Pure Type System conversion is always typable

Vincent Siles 1, 2, 3 Hugo Herbelin 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : 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 toward this equivalence has been made by Adams for a particular class of \emph{Pure Type Systems} (PTS) called functional. Then, his result has been relaxed to all semi-full PTS in previous work. In this paper, we finally give a positive answer to the general issue, and prove that equivalence holds for any Pure Type System.
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Vincent Siles, Hugo Herbelin. Pure Type System conversion is always typable. Journal of Functional Programming, Cambridge University Press (CUP), 2012, 22 (2), pp.153 - 180. ⟨10.1017/S0956796812000044⟩. ⟨inria-00497177v2⟩

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