Author:
SILES VINCENT,HERBELIN HUGO
Abstract
AbstractPure 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 ofPure 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.
Publisher
Cambridge University Press (CUP)
Reference25 articles.
1. Werner B. (1994) Une théorie des Constructions Inductives. Ph.D. thesis, Université Paris, France.
2. Siles V. (2010) Formalization of Equivalence Between PTS and PTSe. http://www.lix.polytechnique.fr/vsiles/coq/PTSATR.html.
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