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Pure Type System conversion is always typable

Part of: JFP Research Articles

Published online by Cambridge University Press:  16 March 2012

VINCENT SILES  and
HUGO HERBELIN
VINCENT SILES
Affiliation:
Ecole Polytechnique/INRIA/Laboratoire PPS, Equipe πr2 (e-mail: vincent.siles@polytechnique.edu)
HUGO HERBELIN
Affiliation:
INRIA/Laboratoire PPS, Equipe πr2 (e-mail: hugo.herbelin@inria.fr)
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Abstract

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Pure Type Systems are usually described in two different ways, one that uses an external notion of computation like beta-reduction, and one that relies on a typed judgment of equality, directly in the typing system. For a long time, the question was open to know whether both presentations described the same theory. A first step towards this equivalence has been made by Adams for a particular class of Pure Type Systems (PTS) called functional. Then, his result has been relaxed to all semi-full PTSs in previous work. In this paper, we finally give a positive answer to the general question, and prove that equivalence holds for any Pure Type System.

Type
Articles
Information
Journal of Functional Programming , Volume 22 , Issue 2 , March 2012 , pp. 153 - 180
Copyright
Copyright © Cambridge University Press 2012

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