Types, equations, dimensions and the Pi theorem

Botta, Nicola; Jansson, Patrik

doi:10.48550/arXiv.2308.09481

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Types, equations, dimensions and the Pi theorem

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Botta, Nicola
Potsdam Institute for Climate Impact Research;

Jansson, Patrik
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https://arxiv.org/abs/2308.09481
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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

Cite as: https://publications.pik-potsdam.de/pubman/item/item_34276

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.