9,817 research outputs found
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
Proving Correctness of Imperative Programs by Linearizing Constrained Horn Clauses
We present a method for verifying the correctness of imperative programs
which is based on the automated transformation of their specifications. Given a
program prog, we consider a partial correctness specification of the form
prog , where the assertions and are
predicates defined by a set Spec of possibly recursive Horn clauses with linear
arithmetic (LA) constraints in their premise (also called constrained Horn
clauses). The verification method consists in constructing a set PC of
constrained Horn clauses whose satisfiability implies that prog
is valid. We highlight some limitations of state-of-the-art
constrained Horn clause solving methods, here called LA-solving methods, which
prove the satisfiability of the clauses by looking for linear arithmetic
interpretations of the predicates. In particular, we prove that there exist
some specifications that cannot be proved valid by any of those LA-solving
methods. These specifications require the proof of satisfiability of a set PC
of constrained Horn clauses that contain nonlinear clauses (that is, clauses
with more than one atom in their premise). Then, we present a transformation,
called linearization, that converts PC into a set of linear clauses (that is,
clauses with at most one atom in their premise). We show that several
specifications that could not be proved valid by LA-solving methods, can be
proved valid after linearization. We also present a strategy for performing
linearization in an automatic way and we report on some experimental results
obtained by using a preliminary implementation of our method.Comment: To appear in Theory and Practice of Logic Programming (TPLP),
Proceedings of ICLP 201
Enhancing Predicate Pairing with Abstraction for Relational Verification
Relational verification is a technique that aims at proving properties that
relate two different program fragments, or two different program runs. It has
been shown that constrained Horn clauses (CHCs) can effectively be used for
relational verification by applying a CHC transformation, called predicate
pairing, which allows the CHC solver to infer relations among arguments of
different predicates. In this paper we study how the effects of the predicate
pairing transformation can be enhanced by using various abstract domains based
on linear arithmetic (i.e., the domain of convex polyhedra and some of its
subdomains) during the transformation. After presenting an algorithm for
predicate pairing with abstraction, we report on the experiments we have
performed on over a hundred relational verification problems by using various
abstract domains. The experiments have been performed by using the VeriMAP
transformation and verification system, together with the Parma Polyhedra
Library (PPL) and the Z3 solver for CHCs.Comment: Pre-proceedings paper presented at the 27th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur,
Belgium, 10-12 October 2017 (arXiv:1708.07854
Programming in logic without logic programming
In previous work, we proposed a logic-based framework in which computation is
the execution of actions in an attempt to make reactive rules of the form if
antecedent then consequent true in a canonical model of a logic program
determined by an initial state, sequence of events, and the resulting sequence
of subsequent states. In this model-theoretic semantics, reactive rules are the
driving force, and logic programs play only a supporting role.
In the canonical model, states, actions and other events are represented with
timestamps. But in the operational semantics, for the sake of efficiency,
timestamps are omitted and only the current state is maintained. State
transitions are performed reactively by executing actions to make the
consequents of rules true whenever the antecedents become true. This
operational semantics is sound, but incomplete. It cannot make reactive rules
true by preventing their antecedents from becoming true, or by proactively
making their consequents true before their antecedents become true.
In this paper, we characterize the notion of reactive model, and prove that
the operational semantics can generate all and only such models. In order to
focus on the main issues, we omit the logic programming component of the
framework.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Recommended from our members
AUnit - a testing framework for alloy
textWriting declarative models of software designs and analyzing them to detect defects is an effective methodology for developing more dependable software systems. However, writing such models correctly can be challenging for practitioners who may not be proficient in declarative programming, and their models themselves may be buggy. We introduce the foundations of a novel test automation framework, AUnit, which we envision for testing declarative models written in Alloy -- a first-order, relational language that is supported by its SAT-based analyzer. We take inspiration from the success of the family of xUnit frameworks that are used widely in practice for test automation, albeit for imperative or object-oriented programs. The key novelty of our work is to define a basis for unit testing for Alloy, specifically, to define the concepts of test case and test coverage as well as coverage criteria for declarative models. We reduce the problems of declarative test execution and coverage computation to partial evaluation without requiring SAT solving. Our vision is to blend how developers write unit tests in commonly used programming languages with how Alloy users formulate their models in Alloy, thereby facilitating the development and testing of Alloy models for both new Alloy users as well as experts. We illustrate our ideas using a small but complex Alloy model. While we focus on Alloy, our ideas generalize to other declarative languages (such as Z, B, ASM).Electrical and Computer Engineerin
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