Abstract interpretation is a theory of semantics approximation which is usedfor the construction of semantics-basedprogram analysis algorithms (sometimes called“data flow analysis”), the comparison of formal semantics (e.g., construction of a denotational semantics from an operational one), the design of proof methods, etc. Automatic program analysers are used for determining statically conservative approximations of dynamic properties of programs. Such properties of the run-time behavior of programs are useful for debugging (e.g., type inference), code optimization (e.g., compile-time garbage collection, useless occur-check elimination), program transformation (e.g., partial evaluation, parallelization), andeven program correctness proofs (e.g., termination proof). After a few simple introductory examples, we recall the classical framework for abstract interpretation of programs. Starting from a standardoperational semantics formalizedas a transition system, classes of program properties are first encapsulatedin collecting semantics expressedas fixpoints on partial orders representing concrete program properties. We consider invariance properties characterizing the descendant states of the initial states (corresponding to top/down or forward analyses), the ascendant states of the final states (corresponding to bottom/up or backward analyses) as well as a combination

The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis.

Interpretation of Logic Programs Roberto Barbuti , Roberto Giacobazzi , Giorgio Levi Dipartimento di Informatica Universit`a di Pisa Corso Italia 40, 56125 Pisa fbarbuti,giaco,levig@di.unipi.it in ACM Transactions on Programming Languages and Systems Vol 15, January 1993 Abstract The theory of abstract interpretation provides a formal framework to develop advanced dataflow analysis tools. The idea is to define a non-standard semantics which is able to compute, in finite time, an approximated model of the program. In this paper we define an abstract interpretation framework based on a fixpoint approach to the semantics. This leads to the definition, by means of a suitable set of operators, of an abstract fixpoint characterization of a -model associated with the program. Thus, we obtain a specializable abstract framework for bottom-up abstract interpretations of definite logic programs. The specialization of the framework is shown on two examples, namely ground dependence analysis and depth-k analysis.

Abstract This paper presents a formal framework for the bottom-up abstract interpretation of logic programs which can be applied to approximate answer substitutions, partial an- swer substitutions and call patterns for a given program and arbitrary initial goal. The framework is based on a T P like semantics defined over a Herbrand universe with vari-ables which has previously been shown to determine the answer substitutions for arbitrary initial goals. The first part of the paper reconstructs this semantics to provide a more adequate basis for abstract interpretation. A notion of abstract substitution is introduced and shown to determine an abstract semantic function which for a given program can be applied to approximate the answer substitutions for an arbitrary initial goal.

We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. The idea is to abstract away from standard semantic objects by focusing on the general properties of any --possibly non-standard -- semantic definition. In constraint logic programming, this corresponds to a suitable definition of the constraint system supporting the semantic definition. An algebraic structure is introduced to formalize the notion of a constraint system, thus making classical mathematical results applicable. Both top-down and bottom-up semantics are considered. Non-standard semantics for constraint logic programs can then be formally specified using the same techniques used to define standard semantics. Different nonstandard semantics for constraint logic languages can be specified in this ...

We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. "Generalized semantics" abstract away from standard semantics objects, by focusing on the general properties of any (possibly non-standard) semantics definition. In constraint logic programming, this corresponds to a suitable definition of the constraint system supporting the semantics definition. An algebraic structure is introduced to formalize the constraint system notion, thus making applicable classical mathematical results and both a top-down and bottom-up semantics are considered. Non-standard semantics for CLP can then be formally specified by means of the same techniques used to define standard semantics. Different non-standard semantics for constraint logic languages can be specified in this framework: e.g. abstract interpretation, machine level traces and any computation based on an instance of the constraint system.

In this paper we propose a denotational semantics for Prolog and an approach to the abstract interpretation of Prolog programs; we deal with the control rules of Prolog and the cut operator. Moreover, we get a simple denotation for negation as finite failure. The abstract analysis is proposed both for computed answers analysis and for call patterns analysis. In both cases the abstract semantics is finitely computable. Two examples show the usefulness of our approach for the analysis of Prolog programs. 1 Introduction A semantics can be useful as a tool for program understanding, as a tool for defining an equivalence relation between programs (in relation to program transformations), or as a tool for program analysis. The latter is our main interest. The first question to be answered is why we look for a new semantics of a subset of Prolog (more precisely, of Prolog without database and set operations). There exist many formalizations for subsets of Prolog, and there exists even a for...

This paper proposes to specify semantic definitions for logic programming languages such as Prolog in terms of an oracle which specifies the control strategy and identifies which clauses are to be applied to resolve a given goal. The approach is quite general. It is applicable to Prolog to specify both operational and declarative semantics as well as other logic programming languages. Previous semantic definitions for Prolog typically encode the sequential depth-first search of the language into various mathematical frameworks. Such semantics mimic a Prolog interpreter in the sense that following the "leftmost" infinite path in the computation tree excludes computation to the right of this path from being considered by the semantics. The basic idea in this paper is to abstract away from the sequential control of Prolog and to provide a declarative characterization of the clauses to apply to a given goal. The decision whether or not to apply a clause is viewed as a query to an oracle wh...

ing Synchronization in Concurrent Constraint Programming ? Enea Zaffanella 1 Roberto Giacobazzi 2 Giorgio Levi 1 1 Dipartimento di Informatica, Universit`a di Pisa Corso Italia 40, 56125 Pisa (zaffanel,levi)@di.unipi.it 2 LIX, Laboratoire d'Informatique, ' Ecole Polytechnique 91128 Palaiseau cedex giaco@lix.polytechnique.fr Abstract. Because of synchronization based on blocking ask, some of the most important techniques for data flow analysis of (sequential) constraint logic programs (clp) are no longer applicable to cc languages. In particular, the generalized approach to the semantics, intended to factorize the (standard) semantics so as to make explicit the domain-dependent features (i.e. operators and semantic objects which may be influenced by abstraction) becomes useless for relevant applications. A possible solution to this problem is based on a more abstract (non-standard) semantics: the success semantics, which models non suspended computations only. With a program tr...

: A sound and complete semantics is given for sequential, depth-first logic programming with a version of negation as failure. The semantics is logical in the sense that it is built up only from valuation functions (multi-valued logic interpretations in the style of Fitting and Kunen) and logically-motivated equivalence relations between formulas. The notion of predicate folding and unfolding with respect to a program (Tamaki, Sato, Levi et al.) and the universal notion of "disjunctive unfolding" (Andrews) are important elements of this semantics. The negation used is the version which returns an error indication whenever it is invoked on a non-ground goal. It is theoretically interesting that this form of negation, along with the left-to-right processing of depth-first logic programming, can be characterized logically with four-valued interpretations over an extended alphabet of terms. The fourth truth value, N , can be read operationally as "floundering on negation". The extension of...