Condensing Lemmas for Pure Type Systems with Universes

Authors:
Blas C. Ruiz Jiménez
Affiliations:
-
Venue:
AMAST '98 Proceedings of the 7th International Conference on Algebraic Methodology and Software Technology
Year:
1999

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Abstract

Pure Type Systems with universes (γPTS) provide a right frame to model programming languages features and are the core of Logical Frameworks, widely used in theorem proof systems. For these systems some authors propose a single rule, which includes both typing under β-conversion and the relation between universes. Our proposal adds an independent rule parameterized over a relation γ between sorts. Non trivial properties of the PTS like the weak strengthening lemma can be obtained in γPTS by extending a method proposed by van Benthem Jutting and using weak-closure for γreduction. This lemma is important due to two main reasons: (1) it provides a condensing lemma that determines in the underlying logic system a cut rule that simplifies the task in proof assistant systems; (2) the proof of type checking decidability can be eased in some normalizing systems.