Fitting Semantics for Conditional Term Rewriting

This paper investigates the semantics of conditional term rewriting systems with negation which do not satisfy useful properties like termination. It is shown that the approach used by Fitting [5] for Prolog-style logic programs is applicable in this context. A monotone operator is developed, whose fixpoints describe the semantics of conditional rewriting. Several examples illustrate this semantics for non-terminating rewrite systems which could not be easily handled by previous approaches

Logic Programming as Constructivism

The features of logic programming that seem unconventional from the viewpoint of classical logic can be explained in terms of constructivistic logic. We motivate and propose a constructivistic proof theory of non-Horn logic programming. Then, we apply this formalization for establishing results of practical interest. First, we show that 'stratification can be motivated in a simple and intuitive way. Relying on similar motivations, we introduce the larger classes of 'loosely stratified' and 'constructively consistent' programs. Second, we give a formal basis for introducing quantifiers into queries and logic programs by defining 'constructively domain independent* formulas. Third, we extend the Generalized Magic Sets procedure to loosely stratified and constructively consistent programs, by relying on a 'conditional fixpoini procedure

The Sigma-Semantics: A Comprehensive Semantics for Functional Programs

A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns

The Sigma-Semantics: A Comprehensive Semantics for Functional Programs

A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns

CASL for CafeOBJ Users

Casl is an expressive language for the algebraic specificationof software requirements, design, and architecture. It has been developed by an open collaborative effort called CoFI (Common Framework Initiative for algebraic specification and development). Casl combines the best features of many previous main-stream algebraic specification languages, and it should provide a focus for future research and development in the use of algebraic techniques, as well facilitating interoperability ofexisting and future tools. This paper presents Casl for users of the CafeOBJ framework, focusing on the relationship between the two languages. It first considers those constructs of CafeOBJ that have direct counterparts in Casl, and then (briefly) those that do not. It also motivates various Casl constructsthat are not provided by CafeOBJ. Finally, it gives a concise overview of Casl, and illustrates how some CafeOBJ specifications may be expressed in Casl