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A Profunctorial Scott Semantics

Author Zeinab Galal

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Zeinab Galal
  • Université de Paris, IRIF, CNRS, Paris, France

Acknowledgements

I thank Thomas Ehrhard, Marcelo Fiore, Chaitanya Leena Subramaniam and Christine Tasson for helpful discussions on this article and the referees for their valuable feedback.

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Zeinab Galal. A Profunctorial Scott Semantics. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.FSCD.2020.16

Abstract

In this paper, we study the bicategory of profunctors with the free finite coproduct pseudo-comonad and show that it constitutes a model of linear logic that generalizes the Scott model. We formalize the connection between the two models as a change of base for enriched categories which induces a pseudo-functor that preserves all the linear logic structure. We prove that morphisms in the co-Kleisli bicategory correspond to the concept of strongly finitary functors (sifted colimits preserving functors) between presheaf categories. We further show that this model provides solutions of recursive type equations which provides 2-dimensional models of the pure lambda calculus and we also exhibit a fixed point operator on terms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Categorical semantics
Keywords
  • Linear Logic
  • Scott Semantics
  • Profunctors

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