M. R. K. Krishna Rao

Modular proofs for completeness of hierarchical term rewriting systems

Abstract In this paper, we study modular aspects of hierarchical combinations of term rewriting systems. A combination R 0 ∪ R 1 is hierarchical if the defined symbols of the two subsystems R 0 and R 1 are disjoint, some of the defined symbols of R 0 are constructors in R 1 and the defined symbols of R 1 do not occur in R 0. It is shown that in hierarchical combinations, a reduction can increase the rank of a term. Therefore, techniques employed in proving the modularity results for direct sums and constructor sharing systems are not applicable for hierarchical combinations. We propose a set of sufficient conditions for the modularity of completeness of hierarchical combinations. The sufficient conditions are syntactic ones (about recursion) and can be easily tested for finite systems. First, the modularity of strong innermost normalization (SIN) for a class of hierarchical combinations is established. By imposing a restriction that R 0 ∪ R 1 is an overlay system, the modularity of local confluence is established for this class. Then the modularity of completeness is obtained using a recent result relating strong innermost normalization and termination properties of locally confluent overlay systems.

Transformational methodology for proving termination of logic programs

Abstract A methodology for proving the termination of well-moded logic programs is developed by reducing the termination problem of logic programs to that of term rewriting systems. A transformation procedure is presented to derive a term rewriting system from a given well-moded logic program such that the termination of the derived rewrite system implies the termination of the logic program for all well-moded queries under a class of selection rules. This facilitates applicability of a vast source of termination orderings proposed in the literature on term rewriting, for proving termination of logic programs. The termination of various benchmark programs has been established with this approach. Unlike other mechanizable approaches, the proposed approach does not require any preprocessing and works well, even in the presence of mutual recursion. The transformation has also been implemented as a front end to Rewrite Rule Laboratory (RRL) and has been used in establishing termination of nontrivial Prolog programs such as a prototype compiler for ProCoS, PL 0 language.

Simple Termination of Hierarchical Combinations of Term Rewriting Systems

In this paper, we study modular aspects of hierarchical combinations of term rewriting systems. A class of hierarchical combinations is identified for which simple termination is modular. Our result generalizes Kurihara and Ohuchis result on modularity of simple termination of rewrite systems with shared constructors. The result is extended to conditional term rewriting systems generalizing Ohlebuschs result.

A Transformational Methodology for Proving Termination of Logic Programs

An approach for proving termination of well-moded logic programs is given by transforming a given logic program into a term rewriting system. It is proved that the termination of the derived rewriting system implies the termination of the corresponding logic program for well-moded queries under any selection rule implied by the given modings. The approach is mechanizable using termination orderings proposed in the term rewriting literature. Unlike Ullman and van Gelders approach and Plumers method, no preprocessing is needed, and the approach works well even in the presence of mutual recursion. This approach has been used recently to show termination of the Prolog implementation of compiler for ProCoS level 0 language PL0 developed at Oxford University.

Completeness of Hierarchical Combinations of term Rewriting Systems

In this paper, we propose a sufficient condition for modularity of completeness of hierarchical combinations. The sufficient condition is a syntactic one (about recursion) based on constructor discipline. Our result generalizes Middeldorp and Toyamas result on modularity of completeness for shared constructor systems.

Learning from Entailment of Logic Programs with Local Variables

In this paper, we study exact learning of logic programs from entailment and present a polynomial time algorithm to learn a rich class of logic programs that allow local variables and include many standard programs like append, merge, split, delete, member, prefix, suffix, length, reverse, append/4 on lists, tree traversal programs on binary trees and addition, multiplication, exponentiation on natural numbers. Grafting a few aspects of incremental learning [9] onto the framework of learning from entailment [3], we generalize the existing results to allow local variables, which play an important role of sideways information passing in the paradigm of logic programming.

Semi-Completeness of Hierarchical and Super-Hierarchical Combinations of Term Rewriting Systems

In this paper, we study modular aspects of hierarchical and super hierarchical combinations of term rewriting systems. In particular, a sufficient condition for modularity of semi-completeness of hierarchical and super hierarchical combinations is proposed. We first establish modularity of weak normalization for this class (defined by the sufficient condition) and modularity of semi-completeness for a class of crosswise independent unions. From these results, we obtain modularity of semi-completeness for a class of hierarchical and super hierarchical combinations. Our results generalize the semi-completeness results of Ohlebusch [14] and Middeldorp and Toyama [13]. The notion of crosswise independent unions is a generalization of both constructor sharing unions as well as Plumps crosswise disjoint unions.

Rewriting Concepts in the Study of Termination of Logic Programs

A characterization of terminating logic programs is proposed. The approach is to relate the termination property of logic programs with that of term rewriting systems and use various termination techniques of rewriting in characterizing and proving termination of logic programs. The characterization is given using a new concept, unification closure. The concept of unification closure is closely related to the concepts of forward closure and overlap closure used in term rewriting literature to characterize the termination of linear term rewriting systems. Equivalence of our characterization with that based on level mappings is proved. Com-putability of the unification closure for a class of logic programs satisfying the bounded term-size property is established. The mechanizability and practicality of the approach is discussed.

Principles of curriculum design and revision: a case study in implementing computing curricula CC2001

Our department has recently revisited its computer science program in the light of IEEE/ACM Computing Curricula 2001 (CC2001) recommendations, taking into consideration the ABETs Criteria for Accrediting Computing programs (CAC 04-05). The effort resulted in a revised curriculum. This paper presents the different decisions we made with regard to the curriculum orientation, knowledge units coverage, transition management, and monitoring and assessment. The paper also sheds some light on challenges faced. Tables provided in the paper show that the curriculum successfully implements CC2001 recommendations while satisfying the CAC 04-05.

Some classes of Prolog programs inferable from positive data

In this paper, we identify a class of Prolog programs inferable from positive data. Our approach is based on moding information and linear predicate inequalities between input terms and output terms. Our results generalize the results of Arimura and Shinohara [4]. Standard programs for reverse, quick-sort, merge-sort are a few examples of programs that can be handled by our results but not by the earlier results of [4]. The generality of our results follows from the fact that we treat logical variables as transmitters for broadcasting communication, whereas Arimura and Shinohara [4] treat them as point-to-point communication channels.