Preserving model structure and constraints in scientific computing
In this paper, we look at how model structure and constraints can be incorporated into scientific computing using functional programming and, implicitly, category theory, in a way that constraints are automatically satisfied. Category theory is the study of different types of objects (e.g., sets, gr...
Saved in:
| Published in: | Measurement. Sensors Vol. 38; p. 101796 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Ltd
01.05.2025
|
| Subjects: | |
| ISSN: | 2665-9174, 2665-9174 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper, we look at how model structure and constraints can be incorporated into scientific computing using functional programming and, implicitly, category theory, in a way that constraints are automatically satisfied. Category theory is the study of different types of objects (e.g., sets, groups, vector spaces) and mappings between them (e.g., functions, homomorphisms, matrices) and is used in mathematics to model the underlying structure associated with systems we wish to describe and how this underlying structure is preserved under transformations. In this paper, we look at the structure associated with the representation of, and calculations using, quantitative data. In particular, we describe how measurement data can be represented in terms of the product C × D of two groups: the first, C, the counting algebra, and the second, D, the dimension algebra. Different but equivalent unit systems are related through group isomorphisms. The structure associated with this representation can be embedded in software using functional programming. |
|---|---|
| AbstractList | In this paper, we look at how model structure and constraints can be incorporated into scientific computing using functional programming and, implicitly, category theory, in a way that constraints are automatically satisfied. Category theory is the study of different types of objects (e.g., sets, groups, vector spaces) and mappings between them (e.g., functions, homomorphisms, matrices) and is used in mathematics to model the underlying structure associated with systems we wish to describe and how this underlying structure is preserved under transformations. In this paper, we look at the structure associated with the representation of, and calculations using, quantitative data. In particular, we describe how measurement data can be represented in terms of the product C × D of two groups: the first, C, the counting algebra, and the second, D, the dimension algebra. Different but equivalent unit systems are related through group isomorphisms. The structure associated with this representation can be embedded in software using functional programming. |
| ArticleNumber | 101796 |
| Author | Forbes, Alistair Videla, Andre Forsberg, Fredrik Nordvall McBride, Conor Lines, Keith |
| Author_xml | – sequence: 1 givenname: Alistair surname: Forbes fullname: Forbes, Alistair email: alistair.forbes@npl.co.uk organization: National Physical Laboratory, Teddington, UK – sequence: 2 givenname: Keith surname: Lines fullname: Lines, Keith organization: National Physical Laboratory, Teddington, UK – sequence: 3 givenname: Fredrik Nordvall surname: Forsberg fullname: Forsberg, Fredrik Nordvall organization: University of Strathclyde, Glasgow, UK – sequence: 4 givenname: Conor surname: McBride fullname: McBride, Conor organization: University of Strathclyde, Glasgow, UK – sequence: 5 givenname: Andre surname: Videla fullname: Videla, Andre organization: University of Strathclyde, Glasgow, UK |
