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  Types, equations, dimensions and the Pi theorem

Botta, N., Jansson, P. (in press): Types, equations, dimensions and the Pi theorem. - Journal of Functional Programming.
https://doi.org/10.48550/arXiv.2308.09481

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Item Permalink: https://publications.pik-potsdam.de/pubman/item/item_34276 Version Permalink: https://publications.pik-potsdam.de/pubman/item/item_34276_1
Genre: Journal Article

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Botta_2026_2308.09481v5.pdf (Preprint), 578KB
 
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https://arxiv.org/abs/2308.09481 (Preprint)
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 Creators:
Botta, Nicola1, Author                 
Jansson, Patrik 2, Author
Affiliations:
1Potsdam Institute for Climate Impact Research, ou_persistent13              
2External Organizations, ou_persistent22              

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 Abstract: The languages of mathematical physics and modelling are endowed with a rich "grammar of dimensions" that common abstractions of programming languages fail to represent. We propose a dependently typed domain-specific language (embedded in Idris) that captures this grammar. We apply it to formalize basic notions of dimensional analysis: those of dimension function, physical quantity, homomorphic measurement, the covariance principle and Buckingham's Pi theorem. We hope that the language makes mathematical physics more accessible to computer scientists and functional programming more palatable to modellers and physicists.

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Language(s): eng - English
 Dates: 2026-03-17
 Publication Status: Accepted / In Press
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.48550/arXiv.2308.09481
MDB-ID: No MDB - stored outside PIK (see locators/paper)
PIKDOMAIN: RD4 - Complexity Science
Organisational keyword: RD4 - Complexity Science
Model / method: Quantitative Methods
Model / method: Qualitative Methods
OATYPE: Diamond
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Title: Journal of Functional Programming
Source Genre: Journal, SCI, Scopus, oa-diamond
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Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/journal-functional-programming
Publisher: Episciences