Tabling, Rational Terms, and Coinduction Finally Together!

To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling often improves computational performance. Rational term are terms with one or more infinite sub-terms but with a finite representation. Rational terms can be generated in Prolog by omitting the occurs check when unifying two terms. Applications of rational terms include definite clause grammars, constraint handling systems, and coinduction. In this paper, we report our extension of YAP's Prolog tabling mechanism to support rational terms. We describe the internal representation of rational terms within the table space and prove its correctness. We then use this extension to implement a tabling based approach to coinduction. We compare our approach with current coinductive transformations and describe the implementation. In addition, we present an algorithm that ensures a canonical representation for rational terms.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Coinduction Plain and Simple

Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming. Second, it reviews and slightly extends the formalism commonly used for specifying codata. Third, it generalizes the coinduction proof principle, which has been originally specified for the equality predicate only, to other predicates. This generalization makes the coinduction proof principle more intuitive and stresses its closeness with structural induction. The article finally suggests in its conclusion extensions of functional and logic programming with limited and decidable forms of the generalized coinduction proof principle