Regular Article
Alpha-Conversion and Typability,☆☆

DEDICATED TO THE MEMORY OF ALONZO CHURCH
https://doi.org/10.1006/inco.1998.2756Get rights and content
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Abstract

There are two results in this paper. We first prove that alpha-conversion on types can be eliminated from the second-orderλ-calculusFof Girard and Reynolds without affecting the typing power of the system. On the other hand we show that it is impossible to eliminate alpha-conversion on universally quantified variables in the higher-orderλ-calculusFωof Girard, by exhibiting a term which is typable inFωwith alpha-conversion but not typable inFωwithout alpha-conversion.

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This work is partly supported by NSF grant CCR-9113196, by Polish KBN grant No. 2 1192 91 01 and by ESPRIT Basic Research Action grant No. 7232, “Gentzen”.

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