HAL: inria-00497177, version 2

DOI: 10.1017/S0956796812000044

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Journal of Functional Programming 22, 2 (2012) 153 - 180

Available versions

v1 (2010-07-02)

v2 (2011-12-18)

Pure Type System conversion is always typable

Vincent Siles 1, 2, 3, Hugo Herbelin 1, 2

(2012-05-10)

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.

1:	Preuves, Programmes et Systèmes (PPS)
	CNRS : UMR7126 – Université Paris VII - Paris Diderot
2:	PI.R2 (INRIA Paris - Rocquencourt)
	INRIA – Université Paris VII - Paris Diderot – CNRS : UMR7126
3:	Laboratoire d'informatique de l'école polytechnique (LIX)
	CNRS : UMR7161 – Polytechnique - X

Domain

:

Computer Science/Programming Languages

Keywords: Pure Type System – Judgemental Equality – Church-Rosser – Subject Reduction – Injectivity

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From: Vincent Siles <>

Submitted on: Sunday, 18 December 2011 10:10:40

Updated on: Friday, 11 May 2012 10:55:05