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On the Semantics of Coinductive Types in Martin-Löf Type Theory

  • Federico De Marchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3629)

Abstract

There are several approaches to the problem of giving a categorical semantics to Martin-Löf type theory with dependent sums and products and extensional equality types. The most established one relies on the notion of a type-category (or category with attributes) with \({\it \Sigma}\) and \({\it \Pi}\) types. We extend such a semantics by introducing coinductive types both on the syntactic level and in a type-category. Soundness of the semantics is preserved.

As an example of such a category, we prove that the type-category built over a locally cartesian closed category \({\mathcal C}\) admits coinductive types whenever \({\mathcal C}\) has final coalgebras for all polynomial functors.

Keywords

Type Theory Categorical Semantic Canonical Projection Syntactic Category Coherence Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Federico De Marchi
    • 1
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands

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