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Restrictable Variants: A Simple and Practical Alternative to Extensible Variants

Authors Magnus Madsen , Jonathan Lindegaard Starup , Matthew Lutze

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Author Details

Magnus Madsen
  • Department of Computer Science, Aarhus University, Denmark
Jonathan Lindegaard Starup
  • Department of Computer Science, Aarhus University, Denmark
Matthew Lutze
  • Department of Computer Science, Aarhus University, Denmark

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Magnus Madsen, Jonathan Lindegaard Starup, and Matthew Lutze. Restrictable Variants: A Simple and Practical Alternative to Extensible Variants. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 17:1-17:27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We propose restrictable variants as a simple and practical alternative to extensible variants. Restrictable variants combine nominal and structural typing: a restrictable variant is an algebraic data type indexed by a type-level set formula that captures its set of active labels. We introduce new pattern-matching constructs that allows programmers to write functions that only match on a subset of variants, i.e., pattern-matches may be non-exhaustive. We then present a type system for restrictable variants which ensures that such non-exhaustive matches cannot get stuck at runtime. An essential feature of restrictable variants is that the type system can capture structure-preserving transformations: specifically the introduction and elimination of variants. This property is important for writing reusable functions, yet many row-based extensible variant systems lack it. In this paper, we present a calculus with restrictable variants, two partial pattern-matching constructs, and a type system that ensures progress and preservation. The type system extends Hindley-Milner with restrictable variants and supports type inference with an extension of Algorithm W with Boolean unification. We implement restrictable variants as an extension of the Flix programming language and conduct a few case studies to illustrate their practical usefulness.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
  • restrictable variants
  • extensible variants
  • refinement types
  • Boolean unification


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