Editing Dimensional analysis (section)

== Programming languages ==
Dimensional correctness as part of [[type checking]] has been studied since 1977.<ref>{{cite journal |last=Gehani |first=N. |year=1977 |title=Units of measure as a data attribute |journal=Comput. Lang. |volume=2 |issue=3 |pages=93–111 |doi=10.1016/0096-0551(77)90010-8}}</ref>
Implementations for Ada<ref>{{cite journal |last=Gehani |first=N. |date=June 1985 |title=Ada's derived types and units of measure |journal=Software: Practice and Experience |volume=15 |issue=6 |pages=555–569 |doi=10.1002/spe.4380150604 |s2cid=40558757}}</ref> and C++<ref>{{cite journal |last1=Cmelik |first1=R. F. |last2=Gehani |first2=N. H. |date=May 1988 |title=Dimensional analysis with C++ |journal=IEEE Software |volume=5 |issue=3 |pages=21–27 |doi=10.1109/52.2021 |s2cid=22450087}}</ref> were described in 1985 and 1988.
Kennedy's 1996 thesis describes an implementation in [[Standard ML]],<ref>{{cite thesis |first=Andrew J. |last=Kennedy |title=Programming languages and dimensions |type=Phd |date=April 1996 |publisher=University of Cambridge |id=UCAM-CL-TR-391 |issn=1476-2986 |volume=391 |url=http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-391.html}}</ref> and later in [[F Sharp (programming language)|F#]].<ref>{{cite book |last=Kennedy |first=A. |title=Central European Functional Programming School. CEFP 2009 |publisher=Springer |year=2010 |isbn=978-3-642-17684-5 |editor-last=Horváth |editor-first=Z. |series=Lecture Notes in Computer Science |volume=6299 |pages=268–305 |chapter=Types for Units-of-Measure: Theory and Practice |citeseerx=10.1.1.174.6901 |doi=10.1007/978-3-642-17685-2_8 |editor2-last=Plasmeijer |editor2-first=R. |editor3-last=Zsók |editor3-first=V.}}</ref> There are implementations for [[Haskell]],<ref>{{cite journal |last=Gundry |first=Adam |date=December 2015 |title=A typechecker plugin for units of measure: domain-specific constraint solving in GHC Haskell |url=http://adam.gundry.co.uk/pub/typechecker-plugins/typechecker-plugins-2015-07-17.pdf |url-status=live |journal=SIGPLAN Notices |volume=50 |issue=12 |pages=11–22 |doi=10.1145/2887747.2804305 |archive-url=https://web.archive.org/web/20170810000458/http://adam.gundry.co.uk/pub/typechecker-plugins/typechecker-plugins-2015-07-17.pdf |archive-date=2017-08-10}}</ref> [[OCaml]],<ref>{{cite book |last1=Garrigue |first1=J. |title=28ièmes Journées Francophones des Langaeges Applicatifs, Jan 2017, Gourette, France |last2=Ly |first2=D. |year=2017 |language=fr |chapter=Des unités dans le typeur |id=hal-01503084 |chapter-url=https://www.math.nagoya-u.ac.jp/~garrigue/papers/ocamldim.pdf |archive-url=https://web.archive.org/web/20201110105231/https://www.math.nagoya-u.ac.jp/~garrigue/papers/ocamldim.pdf |archive-date=2020-11-10 |url-status=live}}</ref> and [[Rust (programming language)|Rust]],<ref>{{cite web |last=Teller |first=David |date=January 2020 |title=Units of Measure in Rust with Refinement Types |url=https://yoric.github.io/post/uom.rs/}}</ref> Python,<ref>{{cite web |last=Grecco |first=Hernan E. |date=2022 |title=Pint: makes units easy |url=https://pint.readthedocs.io/en/stable/}}</ref> and a code checker for [[Fortran]].<ref>{{cite web |date=2018 |title=CamFort: Specify, verify, and refactor Fortran code |url=https://camfort.github.io/ |publisher=University of Cambridge; University of Kent}}</ref><ref>{{cite book |last1=Bennich-Björkman |first1=O. |title=Proceedings of the 11th ACM SIGPLAN International Conference on Software Language Engineering |last2=McKeever |first2=S. |date=2018 |isbn=978-1-4503-6029-6 |pages=121–132 |chapter=The next 700 unit of measurement checkers |doi=10.1145/3276604.3276613 |s2cid=53089559}}</ref><br />
