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Quantitative Polynomial Functors (Early Ideas)

Authors Georgi Nakov, Fredrik Nordvall Forsberg

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Georgi Nakov
  • Department of Computer and Information Sciences, University of Strathclyde, UK
Fredrik Nordvall Forsberg
  • Department of Computer and Information Sciences, University of Strathclyde, UK

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Georgi Nakov and Fredrik Nordvall Forsberg. Quantitative Polynomial Functors (Early Ideas). In 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 211, pp. 22:1-22:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CALCO.2021.22

Abstract

We investigate containers and polynomial functors in Quantitative Type Theory, and give initial algebra semantics of inductive data types in the presence of linearity. We show that reasoning by induction is supported, and equivalent to initiality, also in the linear setting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Linear logic
Keywords
  • quantitative type theory
  • polynomial functors
  • inductive data types

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References

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