Moreno Falaschi

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.

Partial evaluation of functional logic programs

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. In this article, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. The method is formalized within the theoretical framework established by Lloyd and Shepherdson for the partial deduction of logic programs, which we have generalized for dealing with functional computations. A generic specialization algorithm is proposed which does not depend on the eager or lazy nature of the narrower being used. To the best of our knowledge, this is the first generic algorithm for the specialization of functional logic programs. We also discuss the relation to work on partial evaluation in functional programming, term-rewriting systems, and logic programming. Finally, we present some experimental results with an implementation of the algorithm which show in practice that the narrowing-driven partial evaluator effectively combines the propagation of partial data structures (by means of logical variables and unification) with better opportunities for optimization (thanks to the functional dimension).

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).

Specialization of lazy functional logic programs

Partial evaluation is a method for program specialization based on fold/unfold transformations [8, 25]. Partial evaluation of pure functional programs uses mainly static values of given data to specialize the program [15, 44]. In logic programming, the so-called static/dynamic distinction is hardly present, whereas considerations of determinacy and choice points are far more important for control [12]. We discuss these issues in the context of a (lazy) functional logic language. We formalize a two-phase specialization method for a non-strict, first order, integrated language which makes use of lazy narrowing to specialize the program w.r. t. a goal. The basic algorithm (first phase) is formalized as an instance of the framework for the partial evaluation of functional logic programs of [2, 3], using lazy narrowing. However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy. A post-processing renaming scheme (second phase) is necessary which we describe and illustrate on the well-known matching example. This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies. We show that our method preserves the lazy narrowing semantics and that the inclusion of simplification steps in narrowing derivations can improve control during specialization.

Suspension analyses for concurrent logic programs

Concurrent logic languages specify reactive systems which consist of collections of communicating processes. The presence of unintended suspended computations is a common programming error which is difficult to detect using standard debugging and testing techniques. We develop a number of analyses, based on abstract interpretation, which succeed if a program is definitely suspension free. If an analysis fails, the program may, or may not, be suspension free. Examples demonstrate that the analyses are practically useful. They are conceptually simple and easy to justify because they are based directly on the transition system semantics of concurrent logic programs. A naive analysis must consider all scheduling policies. However, it is proven that for our analyses it suffices to consider only one scheduling policy, allowing for efficient implementation.

Abstract Diagnosis of Functional Programs

We present a generic scheme for the declarative debugging of functional programs modeled as term rewriting systems. We associate to our programs a semantics based on a (continuous) immediate consequence operator, \( T_\mathcal{R} \), which models the (values/normal forms) semantics of \( \mathcal{R} \) . Then, we develop an effective debugging methodology which is based on abstract interpretation: by approximating the intended specification of the semantics of \( \mathcal{R} \) we derive a finitely terminating bottom-up diagnosis method, which can be used statically. Our debugging framework does not require the user to either provide error symptoms in advance or answer questions concerning program correctness. We have made available a prototypical implementation in Haskell and have tested it on some non trivial examples.

Narrowing-Driven Partial Evaluation of Functional Logic Programs

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. Formal methods of transformation of functional logic programs can be based on this well-established operational semantics. In this paper, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs. We illustrate our method with several examples and discuss the relation with Supercompilation and Partial Evaluation. To the best of our knowledge, this is the first formal approach to partial evaluation of functional logic programs.

Automatic verification of timed concurrent constraint programs

The language Timed Concurrent Constraint (tccp) is the extension over time of the Concurrent Constraint Programming (cc) paradigm that allows us to specify concurrent systems where timing is critical, for example reactive systems. Systems which may have an infinite number of states can be specified in tccp. Model checking is a technique which is able to verify finite-state systems with a huge number of states in an automatic way. In the last years several studies have investigated how to extend model checking techniques to systems with an infinite number of states. In this paper we propose an approach which exploits the computation model of tccp. Constraint based computations allow us to define a methodology for applying a model checking algorithm to (a class of) infinite-state systems. We extend the classical algorithm of model checking for LTL to a specific logic defined for the verification of tccp and to the tccp Structure which we define in this work for modeling the program behavior. We define a restriction on the time in order to get a finite model and then we develop some illustrative examples. To the best of our knowledge this is the first approach that defines a model checking methodology for tccp.

Compositional analysis for concurrent constraint programming

A framework for the analysis of concurrent constraint programming (CCP) is proposed. The approach is based on simple denotational semantics that approximate the usual semantics in the sense that they give a superset of the input-output relation of a CCP program. Analyses based on these semantics can be easily and efficiently implemented using standard techniques from the analysis of logic programs.<<ETX>>

A synchronization logic: Axiomatics and formal semantics of generalized horn clauses

An extension of Horn clause logic is defined based on the introduction of a synchronization operator. Generalized Horn clauses (GHC) are introduced through an informal description of their operational semantics, which allows discussion of some typical synchronization problems. GHC are first considered formally as a programming language by defining the syntax, the operational semantics, the model-theoretic semantics, and the fixed-point semantics. The above mentioned semantics are given in the Van Emden-Kowalski style (1976, J. Assoc. Comput. Mach. 23, 733–742) and are proved equivalent. GHC are then characterized as axiomatic theories. A set of axiom schemata concerned with the newly introduced synchronization operator is defined and it is proved that the operational semantics inference rule is both sound and complete. Finally, the relation between GHC and Horn clauses is analyzed, and it is proved that Horn clause logic is strictly included in the generalized Horn clause logic.