Pure type systems with explicit substitution

Authors:
Roel Bloo
Affiliations:
Faculty of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands. E-mail: c.j.bloo@tue.nl
Venue:
Mathematical Structures in Computer Science
Year:
2001

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Abstract

We define an extension of pure type systems with explicit substitution. We show that the type systems with explicit substitution are strongly normalizing iff their ordinary counterparts are. Subject reduction is shown to fail in general but a weaker, though still useful, subject reduction property is established. A more complicated extension is proposed for which subject reduction does hold in general.