| BookMark | eNp9kE1OwzAQhS1UJErpDVjkAglj13GSDRJU_EmVYAFry7XHyFHjVLZTiduTEBasWM1o5r2nme-SLHzvkZBrCgUFKm7aokMV0RcMGJ9GVSPOyJIJUeYNrfjiT39B1jG2AMDqUcj4kty_BYwYTs5_Zl1v8JDFFAadhoCZ8ibTvR8HyvkUM-ezqB365KzT46Y7Dmn0XZFzqw4R1791RT4eH963z_nu9elle7fLNaNC5HUDFaOmMRZ0XQPojbKlUUJRBAp7tFzsuWFgOWfMGC5KaKyqkfFJpurNivA5V4c-xoBWHoPrVPiSFOSEQrZyRiEnFHJGMdpuZxuOt50cBvnzhEbjAuokTe_-D_gGhvprzg |
| Cites_doi | 10.1088/0026-1394/51/4/S183 10.1016/0263-2241(84)90020-4 10.1371/journal.pone.0024274 10.21014/actaimeko.v12i1.1412 10.1016/0096-0551(77)90010-8 |
| ContentType | Journal Article |
| Copyright | 2024 |
| Copyright_xml | – notice: 2024 |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.measen.2024.101796 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2665-9174 |
| ExternalDocumentID | 10_1016_j_measen_2024_101796 S2665917424007724 |
| GroupedDBID | 0R~ 53G 6I. AAEDW AAFTH AALRI AAXUO AAYWO ACVFH ADCNI ADVLN AEUPX AFJKZ AFPUW AIGII AITUG AKBMS AKYEP ALMA_UNASSIGNED_HOLDINGS AMRAJ APXCP EBS EJD FDB GROUPED_DOAJ M41 M~E OK1 ROL AAYXX CITATION |
| ID | FETCH-LOGICAL-c2166-890721d9df0c8800c3af5da6a1e010bef46b4d20f4422dd46509fa8e24f5daa83 |
| ISSN | 2665-9174 |
| IngestDate | Sat Nov 29 07:44:31 EST 2025 Sat Aug 16 17:02:35 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Numerical computation Functional programming Dimensioned variable Units of measurement |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c2166-890721d9df0c8800c3af5da6a1e010bef46b4d20f4422dd46509fa8e24f5daa83 |
| OpenAccessLink | http://dx.doi.org/10.1016/j.measen.2024.101796 |
| ParticipantIDs | crossref_primary_10_1016_j_measen_2024_101796 elsevier_sciencedirect_doi_10_1016_j_measen_2024_101796 |
| PublicationCentury | 2000 |
| PublicationDate | May 2025 2025-05-00 |
| PublicationDateYYYYMMDD | 2025-05-01 |
| PublicationDate_xml | – month: 05 year: 2025 text: May 2025 |
| PublicationDecade | 2020 |
| PublicationTitle | Measurement. Sensors |
| PublicationYear | 2025 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Bennich-Bjorkman, McKeever (bib18) 2018 Nielsen (bib4) 2014; 51 Finkelstein, Leaning (bib9) 1984; 2 Kennedy (bib17) 2010 Lambek, Scott (bib7) 1986 McBride, Nordvall Forsberg (bib20) 2022; vol. XII Forbes (bib21) 2009 Spivak (bib2) 2013 (bib13) 2019 Golub, Van Loan (bib23) 2013 Alvin Howard (bib6) 1980 Hart (bib10) 1995 Spivak, Ologs (bib8) January 2012; 7 Gehani (bib15) January 1977; 2 Hall (bib19) 2022 Gill, Murray, Wright (bib22) 1981 (bib25) 2011; 102 McBride, Nakov, Forsberg (bib26) 2023; 12 MacLane (bib1) 1971; vol. 5 Hanisch, Chalk, Coulon, Cox, Emmerson (bib12) May 2022; 605 Thompson, Taylor (bib14) 2008 Hansen, Rischel (bib16) 2013 Hall (bib11) January 2002, 2002 McBride, Nakov, Nordvall Forsberg (bib3) 2022 (bib24) 2008; 100 Brooks Curry, Feys (bib5) 1958; vol. 1 McBride, Nakov, Nordvall Forsberg, Videla, Forbes, Lines (bib27) August, 2024 Spivak (10.1016/j.measen.2024.101796_bib8) 2012; 7 Nielsen (10.1016/j.measen.2024.101796_bib4) 2014; 51 McBride (10.1016/j.measen.2024.101796_bib20) 2022; vol. XII Finkelstein (10.1016/j.measen.2024.101796_bib9) 1984; 2 Hall (10.1016/j.measen.2024.101796_bib19) 2022 Hart (10.1016/j.measen.2024.101796_bib10) 1995 Hanisch (10.1016/j.measen.2024.101796_bib12) 2022; 605 Spivak (10.1016/j.measen.2024.101796_bib2) 2013 McBride (10.1016/j.measen.2024.101796_bib27) 2024 Alvin Howard (10.1016/j.measen.2024.101796_bib6) 1980 Hall (10.1016/j.measen.2024.101796_bib11) 2002 Gill (10.1016/j.measen.2024.101796_bib22) 1981 MacLane (10.1016/j.measen.2024.101796_bib1) 1971; vol. 5 McBride (10.1016/j.measen.2024.101796_bib3) 2022 (10.1016/j.measen.2024.101796_bib24) 2008; 100 Golub (10.1016/j.measen.2024.101796_bib23) 2013 (10.1016/j.measen.2024.101796_bib13) 2019 Bennich-Bjorkman (10.1016/j.measen.2024.101796_bib18) 2018 Gehani (10.1016/j.measen.2024.101796_bib15) 1977; 2 Brooks Curry (10.1016/j.measen.2024.101796_bib5) 1958; vol. 1 Hansen (10.1016/j.measen.2024.101796_bib16) 2013 Lambek (10.1016/j.measen.2024.101796_bib7) 1986 (10.1016/j.measen.2024.101796_bib25) 2011; 102 Thompson (10.1016/j.measen.2024.101796_bib14) 2008 Forbes (10.1016/j.measen.2024.101796_bib21) 2009 Kennedy (10.1016/j.measen.2024.101796_bib17) 2010 McBride (10.1016/j.measen.2024.101796_bib26) 2023; 12 |
| References_xml | – volume: 102 start-page: 2011 year: 2011 ident: bib25 article-title: Evaluation of measurement data — supplement 2 to the “Guide to the expression of uncertainty in measurement” — extension to any number of output quantities publication-title: Joint Committee for Guides in Metrology, JCGM – volume: 7 year: January 2012 ident: bib8 article-title: A categorical framework for knowledge representation publication-title: PLoS One – year: 2013 ident: bib16 article-title: Functional Programming Using F♯ – year: 1980 ident: bib6 article-title: The formulae-as-types notion of construction publication-title: Essays on Combinatory Logic, Lambda Calculus, and Formalism – year: 1986 ident: bib7 article-title: Introduction to Higher Order Categorical Logic – start-page: 273 year: 2022 end-page: 284 ident: bib19 article-title: Software representation of measured physical quantities publication-title: Advanced Mathematical Tools in Metrology and Testing, XII – year: 2022 ident: bib3 article-title: Expressive type systems for metrology publication-title: IMEKO TC6 International Conference on Metrology and Digital Transformation – year: 1995 ident: bib10 article-title: Multidimensional Analysis: Algebras and Systems for Science and Engineering – start-page: 268 year: 2010 end-page: 305 ident: bib17 article-title: Types for units-of-measure: theory and practice publication-title: Central European Functional Programming School: Hungary, May 21-23, 2009 – volume: vol. XII start-page: 331 year: 2022 end-page: 345 ident: bib20 article-title: Type systems for programs respecting dimensions publication-title: Advanced Mathematical Tools in Metrology – year: 2019 ident: bib13 article-title: The International System of Units (SI Brochure (EN)) – start-page: 147 year: 2009 end-page: 176 ident: bib21 article-title: Parameter estimation based on least squares methods publication-title: Data Modeling for Metrology and Testing in Measurement Science – volume: vol. 5 year: 1971 ident: bib1 publication-title: Categories for the Working Mathematician – volume: 12 year: 2023 ident: bib26 article-title: Measuring with confidence: leveraging expressive type systems for correct-by-construction software publication-title: Acta IMEKO – year: 2013 ident: bib2 article-title: Category Theory for Scientists – volume: vol. 1 year: 1958 ident: bib5 publication-title: Combinatory Logic – year: January 2002, 2002 ident: bib11 article-title: Software support for physical quantities publication-title: Proceedings of the 9th Electronics New Zealand Conference – volume: 605 year: May 2022 ident: bib12 article-title: Unclear units stymie science publication-title: Nature – year: 2008 ident: bib14 article-title: NIST Special Publication 811: Guide for the Use of the