Show HN: Numbat – A programming language with physical dimensions as types

How does something like `let y: Time = 1 year` work? Does it take into consideration the idea of leap years and leap seconds, counting a single year as 365.2422 days[0]? Or does it count as 365 days?<p>I got curious and installed the CLI tool[1] and found that it does indeed account for leap second &#x2F; leap years:<p>&gt;&gt;&gt; let jahr: Time = 1 year<p>&gt;&gt;&gt; let tage: Time = jahr -&gt; days<p>&gt;&gt;&gt; tage<p><pre><code> = 365.243 day [Time] </code></pre> References:<p>0: <a href="https:&#x2F;&#x2F;museum.seiko.co.jp&#x2F;en&#x2F;knowledge&#x2F;story_01&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;museum.seiko.co.jp&#x2F;en&#x2F;knowledge&#x2F;story_01&#x2F;</a><p>1: <a href="https:&#x2F;&#x2F;numbat.dev&#x2F;doc&#x2F;cli-installation.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;numbat.dev&#x2F;doc&#x2F;cli-installation.html</a>

How does Numbat infer the type&#x2F;unit for operations that involve transcendental functions like the trigonometric functions and the natural logarithm? How about for exponents that are not integers (rational or irrational)?<p>I&#x27;ve seen from to time some empirical equations that result to this. Usually, it&#x27;s just hand-waved away and the non-integer units are ignored or dropped when the transcendental function is evaluated. I guess the trivial answer is probably add an extra factor with a value of 1 with the reciprocal units to result to the said type 1 for dimensionless units?

the classic problem for such number systems is linear algebra <a href="https:&#x2F;&#x2F;yosefk.com&#x2F;blog&#x2F;can-your-static-type-system-handle-linear-algebra.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;yosefk.com&#x2F;blog&#x2F;can-your-static-type-system-handle-l...</a><p>the issue is that each column and each row of a matrix can have different units. worse, gauss-jordan elimination chooses which rows to operate on dynamically. there is eventually a solution to this problem in c++ far down the comments thread<p>i don&#x27;t see anything in <a href="https:&#x2F;&#x2F;numbat.dev&#x2F;doc&#x2F;type-system.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;numbat.dev&#x2F;doc&#x2F;type-system.html</a> about aggregate types such as vectors, matrices, maps, arrays, lists, trees, records, etc., though it does have a suggestively named scalar type. i wonder how it handles this sort of thing

If I’m reading this correctly, the Frink language has similar features (and also seems darn useful!) <a href="https:&#x2F;&#x2F;frinklang.org&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;frinklang.org&#x2F;</a>

A month cannot be unambiguously represented as a length of time, as the length of a month is variable.

Still reading the article, and really intrigued by and love this idea. But can I just say that I find this intro extremely well written. I feel like the writer is reading my thought process almost. Wvery time I start to form questions about decisions made in the language, it seems to answer them one or two paragraphs later. I feel like this is incredibly rare and yet incredibly important in an intro piece. Nicely done on the author[&#x27;s]&#x2F;[s&#x27;] part.

This is really cool!<p>If the author is around, I notice in the README you mention the GNU units program, which I use quite a bit. I&#x27;m curious if you&#x27;ve made any notable divergences from it?

First project I&#x27;ve ever seen that made me instantly sponsor it. Then to only find out you wrote fd and hexyl and some other classics. Great work.

In theory it can help to compute how many ore belts I need for producing full belt of white sciences in Factorio?

Impressive!<p>One thing I find unintuitive is the implementation of variable length units (like months or years) as an averaged constant. Then again, perhaps that’s the point - and e.g. working with months without specifying a calendar is just unintuitive.

Can it be used as a date calculator? I didn&#x27;t see a way to specify &quot;today&quot; or &quot;tomorrow&quot;. Like &quot;today&quot; + 14 days etc.

Apparently this replaces <a href="https:&#x2F;&#x2F;github.com&#x2F;sharkdp&#x2F;insect">https:&#x2F;&#x2F;github.com&#x2F;sharkdp&#x2F;insect</a>

It’s interesting that they support currency units. Wonder how the conversion works. Probably have to provide conversion factor as well?

Modeling compile-time units was one of the memes of c++ 11. One of many examples:<p><a href="https:&#x2F;&#x2F;benjaminjurke.com&#x2F;content&#x2F;articles&#x2F;2015&#x2F;compile-time-numerical-unit-dimension-checking&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;benjaminjurke.com&#x2F;content&#x2F;articles&#x2F;2015&#x2F;compile-time...</a>

So if I try to get the Falcon to do the Kessel run in two Parsecs, Numbat will raise an exception.

