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.CSL.2023.3
URN: urn:nbn:de:0030-drops-174648
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Miller, Dale ; Wu, Jui-Hsuan

A Positive Perspective on Term Representation (Invited Talk)

LIPIcs-CSL-2023-3.pdf (0.8 MB)


We use the focused proof system LJF as a framework for describing term structures and substitution. Since the proof theory of LJF does not pick a canonical polarization for primitive types, two different approaches to term representation arise. When primitive types are given the negative polarity, LJF proofs encode terms as tree-like structures in a familiar fashion. In this situation, cut elimination also yields the familiar notion of substitution. On the other hand, when primitive types are given the positive polarity, LJF proofs yield a structure in which explicit sharing of term structures is possible. Such a representation of terms provides an explicit method for sharing term structures. In this setting, cut elimination yields a different notion of substitution. We illustrate these two approaches to term representation by applying them to the encoding of untyped λ-terms. We also exploit concurrency theory techniques - namely traces and simulation - to compare untyped λ-terms using such different structuring disciplines.

BibTeX - Entry

  author =	{Miller, Dale and Wu, Jui-Hsuan},
  title =	{{A Positive Perspective on Term Representation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-174648},
  doi =		{10.4230/LIPIcs.CSL.2023.3},
  annote =	{Keywords: term representation, sharing, focused proof systems}

Keywords: term representation, sharing, focused proof systems
Collection: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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