Griffioen's 2019 thesis extended Kennedy's [[Hindley–Milner type system]] to support Hart's matrices.<ref>{{harvnb|Hart|1995}}</ref><ref>{{cite thesis |first=P. |last=Griffioen |title=A unit-aware matrix language and its application in control and auditing |publisher=University of Amsterdam |year=2019 |url=https://pure.uva.nl/ws/files/42206706/Thesis.pdf |archive-url=https://web.archive.org/web/20200221072448/https://pure.uva.nl/ws/files/42206706/Thesis.pdf |archive-date=2020-02-21 |url-status=live |hdl=11245.1/fd7be191-700f-4468-a329-4c8ecd9007ba}}</ref>
McBride and Nordvall-Forsberg show how to use [[dependent type]]s to extend type systems for units of measure.<ref>{{cite book |last1=McBride |first1=Conor |url= |title=Advanced Mathematical and Computational Tools in Metrology and Testing XII |last2=Nordvall-Forsberg |first2=Fredrik |date=2022 |publisher=World Scientific |isbn=9789811242380 |series=Advances in Mathematics for Applied Sciences |pages=331–345 |chapter=Type systems for programs respecting dimensions |doi=10.1142/9789811242380_0020 |author-link=Conor McBride |chapter-url=https://strathprints.strath.ac.uk/76626/1/McBride_etal_amctmtxii2021_type_systems_for_programs_respecting_dimensions.pdf |archive-url=https://web.archive.org/web/20220517115417/https://strathprints.strath.ac.uk/76626/1/McBride_etal_amctmtxii2021_type_systems_for_programs_respecting_dimensions.pdf |archive-date=2022-05-17 |url-status=live |s2cid=243831207}}</ref>

Mathematica 13.2 has a function for transformations with quantities named NondimensionalizationTransform that applies a nondimensionalization transform to an equation.<ref>{{Cite web |title=NondimensionalizationTransform—Wolfram Language Documentation |url=https://reference.wolfram.com/language/ref/NondimensionalizationTransform.html.en |access-date=2023-04-19 |website=reference.wolfram.com}}</ref> Mathematica also has a function to find the dimensions of a unit such as 1 J named UnitDimensions.<ref>{{Cite web |title=UnitDimensions—Wolfram Language Documentation |url=https://reference.wolfram.com/language/ref/UnitDimensions.html.en |access-date=2023-04-19 |website=reference.wolfram.com}}</ref> Mathematica also has a function that will find dimensionally equivalent combinations of a subset of physical quantities named DimensionalCombations.<ref>{{Cite web |title=DimensionalCombinations—Wolfram Language Documentation |url=https://reference.wolfram.com/language/ref/DimensionalCombinations.html.en |access-date=2023-04-19 |website=reference.wolfram.com}}</ref> Mathematica can also factor out certain dimension with UnitDimensions by specifying an argument to the function UnityDimensions.<ref name=":0">{{Cite web |title=UnityDimensions—Wolfram Language Documentation |url=https://reference.wolfram.com/language/ref/UnityDimensions.html.en |access-date=2023-04-19 |website=reference.wolfram.com}}</ref> For example, you can use UnityDimensions to factor out angles.<ref name=":0" /> In addition to UnitDimensions, Mathematica can find the dimensions of a QuantityVariable with the function QuantityVariableDimensions.<ref>{{Cite web |title=QuantityVariableDimensions—Wolfram Language Documentation |url=https://reference.wolfram.com/language/ref/QuantityVariableDimensions.html.en |access-date=2023-04-19 |website=reference.wolfram.com}}</ref>