Work

Types, equations, dimensions and the Pi theorem

Year: 2026

Type: article

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.

Source: Journal of Functional Programming

DOI: 10.46298/jfp.17762

Authors: Nicola Botta, Patrik Jansson

Institutions: Potsdam Institute for Climate Impact Research, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,660

Funder: European Commission