### 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 language | English |
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Pages (from-to) | 223-231 |

Number of pages | 9 |

Journal | Theoretical Computer Science |

Volume | 56 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 1988 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Sekimoto, S., & Hirokawa, S. (1988). One-step recurrent terms in λ-β-calculus.

*Theoretical Computer Science*,*56*(2), 223-231. https://doi.org/10.1016/0304-3975(88)90079-5