A Productivity Checker For Logic Programming

ASU Author/Contributor (non-ASU co-authors, if there are any, appear on document)
Patricia Johann Ph.D, Professor (Creator)
Appalachian State University (ASU )
Web Site: https://library.appstate.edu/

Abstract: Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a practical work-around for this problem, by making a clear distinction between whether a program is meant to be understood inductively or coinductively. For programs meant to be understood inductively, termination must be guaranteed, whereas for programs meant to be understood coinductively, productive non- termination (or “productivity”) must be ensured. In practice, such classification helps to better understand and implement some non-terminating computations. Logic programming was one of the first declarative languages to make this distinction: in the 1980’s, Lloyd and van Emden’s “computations at infinity” captured the big-step operational semantics of derivations that produce infinite terms as answers. In modern terms, computations at infinity describe “global productivity” of computations in logic programming. Most programming languages featuring coinduction also provide an observational, or small-step, notion of productivity as a computational counterpart to global productivity. This kind of productivity is ensured by checking that finite initial fragments of infinite computations can always be observed to produce finite portions of their infinite answer terms. In this paper we introduce a notion of observational productivity for logic programming as an algorithmic approximation of global productivity, give an effective procedure for semi-deciding observational productivity, and offer an implemented automated observational productivity checker for logic programs.

Additional Information

Komendantskaya, E., Johann, P., & Schmidt, M. (2016). A Productivity Checker for Logic Programming. Logic- Based Program Synthesis and Transformation 2016 (LOPSTR '16), pp. 168-186. NC Docks permission to re-print granted by author(s). Publisher version of record available at: https://arxiv.org/abs/1608.04415
Language: English
Date: 2016
Logic programming, corecursion, coinduction, termination, productivity

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