Parallel reduction in type free λμ-calculus

Kensuke Baba, Sachio Hirokawa, Ken Etsu Fujita

    Research output: Contribution to journalConference articlepeer-review

    20 Citations (Scopus)


    The typed λμ-calculus is known to be strongly normalizing and weakly Church-Rosser, and hence becomes confluent. In fact, Parigot formulated a parallel reduction to prove confluence of the typed λμ-calculus by "Tait-and-Martin-Löf" method. However, the diamond property does not hold for his parallel reduction. The confluence for type-free λμ-calculus cannot be derived from that of the typed λμ-calculus and is not confirmed yet as far as we know. We analyze granularity of the reduction rules, and then introduce a new parallel reduction such that both renaming reduction and consecutive structural reductions are considered as one step parallel reduction. It is shown that the new formulation of parallel reduction has the diamond property, which yields a correct proof of the confluence for type free λμ-calculus. The diamond property of the new parallel reduction is also applicable to a call-by-value version of the λμ-calculus containing the symmetric structural reduction rule.

    Original languageEnglish
    Pages (from-to)52-66
    Number of pages15
    JournalElectronic Notes in Theoretical Computer Science
    Publication statusPublished - Jan 2001
    EventComputing: The Australasian Theory Symposium (CATS 2001) - Gold Coast, Australia
    Duration: Jan 29 2001Jan 30 2001

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • General Computer Science


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