We describe a denotational semantics for a sequential functional language with random number generation over a countably infinite set (the natural numbers), and prove that it is fully abstract with respect to may-and-must testing.

Our model is based on biordered sets similar to Berry’s bidomains, and stable, monotone functions. However, (as in prior models of unbounded non-determinism) these functions may not be continuous. Working in a biordered setting allows us to exploit the different properties of both extensional and stable orders to construct a Cartesian closed category of sequential, discontinuous functions, with least and greatest fixpoints having strong enough properties to prove computational adequacy.

We establish full abstraction of the semantics by showing that it contains a simple, first-order “universal type-object” within which all types may be embedded using functions defined by (countable) ordinal induction.


Operational Semantic Functional Language Denotational Semantic Stable Order Game Semantic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • James Laird
    • 1
  1. 1.Dept. of InformaticsUniversity of SussexUK

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