Inductive and Functional Types in Ludics

Pavaux, Alice

doi:10.4230/LIPIcs.CSL.2017.34

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LIPIcs.CSL.2017.34.pdf

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DOI: 10.4230/LIPIcs.CSL.2017.34
URN: urn:nbn:de:0030-drops-77035

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Alice Pavaux

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Alice Pavaux. Inductive and Functional Types in Ludics. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 34:1-34:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.CSL.2017.34

Abstract

Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their structure following a game semantics approach. Inductive types are interpreted as least fixed points, and we prove an internal completeness result giving an explicit construction for such fixed points. The interactive properties of the ludics interpretation of inductive and functional types are then studied. In particular, we identify which higher-order functions types fail to satisfy type safety, and we give a computational explanation.

Keywords

Ludics
Inductive types
Fixed point
Linear logic
Game semantics

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