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.ITP.2022.7
URN: urn:nbn:de:0030-drops-167165
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Biernacka, Małgorzata ; Charatonik, Witold ; Drab, Tomasz

The Zoo of Lambda-Calculus Reduction Strategies, And Coq

LIPIcs-ITP-2022-7.pdf (0.8 MB)


We present a generic framework for the specification and reasoning about reduction strategies in the lambda calculus, representable as sets of term decompositions. It is provided as a Coq formalization that features a novel format of phased strategies. It facilitates concise description and algebraic reasoning about properties of reduction strategies. The formalization accommodates many well-known strategies, both weak and strong, such as call by name, call by value, head reduction, normal order, full β-reduction, etc. We illustrate the use of the framework as a tool to inspect and categorize the "zoo" of existing strategies, as well as to discover and study new ones with particular properties.

BibTeX - Entry

  author =	{Biernacka, Ma{\l}gorzata and Charatonik, Witold and Drab, Tomasz},
  title =	{{The Zoo of Lambda-Calculus Reduction Strategies, And Coq}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-167165},
  doi =		{10.4230/LIPIcs.ITP.2022.7},
  annote =	{Keywords: Lambda calculus, Reduction strategies, Coq}

Keywords: Lambda calculus, Reduction strategies, Coq
Collection: 13th International Conference on Interactive Theorem Proving (ITP 2022)
Issue Date: 2022
Date of publication: 03.08.2022
Supplementary Material: Software (Source Code): archived at:

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