Unit Types : A Radical Proposal

[John Bugner]

In the time library ( package.elm-lang.org/packages/elm-lang/core/4.0.3/Time ), there are many functions under the "Units" heading. Under the function `millisecond`, it says:

>Units of time, making it easier to specify things like a half-second (500 * millisecond) without remembering Elm’s underlying units of time.

I find this underwhelming, because nothing forces me to use these unit functions. I could write `every 5 toMsg` and the compiler will not stop me. How long of a time am I actually specifying? Probably 5 milliseconds, because I infer that it's probably using the same unit as JavaScript, but I can't know for sure. A beginner might think 5 seconds, because it's the unit that has no prefixes, or 5 minutes if 5 minutes seems appropriate to what the application does. This is very bad; There should never be doubt about what unit is being used, and the compiler should enforce this unit correctness. Currently, Elm can't do this, because `Time` is just an alias for `Float`.

To prevent this kind of error, I propose a new language construct that I call a "unit type". It would have the following properties:

(1) A definition that would look (very roughly) like this:

```

type unit Time as Float

    = Second

    | Millisecond == Second 0.0001

    | Nanosecond == Millisecond 0.0001

    | Minute == Second 60

    | Hour == Minute 60

    | Day == Hour 24

    | Year == Day 365

```

The point of the definition is to:

(a) Provide an easy way to define different units that measure the same thing (in this case, time, but you could do the same thing for length/height/depth in either metric or US imperial units) as constructors.

(b) Tell how they are related to eachother. (A minute is 60 seconds, an hour is 60 minutes, etc.) The compiler would check that all relations of the constructors eventually flow to a single base unit (in this case, `Second`). A cycle would be disallowed.

(c) Tell what type the unit is based on (in this case, `Float`). (Perhaps non-number types would be disallowed.)

(2) Given that `every` still has the same signature: `Time -> (Time -> msg) -> Sub msg`, `every 5 toMsg` would cause a compile-time error, because the types don't match; The function expects a number with a `Time` unit, but receives `5`, which is just a raw number (a number without any unit).

(3) When writing a function that has a parameter of type `Time`, pattern matching only matches the base unit constructor, not every constructor like a normal (data/enum) type. The compiler would automatically convert the other units to the base unit with the conversions that the programmer provided in the definition.

(4) Comparison, addition, and subtraction would be automatically implemented for the type, so two times of any combination of constructors could be compared, added, or subtracted with ease. `(Minute 5) - (Second 20) == (Millisecond 280000)` would "just work". "Time + Float" (or "Time + Length") would cause a compile-time error.

(5) Perhaps compound unit types like "Time^2" would be supported, so a "Time * Time" would yield "Time^2", "Time * Float" would yield "Time", and "Time * Length" would yield just that: "Time * Length". ("Force" would be an alias of "Mass * Length / (Second^2)".)

I know that this is a very radical proposal, (I don't know of any language that has a feature like this.) but I bring it up anyways, because although it's been 18 years since the mars probe crashed because of a unit error (one module assumed that the number it was getting was in metric units, and another assumed that it was getting it in US imperial units) ( https://en.wikipedia.org/wiki/Mars_Climate_Orbiter ), I'm amazed that since then, programming languages have done nothing to prevent this kind of error from happening again, besides just admonishing programmers to be careful. (As if the NASA programmers at the time weren't already trying to!)

Letting `5` be a legal unitless `Time` value is just as silly and dangerous as letting `bool a = 2;` be a legal statement in C. data/enum types prevent this from happening to `Bool` in Elm, and unit types could prevent the same kind of thing from happening to `Time`.

Questions, comments, related thoughts, etc are welcome.

[Duane Johnson]

This would be a nice fix to the Radians / Degrees issue too. Every language seems to settle on one or the other as "the base unit" but newcomers have to learn the assumption or face bad accidental outputs.

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[art yerkes]

F# is kind of radical in that it has units.

https://fsharpforfunandprofit.com/posts/units-of-measure/

It's not perfect, but it could serve as a starting point for evaluating different ways of having units as part of a language.

[Duane Johnson]

On Thu, Jul 28, 2016 at 1:11 PM, art yerkes <art.y...@gmail.com> wrote:

F# is kind of radical in that it has units.

https://fsharpforfunandprofit.com/posts/units-of-measure/

Wow, very neat! I like that F# keeps the units after the number, actually adding to readability.

[Joey Eremondi]

There is also some prior art with Haskell for this:

https://hackage.haskell.org/package/uom-plugin

https://hackage.haskell.org/package/units

https://hackage.haskell.org/package/Measure

--

[OvermindDL1]

Could possible do it 'now' with

```elm

type Time

  = Time_Value Float

milliseconds m = seconds <| m/1000

seconds s = Time_Value s

minutes m = seconds <| m*60

from_json json =

  Json.Decode.decodeString Json.Decode.float json |> Result.map (\t -> Time_Value t)

to_seconds (Time_Value t) = t

to_minutes t = 60 * (to_seconds t)

to_json t = Json.Encode.float <| to_seconds t

```

If you do not expose the constructor of the type then it should be a fully opaque type, only able to be constructed via things like `milliseconds 500` or so.

