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Conservativity of equality reflection over intensional type theory

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1158)


We investigate the relationship between intensional and extensional formulations of Martin-Löf type theory. We exhibit two principles which are not provable in the intensional formulation: uniqueness of identity and functional extensionality. We show that extensional type theory is conservative over the intensional one extended by these two principles, meaning that the same types are inhabited, whenever they make sense. The proof is non-constructive because it uses set-theoretic quotienting and choice of representatives.


  • Type Theory
  • Identity Type
  • Elimination Rule
  • Functional Extensionality
  • Canonical Element

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© 1996 Springer-Verlag Berlin Heidelberg

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Hofmann, M. (1996). Conservativity of equality reflection over intensional type theory. In: Berardi, S., Coppo, M. (eds) Types for Proofs and Programs. TYPES 1995. Lecture Notes in Computer Science, vol 1158. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61780-8

  • Online ISBN: 978-3-540-70722-6

  • eBook Packages: Springer Book Archive