International System of Units (SI) – start-page: 26 year: August, 2024 end-page: 29 ident: bib27 article-title: LabMate: a prospectus for types for MATLAB publication-title: IMEKO World Congress – start-page: 121 year: 2018 end-page: 132 ident: bib18 article-title: The next 700 unit of measurement checkers publication-title: Software Language Engineering – year: 2013 ident: bib23 article-title: Matrix Computations – year: 1981 ident: bib22 article-title: Practical Optimization – volume: 100 start-page: 2008 year: 2008 ident: bib24 article-title: Evaluation of measurement data — guide to the expression of uncertainty in measurement publication-title: Joint Committee for Guides in Metrology, JCGM – volume: 51 start-page: S183 year: 2014 ident: bib4 article-title: Evaluation of mass measurements in accordance with the GUM publication-title: Metrologia – volume: 2 start-page: 25 year: 1984 end-page: 34 ident: bib9 article-title: A review of the fundamental concepts of measurement publication-title: Measurement – volume: 2 start-page: 93 year: January 1977 end-page: 111 ident: bib15 article-title: Units of measure as a data attribute publication-title: Comput. Lang. – volume: 51 start-page: S183 year: 2014 ident: 10.1016/j.measen.2024.101796_bib4 article-title: Evaluation of mass measurements in accordance with the GUM publication-title: Metrologia doi: 10.1088/0026-1394/51/4/S183 – year: 1980 ident: 10.1016/j.measen.2024.101796_bib6 article-title: The formulae-as-types notion of construction – volume: vol. XII start-page: 331 year: 2022 ident: 10.1016/j.measen.2024.101796_bib20 article-title: Type systems for programs respecting dimensions – volume: 2 start-page: 25 issue: 1 year: 1984 ident: 10.1016/j.measen.2024.101796_bib9 article-title: A review of the fundamental concepts of measurement publication-title: Measurement doi: 10.1016/0263-2241(84)90020-4 – volume: vol. 1 year: 1958 ident: 10.1016/j.measen.2024.101796_bib5 – volume: 102 start-page: 2011 year: 2011 ident: 10.1016/j.measen.2024.101796_bib25 article-title: Evaluation of measurement data — supplement 2 to the “Guide to the expression of uncertainty in measurement” — extension to any number of output quantities publication-title: Joint Committee for Guides in Metrology, JCGM – volume: 100 start-page: 2008 year: 2008 ident: 10.1016/j.measen.2024.101796_bib24 article-title: Evaluation of measurement data — guide to the expression of uncertainty in measurement publication-title: Joint Committee for Guides in Metrology, JCGM – volume: vol. 5 year: 1971 ident: 10.1016/j.measen.2024.101796_bib1 – year: 2019 ident: 10.1016/j.measen.2024.101796_bib13 – year: 2022 ident: 10.1016/j.measen.2024.101796_bib3 article-title: Expressive type systems for metrology – volume: 605 year: 2022 ident: 10.1016/j.measen.2024.101796_bib12 article-title: Unclear units stymie science publication-title: Nature – start-page: 26 year: 2024 ident: 10.1016/j.measen.2024.101796_bib27 article-title: LabMate: a prospectus for types for MATLAB – volume: 7 issue: 1 year: 2012 ident: 10.1016/j.measen.2024.101796_bib8 article-title: A categorical framework for knowledge representation publication-title: PLoS One doi: 10.1371/journal.pone.0024274 – volume: 12 issue: 1 year: 2023 ident: 10.1016/j.measen.2024.101796_bib26 article-title: Measuring with confidence: leveraging expressive type systems for correct-by-construction software publication-title: Acta IMEKO doi: 10.21014/actaimeko.v12i1.1412 – year: 1995 ident: 10.1016/j.measen.2024.101796_bib10 – year: 2013 ident: 