[John Bugner]

>This would be a nice fix to the Radians / Degrees issue too. Every language seems to settle on one or the other as "the base unit" but newcomers have to learn the assumption or face bad accidental outputs.

Yes, `degrees`, `radians`, and `turns` in `Basics` suffer the same problem.

>F# is kind of radical in that it has units.

I didn't know this! (I have heard of F#, but I had never used or read some of its code.) It pleases me to know that I'm not the only one to think that is a problem, and that it can be solved by this solution! (F#'s implementation seems slightly different from what I am imagining, but close enough.)

I'm curious though, does F# use its unit/measure types widely? or do common library functions (like those about time, angles, etc) still take a raw float type where it could take a unit/measure float type? How often do common 3rd-party libraries use this feature? How often do average-joe programmers use this feature?

>Could possible do it 'now' with

>...

>If you do not expose the constructor of the type then it should be a fully opaque type, only able to be constructed via things like `milliseconds 500` or so.

As a work-around that uses only current features, I like this. It's an improvement over the current system of just having `Time` be an alias of `Float`. (Heck, `Angle` isn't even an alias! The angle functions' signatures are just `Float -> Float`!)

[John Bugner]

Also, thinking about this further, any definition of conversions between types is probably best expressed as a function, because a conversion is not always a simple multiple (like 1 yard = 3 feet). Take, for example, the conversion between degrees celsius and degrees fahrenheit. (Note that if `Temp` was a unit type, it's "base" unit should be Kelvin (or Rankine, I suppose.), because Kelvin starts at 0, which lets multiplying temperatures by a raw number make sense.)

[OvermindDL1]

Yep, that is why I like the style that you can do with current code.  :-)

[Max Goldstein]

Here's another piece of prior art, Frink:

http://futureboy.us/frinkdocs/

Also, have you considered that floating point arithmetic might totally screw things up, especially with angles where irrational numbers are involved?

+1 for experimenting with the types we already have.

[Anton Lorenzen]

I just created a small library for this:
https://github.com/anfelor/elm-units

It allows for time to be used like this:
Units.Time.every (30 ::: milliseconds) Tick

[Duane Johnson]

On Fri, Jul 29, 2016 at 10:48 AM, Anton Lorenzen <anf...@posteo.de> wrote:

I just created a small library for this:
https://github.com/anfelor/elm-units

It allows for time to be used like this:
Units.Time.every (30 ::: milliseconds) Tick

Neat! I'm surprised at what can be done with existing syntax and types.

[John Bugner]

I like the clever use of the (:::) function to make its function argument (somewhat) look like a type.

[John Bugner]

Btw, when using (:::) this way, it's nice to set the operator precedence to something lower than 9 so you can say `2 * 5 + 3 ::: radians` without having to put brackets around the numbers. I think `infix 5 :::` gives the right precedence; Looking at the core docs ( https://github.com/elm-lang/core/blob/master/src/Basics.elm ), (+) and (-) are 6, and (==), (/=), etc are 4.

[Max Goldstein]

Just be careful with (:::) in particular. Some other libraries already define it, and there's currently no good way to resolve conflicts.

[Job van der Zwan]

On Thursday, 28 July 2016 20:42:44 UTC+2, John Bugner wrote:

(5) Perhaps compound unit types like "Time^2" would be supported, so a "Time * Time" would yield "Time^2", "Time * Float" would yield "Time", and "Time * Length" would yield just that: "Time * Length". ("Force" would be an alias of "Mass * Length / (Second^2)".)

Here's how Julia handles this, although it seems to require hand-coding all of of the promotion rules:

http://docs.julialang.org/en/release-0.4/devdocs/promote-op/

(understanding this may require a bit of understanding Julia's type system, which lets you define your own types down to the bit-level, complete with custom conversion and promotion rules)

Not sure how that might translate to Elm's type system, but I guess using custom infix operators will be part of it (except for not allowing redefining the built-in ones). Off-topic, but is this really all documentation available on infix operators? Because I don't really think that's good enough:

http://elm-lang.org/docs/syntax#infix-operators 

[John Bugner]

I just realized that Elm already uses this strategy... with `Color`! It has two constructors: RGBA and HSLA ( https://github.com/elm-lang/core/blob/master/src/Color.elm ), but neither is exported. This forces the user to use the various 'creation' functions to create one ( http://package.elm-lang.org/packages/elm-lang/core/4.0.4/Color ). There's no reason why the same thing couldn't be done with an `Angle` type. All the trig functions and angle creation functions in `Basics` should probably be moved to a new `Angle` module too then.