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Linear Rank Intersection Types

Authors Fábio Reis , Sandra Alves , Mário Florido

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Author Details

Fábio Reis
  • DCC-FCUP, University of Porto, Portugal
  • LIACC - Artificial Intelligence and Computer Science Laboratory, University of Porto, Portugal
Sandra Alves
  • DCC-FCUP, University of Porto, Portugal
  • LIACC - Artificial Intelligence and Computer Science Laboratory, University of Porto, Portugal
  • CRACS, INESC-TEC - Centre for Research in Advanced Computing Systems, Porto, Portugal
Mário Florido
  • DCC-FCUP, University of Porto, Portugal
  • LIACC - Artificial Intelligence and Computer Science Laboratory, University of Porto, Portugal

Funding

  • Reis, Fábio: This work was partially financially supported by Base Funding - UIDB/00027/2020 of the Artificial Intelligence and Computer Science Laboratory - LIACC - funded by national funds through the FCT/MCTES (PIDDAC).
  • Alves, Sandra: Partially supported by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project LA/P/0063/2020.
  • Florido, Mário: This work was partially financially supported by Base Funding - UIDB/00027/2020 of the Artificial Intelligence and Computer Science Laboratory - LIACC - funded by national funds through the FCT/MCTES (PIDDAC).

Cite AsGet BibTex

Fábio Reis, Sandra Alves, and Mário Florido. Linear Rank Intersection Types. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.TYPES.2022.8

Abstract

Non-idempotent intersection types provide quantitative information about typed programs, and have been used to obtain time and space complexity measures. Intersection type systems characterize termination, so restrictions need to be made in order to make typability decidable. One such restriction consists in using a notion of finite rank for the idempotent intersection types. In this work, we define a new notion of rank for the non-idempotent intersection types. We then define a novel type system and a type inference algorithm for the λ-calculus, using the new notion of rank 2. In the second part of this work, we extend the type system and the type inference algorithm to use the quantitative properties of the non-idempotent intersection types to infer quantitative information related to resource usage.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
Keywords
  • Lambda-Calculus
  • Intersection Types
  • Quantitative Types
  • Tight Typings

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