Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Pistone, Paolo; Tranchini, Luca https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-142652
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What’s Decidable About (Atomic) Polymorphism?

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Abstract

Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we investigate System Fat, or atomic System F, a very weak predicative fragment of System F whose typable terms coincide with the simply typable ones. We show that the type-checking problem for Fat is decidable and we propose an algorithm which sheds some new light on the source of undecidability in full System F. Moreover, we investigate free theorems and contextual equivalence in this fragment, and we show that the latter, unlike in the simply typed lambda-calculus, is undecidable.

BibTeX - Entry

@InProceedings{pistone_et_al:LIPIcs.FSCD.2021.27,
  author =	{Pistone, Paolo and Tranchini, Luca},
  title =	{{What’s Decidable About (Atomic) Polymorphism?}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{27:1--27:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14265},
  URN =		{urn:nbn:de:0030-drops-142652},
  doi =		{10.4230/LIPIcs.FSCD.2021.27},
  annote =	{Keywords: Atomic System F, Predicative Polymorphism, ML-Polymorphism, Type-Checking, Contextual Equivalence, Free Theorems}
}

Keywords: Atomic System F, Predicative Polymorphism, ML-Polymorphism, Type-Checking, Contextual Equivalence, Free Theorems
Seminar: 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)
Issue date: 2021
Date of publication: 06.07.2021


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