Higher-Precision Groundness Analysis. Codish, M., Genaim, S., Søndergaard, H., & Stuckey, P. J. In Logic Programming: Proceedings of the 17th International Conference, volume 2237, of Lecture Notes in Computer Science, pages 135–149, 2001. Springer.
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Groundness analysis of logic programs using Pos-based abstract interpretation is one of the clear success stories of the last decade in the area of logic program analysis. In this work we identify two problems with the Pos domain, the multiplicity and sign problems, that arise independently in groundness and uniqueness analysis. We describe how these problems can be solved using an analysis based on a domain Size for inferring term size relations. However this solution has its own shortcomings because it involves a widening operator which leads to a loss of Pos information. Inspired by Pos, Size and the Lsign domain for abstract linear arithmetic constraints we introduce a new domain Lpos, and show how it can be used for groundness and uniqueness analysis. The idea is to use the sign information of Lsign to improve the widening of Size so that it does not lose Pos information. We prove that the resulting analyses using Lpos are uniformly more precise than those using Pos.
@Inproceedings{Cod-Gen-Son-Stu_ICLP01,
  author    = {Michael Codish and 
		Samir Genaim and 
		Harald S{\o}ndergaard and 
		Peter J. Stuckey},
  title     = {Higher-Precision Groundness Analysis},
  editor    = {P. Codognet},
  booktitle = {Logic Programming: Proceedings of the 17th International 
		Conference},
  series    = {Lecture Notes in Computer Science},
  volume    = {2237},
  pages     = {135--149},
  publisher = {Springer},
  year      = {2001},
  doi       = {10.1007/3-540-45635-x_17},
  abstract  = {Groundness analysis of logic programs using Pos-based abstract
		interpretation is one of the clear success stories of the last
		decade in the area of logic program analysis. In this work we
		identify two problems with the Pos domain, the multiplicity and
		sign problems, that arise independently in groundness and 
		uniqueness analysis. We describe how these problems can be 
		solved using an analysis based on a domain Size for inferring 
		term size relations.  However this solution has its own 
		shortcomings because it involves a widening operator which leads
		to a loss of Pos information. Inspired by Pos, Size and the
		Lsign domain for abstract linear arithmetic constraints we
		introduce a new domain Lpos, and show how it can be used for
		groundness and uniqueness analysis. The idea is to use the sign
		information of Lsign to improve the widening of Size so that
		it does not lose Pos information. We prove that the resulting 
		analyses using Lpos are uniformly more precise than those using
		Pos.},
  keywords  = {Boolean logic, Abstract domains, Abstract interpretation, Logic programming},
}

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