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A Predicative Strong Normalisation Proof for a -calculus with Interleaving Inductive Types
 

Summary: A Predicative Strong Normalisation Proof for a
-calculus with Interleaving Inductive Types
Andreas Abel 1 and Thorsten Altenkirch 2
1 Department of Computer Science,
University of Munich
abel@informatik.uni-muenchen.de
2 School of Computer Science & Information Technology,
University of Nottingham
txa@cs.nott.ac.uk
Abstract. We present a new strong normalisation proof for a -calculus
with interleaving strictly positive inductive types   which avoids the use
of impredicative reasoning, i.e., the theorem of Knaster-Tarski. Instead
it only uses predicative, i.e., strictly positive inductive de nitions on the
metalevel. To achieve this we show that every strictly positive operator
on types gives rise to an operator on saturated sets which is not only
monotone but also (deterministically) set based { a concept introduced
by Peter Aczel in the context of intuitionistic set theory. We also extend
this to coinductive types using greatest xpoints of strictly monotone
operators on the metalevel.
1 Introduction

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universit√§t M√ľnchen

 

Collections: Computer Technologies and Information Sciences