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.

This article considers static analysis based on abstract interpretation of logic programs over combined domains. It is known that analyses over combined domains provide more information potentially than obtained by the independent analyses. However, the construction of a combined analysis often requires redefining the basic operations for the combined domain. A practical ap-proach to maintain precision in combined analyses of logic programs which reuses the individual analyses and does not redefine the basic operations is illustrated, The advantages of the approach are that (1) proofs of correctness for the new domains are not required and (2) implementations can be reused. The approach is demonstrated by showing that a combined sharing analysis — constructed from “old” proposals — compares well with other “new” proposals suggested in recent

This paper describes a semantic basis for a compositional approach to the analysis of logic programs. A logic program is viewed as consisting of a set of modules, each module defining a subset of the program's predicates. Analyses are constructed by considering abstract interpretations of a compositional semantics. The abstract meaning of a module corresponds to its analysis and composition of abstract meanings corresponds to composition of analyses. Such an approach is essential for large program development so that altering one module does not require re-analysis of the entire program. A compositional analysis for ground dependencies is included to illustrate the approach. To the best of our knowledge this is the first account of a compositional framework for the analysis of (logic) programs. 1 Introduction It is widely acknowledged that as the size of a program increases, it becomes impractical to maintain it as a single monolithic structure. Instead, the program has to be...

This paper presents a new notion of typing for logic programs which generalizes the notion of directional types. The generation of type dependencies for a logic program is fully automatic with respect to a given domain of types. The analysis method is based on a novel combination of program abstraction and ACI-unification which is shown to be correct and optimal. Type dependencies are obtained by abstracting programs, replacing concrete terms by their types, and evaluating the meaning of the abstract programs using a standard semantics for logic programs enhanced by ACI-unification. This approach is generic and can be used with any standard semantics. The method is both theoretically clean and easy to implement using general purpose tools. The proposed domain of types is condensing which means that analyses can be carried out in both top-down or bottom-up frameworks with no loss of precision for goal-independent analyses. The proposed method has been fully implemented within a bottom-up approach and the experimental results are promising.

The constraint logic programming paradigm CLP(X) (CLP for short) has been proposed by Jaffar and Lassez in order to integrate a generic computational mechanism based on constraints with the logic programming framework. This paradigm retains the semantic properties of logic languages, namely the existence of equivalent operational, model theoretic and fixpoint semantics. Moreover, since computation is performed over the particular domain of computation X , CLP(X) programs have an equivalent "algebraic" semantics, i.e. a semantics which is defined directly on the algebraic structure of the domain X . In this paper we propose an extension of such a semantics, for the success set case, in order to fully characterize the operational behaviour of programs. We introduce a framework for defining various notions of models, each corresponding to a specific operationally observable property. The construction is based on a new notion of interpretation (set of constrained atoms), on a natural exten...

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 ...

. This paper illustrates the application of abstract compilation using multiple incarnations of the domain Prop in deriving type dependencies for logic programs. We illustrate how dependencies can be derived in the presence of both monomorphic and polymorphic type information. Type dependencies generalize the recently proposed notion of directional types as well as the more common notion of groundness dependencies. Directional types have proven useful in a number of applications such as in proving termination. These applications, however, are based on type declarations. The main contribution of this paper is in the simplicity in which non-trivial type dependencies are inferred using abstract compilation and by associating each type with an incarnation of Prop. We illustrate the use of a semantics for open logic programs in maintaining space efficient analyses. Time efficiency is also maintained due to approximation of the type domain in a boolean lattice calling on results of universal...

The goal of this paper is to construct a semantic basis for the abstract interpretation of Prolog programs. Prolog is a well-known logic programming language which applies a depth-first search strategy in order to provide a practical approximation of Horn clause logic. While pure logic programming has clean fixpoint, model-theoretic and operational semantics the situation for Prolog is different. Difficulties in capturing the declarative meaning of Prolog programs have led to various semantic definitions which attempt to encode the search strategy in different mathematical frameworks. However semantic based analyses of Prolog are typically achieved by abstracting the more simple but less precise declarative semantics of pure logic Programs. We propose instead to model Prolog control in a simple constraint logic language which is presented together with its declarative and operational semantics. This enables us to maintain the usual approach to declarative semantics of logic programs wh...

The declarative semantics of definite logic programs is the basis of an elegant and practical framework for their static analysis. We define a core semantics parameterised by a preinterpretation of the language underlying the program. The concrete semantics is given by an extended Herbrand interpretation, capturing the correct answers of a program. The semantics is computed as the least fixed point of an immediate consequences operator. An abstract semantics is specified simply by giving, for each constant and function in the program, a denotation in an abstract domain of interpretation. No abstract operations such as abstract unification need to be defined. The directness and simplicity of this approach is then illustrated by specifying and implementing a number of abstract interpretations. These include various mode analyses, analyses on the structure of lists and the length of lists, and simple and polymorphic types. The implementations used for the experiments are based on abstract...