16,449 research outputs found
Formal Proof of SCHUR Conjugate Function
The main goal of our work is to formally prove the correctness of the key
commands of the SCHUR software, an interactive program for calculating with
characters of Lie groups and symmetric functions. The core of the computations
relies on enumeration and manipulation of combinatorial structures. As a first
"proof of concept", we present a formal proof of the conjugate function,
written in C. This function computes the conjugate of an integer partition. To
formally prove this program, we use the Frama-C software. It allows us to
annotate C functions and to generate proof obligations, which are proved using
several automated theorem provers. In this paper, we also draw on methodology,
discussing on how to formally prove this kind of program.Comment: To appear in CALCULEMUS 201
Verification of Imperative Programs by Constraint Logic Program Transformation
We present a method for verifying partial correctness properties of
imperative programs that manipulate integers and arrays by using techniques
based on the transformation of constraint logic programs (CLP). We use CLP as a
metalanguage for representing imperative programs, their executions, and their
properties. First, we encode the correctness of an imperative program, say
prog, as the negation of a predicate 'incorrect' defined by a CLP program T. By
construction, 'incorrect' holds in the least model of T if and only if the
execution of prog from an initial configuration eventually halts in an error
configuration. Then, we apply to program T a sequence of transformations that
preserve its least model semantics. These transformations are based on
well-known transformation rules, such as unfolding and folding, guided by
suitable transformation strategies, such as specialization and generalization.
The objective of the transformations is to derive a new CLP program TransfT
where the predicate 'incorrect' is defined either by (i) the fact 'incorrect.'
(and in this case prog is not correct), or by (ii) the empty set of clauses
(and in this case prog is correct). In the case where we derive a CLP program
such that neither (i) nor (ii) holds, we iterate the transformation. Since the
problem is undecidable, this process may not terminate. We show through
examples that our method can be applied in a rather systematic way, and is
amenable to automation by transferring to the field of program verification
many techniques developed in the field of program transformation.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
What's Decidable About Sequences?
We present a first-order theory of sequences with integer elements,
Presburger arithmetic, and regular constraints, which can model significant
properties of data structures such as arrays and lists. We give a decision
procedure for the quantifier-free fragment, based on an encoding into the
first-order theory of concatenation; the procedure has PSPACE complexity. The
quantifier-free fragment of the theory of sequences can express properties such
as sortedness and injectivity, as well as Boolean combinations of periodic and
arithmetic facts relating the elements of the sequence and their positions
(e.g., "for all even i's, the element at position i has value i+3 or 2i"). The
resulting expressive power is orthogonal to that of the most expressive
decidable logics for arrays. Some examples demonstrate that the fragment is
also suitable to reason about sequence-manipulating programs within the
standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl
Your Proof Fails? Testing Helps to Find the Reason
Applying deductive verification to formally prove that a program respects its
formal specification is a very complex and time-consuming task due in
particular to the lack of feedback in case of proof failures. Along with a
non-compliance between the code and its specification (due to an error in at
least one of them), possible reasons of a proof failure include a missing or
too weak specification for a called function or a loop, and lack of time or
simply incapacity of the prover to finish a particular proof. This work
proposes a new methodology where test generation helps to identify the reason
of a proof failure and to exhibit a counter-example clearly illustrating the
issue. We describe how to transform an annotated C program into C code suitable
for testing and illustrate the benefits of the method on comprehensive
examples. The method has been implemented in STADY, a plugin of the software
analysis platform FRAMA-C. Initial experiments show that detecting
non-compliances and contract weaknesses allows to precisely diagnose most proof
failures.Comment: 11 pages, 10 figure
A Static Analyzer for Large Safety-Critical Software
We show that abstract interpretation-based static program analysis can be
made efficient and precise enough to formally verify a class of properties for
a family of large programs with few or no false alarms. This is achieved by
refinement of a general purpose static analyzer and later adaptation to
particular programs of the family by the end-user through parametrization. This
is applied to the proof of soundness of data manipulation operations at the
machine level for periodic synchronous safety critical embedded software. The
main novelties are the design principle of static analyzers by refinement and
adaptation through parametrization, the symbolic manipulation of expressions to
improve the precision of abstract transfer functions, the octagon, ellipsoid,
and decision tree abstract domains, all with sound handling of rounding errors
in floating point computations, widening strategies (with thresholds, delayed)
and the automatic determination of the parameters (parametrized packing)
On Verifying Resource Contracts using Code Contracts
In this paper we present an approach to check resource consumption contracts
using an off-the-shelf static analyzer.
We propose a set of annotations to support resource usage specifications, in
particular, dynamic memory consumption constraints. Since dynamic memory may be
recycled by a memory manager, the consumption of this resource is not monotone.
The specification language can express both memory consumption and lifetime
properties in a modular fashion.
We develop a proof-of-concept implementation by extending Code Contracts'
specification language. To verify the correctness of these annotations we rely
on the Code Contracts static verifier and a points-to analysis. We also briefly
discuss possible extensions of our approach to deal with non-linear
expressions.Comment: In Proceedings LAFM 2013, arXiv:1401.056
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