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DOI: 10.4230/LIPIcs.TYPES.2015.6

Efficient Type Checking for Path Polymorphism

Authors: Juan Edi, Andrés Viso, and Eduardo Bonelli

Published in: LIPIcs, Volume 69, 21st International Conference on Types for Proofs and Programs (TYPES 2015) (2018)

Abstract

A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that can operate uniformly over recursively specified applicative data structures. A typical pattern such functions resort to is \dataterm{x}{y} which decomposes a compound, in other words any applicative tree structure, into its parts. We study type-checking for this type system in two stages. First we propose algorithms for checking type equivalence and subtyping based on coinductive characterizations of those relations. We then formulate a syntax-directed presentation and prove its equivalence with the original one. This yields a type-checking algorithm which unfortunately has exponential time complexity in the worst case. A second algorithm is then proposed, based on automata techniques, which yields a polynomial-time type-checking algorithm.

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Juan Edi, Andrés Viso, and Eduardo Bonelli. Efficient Type Checking for Path Polymorphism. In 21st International Conference on Types for Proofs and Programs (TYPES 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 69, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{edi_et_al:LIPIcs.TYPES.2015.6,
  author =	{Edi, Juan and Viso, Andr\'{e}s and Bonelli, Eduardo},
  title =	{{Efficient Type Checking for Path Polymorphism}},
  booktitle =	{21st International Conference on Types for Proofs and Programs (TYPES 2015)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-030-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{69},
  editor =	{Uustalu, Tarmo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2015.6},
  URN =		{urn:nbn:de:0030-drops-84761},
  doi =		{10.4230/LIPIcs.TYPES.2015.6},
  annote =	{Keywords: lambda-calculus, pattern matching, path polymorphism, type checking}
}

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Efficient Type Checking for Path Polymorphism

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