A formalized proof of strong normalization for guarded recursive types

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• We consider a simplified version of Nakano’s guarded fixed-point types in a representation by infinite type expressions, defined coinductively. Smallstep reduction is parametrized by a natural number “depth” that expresses under how many guards we may step during evaluation. We prove that reduction is strongly normalizing for any depth. The proof involves a typed inductive notion of strong normalization and a Kripke model of types in two dimensions: depth and typing context. Our results have been formalized in Agda and serve as a case study of reasoning about a language with coinductive type expressions.

Subject headings

NATURVETENSKAP  -- Data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences (hsv//eng)

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ref (subject category)

kon (subject category)