This is great. I want this as an addon to JS and Python.

Cool that you can use actual 1 × 2 multiplication sign or 4 ⋅ 8 instead of that kludge of an asterisk *

&gt; On the other hand, 3 months + 2 lightyears is ill-typed, because the right-hand side is of type Length. You can change ‘years’ to ‘lightyears’ in the example above to see the resulting compiler error.<p>Why not both? Make lightyears both Length and Time

I can&#x27;t resist mentioning F# Units of Measure aka UoM :)<p><a href="https:&#x2F;&#x2F;learn.microsoft.com&#x2F;en-us&#x2F;dotnet&#x2F;fsharp&#x2F;language-reference&#x2F;units-of-measure" rel="nofollow noreferrer">https:&#x2F;&#x2F;learn.microsoft.com&#x2F;en-us&#x2F;dotnet&#x2F;fsharp&#x2F;language-ref...</a>

Super cool! I love when programming languages try to do more with types.<p>Julia has a neat little library called Unitful.jl[1] which does almost exactly what Numbat does by taking advantage of Julia&#x27;s extremely flexible type system. Extending it to cover all of Numbat&#x27;s functionality could be trivially accomplished in a few lines. In fact, fun type magic like this is pretty much my primary motivation for using Julia in the first place.<p>Not that I want to detract from the author&#x27;s hard work, of course, I&#x27;m just very excited about Julia! Numbat is obviously an awesome project, and I can&#x27;t wait to see where it leads!<p>[1] <a href="https:&#x2F;&#x2F;painterqubits.github.io&#x2F;Unitful.jl&#x2F;stable&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;painterqubits.github.io&#x2F;Unitful.jl&#x2F;stable&#x2F;</a>

Or you could just use Nim [0], where this sort of thing can be implemented in Nim&#x27;s macro system. Then you have a regular programming language combined with CT safe units. :)<p>It even pretty much looks identical to those Numbat snippets!<p><pre><code> import unchained let earth_mass = 5.972168e24.kg let solar_mass = 1.9885e30.kg let lunar_mass = 7.342e22.kg let distance_sun = 1.AU # astronomical unit let distance_moon = 384_400.km let force_sun = G_Newton * earth_mass * solar_mass &#x2F; distance_sun let force_moon = G_Newton * earth_mass * lunar_mass &#x2F; distance_moon echo force_sun &#x2F; force_moon # 69593.6 UnitLess </code></pre> Sorry for the shameless plug. ;) Numbat looks quite cool though and the article talks about a lot of things to think about when writing such a program &#x2F; lib &#x2F; programming language.<p>[0]: <a href="https:&#x2F;&#x2F;github.com&#x2F;SciNim&#x2F;Unchained">https:&#x2F;&#x2F;github.com&#x2F;SciNim&#x2F;Unchained</a>

Frink (<a href="https:&#x2F;&#x2F;frinklang.org&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;frinklang.org&#x2F;</a>) is an older language with similar design goals.<p>Frink runs on the JVM and is also available on Android.<p>I use it as a general purpose calculator on my smartphone.<p>It&#x27;s really nice that Numbat is written in Rust :) Will have to try it out.

Remind me of GNU Units <a href="https:&#x2F;&#x2F;www.gnu.org&#x2F;software&#x2F;units&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.gnu.org&#x2F;software&#x2F;units&#x2F;</a>

Ada’s type system also allows compile-time checking of units like physical dimensions:<p><a href="https:&#x2F;&#x2F;gcc.gnu.org&#x2F;onlinedocs&#x2F;gcc-4.9.4&#x2F;gnat_ugn_unw&#x2F;Performing-Dimensionality-Analysis-in-GNAT.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;gcc.gnu.org&#x2F;onlinedocs&#x2F;gcc-4.9.4&#x2F;gnat_ugn_unw&#x2F;Perfor...</a><p><a href="https:&#x2F;&#x2F;blog.adacore.com&#x2F;uploads&#x2F;dc.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;blog.adacore.com&#x2F;uploads&#x2F;dc.pdf</a>

You don&#x27;t need a new programming language for something that C++ templates with integer constants give you for free.

<i>perform computations with physical units.</i><p>It has units awareness --- not necessarily only <i>physical</i> units.<p>For example; light, temperature and time are measured in units but they are not <i>physical</i> units --- aka 3 dimensional.