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A Deep Quantitative Type System

Authors Giulio Guerrieri , Willem B. Heijltjes, Joseph W.N. Paulus



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Author Details

Giulio Guerrieri
  • University of Bath, Department of Computer Science, UK
Willem B. Heijltjes
  • University of Bath, Department of Computer Science, UK
Joseph W.N. Paulus
  • Rijksuniversiteit Groningen, The Netherlands

Acknowledgements

We would like to thank Ugo Dal Lago, Delia Kesner, Luc Pelissier, Nicolas Wu, and the anonymous referees for their constructive engagement with our work.

Cite AsGet BibTex

Giulio Guerrieri, Willem B. Heijltjes, and Joseph W.N. Paulus. A Deep Quantitative Type System. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 24:1-24:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.CSL.2021.24

Abstract

We investigate intersection types and resource lambda-calculus in deep-inference proof theory. We give a unified type system that is parametric in various aspects: it encompasses resource calculi, intersection-typed lambda-calculus, and simply-typed lambda-calculus; it accommodates both idempotence and non-idempotence; it characterizes strong and weak normalization; and it does so while allowing a range of algebraic laws to determine reduction behaviour, for various quantitative effects. We give a parametric resource calculus with explicit sharing, the "collection calculus", as a Curry-Howard interpretation of the type system, that embodies these computational properties.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • Theory of computation → Lambda calculus
Keywords
  • Lambda-calculus
  • Deep inference
  • Intersection types
  • Resource calculus

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