Catuscia Palamidessi

Declarative modeling of the operational behavior of logic languages

Abstract The paper defines a new declarative semantics for logic programs, which is based on interpretations containing (possibly) non-ground atoms. Two different interpretations are introduced and the corresponding models are defined and compared. The classical results on the Herbrand model semantics of logic programs are shown to hold in the new models too (i.e. existence of a minimal model, fixpoint characterization, etc.). With the new models, we have a stronger soundness and completeness result for SLD-resolution. In particular, one of the two models allows the set of computed answer substitutions to be characterized precisely.

Comparing the expressive power of the synchronous and the asynchronous π-calculus

The Asynchronous ¿-calculus, as recently proposed by Boudol and, independently, by Honda and Tokoro, is a subset of the ¿-calculus which contains no explicit operators for choice and output-prefixing. The communication mechanism of this calculus, however, is powerful enough to simulate output-prefixing, as shown by Boudol, and input-guarded choice, as shown recently by Nestmann and Pierce. A natural question arises, then, whether or not it is possible to embed in it the full ¿-calculus. We show that this is not possible, i.e. there does not exist any uniform, parallel-preserving, translation from the ¿-calculus into the asynchronous ¿-calculus, up to any reasonable notion of equivalence. This result is based on the incapablity of the asynchronous ¿-calculus of breaking certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the ¿-calculus and CCS.

Kernel-LEAF: a logic plus functional language

Abstract Kernel-LEAF is a logic plus functional language based on the flattening technique. It differs from other similar languages because it is able to cope with partial (undefined or non-terminating) functions. This is achieved by introducing the distinction between data structures and (functional) term structures, and by using two kinds of equality. The language has a clean model-theoretic semantics, where the domains of the interpretations are the algebraic CPOs. In these domains the difference between the two equalities corresponds to a different behaviour with respect to continuity. The operational semantics (based on SLD-resolution) is proved sound and complete with respect to the model-theoretic one. Finally, an outermost strategy, more efficient than unrestricted SLD-resolution, but still complete, is presented.

A model-theoretic reconstruction of the operational semantics of logic programs

Abstract In this paper we define a new notion or truth on Herbrand interpretations extended with variables which allows us to capture, by means of suitable models, various observable properties, such as the ground success set, the set of atomic consequences, and the computed answer substitutions. The notion of truth extends the classical one to account for non-ground formulas in the interpretations. The various operational semantics are all models. An ordering on interpretations is defined to overcome the problem that the intersection of a set of models is not necessarily a model. The set of interpretations with this partial order is shown to be a complete lattice, and the greatest lower bound of any set of models is shown to be a model. Thus there exists a least model, which is the least Herbrand model and therefore the ground success set semantics. Richer operational semantics are non-least models, which can, however, be effectively defined by fixpoint constructions. The model corresponding to the computed answer substitutions operational semantics is the most primitive one (the others can easily be obtained from it).

Algebraic properties of idempotent substitutions

This paper presents an algebra of idempotent substitutions whose operations have many properties. We provide an algorithm to compute these operations and we show how they are related to the standard composition. The theory of Logic Programming can be rewritten in terms of these new operations. The advantages are that both the operational and the declarative semantics of Horn Clause Logic can be formalized in a compositional way and the proofs of standard results, like the switching lemma, get easier and more intuitive. Moreover, this formalization can be naturally extended to a parallel computational model, and therefore it can be regarded as a basis for a theory of concurrent logic programming.

SOFSEM 2009: Theory and Practice of Computer Science

SOFSEM 2009: Theory and Practice of Computer Science: 35thnConference on Current Trends in Theory and Practice of ComputernScience : Spindlerův Mlýn, Czech Republic, January 2009,nProceedings of the Conference

Proving concurrent constraint programs correct

We introduce a simple compositional proof system for proving (partial) correctness of concurrent constraint programs (CCP). The proof system is based on a denotational approximation of the strongest postcondition semantics of CCP programs. The proof system is proved to be correct for full CCP and complete for the class of programs in which the denotational semantics characterizes exactly the strongest postcondition. This class includes the so-called confluent CCP, a special case of which is constraint logic programming with dynamic scheduling.

Complementation in abstract interpretation

Reduced product of abstract domains is a rather well-known operation for domain composition in abstract interpretation. In this article, we study its inverse operation, introducing a notion of domain complementation in abstract interpretation. Complementation provides as systematic way to design new abstract domains, and it allows to systematically decompose domains. Also, such an operation allows to simplify domain verification problems, and it yields space-saving representations for complex domains. We show that the complement exists in most coses, and we apply complementation to three well-know abstract domains, notably to Cousot and Cousots interval domain for integer variable analysis, to Cousot and Cousots domain for comportment analysis of functional languages, and to the domain Sharing for aliasing analysis of logic languages.

Nondeterminism and infinite computations in constraint programming

We investigate the semantics of concurrent constraint programming and of various sublanguages, with particular emphasis on nondeterminism and infinite behavior. The aim is to find out what is the minimal structure which a domain must have in order to capture these two aspects. We show that a notion of observables, obtained by the upward-closure of the results of computations, is relatively easy to model even in presence of synchronization. On the contrary, modeling the exact set of results is problematic, even for the simple sublanguage of constraint logic programming. We show that most of the standard topological techniques fail in capturing this more precise notion of observables. The analysis of these failed attempts leads us to consider a categorical approach.

On the Expressiveness of Linearity vs Persistence in the Asychronous Pi-Calculus

We present an expressiveness study of linearity and persistence of processes. We choose the pi-calculus, one of the main representatives of process calculi, as a framework to conduct our study. We consider four fragments of the pi-calculus. Each one singles out a natural source of linearity/persistence also present in other frameworks such as concurrent constraint programming (CCP), linear CCP, and several calculi for security. The study is presented by providing (or proving the non-existence of) encodings among the fragments, a processes-as-formulae interpretation and a reduction from, Minsky machines