## 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 |

### 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}

}

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### 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 λ-term into a λI-term, and show that a λ-term is strongly fi-normalisable if and only if its translation is weakly fi-normalisable. We then prove that the translation preserves typability of λ-terms in various typed λ-calculi. This enables us to establish the equivalence between weak and strong fi-normalisations in these typed λ-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.