Stable Computational Semantics of Conflict-Free Rewrite Systems (Partial Orders with Duplication)

  • Zurab Khasidashvili
  • John Glauert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2706)


We study orderings ⊴S on reductions in the style of Lévy reflecting the growth of information w.r.t. (super)stable sets S of ‘values’ (such as head-normal forms or Böhm-trees). We show that sets of co-initial reductions ordered by ⊴S form finitary ω-algebraic complete lattices, and hence form computation and Scott domains. As a consequence, we obtain a relativized version of the computational semantics proposed by Boudol for term rewriting systems. Furthermore, we give a pure domain-theoretic characterization of the orderings ⊴S in the spirit of Kahn and Plotkin’s concrete domains. These constructions are carried out in the framework of Stable Deterministic Residual Structures, which are abstract reduction systems with an axiomatized residual relations on redexes, that model all orthogonal (or conflict-free) reduction systems as well as many other interesting computation structures.


Complete Lattice Reduction Ordering Initial Reduction Reduction Space Rewrite System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Zurab Khasidashvili
    • 1
  • John Glauert
    • 2
  1. 1.Logic and Validation Technology IntelIDCHaifaIsrael
  2. 2.School of Computing SciencesUEANorwichUK

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