Strong normalization and equi-(co)inductive types

Authors:
Andreas Abel
Affiliations:
Department of Computer Science, University of Munich, München, Germany
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

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Abstract

A type system for the lambda-calculus enriched with recursive and corecursive functions over equi-inductive and -coinductive types is presented in which all well-typed programs are strongly normalizing. The choice of equi-inductive types, instead of the more common iso-inductive types, influences both reduction rules and the strong normalization proof. By embedding iso- into equi-types, the latter ones are recognized as more fundamental. A model based on orthogonality is constructed where a semantical type corresponds to a set of observations, and soundness of the type system is proven.