10.1016/j.measen.2024.101796_bib16 – year: 2013 ident: 10.1016/j.measen.2024.101796_bib2 – start-page: 268 year: 2010 ident: 10.1016/j.measen.2024.101796_bib17 article-title: Types for units-of-measure: theory and practice – year: 1986 ident: 10.1016/j.measen.2024.101796_bib7 – start-page: 121 year: 2018 ident: 10.1016/j.measen.2024.101796_bib18 article-title: The next 700 unit of measurement checkers – start-page: 147 year: 2009 ident: 10.1016/j.measen.2024.101796_bib21 article-title: Parameter estimation based on least squares methods – volume: 2 start-page: 93 issue: 3 year: 1977 ident: 10.1016/j.measen.2024.101796_bib15 article-title: Units of measure as a data attribute publication-title: Comput. Lang. doi: 10.1016/0096-0551(77)90010-8 – year: 2008 ident: 10.1016/j.measen.2024.101796_bib14 – year: 2002 ident: 10.1016/j.measen.2024.101796_bib11 article-title: Software support for physical quantities – year: 1981 ident: 10.1016/j.measen.2024.101796_bib22 – start-page: 273 year: 2022 ident: 10.1016/j.measen.2024.101796_bib19 article-title: Software representation of measured physical quantities – year: 2013 ident: 10.1016/j.measen.2024.101796_bib23 |
| SSID | ssj0002810124 |
| Score | 2.290026 |
| Snippet | In this paper, we look at how model structure and constraints can be incorporated into scientific computing using functional programming and, implicitly,... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 101796 |
| SubjectTerms | Dimensioned variable Functional programming Numerical computation Units of measurement |
| Title | Preserving model structure and constraints in scientific computing |
| URI | https://dx.doi.org/10.1016/j.measen.2024.101796 |
| Volume | 38 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2665-9174 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002810124 issn: 2665-9174 databaseCode: DOA dateStart: 20190101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2665-9174 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002810124 issn: 2665-9174 databaseCode: M~E dateStart: 20190101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELaWwgEOiKcoj8oHbiirXa-T2Me2YoVEqTgUqbco6wekFKfKLlVPSPxzZuw4DrCq6IFLtLK83qzn03g8_vwNIa_nuCYbZjPLYW_Cy4XJhLYisyqH4KRURSH8ReGj8vhYnJ7Kj5PJz3gX5vK8dE5cXcmL_2pqaANj49XZG5h7GBQa4DMYHZ5gdnj-k-GRVIEOwH0OZW7eBInYeFCgMCDEuhAbz4QNFyKRL-TZ5d83cSmLVZ5SDnEKjsWt23T8s2y7VfAy--cYhjYD0feo6SsAvDfN5suo_zrSyZad0V3zFc-NNPz7xE5UB10TpIAPW9d246wEyxMHMDgvWPexBmSowDM1W9p67xu0XXr36f1DsdWzhyTD2fQbnlqhcC3j09T9dyHtPxa4gXYYGW1nVRilwlGqMMotcpuVuURW4IcfKU3HvAAachOGt48XMD1L8O_X2R7gjIKWkwfkfr_boPsBJQ_JxLhH5N5Ig_IxOUh4oR4vdMALBbzQEV5o42jCCx3w8oR8Wr49OXyX9YU1MsXmRZEJiap4Wmo7U-C_Z2pR21zXRT03sD1fGcuLFddsZjlnTGuOKou2FoZx7FaLxVOy41pnnhGaMy1nTGpW15xLwyRfMWNMIWploG-5S7I4G9VF0E-prjPDLinjlFV9DBhiuwqAcO03n9_wl16Quwm4L8kOzK15Re6oy02z7vZ8bmbPY-EXS9yBdw |
| linkProvider | ISSN International Centre |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Preserving+model+structure+and+constraints+in+scientific+computing&rft.jtitle=Measurement.+Sensors&rft.au=Forbes%2C+Alistair&rft.au=Lines%2C+Keith&rft.au=Forsberg%2C+Fredrik+Nordvall&rft.au=McBride%2C+Conor&rft.date=2025-05-01&rft.issn=2665-9174&rft.eissn=2665-9174&rft.volume=38&rft.spage=101796&rft_id=info:doi/10.1016%2Fj.measen.2024.101796&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_measen_2024_101796 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2665-9174&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2665-9174&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2665-9174&client=summon |