One-step recurrent terms in λ-β-calculus

Shoji Sekimoto, Sachio Hirokawa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number2
Publication statusPublished - Feb 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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