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International Static Analysis Symposium

SAS 2017: Static Analysis pp 382–404Cite as

A Gradual Interpretation of Union Types

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10422))

Abstract

Union types allow to capture the possibility of a term to be of several possibly unrelated types. Traditional static approaches to union types are untagged and tagged unions, which present dual advantages in their use. Inspired by recent work on using abstract interpretation to understand gradual typing, we present a novel design for union types, called gradual union types. Gradual union types combine the advantages of tagged and untagged union types, backed by dynamic checks. Seen as a gradual typing discipline, gradual union types are restricted imprecise types that denote a finite number of static types. We apply the Abstracting Gradual Typing (AGT) methodology of Garcia et al. to derive the static and dynamic semantics of a language that supports both gradual unions and the traditional, totally-unknown type. We uncover that gradual unions interact with the unknown type in a way that mandates a stratified approach to AGT, relying on a composition of two distinct abstract interpretations in order to retain optimality. Thanks to the abstract interpretation framework, the resulting language is type safe and satisfies the refined criteria for gradual languages. We also show how to compile such a language to a threesome cast calculus, and prove that the compilation preserves the semantics and properties of the language.

M. Toro—Funded by CONICYT-PCHA/Doctorado Nacional/2015-21150510.

É. Tanter—Partially funded by FONDECYT Project 1150017.

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Notes

  1. 1.

    Similarly to untagged unions, one could design a language whose conditional expression implicitly introduces imprecision, without the need for any ascription (Sect. 2.2); we do not further consider this possible design and use ascriptions explicitly.

  2. 2.

    We use the hat notation to refer to a set of elements X (e.g. is a set of static types, and is a set of sets of static types).

  3. 3.

    The AI framework provides us with definitions for consistent predicates and functions; we will provide some equivalent algorithmic characterizations.

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Acknowledgments

We thank Gabriel Scherer, Ronald Garcia and the anonymous reviewers for their detailed comments and suggestions.

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Authors and Affiliations

  1. PLEIAD Laboratory, Computer Science Department (DCC), University of Chile, Santiago, Chile

    Matías Toro & Éric Tanter

Authors
  1. Matías Toro
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  2. Éric Tanter
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Correspondence to Matías Toro .

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Editors and Affiliations

  1. Dipartimento di Matematica, University of Padova, Padua, Italy

    Francesco Ranzato

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Toro, M., Tanter, É. (2017). A Gradual Interpretation of Union Types. In: Ranzato, F. (eds) Static Analysis. SAS 2017. Lecture Notes in Computer Science(), vol 10422. Springer, Cham. https://doi.org/10.1007/978-3-319-66706-5_19

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  • DOI: https://doi.org/10.1007/978-3-319-66706-5_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66705-8

  • Online ISBN: 978-3-319-66706-5

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