License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2022.18
URN: urn:nbn:de:0030-drops-162994
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16299/
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Kesner, Delia ; Peyrot, Loïc

Solvability for Generalized Applications

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LIPIcs-FSCD-2022-18.pdf (1.0 MB)

Abstract

Solvability is a key notion in the theory of call-by-name lambda-calculus, used in particular to identify meaningful terms. However, adapting this notion to other call-by-name calculi, or extending it to different models of computation - such as call-by-value - , is not straightforward. In this paper, we study solvability for call-by-name and call-by-value lambda-calculi with generalized applications, both variants inspired from von Plato’s natural deduction with generalized elimination rules. We develop an operational as well as a logical theory of solvability for each of them. The operational characterization relies on a notion of solvable reduction for generalized applications, and the logical characterization is given in terms of typability in an appropriate non-idempotent intersection type system. Finally, we show that solvability in generalized applications and solvability in the lambda-calculus are equivalent notions.

BibTeX - Entry

@InProceedings{kesner_et_al:LIPIcs.FSCD.2022.18,
  author =	{Kesner, Delia and Peyrot, Lo\"{i}c},
  title =	{{Solvability for Generalized Applications}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16299},
  URN =		{urn:nbn:de:0030-drops-162994},
  doi =		{10.4230/LIPIcs.FSCD.2022.18},
  annote =	{Keywords: Lambda-calculus, Generalized applications, Solvability, CBN/CBV, Quantitative types}
}

Keywords: Lambda-calculus, Generalized applications, Solvability, CBN/CBV, Quantitative types
Collection: 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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