642-39634-2_2 fatcat:n56eavdz75f6ldiadspg5d36jy

Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL [chapter]

Sascha Böhme, Anthony C. J. Fox, Thomas Sewell, Tjark Weber
2011 Lecture Notes in Computer Science  
The Satisfiability Modulo Theories (SMT) solver Z3 can generate proofs of unsatisfiability.  ...  We present independent reconstruction of unsatisfiability proofs for bit-vector theories in the theorem provers HOL4 and Isabelle/HOL.  ...  The authors are grateful to Nikolaj Bjørner and Leonardo de Moura for their help with Z3.  ... 
doi:10.1007/978-3-642-25379-9_15 fatcat:gesxkp2cm5girliosyngzyuwmi

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.  ...  Automated first-order theorem proving tools, commonly known as ATP tools, prove properties of theorems expressed in (pure classical) first-order logic.  ... 
doi:10.1145/2593882.2593899 dblp:conf/icse/VisserBS14 fatcat:cdgga6syovar5hr4mfzjyyi4se

The Strategy Challenge in SMT Solving [chapter]

Leonardo de Moura, Grant Olney Passmore
2013 Lecture Notes in Computer Science  
We present evidence that the adaptation of ideas of strategy prevalent both within the Argonne and LCF theorem proving paradigms can go a long way towards realizing this goal. Prologue.  ...  We present a challenge to the SMT community: to develop methods through which users can exert strategic control over core heuristic aspects of SMT solvers.  ...  There is a natural view of automated theorem proving as being an exercise in combinatorial search. 2.  ... 
doi:10.1007/978-3-642-36675-8_2 fatcat:op5iarzvnvfkddz5ycsgyzo264

Preface

Silvio Ranise, Ullrich Hustadt
2009 Annals of Mathematics and Artificial Intelligence  
The role of first-order theorem proving as a core domain of automated deduction has been recognized since the first automated procedures were developed in the late 1950s and early 1960s.  ...  logic, manyvalued logic, description logic, and modal logic, strategies and complexity of theorem proving procedures, decision procedures, and applications of first-order theorem proving.  ...  The work by Peter Höfner, Georg Struth and Geoff Sutcliffe illustrates the use of state-of-the-art automated theorem proving (ATP) systems for the verification of refinement laws in demonic refinement  ... 
doi:10.1007/s10472-009-9149-2 fatcat:amorecrlxbhsfmgcaygccikaq4

SMT solvers: new oracles for the HOL theorem prover

Tjark Weber
2011 International Journal on Software Tools for Technology Transfer (STTT)  
This paper describes an integration of Satisfiability Modulo Theories (SMT) solvers with the HOL4 theorem prover.  ...  Proof obligations are passed from the interactive HOL4 prover to the SMT solver, which can often prove them automatically.  ...  the degree of automation available in interactive theorem proving and ultimately enhancing its applicability.  ... 
doi:10.1007/s10009-011-0188-8 fatcat:6pjachis4rdavjufzbf43smdrm

Toward SMT-Based Refinement Types in Agda [article]

Gan Shen, Lindsey Kuper
2021 arXiv   pre-print
and combine the strengths of the two approaches to mechanized theorem proving.  ...  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  ...  CONCLUSION AND FUTURE WORK Theorem-proving systems have historically fallen into two camps [Boutin 1997 ]: interactive theorem proving, exemplified by proof assistants such as Agda, and automated theorem  ... 
arXiv:2110.05771v1 fatcat:6jwhdwhpafaalbb55gidsblaiq

Fast LCF-Style Proof Reconstruction for Z3 [chapter]

Sascha Böhme, Tjark Weber
2010 Lecture Notes in Computer Science  
We present independent reconstruction of these proofs in the theorem provers Isabelle/HOL and HOL4 with particular focus on efficiency.  ...  The Satisfiability Modulo Theories (SMT) solver Z3 can generate proofs of unsatisfiability.  ...  Acknowledgments The authors are grateful to Nikolaj Bjørner and Leonardo de Moura for their help with Z3, to Yeting Ge for his help on proof reconstruction for CVC3, and to Alexander Krauss and Lukas Bulwahn  ... 
doi:10.1007/978-3-642-14052-5_14 fatcat:yvi5yovfijayhmc6nnkj34mfju

