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A simple adequate categorical model for PCF

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Typed Lambda Calculi and Applications (TLCA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1210))

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Abstract

Usually types of PCF are interpreted as cpos and terms as continuous functions. It is then the case that non-termination of a closed term of ground type corresponds to the interpretation being bottom; we say that the semantics is adequate. We shall here present an axiomatic approach to adequacy for PCF in the sense that we will introduce categorical axioms enabling an adequate semantics to be given. We assume the presence of certain “bottom” maps with the role of being the interpretation of non-terminating terms, but the order-structure is left out. This is different from previous approaches where some kind of order-theoretic structure has been considered as part of an adequate categorical model for PCF. We take the point of view that partiality is the fundamental notion from which order-structure should be derived, which is corroborated by the observation that our categorical model induces an order-theoretic model for PCF in a canonical way.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, DK-8000, Aarhus C, Denmark

    Torben Braüner

  2. Basic Research in Computer Science, Center of the Danish Nationsl Research Foundation, Denmark

    Torben Braüner

Authors
  1. Torben Braüner
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Philippe de Groote J. Roger Hindley

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© 1997 Springer-Verlag Berlin Heidelberg

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Braüner, T. (1997). A simple adequate categorical model for PCF. In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_30

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  • DOI: https://doi.org/10.1007/3-540-62688-3_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62688-6

  • Online ISBN: 978-3-540-68438-1

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