We propose a novel formalism, called Frame Logic (abbr., F-logic), that accounts in a clean and declarative fashion for most of the structural aspects of object-oriented and frame-based languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, encapsulation, and others. In a sense, F-logic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts that come from object-oriented programming have direct representation in F-logic; other, secondary aspects of this paradigm are easily modeled as well. The paper also discusses semantic issues pertaining to programming with a deductive object-oriented language based on a subset of F-logic.

A practical procedure for computing a regular approximation of a logic program is given. Regular approximations are useful in a variety of tasks in debugging, program specialisation and compile-time optimisation. The algorithm shown here incorporates optimisations taken from deductive database fixpoint algorithms and efficient bottom-up abstract interpretation techniques. Frameworks for defining regular approximations have been put forward in the past, but the emphasis has usually been on theoretical aspects. Our results contribute mainly to the development of effective analysis tools that can be applied to large programs. Precision of the approximation can be greatly improved by applying query-answer transformations to a program and a goal, thus capturing some argument dependency information. A novel technique is to use transformations based on computation rules other than left-to-right to improve precision further. We give performance results for our procedure on a range of programs. 1

In program analysis, a key notion used to approximate the meaning of a program is that of ignoring inter-variable dependencies. We formalize this notion in logic programming in order to define an approximation to the meaning of a program. The main result proves that this approximation is not only recursive, but that it can be finitely represented in the form of a cyclic term graph. This explicit representation can be used as a starting point for logic program analyzers. A preliminary version appears in the Proceedings, 17 th ACM Symposium on POPL. y School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213-3890 z IBM Thomas J. Watson Research Center, PO Box 218, Yorktown Heights, NY 10598 Section 1: Introduction 1 1 Introduction The problem at hand is: given a logic program, obtain an approximation of its meaning, that is, obtain an approximation of its least model. The definition of the approximation should be declarative (so that results can be proved ab...

. Set constraints are a natural formalism for many problems that arise in program analysis. This paper provides a brief introduction to set constraints: what set constraints are, why they are interesting, the current state of the art, open problems, applications and implementations. 1 Introduction Set constraints are a natural formalism for describing relationships between sets of terms of a free algebra. A set constraint has the form X ` Y , where X and Y are set expressions. Examples of set expressions are 0 (the empty set), ff (a set-valued variable), c(X; Y ) (a constructor application), and the union, intersection, or complement of set expressions. Recently, there has been a great deal of interest in program analysis algorithms based on solving systems of set constraints, including analyses for functional languages [AWL94, Hei94, AW93, AM91, JM79, MR85, Rey69], logic programming languages [AL94, HJ92, HJ90b, Mis84], and imperative languages [HJ91]. In these algorithms, sets of...

We investigate the relationship between set constraints and the monadic class of first-order formulas and show that set constraints are essentially equivalent to the monadic class. From this equivalence we can infer that the satisfiability problem for set constraints is complete for NEXPTIME. More precisely, we prove that this problem has a lower bound of NTIME(c n= log n ). The relationship between set constraints and the monadic class also gives us decidability and complexity results for certain practically useful extensions of set constraints, in particular "negative projections" and subterm equality tests.

. Set constraints are relations between sets of terms. They have been used extensively in various applications in program analysis and type inference. We present several results on the computational complexity of solving systems of set constraints. The systems we study form a natural complexity hierarchy depending on the form of the constraint language. 1 Introduction Systems of set constraints have received considerable attention as a formalism for expressing algorithms in program analysis and type inference. Many algorithms based on set constraints have been proposed and implemented, but very little is known about the computational complexity of solving systems of set constraints. In this paper we present complexity results for a natural hierarchy of decision problems involving set constraints. Set constraints are formal inclusions between expressions representing subsets of T \Sigma , the set of ground terms over a finite ranked alphabet \Sigma . A positive set constraint is an in...

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A set constraint is of the form exp 1 ' exp 2 where exp 1 and exp 2 are set expressions constructed using variables, function symbols, projection symbols, and the set union, intersection and complement symbols. While the satisfiability problem for such constraints is open, restricted classes have been useful in program analysis. The main result herein is a decision procedure for definite set constraints which are of the restricted form a ' exp where a contains only constants, variables and function symbols, and exp is a positive set expression (that is, it does not contain the complement symbol). A conjunction of such constraints, whenever satisfiable, has a least model and the algorithm will output an explicit representation of this model. 1 1 Introduction We consider a formalism for elementary set algebra which is useful for describing properties of programs whose underlying domain of computation is a Herbrand universe. The domain of discourse for this formalism is the powerset of...

Regular tree expressions are a natural formalism for describing the sets of tree-structured values that commonly arise in programs; thus, they are well-suited to applications in program analysis. We describe an implementation of regular tree expressions and our experience with that implementation in the context of the FL type system. A combination of algorithms, optimizations, and fast heuristics for computationally difficult problems yields an implementation efficient enough for practical use. 1 Introduction Regular tree expressions are a natural formalism for describing the sets of tree-structured values that commonly arise in programs. As such, several researchers have proposed using (variations on) regular tree expressions in type inference and program analysis algorithms [JM79, Mis84, MR85, HJ90, HJ91, AM91]. We are not aware of any implementations based on regular tree expressions, however, except for our own work on type analysis for the functional language FL [B + 89]. A p...

We present an algorithm for automatic type checking of logic programs with respect to directional types that describe both the structure of terms and the directionality of predicates. The type checking problem is reduced to a decidable problem on systems of inclusion constraints over set expressions. We discuss some properties of the reduction algorithm, complexity, and present a proof of correctness. 1 1 Introduction Most logic programming languages are untyped. In Prolog, for example, it is considered meaningful to apply any n-ary predicate to any n-tuple of terms. However, it is generally accepted that static type checking has great advantages in detecting programming errors early and for generating efficient executable code. Motivated at least in part by the success of type systems for procedural and functional languages, there is currently considerable interest in finding appropriate definitions of type and welltyping for logic languages. This paper explores the type checki...