Structural Subtyping as Parametric Polymorphism

Wenhao Tang, Daniel Hillerström, James McKinna, Michel Steuwer, Ornela Dardha, Rongxiao Fu, Sam Lindley

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Abstract

Structural subtyping and parametric polymorphism provide similar flexibility and reusability to programmers. For example, both features enable the programmer to provide a wider record as an argument to a function that expects a narrower one. However, the means by which they do so differs substantially, and the precise details of the relationship between them exists, at best, as folklore in literature. In this paper, we systematically study the relative expressive power of structural subtyping and parametric polymorphism. We focus our investigation on establishing the extent to which parametric polymorphism, in the form of row and presence polymorphism, can encode structural subtyping for variant and record types. We base our study on various Church-style λ-calculi extended with records and variants, different forms of structural subtyping, and row and presence polymorphism. We characterise expressiveness by exhibiting compositional translations between calculi. For each translation we prove a type preservation and operational correspondence result. We also prove a number of non-existence results. By imposing restrictions on both source and target types, we reveal further subtleties in the expressiveness landscape, the restrictions enabling otherwise impossible translations to be defined. More specifically, we prove that full subtyping cannot be encoded via polymorphism, but we show that several restricted forms of subtyping can be encoded via particular forms of polymorphism.

Original languageEnglish
Article number260
JournalProceedings of the ACM on Programming Languages
Volume7
Issue numberOOPSLA2
Early online date16 Oct 2023
DOIs
Publication statusPublished - Oct 2023

Keywords

  • expressiveness
  • polymorphism
  • row types
  • subtyping

ASJC Scopus subject areas

  • Software
  • Safety, Risk, Reliability and Quality

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