## Weak and Strong Beta Normalisations in Typed λ-Calculi (1997)

Venue: | In: Proc. of the 3 rd International Conference on Typed Lambda Calculus and Applications, TLCA'97 |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Xi97weakand,

author = {Hongwei Xi},

title = {Weak and Strong Beta Normalisations in Typed λ-Calculi},

booktitle = {In: Proc. of the 3 rd International Conference on Typed Lambda Calculus and Applications, TLCA'97},

year = {1997},

pages = {390--404},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

. We present a technique to study relations between weak and strong fi-normalisations in various typed -calculi. We first introduce a translation which translates a -term into a I-term, and show that a -term is strongly fi-normalisable if and only if its translation is weakly fi-normalisable. We then prove that the translation preserves typability of -terms in various typed -calculi. This enables us to establish the equivalence between weak and strong fi-normalisations in these typed -calculi. This translation can deal with Curry typing as well as Church typing, strengthening some recent closely related results. This may bring some insights into answering whether weak and strong fi-normalisations in all pure type systems are equivalent. 1 Introduction In various typed -calculi, one of the most interesting and important properties on -terms is how they can be fi-reduced to fi-normal forms. A -term M is said to be weakly fi-normalisable (WN fi (M )) if it can be fi-reduced to a fi-n...