Types, equations, dimensions and the Pi theorem
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914400251674624 |
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| author | Botta, Nicola Jansson, Patrik |
| author_facet | Botta, Nicola Jansson, Patrik |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_09481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Types, equations, dimensions and the Pi theorem Botta, Nicola Jansson, Patrik Programming Languages Logic in Computer Science 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. |
| title | Types, equations, dimensions and the Pi theorem |
| topic | Programming Languages Logic in Computer Science |
| url | https://arxiv.org/abs/2308.09481 |