A Proof of Strong Normalization For the Theory of Constructions Using a Kripke-Like Interpretation (1990)
| Venue: | In Workshop on Logical Frameworks--Preliminary Proceedings |
| Citations: | 16 - 0 self |
BibTeX
@INPROCEEDINGS{Coquand90aproof,
author = {Thierry Coquand and Jean Gallier and Le Chesnay Cedex},
title = {A Proof of Strong Normalization For the Theory of Constructions Using a Kripke-Like Interpretation},
booktitle = {In Workshop on Logical Frameworks--Preliminary Proceedings},
year = {1990}
}
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Abstract
. We give a proof that all terms that type-check in the theory of constructions are strongly normalizing (under fi-reduction). The main novelty of this proof is that it uses a "Kripke-like" interpretation of the types and kinds, and that it does not use infinite contexts. We explore some consequences of strong normalization, consistency and decidability of typechecking. We also show that our proof yields another proof of strong normalization for LF (under fi-reduction), using the reducibility method. 1 Introduction We give a proof that all terms that type-check in the theory of constructions are strongly normalizing (under fi-reduction). The main novelty of this proof is that it uses a "Kripkelike " interpretation of the types and kinds, and that it does not use infinite contexts. The idea used for avoiding infinite contexts comes from Coquand's thesis [Coq85]. Our proof yields as a corollary another proof of strong normalization (under fi-reduction) of well-formed terms of LF . In f...
