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2005 Equivalences between Pure Type Systems and Systems of Illative Combinatory Logic
M. W. Bunder, W. J. M. Dekkers
Notre Dame J. Formal Logic 46(2): 181-205 (2005). DOI: 10.1305/ndjfl/1117755149


Pure Type Systems, PTSs, were introduced as a generalization of the type systems of Barendregt's lambda cube and were designed to provide a foundation for actual proof assistants which will verify proofs. Systems of illative combinatory logic or lambda calculus, ICLs, were introduced by Curry and Church as a foundation for logic and mathematics. In an earlier paper we considered two changes to the rules of the PTSs which made these rules more like ICL rules. This led to four kinds of PTSs. Most importantly PTSs are about statements of the form M:A, where M is a term and A a type. In ICLs there are no explicit types and the statements are terms. In this paper we show that for each of the four forms of PTS there is an equivalent form of ICL, sometimes if certain conditions hold.


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M. W. Bunder. W. J. M. Dekkers. "Equivalences between Pure Type Systems and Systems of Illative Combinatory Logic." Notre Dame J. Formal Logic 46 (2) 181 - 205, 2005.


Published: 2005
First available in Project Euclid: 2 June 2005

zbMATH: 1081.03015
MathSciNet: MR2150951
Digital Object Identifier: 10.1305/ndjfl/1117755149

Primary: 03B40

Rights: Copyright © 2005 University of Notre Dame


Vol.46 • No. 2 • 2005
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