The modeling of unit systems with types is fraught with all sorts of inconsistencies and design tradeoffs. There are quantities that have the same dimensions, but shouldn't be compared or allow arithmetic between them. Many issues with Temperature scales and how to interpret differences in these spaces.

I think a pretty well thought out approach to this is the mp-units library in c++ that uses the ISQ(International System of Quantities) [1].

There are some great blog posts on their site about modeling units systems and dimensions. Fingers crossed it may even be added to the standard library in C++29.

[1]: https://mpusz.github.io/mp-units/latest/

I will say that the OpenFOAM C++ library supports dimensions in a more user friendly way than this, with support for both vectors/matrices and for checking units when you take partial derivatives of your quantities.

There is even native support for reading dimensioned values from input files, so your user can specify "speed 12.7 [ft/s]" irrespective of what units you use internally in the code processing that input file. It just gets converted (or throws an error).

See e.g. this, from 4.2.6 onwards: https://doc.cfd.direct/openfoam/user-guide-v12/basic-file-fo...

Author here, thanks for posting!

On the Haskell Discourse [0], someone posted about another Haskell library, units [1], which allows to define unit systems NOT limited to the 7 physical dimensions. For example, adding a base dimension for currency would be nice to model electricity prices in currency per energy.

[0]: https://discourse.haskell.org/t/blog-post-scientific-computi...

[1]: https://hackage.haskell.org/package/units

I have yet to see a language which does units better than F#: https://learn.microsoft.com/en-us/dotnet/fsharp/language-ref... It is one of the main reasons I use F# over other functional languages.

Doing it within an existing type system is more trouble than it’s worth: the algebra of units is simple, but it doesn’t apply to other types without stretching the compiler. It is far easier to have a distinct subsystem with measure types specifically identified.

Also in Julia: https://painterqubits.github.io/Unitful.jl/stable/