Soundness, idempotence and commutativity of set-sharing

It is important that practical data-flow analyzers are backed by reliably proven theoretical results. Abstract interpretation provides a sound mathematical framework and necessary generic properties for an abstract domain to be well-defined and sound with respect to the concrete semantics. In logic programming, the abstract domain Sharing is a standard choice for sharing analysis for both practical work and further theoretical study. In spite of this, we found that there were no satisfactory proofs for the key properties of commutativity and idempotence that are essential for Sharing to be well-defined and that published statements of the soundness of Sharing assume the occurs-check. This paper provides a generalization of the abstraction function for Sharing that can be applied to any language, with or without the occurs-check. Results for soundness, idempotence and commutativity for abstract unification using this abstraction function are proven

A correct, precise and efficient integration of set-sharing, freeness and linearity for the analysis of finite and rational tree languages

It is well known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper, we present a novel combination of set-sharing with freeness and linearity information, which is characterized by an improved abstract unification operator. We provide a new abstraction function and prove the correctness of the analysis for both the finite tree and the rational tree cases. Moreover, we show that the same notion of redundant information as identified in Bagnara et al. (2000) and Zaffanella et al. (2002) also applies to this abstract domain combination: this allows for the implementation of an abstract unification operator running in polynomial time and achieving the same precision on all the considered observable properties

Abstract Analysis of Universal Properties for tccp

[EN] The Timed Concurrent Constraint Language (tccp) is a time extension of the concurrent constraint paradigm of Saraswat. tccp was defined to model reactive systems, where infinite behaviors arise naturally. In previous works, a semantic framework and abstract diagnosis method for the language has been defined. On the basis of that semantic framework, this paper proposes an abstract semantics that, together with a widening operator, is suitable for the definition of different analyses for tccp programs. The abstract semantics is correct and can be represented as a finite graph where each node represents a hypothetical computational step of the program containing approximated information for the variables. The widening operator allows us to guarantee the convergence of the abstract fixpoint computation.This work has been supported by the Andalusian Excellence Project P11-TIC7659. This work has been partially supported by the EU (FEDER) and the Spanish MINECO under grant TIN 2013-45732-C4-1-P (DAMAS) and by Generalitat Valenciana PROMETEOII/2015/013Comini, M.; Gallardo Melgarejo, MDM.; Titolo, L.; Villanueva, A. (2015). Abstract Analysis of Universal Properties for tccp. Lecture Notes in Computer Science. 163-178. https://doi.org/10.1007/978-3-319-27436-2_10S163178Alpuente, M., Gallardo, M.M., Pimentel, E., Villanueva, A.: A semantic framework for the abstract model checking of tccp programs. Theor. Comput. Sci. 346(1), 58–95 (2005)Bagnara, R., Hill, P.M., Ricci, E., Zaffanella, E.: Precise widening operators for convex polyhedra. Sci Comput. Program. 58(1–2), 28–56 (2005)Comini, M., Titolo, L., Villanueva, A.: Abstract diagnosis for timed concurrent constraint programs. Theor. Pract. Log. Program. 11(4–5), 487–502 (2011)Comini, M., Titolo, L., Villanueva, A.: A condensed goal-independent bottom-up fixpoint modeling the behavior of tccp. Technical report, DSIC, Universitat Politècnica de València (2013). http://riunet.upv.es/handle/10251/34328Cousot, P., Cousot, R.: Abstract Interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the 4th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, Los Angeles, California, January 17–19, pp. 238–252. ACM Press, New York (1977)de Boer, F.S., Gabbrielli, M., Meo, M.C.: A timed concurrent constraint language. Inf. Comput. 161(1), 45–83 (2000)Falaschi, M. Gabbrielli, M., Marriott, K., Palamidessi, C.: Compositional analysis for concurrent constraint programming. In: Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science, pp. 210–221. IEEE Computer Society Press, Los Alamitos (1993)Falaschi, M., Olarte, C., Palamidessi, C.: Abstract interpretation of temporal concurrent constraint programs. Theor. Pract. Log. Program. (TPLP) 15(3), 312–357 (2015)Falaschi, M., Villanueva, A.: Automatic verification of timed concurrent constraint programs. Theor. Pract. Log. Program. 6(3), 265–300 (2006)Saraswat, V.A.: Concurrent Constraint Programming. The MIT Press, Cambridge (1993)Zaffanella, E., Giacobazzi, R., Levi, G.: Abstracting synchronization in concurrent constraint programming. J. Funct. Log. Program. 6, 1997 (1997

Multivariant Assertion-based Guidance in Abstract Interpretation

Approximations during program analysis are a necessary evil, as they ensure essential properties, such as soundness and termination of the analysis, but they also imply not always producing useful results. Automatic techniques have been studied to prevent precision loss, typically at the expense of larger resource consumption. In both cases (i.e., when analysis produces inaccurate results and when resource consumption is too high), it is necessary to have some means for users to provide information to guide analysis and thus improve precision and/or performance. We present techniques for supporting within an abstract interpretation framework a rich set of assertions that can deal with multivariance/context-sensitivity, and can handle different run-time semantics for those assertions that cannot be discharged at compile time. We show how the proposed approach can be applied to both improving precision and accelerating analysis. We also provide some formal results on the effects of such assertions on the analysis results.Comment: Pre-proceedings paper presented at the 28th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt am Main, Germany, 4-6 September 2018 (arXiv:1808.03326

Concurrent and Reactive Constraint Programming

The Italian Logic Programming community has given several contributions to the theory of Concurrent Constraint Programming. In particular, in the topics of semantics, verification, and timed extensions. In this paper we review the main lines of research and contributions of the community in this fiel

Strategic directions in constraint programming

An abstract is not available

Speeding up Static Analysis with the Split Operator

In the context of static analysis based on Abstract Interpretation, we propose a new abstract operator modeling the split of control flow paths: The goal of the operator is to enable a more efficient analysis when using abstract domains that are computationally expensive, having no effect on precision. Focusing on the case of conditional branches guarded by numeric linear constraints, we provide a preliminary experimental evaluation showing that, by using the split operator, we can achieve significant efficiency improvements for a static analysis based on the domain of convex polyhedra. We also briefly discuss the applicability of this new operator to different, possibly non-numeric abstract domains

Reverse engineering with P-stable abstractions

The analysis of legacy systems such as electro-mechanical circuits requires the extraction of the underlying specification from a high level point of view. We consider P-stable abstraction, an analysis for transition systems that synthesizes the properties of a given set of events in terms of their eventual and stable effects on the system state. The abstract transitions simulate convergent runs of the concrete model and correspond to a set of temporal properties which are satisfied. We show an application of the P-stable abstraction on a relay-based circuit, showing its ability to extract a high level description of the implemented behaviour