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Strong Normalization and Equi-(co)inductive Types

Summary: Strong Normalization and
Equi-(co)inductive Types
Andreas Abel #
Department of Computer Science, University of Munich
Oettingenstr.67, D-80538 MŁnchen, Germany
Abstract. A type system for the lambda-calculus enriched with recur-
sive 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, inuences both reduction rules and the strong normal-
ization proof. By embedding iso- into equi-types, the latter ones are
recognized as more fundamental. A model based on orthogonality is con-
structed where a semantical type corresponds to a set of observations,
and soundness of the type system is proven.
1 Introduction
Theorem provers based on the Curry-Howard-Isomorphism, such as Agda, Coq,
Epigram, or LEGO are built on dependent types and use inductive and coin-
ductive types to formalize data structures, object languages, logics, judgments,
derivations, etc. Proofs by induction or coinduction are represented as recursive


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


Collections: Computer Technologies and Information Sciences