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.TYPES.2022.6
URN: urn:nbn:de:0030-drops-184498
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Stassen, Philipp ; Gratzer, Daniel ; Birkedal, Lars

{mitten}: A Flexible Multimodal Proof Assistant

LIPIcs-TYPES-2022-6.pdf (0.9 MB)


Recently, there has been a growing interest in type theories which include modalities, unary type constructors which need not commute with substitution. Here we focus on MTT [Daniel Gratzer et al., 2021], a general modal type theory which can internalize arbitrary collections of (dependent) right adjoints [Birkedal et al., 2020]. These modalities are specified by mode theories [Licata and Shulman, 2016], 2-categories whose objects corresponds to modes, morphisms to modalities, and 2-cells to natural transformations between modalities. We contribute a defunctionalized NbE algorithm which reduces the type-checking problem for MTT to deciding the word problem for the mode theory. The algorithm is restricted to the class of preordered mode theories - mode theories with at most one 2-cell between any pair of modalities. Crucially, the normalization algorithm does not depend on the particulars of the mode theory and can be applied without change to any preordered collection of modalities. Furthermore, we specify a bidirectional syntax for MTT together with a type-checking algorithm. We further contribute mitten, a flexible experimental proof assistant implementing these algorithms which supports all decidable preordered mode theories without alteration.

BibTeX - Entry

  author =	{Stassen, Philipp and Gratzer, Daniel and Birkedal, Lars},
  title =	{{\{mitten\}: A Flexible Multimodal Proof Assistant}},
  booktitle =	{28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-285-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{269},
  editor =	{Kesner, Delia and P\'{e}drot, Pierre-Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-184498},
  doi =		{10.4230/LIPIcs.TYPES.2022.6},
  annote =	{Keywords: Dependent type theory, guarded recursion, modal type theory, proof assistants}

Keywords: Dependent type theory, guarded recursion, modal type theory, proof assistants
Collection: 28th International Conference on Types for Proofs and Programs (TYPES 2022)
Issue Date: 2023
Date of publication: 28.07.2023

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