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 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.

. 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 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...

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...

Approximate descriptions of the success set of a program have many uses in program development and optimisation. For untyped logic programming languages, regular approximation is a practical and useful tool. In this paper we consider the problem of approximating the meaning of programs in which some #polymorphic# type information is given. This situation can arise in constraint logic programming languages. In untyped languages the user could impose types on selected symbols. Even in strongly typed languages wemay be able to derive more precise descriptions of the meaning, or to consider restricted uses of polymorphic typed predicates. We propose a practical two-stage method: #rst the original program is transformed by replacing typed arguments by corresponding polymorphic type terms. For well-typed programs the resulting program is an abstraction of the original. Second, an established algorithm for regular approximation is applied to the transformed program. The algorithm is guaranteed to terminate without using arti#cial techniques such as depth-k bounds on #type# terms. The derived description combines polymorphic type terms, including union types, with regular descriptions of untyped terms. The method allows goal-dependent analysis as well as goal-independent analysis of a complete program. We show some experimental results demonstrating the speed and precision of the method and show that it scales up well when applied to larger programs.

. This paper proposes a tool to support reasoning about (partial) correctness of constraint logic programs. The tool infers a specification that approximates the semantics of a given program. The semantics of interest is an operational "call-success" semantics. The main intended application is program debugging. We consider a restricted class of specifications, which are regular types of constrained atoms. Our type inference approach is based on bottom-up abstract interpretation, which is used to approximate the declarative semantics (c-semantics). By using "magic transformations" we can describe the call-success semantics of a program by the declarative semantics of another program. We are focused on CLP over finite domains. Our prototype program analyzer works for the programming language CHIP. 1 Introduction and motivation In this paper we are interested in supporting reasoning about program correctness in the context of CLP (constraint logic programming). Speaking informally, a pr...

INTERPRETATION LUNJIN LU LIX Ecole Polytechnique 91128 Palaiseau Cedex France Abstract In this paper, we first introduce a notion of polymorphic abstract interpretation that formalises a polymorphic analysis as a generalisation of possibly infinitely many monomorphic analyses in the sense that the results of the monomorphic analyses can be obtained as instances of that of the polymorphic analysis. We then present a polymorphic type analysis of logic programs in terms of an abstract domain for polymorphic descriptions of type information and two operators on the abstract domain, namely the least upper bound operator and the abstract unification operator. The abstract domain captures type information more precisely than other abstract domains for similar purposes. The abstract unification operator for the polymorphic type analysis is designed by lifting the abstract unification operator for a monomorphic type analysis in logic programs, which simplifies the proof of the safeness of the...

Generic systems for the analysis of logic programs have been proposed over the last decade or so. Considerable progress has been made in terms of frameworks, algorithms, abstract domains and implementations. A number of generic top-down procedural frameworks are widely available. However, implementation e#orts for bottom-up declarative frameworks are in a preliminary stage. In this thesis

Regular types are a powerful tool for computing very precise descriptive types for logic programs. However, in the context of real-life, modular Prolog programs, the accurate results obtained by regular types often come at the price of efficiency. In this paper we propose a combination of techniques aimed at improving analysis efficiency in this context. As a first technique we allow optionally reducing the accuracy of inferred types by using only the types defined by the user or present in the libraries. We claim that, for the purpose of verifying type signatures given in the form of assertions the precision obtained using this approach is sufficient, and show that analysis times can be reduced significantly. Our second technique is aimed at dealing with situations where we would like to limit the amount of reanalysis performed, especially for library modules. Borrowing some ideas from polymorphic type systems, we show how to solve the problem by admitting parameters in type specifications. This allows us to compose new call patterns with some precomputed analysis info without losing any information. We argue that together these two techniques contribute to the practical and scalable analysis and verification of types in Prolog programs.