Normalisation for higher-order calculi with explicit substitutions

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Abstract

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinite derivations) in the λ-calculus may lose this status in its ES-based implementation. This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems we show that needed strategies normalise in the ES-based implementation of any orthogonal pattern higher-order rewrite system.

Original languageEnglish
Pages (from-to)91-125
Number of pages35
JournalTheoretical Computer Science
Volume333
Issue number1-2
DOIs
StatePublished - 1 Mar 2005
EventFoundations of Software Science and Computation Structures - Warsaw, Poland
Duration: 7 Apr 20039 Apr 2003

Keywords

  • Explicit substitutions
  • Higher-order rewriting
  • Lamda calculus
  • Needed-strategies
  • Normalisation

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