 
Summary: Syntactical Strong Normalization for
Intersection Types with Term Rewriting Rules
Andreas Abel
Institut f¨ur Informatik
LudwigMaximiliansUniversit¨at M¨unchen
4 June 2007
Abstract
We investigate the intersection type system of Coquand and Spiwack
with rewrite rules and natural numbers and give an elementary proof of
strong normalization which can be formalized in a weak metatheory.
1 Introduction
For typed calculi which are used as languages for theorem provers, such as
Agda, Coq, LEGO or Isabelle, normalization is a crucial property; the con
sistency of these provers depend on it. Usually, normalization is proven by a
model construction, but recently, syntactical normalization proofs have received
some interest [Val01, Dav01, JM03]. One advantage of syntactical proofs is that
they explain better why a calculus is normalizing; in such proofs one can see
what actually decreases in each reduction step. Another advantage is that they
can be formalized in weak logical theories. For instance, a syntactic normal
ization proof [Abe04] of the simplytyped calculus (STL) can be carried out
