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From Qualitative to Quantitative Semantics

By Change of Base
  • James LairdEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10203)

Abstract

We give a general description of the transition from qualitative models of programming languages to quantitative ones, as a change of base for enriched categories. This is induced by a monoidal functor from the category of coherence spaces to the category of modules over a complete semiring \({\mathcal {R}}\). Using the properties of this functor, we characterise the requirements for the change of base to preserve the structure of a Lafont category (model of linear type theory with free exponential), and thus to give an adequate semantics of erratic PCF with scalar weights from \({\mathcal {R}}\). Moreover, this model comes with a meaning-preserving functor from the original, qualitative one, which we may use to interpret side-effects such as state. As an example, we show that the game semantics of Idealized Algol bears a natural enrichment over the category of coherence spaces, and thus gives rise by change of base to a \({\mathcal {R}}\)-weighted model, which is fully abstract. We relate this to existing categories of probabilistic games and slot games.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of BathBathUK

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