Program Verification using Constraint Handling Rules and Array Constraint Generalizations^*

Issue title: Special Issue on the 29th Italian Conference on Computational Logic: CILC 2014

Guest editors: Laura Giordano, Valentina Gliozzi, Alberto Pettorossi and Gian Luca Pozzato

Article type: Research Article

Authors: De Angelis, Emanuele^a | Fioravanti, Fabio^b | Pettorossi, Alberto^{c; †} | Proietti, Maurizio^d

Affiliations: [a] University of Chieti-Pescara, Viale Pindaro 42, 65127, Pescara, Italy. emanuele.deangelis@unich.it | [b] University of Chieti-Pescara, Viale Pindaro 42, 65127, Pescara, Italy. fabio.fioravanti@unich.it | [c] University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy. pettorossi@info.uniroma2.it; adp@iasi.cnr.it | [d] IASI-CNR, Via dei Taurini 19, 00185 Rome, Italy. maurizio.proietti@iasi.cnr.it

Correspondence: [†] Address for correspondence: University of Rome Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy

Note: [*] This work has been partially supported by the National Group of Computing Science (GNCS-INDAM). E. De Angelis, F. Fioravanti, and A. Pettorossi are research associates at IASI-CNR, Rome, Italy.

Abstract: The transformation of constraint logic programs (CLP programs) has been shown to be an effective methodology for verifying properties of imperative programs. By following this methodology, we encode the negation of a partial correctness property of an imperative program prog as a predicate incorrect defined by a CLP program T, and we show that prog is correct by transforming T into the empty program (and thus incorrect does not hold) through the application of semantics preserving transformation rules. We can also show that prog is incorrect by transforming T into a program with the fact incorrect (and thus incorrect does hold). Some of the transformation rules perform replacements of constraints that are based on properties of the data structures manipulated by the program prog. In this paper we show that Constraint Handling Rules (CHR) are a suitable formalism for representing and applying constraint replacements during the transformation of CLP programs. In particular, we consider programs that manipulate integer arrays and we present a CHR encoding of a constraint replacement strategy based on the theory of arrays. We also propose a novel generalization strategy for constraints on integer arrays that combines CHR constraint replacements with various generalization operators on integer constraints, such as widening and convex hull. Generalization is controlled by additional constraints that relate the variable identifiers in the imperative program prog and the CLP representation of their values. The method presented in this paper has been implemented and we have demonstrated its effectiveness on a set of benchmark programs taken from the literature.

Keywords: Constraint Handling Rules, Constraint logic programming, Program transformation, Program verification

DOI: 10.3233/FI-2017-1461

Journal: Fundamenta Informaticae, vol. 150, no. 1, pp. 73-117, 2017