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On Classical PCF, Linear Logic and the MIX Rule

Authors Shahin Amini, Thomas Erhard

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Shahin Amini
Thomas Erhard

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Shahin Amini and Thomas Erhard. On Classical PCF, Linear Logic and the MIX Rule. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 582-596, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.CSL.2015.582

Abstract

We study a classical version of PCF from a semantical point of view. We define a general notion of model based on categorical models of Linear Logic, in the spirit of earlier work by Girard, Regnier and Laurent. We give a concrete example based on the relational model of Linear Logic, that we present as a non-idempotents intersection type system, and we prove an Adequacy Theorem using ideas introduced by Krivine. Following Danos and Krivine, we also consider an extension of this language with a MIX construction introducing a form of must non-determinism; in this language, a program of type integer can have more than one value (or no value at all, raising an error). We propose a refinement of the relational model of classical PCF in which programs of type integer are single valued; this model rejects the MIX syntactical constructs (and the MIX rule of Linear Logic).
Keywords
  • lambda-calculus
  • linear logic
  • classical logic
  • denotational semantics

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