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Pregrammars and Intersection Types

Author Sabine Broda

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Author Details

Sabine Broda
  • CMUP, Departamento de Ciência de Computadores, Faculdade de Ciências, University of Porto, Portugal

Funding

The author was partially supported by CMUP, which is financed by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project with reference UIDB/00144/2020.

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Sabine Broda. Pregrammars and Intersection Types. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CSL.2021.14

Abstract

A representation of intersection types in terms of pregrammars is presented. Pregrammar based rewriting relations, corresponding respectively to type checking and inhabitation are defined and the latter is used to implement a Wajsberg/Ben-Yelles style alternating semi-decision algorithm for inhabitation. The usefulness of the framework is illustrated by revisiting and partially extending standard inhabitation related results for intersection types, as well as establishing new ones. It is shown how the notion of bounded multiset dimension emerges naturally and the relation between the two settings is clarified. A meaningful rank independent superset of the set of rank 2 types is identified for which EXPSPACE-completeness for inhabitation as well as for counting is proved. Finally, a standard result on negatively non-duplicated simple types is extended to intersection types.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Logic
  • Theory of computation → Lambda calculus
Keywords
  • Intersection Types
  • Pregrammars
  • Inhabitation

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