 
Summary: Strong Normalization and
Equi(co)inductive Types
Andreas Abel #
Department of Computer Science, University of Munich
Oettingenstr.67, D80538 München, Germany
abel@tcs.ifi.lmu.de
Abstract. A type system for the lambdacalculus enriched with recur
sive and corecursive functions over equiinductive and coinductive types
is presented in which all welltyped programs are strongly normalizing.
The choice of equiinductive types, instead of the more common iso
inductive types, inuences both reduction rules and the strong normal
ization proof. By embedding iso into equitypes, 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 CurryHowardIsomorphism, 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
