One-step recurrent terms in λ-β-calculus

Shoji Sekimoto, Sachio Hirokawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A necessary and sufficient condition for cycling reductions to be recurrent is given. A one-step recurrent term is a term in λ-β-calculus whose one-step reductums are all reducible to the term. It is a weakened notion of minimal form or recurrent term in the λ-β-calculus. In this note, a one-step recurrent term which is not recurrent is shown. That term becomes a counter- example for a conjecture presented by Klop. By analysis of the reduction cycles of one-step recurrent terms, a necessary and sufficient condition for a one-step recurrent term to be recurrent is given.

Original languageEnglish
Pages (from-to)223-231
Number of pages9
JournalTheoretical Computer Science
Volume56
Issue number2
DOIs
Publication statusPublished - Feb 1988
Externally publishedYes

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Calculus
Term
Necessary Conditions
Sufficient Conditions
Cycling
Counterexample
Cycle

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

One-step recurrent terms in λ-β-calculus. / Sekimoto, Shoji; Hirokawa, Sachio.

In: Theoretical Computer Science, Vol. 56, No. 2, 02.1988, p. 223-231.

Research output: Contribution to journalArticle

Sekimoto, Shoji ; Hirokawa, Sachio. / One-step recurrent terms in λ-β-calculus. In: Theoretical Computer Science. 1988 ; Vol. 56, No. 2. pp. 223-231.
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