A simple model for quotient types

  • Martin Hofmann
Conference paper

DOI: 10.1007/BFb0014055

Part of the Lecture Notes in Computer Science book series (LNCS, volume 902)
Cite this paper as:
Hofmann M. (1995) A simple model for quotient types. In: Dezani-Ciancaglini M., Plotkin G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg

Abstract

We give an interpretation of quotient types within in a dependent type theory with an impredicative universe of propositions (Calculus of Constructions). In the model, type dependency arises only at the propositional level, therefore universes and large eliminations cannot be interpreted. In exchange, the model is much simpler and more intuitive than the one proposed by the author in [10]. Moreover, we interpret a choice operator for quotient types that, under certain restrictions, allows one to recover a representative from an equivalence class. Since the model is constructed syntactically, the interpretation function from the syntax with quotient types to the model gives rise to a procedure which eliminates quotient types by replacing propositional equality by equality relations defined by induction on the type structure (“book equalities”).

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Martin Hofmann
    • 1
  1. 1.Department of Computer ScienceUniversity of Edinburgh JCMB, KBEdinburghScotland

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