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The Duality of Subtyping (Artifact)

Authors: Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman

Published in: DARTS, Volume 6, Issue 2, Special Issue of the 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract

This artifact contains the Coq formalization associated with the paper The Duality of Subtyping submitted in ECOOP 2020. This document explains how to run the Coq formalization. Artifact can either be compiled in the pre-built docker image with all the dependencies installed or it could be built from the scratch. Sections 1-7 explain the basic information about the artifact. Section A explains how to get the docker image for the artifact. Section B explains the prerequisites and the steps to run coq files from scratch. Section C explains coq files briefly. Section D shows the correspondence between important lemmas discussed in paper and their respective Coq formalization. The term MonoTyping used in artifact corresponds to the standard subtyping systems.

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Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman. The Duality of Subtyping (Artifact). In Special Issue of the 34th European Conference on Object-Oriented Programming (ECOOP 2020). Dagstuhl Artifacts Series (DARTS), Volume 6, Issue 2, pp. 8:1-8:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Article{oliveira_et_al:DARTS.6.2.8,
  author =	{Oliveira, Bruno C. d. S. and Shaobo, Cui and Rehman, Baber},
  title =	{{The Duality of Subtyping (Artifact)}},
  pages =	{8:1--8:6},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2020},
  volume =	{6},
  number =	{2},
  editor =	{Oliveira, Bruno C. d. S. and Shaobo, Cui and Rehman, Baber},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.6.2.8},
  URN =		{urn:nbn:de:0030-drops-132051},
  doi =		{10.4230/DARTS.6.2.8},
  annote =	{Keywords: DuoTyping, OOP, Duality, Subtyping, Supertyping}
}

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DOI: 10.4230/LIPIcs.ECOOP.2020.29

The Duality of Subtyping

Authors: Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman

Published in: LIPIcs, Volume 166, 34th European Conference on Object-Oriented Programming (ECOOP 2020)

Abstract

Subtyping is a concept frequently encountered in many programming languages and calculi. Various forms of subtyping exist for different type system features, including intersection types, union types or bounded quantification. Normally these features are designed independently of each other, without exploiting obvious similarities (or dualities) between features. This paper proposes a novel methodology for designing subtyping relations that exploits duality between features. At the core of our methodology is a generalization of subtyping relations, which we call Duotyping. Duotyping is parameterized by the mode of the relation. One of these modes is the usual subtyping, while another mode is supertyping (the dual of subtyping). Using the mode it is possible to generalize the usual rules of subtyping to account not only for the intended behaviour of one particular language construct, but also of its dual. Duotyping brings multiple benefits, including: shorter specifications and implementations, dual features that come essentially for free, as well as new proof techniques for various properties of subtyping. To evaluate a design based on Duotyping against traditional designs, we formalized various calculi with common OOP features (including union types, intersection types and bounded quantification) in Coq in both styles. Our results show that the metatheory when using Duotyping does not come at a significant cost: the metatheory with Duotyping has similar complexity and size compared to the metatheory for traditional designs. However, we discover new features as duals to well-known features. Furthermore, we also show that Duotyping can significantly simplify transitivity proofs for many of the calculi studied by us.

Cite as

Bruno C. d. S. Oliveira, Cui Shaobo, and Baber Rehman. The Duality of Subtyping. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 166, pp. 29:1-29:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{oliveira_et_al:LIPIcs.ECOOP.2020.29,
  author =	{Oliveira, Bruno C. d. S. and Shaobo, Cui and Rehman, Baber},
  title =	{{The Duality of Subtyping}},
  booktitle =	{34th European Conference on Object-Oriented Programming (ECOOP 2020)},
  pages =	{29:1--29:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-154-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{166},
  editor =	{Hirschfeld, Robert and Pape, Tobias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2020.29},
  URN =		{urn:nbn:de:0030-drops-131864},
  doi =		{10.4230/LIPIcs.ECOOP.2020.29},
  annote =	{Keywords: DuoTyping, OOP, Duality, Subtyping, Supertyping}
}

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