License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2018.37
URN: urn:nbn:de:0030-drops-99367
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9936/
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Honsell, Furio ; Liquori, Luigi ; Stolze, Claude ; Scagnetto, Ivan

The Delta-Framework

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Abstract

We introduce the Delta-framework, LF_Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union. Strong proof-functional connectives take into account the shape of logical proofs, thus reflecting polymorphic features of proofs in formulae. This is in contrast to classical or intuitionistic connectives where the meaning of a compound formula depends only on the truth value or the provability of its subformulae. Our framework encompasses a wide range of type disciplines. Moreover, since relevant implication permits to express subtyping, LF_Delta subsumes also Pfenning's refinement types. We discuss the design decisions which have led us to the formulation of LF_Delta, study its metatheory, and provide various examples of applications. Our strong proof-functional type theory can be plugged in existing common proof assistants.

BibTeX - Entry

@InProceedings{honsell_et_al:LIPIcs:2018:9936,
  author =	{Furio Honsell and Luigi Liquori and Claude Stolze and Ivan Scagnetto},
  title =	{{The Delta-Framework}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{37:1--37:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9936},
  URN =		{urn:nbn:de:0030-drops-99367},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.37},
  annote =	{Keywords: Logic of programs, type theory, lambda-calculus}
}

Keywords: Logic of programs, type theory, lambda-calculus
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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