## Perpetuality and Uniform Normalization (1997)

Venue: | In Proc. of the 6 th International Conference on Algebraic and Logic Programming, ALP'97 |

Citations: | 4 - 2 self |

### BibTeX

@INPROCEEDINGS{Khasidashvili97perpetualityand,

author = {Zurab Khasidashvili and Mizuhito Ogawa},

title = {Perpetuality and Uniform Normalization},

booktitle = {In Proc. of the 6 th International Conference on Algebraic and Logic Programming, ALP'97},

year = {1997},

pages = {240--255},

publisher = {Submitted}

}

### OpenURL

### Abstract

. We define a perpetual one-step reduction strategy which enables one to construct minimal (w.r.t. L'evy's ordering \Theta on reductions) infinite reductions in Conditional Orthogonal Expression Reduction Systems. We use this strategy to derive two characterizations of perpetual redexes, i.e., redexes whose contractions retain the existence of infinite reductions. These characterizations generalize existing related criteria for perpetuality of redexes. We give a number of applications of our results, demonstrating their usefulness. In particular, we prove equivalence of weak and strong normalization (the uniform normalization property) for various restricted -calculi, which cannot be derived from previously known perpetuality criteria. 1 Introduction The objective of this paper is to study sufficient conditions for uniform normalization, UN, of a term in an orthogonal (first or higher-order) rewrite system, and for the UN property of the rewrite system itself. Here a term is UN if ei...