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A Semantic Normalization Proof for System T Lisa Allali1

Summary: A Semantic Normalization Proof for System T
Lisa Allali1
and Paul Brauner2
1 ´Ecole Polytechnique, INRIA & R´egion Ile de France allali@lix.polytechnique.fr
INPL & LORIA paul.brauner@loria.fr
Abstract. Semantics methods have been used to prove cut elimination theorems
for a long time. It is only recently that they have been extended to prove strong
normalization results. For instance using the notion of super-consistency that is
a semantic criterion for theories expressed in deduction modulo implying strong
normalization. However, the strong normalization of System T has always been
reluctant to such semantic methods. In this paper we give a semantic normaliza-
tion proof of system T using the super consistency of some theory.
1 Introduction
When building a new theory, there are several criteria one wants this theory to meet.
In particular the cut elimination property which means that the cut rule is redundant.
This property ensures the consistency of the theory. In an intuitionistic framework (as
it is the case in the present paper) it also gives the so-called witness property: if a proof
is ending by the introduction of the existential quantifier one can exhibit a witness of
this existence. Normalization of a theory is also a desirable property. It ensures the


Source: Allali, Lisa - Laboratoire d’Informatique, École Polytechnique


Collections: Computer Technologies and Information Sciences