Tabling, Rational Terms, and Coinduction Finally Together!

Abstract

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

Flexible coinductive logic programming

“…CoLP has been initially proposed by Simon et al (2006;2006;2007) as a convenient subparadigm of logic programming to model circularity; it was soon recognized the limitation of its expressive power that does not allow mutually recursive inductive and coinductive predicates, or predicates whose correct interpretation is neither the least, nor the greatest fixed point. Moura et al (2013;2014) and Ancona (2013) have proposed implementations of coLP based on refinements of the Simon's original proposal with the main aim of making them more portable and flexible. Ancona has extended coLP by introducing a finally clause, allowing the user to define the specific behavior of a predicate when solved by coinductive hypothesis.…”

Coaxioms: flexible coinductive definitions by inference systems

“…Since coSLD aims to capture all coinductively derivable atoms, it accepts all cyclic proofs, but in some cases this behaviour is too rigid. To allow more flexible behaviours, in [Anc13,MRM14] other operational models are provided. In particular, the notion of finally clause, introduce by Ancona [Anc13], allows the programmer to specify a fact that should be resolved when a cycle is detected, instead of simply accepting the atom.…”

A Theoretical Perspective of Coinductive Logic Programming

“…Two papers have been recently published in the time spanning the period between the appearance of the conference version and the completion of the revision of the journal version of this work, witnessing the interest toward this sub-paradigm of Logic Programming. Moura [24] presents a portable implementation of co-LP very close to [2] (both based on refinements of the Simon's original proposal [31]), which has been embedded in a tabled Prolog [20], exploiting tabling for storing hypothesis. The work of Moura relates to the implementation of Logtalk, an open source object-oriented logic programming language supporting co-LP; both [20] and [2] propose a more flexible implementation than that provided in [31], with similar mechanisms to allow the user to specify customized behavior in case of the application of the coinductive rule.…”