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Pure Type Systems With More Liberal Rules, Martin W. Bunder, Wil Dekkers

Faculty of Engineering and Information Sciences - Papers: Part A

Pure Type Systems. PTSs, introduced as a generalisation of the type systems of Barendregt's lambda-cube, provide a foundation for actual proof assistants, aiming at the mechanic verification of formal proofs. In this paper we consider simplifications of some of the rules of PTSs. This is of independent interest for PTSs as this produces more flexible PTS-like systems, but it will also help, in a later paper, to bridge the gap between PTSs and systems of Illative Combinatory Logic.

First we consider a simplification of the start and weakening rules of PTSs. which allows contexts to be sets of statements, and …