Paper: A Stability Theorem in Rewriting Theory (at LICS 1998)

Authors: Paul-André Melliès

Abstract

One key property of the λ-calculus is that there exists a minimal computation (the head-reduction) M→^eV from a λ-term M to the set of its head-normal forms. Minimality here means categorical “reflectivity” i.e. that every reduction path M→^fW to a head-normal form W factors (up to redex permutation) to a path M→^eV→^hW. This paper establishes a stability a la Berry or poly-reflectivity theorem [D, La, T] which extends the minimality property to rewriting systems with critical pairs. The theorem is proved in the setting of axiomatic rewriting systems where sets of head-normal forms are characterised by their frontier property in the spirit of J. Glauert and Z. Khasidashvili (1996)

BibTeX

  @InProceedings{Mellis-AStabilityTheoremin,
    author = 	 {Paul-André Melliès},
    title = 	 {A Stability Theorem in Rewriting Theory},
    booktitle =  {Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1998)},
    year =	 {1998},
    month =	 {June}, 
    pages =      {287--298},
    location =   {Indianapolis, IN, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }