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Proving termination of GHC programs

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Abstract

A transformational approach for proving termination of parallel logic programs such as GHC programs is proposed. A transformation from GHC programs to term rewriting systems is developed; it exploits the fact that unifications in GHC-resolution correspond to matchings. The termination of a GHC program for a class of queries is implied by the termination of the resulting rewrite system. This approach facilitates the applicability of a wide range of termination techniques developed for rewrite systems in proving termination of GHC programs. The method consists of three steps: (a) deriving moding information from a given GHC program, (b) transforming the GHC program into a term rewriting system using the moding information, and finally (c) proving termination of the resulting rewrite system. Using this method, the termination of many benchmark GHC programs such as quick-sort, merge-sort, merge, split, fair-split and append, etc., can be proved.

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Authors and Affiliations

  1. Computer Science Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, 400 005, Bombay, India

    M. R. K. Krishna Rao & R. K. Shyamasundar

  2. Department of Computer Science, SUNY at Albany, 12222, NY, USA

    D. Kapur

Authors
  1. M. R. K. Krishna Rao
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  2. D. Kapur
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  3. R. K. Shyamasundar
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Corresponding author

Correspondence to M. R. K. Krishna Rao.

Additional information

This is a revised and extended version of Ref. 12). The work was partially supported by the NSF Indo-US grant INT-9416687

Kapur was partially supported by NSF Grant nos. CCR-8906678 and INT-9014074.

M. R. K. Krishna Rao, Ph.D.: He currently works as a senior research fellow at Griffith University, Brisbane, Australia. His current interests are in the areas of logic programming, modular aspects and noncopying implementations of term rewriting, learning logic programs from examples and conuterexamples and dynamics of mental states in rational agent architectures. He received his Ph.D in computer science from Tata Institute of Fundamental Research (TIFR), Bombay in 1993 and worked at TIFR and Max Planck Institut für Informatik, Saarbrücken until January 1997.

Deepak Kapur, Ph.D.: He currently works as a professor at the State University of New York at Albany. His research interests are in the areas of automated reasoning, term rewriting, constraint solving, algebraic and geometric reasoning and its applications in computer vision, symbolic computation, formal methods, specification and verification. He obtained his Ph.D. in Computer Science from MIT in 1980. He worked at General Electric Corporate Research and Development until 1987. Prof. Kapur is the editor-in-chief of the Journal of Automated Reasoning. He also serves on the editorial boards of Journal of Logic Programming, Journal on Constraints, and Journal of Applicable Algebra in Engineering, Communication and Computer Science.

R. K. Shyamasundar, Ph.D.: He currently works as a professor at Tata Institute of Fundamental Research (TIFR), Bombay. His current intersts are in the areas of logic programming, reactive and real time programming, constraint solving, formal methods, specification and verification. He received his Ph.D in computer science from Indian Institute of Science, Bangalore in 1975 and has been a faculty member at Tata Institute of Fundamental Research since then. He has been a visiting/regular faculty member at Technological University of Eindhoven, University of Utrecht, IBM TJ Watson Research Centre, Pennsylvania State University, University of Illinois at Urbana-Champaign, INRIA and ENSMP, France. He has served on (and chaired) Program Committees of many International Conferences and has been on the Editorial Committees.

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Krishna Rao, M.R.K., Kapur, D. & Shyamasundar, R.K. Proving termination of GHC programs. New Gener Comput 15, 293–338 (1997). https://doi.org/10.1007/BF03037949

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