Alpha-Conversion and Typability

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 q...

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Veröffentlicht in:	Information and computation 1999-04, Vol.150 (1), p.1-21
Hauptverfasser:	Kfoury, A.J., Ronchi della Rocca, S., Tiuryn, J., Urzyczyn, P.
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology General logic Logic and foundations Mathematical logic, foundations, set theory Mathematics Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	0890-5401 1090-2651
DOI:	10.1006/inco.1998.2756