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Publications : Claire DrossBack
Claire Dross, Sylvain Conchon, Johannes Kanig, and Andrei Paskevich.
Reasoning with triggers.
Research Report RR-7986, INRIA, June 2012.
[ bib |
full paper on HAL |
SMT solvers can decide the satisfiability of ground formulas modulo a combination of built-in theories. Adding a built-in theory to a given SMT solver is a complex and time consuming task that requires internal knowledge of the solver. However, many theories can be easily expressed using first-order formulas. Unfortunately, since universal quantifiers are not handled in a complete way by SMT solvers, these axiomatics cannot be used as decision procedures. In this paper, we show how to extend a generic SMT solver to accept a custom theory description and behave as a decision procedure for that theory, provided that the described theory is complete and terminating in a precise sense. The description language consists of first-order axioms with triggers, an instantiation mechanism that is found in many SMT solvers. This mechanism, which usually lacks a clear semantics in existing languages and tools, is rigorously defined here; this definition can be used to prove completeness and termination of the theory. We demonstrate on two examples, how such proofs can be achieved in our formalism.
Keywords: Quantifiers, Triggers, SMT Solvers, Theories
|||Claire Dross, Sylvain Conchon, Johannes Kanig, and Andrei Paskevich. Reasoning with triggers. In Pascal Fontaine and Amit Goel, editors, SMT workshop, Manchester, UK, 2012. http://smt2012.loria.fr/. [ bib ]|
Claire Dross, Jean-Christophe Filliātre, and Yannick Moy.
Correct Code Containing Containers.
In 5th International Conference on Tests and Proofs (TAP'11),
volume 6706 of Lecture Notes in Computer Science, pages 102-118,
Zurich, June 2011. Springer.
[ bib |
For critical software development, containers such as lists, vectors, sets or maps are an attractive alternative to ad-hoc data structures based on pointers. As standards like DO-178C put formal verification and testing on an equal footing, it is important to give users the ability to apply both to the verification of code using containers. In this paper, we present a definition of containers whose aim is to facilitate their use in certified software, using modern proof technology and novel specification languages. Correct usage of containers and user-provided correctness properties can be checked either by execution during testing or by formal proof with an automatic prover. We present a formal semantics for containers and an axiomatization of this semantics targeted at automatic provers. We have proved in Coq that the formal semantics is consistent and that the axiomatization thereof is correct.
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