97 research outputs found
Cell morphing: from array programs to array-free Horn clauses
International audienceAutomatically verifying safety properties of programs is hard.Many approaches exist for verifying programs operating on Boolean and integer values (e.g. abstract interpretation, counterexample-guided abstraction refinement using interpolants), but transposing them to array properties has been fraught with difficulties.Our work addresses that issue with a powerful and flexible abstractionthat morphes concrete array cells into a finite set of abstractones. This abstraction is parametric both in precision and in theback-end analysis used.From our programs with arrays, we generate nonlinear Horn clauses overscalar variables only, in a common format with clear and unambiguouslogical semantics, for which there exist several solvers. We thusavoid the use of solvers operating over arrays, which are still veryimmature.Experiments with our prototype VAPHOR show that this approach can proveautomatically and without user annotationsthe functional correctness of several classical examples, including \emph{selection sort}, \emph{bubble sort}, \emph{insertion sort}, as well as examples from literature on array analysis
Higher-order Program Verification as Satisfiability Modulo Theories with Algebraic Data-types
We report on work in progress on automatic procedures for proving properties
of programs written in higher-order functional languages. Our approach encodes
higher-order programs directly as first-order SMT problems over Horn clauses.
It is straight-forward to reduce Hoare-style verification of first-order
programs into satisfiability of Horn clauses. The presence of closures offers
several challenges: relatively complete proof systems have to account for
closures; and in practice, the effectiveness of search procedures depend on
encoding strategies and capabilities of underlying solvers. We here use
algebraic data-types to encode closures and rely on solvers that support
algebraic data-types. The viability of the approach is examined using examples
from the literature on higher-order program verification
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
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