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Computational Adequacy in an Elementary Topos

  • Alex K. Simpson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)

Abstract

We place simple axioms on an elementary topos which suffice for it to provide a denotational model of call-by-value PCF with sum and product types. The model is synthetic in the sense that types are interpreted by their set-theoretic counterparts within the topos. The main result characterises when the model is computationally adequate with respect to the operational semantics of the programming language. We prove that computational adequacy holds if and only if the topos is 1-consistent (i.e. its internal logic validates only true Σ\(^{\rm 0}_{\rm 1}\)-sentences).

Keywords

Operational Semantic Full Subcategory Algebra Homomorphism Domain Theory Internal Logic 
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 1999

Authors and Affiliations

  • Alex K. Simpson
    • 1
  1. 1.LFCS, Division of InformaticsUniversity of EdinburghEdinburgh

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