Minimal relative normalization in orthogonal expression reduction systems

  • John Glauert
  • Zurab Khasidashvili
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1180)


In previous papers, the authors studied normalization relative to desirable sets S of ‘partial results’, where it is shown that such sets must be stable. For example, the sets of normal forms, head-normal-forms, and weak head-normal-forms in the λ-calculus, are all stable. They showed that, for any stable S, S-needed reductions are S-normalizing. This paper continues the investigation into the theory of relative normalization. In particular, we prove existence of minimal normalizing reductions for regular stable sets of results. All the above mentioned sets are regular. We give a sufficient and necessary criterion for a normalizing reduction (w.r.t. a regular stable S) to be minimal. Finally, we establish a relationship between relative minimal and optimal reductions, revealing a conflict between minimality and optimality: for regular stable sets of results, a term need not possess a reduction that is minimal and optimal at the same time.


Normal Form Relative Normalization Minimal Reduction Lambda Calculus Optimal Reduction 
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 1996

Authors and Affiliations

  • John Glauert
    • 1
  • Zurab Khasidashvili
    • 1
  1. 1.School of Information SystemsUEANorwichEngland

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