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On Mints' reduction for ccc-calculus

  • Yohji Akama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)

Abstract

In this paper, we present a divide- and-conquer lemma to infer the SN+CR (Strongly Normalization and Church-Rosser) property of a reduction system from that property of its subsystems. Then we apply the lemma to show the property of Mints' reduction for ccc-calculus with restricted η-expansion and restricted π-expansion. In the course of the proof, we obtain some relations of the two restricted expansions against traditional reductions. Among others, we get a simple characterization of the restricted η-expansion in terms of traditional β- and η-reductions, and a similar characterization for the restricted π-expansion.

Keywords

Normal Form Induction Hypothesis Atomic Type Reduction System Proof Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Yohji Akama
    • 1
  1. 1.Department of Information ScienceTokyo Institute of TechnologyTokyoJapan

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