Eyal Yardeni

Logic programs as types for logic programs

Optimistic type systems for logic programs are considered. In such systems types are conservative approximations to the success set of the program predicates. The use of logic programs to describe types is proposed. It is argued that this approach unifies the denotational and operational approaches to descriptive type systems and is simpler and more natural than previous approaches. The focus is on the use of unary-predicate programs to describe the types. A proper class of unary-predicate programs is identified, and it is shown that it is expensive enough to express several notions of types. An analogy with two-way automata and a correspondence with alternating algorithms are used to obtain a complexity characterization of type inference and type checking. This characterization is facilitated by the use of logic programs to represent types.<<ETX>>

Bottom-up abstract interpretation of logic programs

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 answer substitutions and call patterns for a given program and arbitrary initial goal. The framework is based on a Tp-like semantics defined over a Herbrand universe with variables 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 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. The second part of the paper extends the bottom-up approach to provide approximations of both partial answer substitutions and call patterns. This is achieved by applying Magic Sets and other existing techniques to transform a program in such a way that the answer substitutions of the transformed program correspond to the partial answer substitutions and call patterns of the original program. This facilitates the analysis of concurrent logic programs (ignoring synchronization) and provides a collecting semantics which characterizes both success and call patterns.

A type system for logic program

Abstract A theory for a type system for logic programs is developed which addressesthe question of well-typing, type inference, and compile-time and run-time type checking. A type is a recursively enumerable set of ground atoms, which is tuple-distributive. The association of a type to a program is intended to mean that only ground atoms that are elements of the type may be derived from the program. A declarative definition of well-typed programs is formulated, based on an intuitive approach related to the fixpoint semantics of logic programs. Whether a program is well typed is undecidable in general. We define a restricted class of types, called regular types, for which type checking is decidable. Regular unary logic programs are proposed as a specification language for regular types. An algorithm for type-checking a logic program with respect to a regular type definition is described, and its complexity is analyzed. Finally, the practicality of the type system is discussed, and some examples are shown. The type system has been implemented in FCP for FCP and is incorporated in the Logix system.

The languages FCP(:) and FCP(:,?)

The language FCP(:,?) is the outcome of attempts to integrate the best of several flat concurrent logic programming languages, including Flat GHC, FCP (↓, |) and Flat Concurrent Prolog, in a single consistent framework. FCP(:) is a subset of FCP(:, ?), which is a variant of FPP(↓, |) and employs concepts of the concurrent constraint framework of cc(↓, |). FCP(:, ?) is a language which is strong enough to accommodate all useful concurrent logic programming techniques, including those which rely on atomic test unification and read-only variables, yet incorporates the weaker languages mentioned as subsets. This allows the programmer to remain within a simple subset of the language such as Flat GHC when the full power of atomic unification or read-only variables is not needed.