Automating Algebraic Methods in Isabelle [chapter]

Walter Guttmann, Georg Struth, Tjark Weber
2011 Lecture Notes in Computer Science  
Isabelle has recently been extended by automated theorem provers and SMT solvers. We use these integrated tools for automatically proving several rather intricate refinement and termination theorems.  ...  These results show, for the first time, that Isabelle's tool integration makes automated algebraic reasoning particularly simple. This is a step towards increasing the automation of formal methods.  ...  They are particularly suitable for automation [18, 20] ; automated theorem proving (ATP) systems were, in fact, instrumental for developing some recent variants [10] .  ... 
doi:10.1007/978-3-642-24559-6_41 fatcat:5jpfr7dazveyddlinhogksywjq

Mostly-automated verification of low-level programs in computational separation logic

Adam Chlipala
2011 Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation - PLDI '11  
Prove module correctness theorem.  ...  Classical verification with SMT solvers Interactive theorem-proving in higher-order logic Complex trigger mechanism for quantifier instantiation Complex program annotation scheme needed  ... 
doi:10.1145/1993498.1993526 dblp:conf/pldi/Chlipala11 fatcat:4wy6impkbfhgnfvf4pkl6dopiu

Mostly-automated verification of low-level programs in computational separation logic

Adam Chlipala
2012 SIGPLAN notices  
Prove module correctness theorem.  ...  Classical verification with SMT solvers Interactive theorem-proving in higher-order logic Complex trigger mechanism for quantifier instantiation Complex program annotation scheme needed  ... 
doi:10.1145/2345156.1993526 fatcat:zwsxr3hh6fb7zihxec76adrd4i

Mostly-automated verification of low-level programs in computational separation logic

Adam Chlipala
2011 SIGPLAN notices  
Prove module correctness theorem.  ...  Classical verification with SMT solvers Interactive theorem-proving in higher-order logic Complex trigger mechanism for quantifier instantiation Complex program annotation scheme needed  ... 
doi:10.1145/1993316.1993526 fatcat:bapo4dbuqje7pf4oocozl4qe2q

Towards Automated Strategies in Satisfiability Modulo Theory [chapter]

Nicolás Gálvez Ramírez, Youssef Hamadi, Eric Monfroy, Frédéric Saubion
2016 Lecture Notes in Computer Science  
Résumé en anglais SMT solvers include many heuristic components in order to ease the theorem proving process for different logics and problems.  ...  Evidence of improvement is shown and the basis for future works with evolutionary and/or learning-based algorithms are raised. Publié sur Okina (http://okina.univ-angers.fr)  ... 
doi:10.1007/978-3-319-30668-1_15 fatcat:sacuww5v55g4lohoyr2bpmydme

Practical Aspects of Automated Deduction for Program Verification

Wolfgang Ahrendt, Bernhard Beckert, Martin Giese, Philipp Rümmer
2010 Künstliche Intelligenz  
Program verification is an increasingly important application area for automated deduction. The field has outgrown the area of academic case studies, and industry is showing serious interest.  ...  Over the last years, technologies for the formal specification and verification of software -using logic-based specification languages and automated deduction -have matured and can be expected to complement  ...  Although the integration of SMT solvers with first-order theorem provers is an active area of research, until now such tasks are the domain of interactive systems.  ... 
doi:10.1007/s13218-010-0001-y fatcat:oungj4soo5dkzpaz4botsf22hq

Verification of Control Systems Implemented in Simulink with Assertion Checks and Theorem Proving: A Case Study [article]

Dejanira Araiza-Illan, Kerstin Eder, Arthur Richards
2015 arXiv   pre-print
An automatic translation tool from Simulink to the language of the theorem proving tool Why3 is also presented.  ...  We compare performing only assertion checks against the use of theorem proving, to highlight the advantages of the latter.  ...  proving with SMT solvers, if they include system variables.  ... 
arXiv:1505.05699v2 fatcat:sersezqkhzasnipkavks6oqcqe
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