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Summary: Strong Normalization and
Equi-(co)inductive Types
Andreas Abel
heprtment of gomputer ieneD niversity of wunih
yettingenstrFTUD hEVHSQV wünhenD qermny
abel@tcs.ifi.lmu.de
Abstract. e type system for the lmdElulus enrihed with reurE
sive nd oreursive funtions over equiEindutive nd Eoindutive types
is presented in whih ll wellEtyped progrms re strongly normlizingF
he hoie of equiEindutive typesD insted of the more ommon isoE
indutive typesD in)uenes oth redution rules nd the strong normlE
iztion proofF fy emedding isoE into equiEtypesD the ltter ones re
reognized s more fundmentlF e model sed on orthogonlity is onE
struted where semntil type orresponds to set of oservtionsD
nd soundness of the type system is provenF
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
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