### 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 |
---|---|

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 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

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

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

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 56, no. 2, pp. 223-231. https://doi.org/10.1016/0304-3975(88)90079-5

}

TY - JOUR

T1 - One-step recurrent terms in λ-β-calculus

AU - Sekimoto, Shoji

AU - Hirokawa, Sachio

PY - 1988/2

Y1 - 1988/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023961089&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023961089&partnerID=8YFLogxK

U2 - 10.1016/0304-3975(88)90079-5

DO - 10.1016/0304-3975(88)90079-5

M3 - Article

AN - SCOPUS:0023961089

VL - 56

SP - 223

EP - 231

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 2

ER -