[eyelidlessness]

If you look upthread, there was a mention of F# unit types. Taking off my programmer hat and returning to my middle school anecdote which also evidently made no sense: expression of a unit without a value is (or should be to my mind, based on my education) a cast, not a computation of N+1 values.

- 1 is unitless

- 1 * m casts the value to a value 1 of unit m = 1m

- 1 * m * m casts the value 1 * m = 1m to 1m then casts 1m to m which = 1m

Admittedly my educational background here might be wildly unconventional but it certainly prepared me for interoperable unit types as a concept without changing values (~precision considerations).

[linkdd]

> If you look upthread, there was a mention of F# unit types.

And the syntax is `3<unit>` not `3 * unit`

- 1 is a scalar - 1m is a quantity - 2 * 1m "casts" 2 to a meter, but really this is just multiplying a quantity by a scalar - 2 * 1m * 1m "casts" 2 to meter², multiplying 2 quantities then by a scalar

I insist, `1 * m` does not make sense. This is not a valid mathematical expression, because a unit can never be on its own without a value.

> expression of a unit without a value is (or should be to my mind, based on my education) a cast

There is no casting in math. Mainly because there is no types, only objects with operations. A vector is not a scalar and you can't cast it into a scalar.

A quantity is not a scalar either, and you can't cast one into another.

A quantity is an object, you can multiply 2 quantities together, but you can't add them if they are different. You can multiply a quantity to a scalar, but you still can't add a scalar to a quantity.

[eyelidlessness]

> And the syntax is `3<unit>` not `3 * unit`

Well, yeah, F# represents this at the type level. Which I’ve said elsewhere in the discussion is preferable. Not knowing Go, but knowing it only recently gained generics, I read multiplying by `time.Seconds` (which does not have a visible 1 associated with it) as perhaps performing an operator-overloaded type cast to a value/type with the Seconds unit assigned to it. I’ve since learned that Go also does not support operator overloading, so I now know that wouldn’t be the case. But had that been the case, it isn’t inconceivable that unitlessValue * valuelessUnit * valuelessUnit = unitlessValue * valuelessUnit. Because…

> I insist, `1 * m` does not make sense. This is not a valid mathematical expression, because a unit can never be on its own without a value.

Well, if you insist! But you seem to be imposing “mathematical expression” on an expression space where that’s already not the case? Whatever you may think of operator overloading, it is a thing that exists and it is a thing that “makes sense” to people using it idiomatically.

Even in languages without overloading, expressions which look like maths don’t necessarily have a corresponding mathematical representation. An equals infix operator in maths is a statement, establishing an immutable fact. Some languages like Erlang honor this, many (most? I strongly suspect most) don’t! I couldn’t guess without researching it also treat infix = statements as an expression which evaluated to a value.

The syntax of infix operators is generally inspired by mathematical notation, but it’s hardly beholden to that. The syntax of programming languages generally is not beholden to mathematical notation. Reacting as if it’s impossibly absurd that someone might read 1 * time.Seconds * time.Seconds as anything other than 1 * 1s * 1s is just snobbery.

Not knowing Go, I focused on the syntax and the explicit values, and tried to build a syntax tree on top of it. I’m not a fan of infix operators, and I am a fan of lisps, so my mental syntax model was (* (* 1 time.Seconds) time.Seconds)), which still doesn’t “make sense” mathematically, but it can make sense if `*` is a polymorphic function which accepts unquantified units.

[linkdd]

> Not knowing Go, but knowing it only recently gained generics, I read multiplying by `time.Seconds` (which does not have a visible 1 associated with it) as perhaps performing an operator-overloaded type cast to a value/type with the Seconds unit assigned to it.

This sums up your incomprehension. `time.Seconds` is just a constant. An integer with the value `1_000_000` meaning 1 million of nanoseconds.

In an expression of the form `a * b` you should always read `a` and `b` as constants. This is true for EVERY programming language.

> it isn’t inconceivable that unitlessValue * valuelessUnit * valuelessUnit = unitlessValue * valuelessUnit.

It is. For example, what would be the meaning of this:

  struct Foo {
    // ...
  }

  2 * Foo

Valueless unit (or any type) is just not a thing, not in math, not in any programming language.

> But you seem to be imposing “mathematical expression” on an expression space where that’s already not the case? Whatever you may think of operator overloading, it is a thing that exists and it is a thing that “makes sense” to people using it idiomatically.

Operator overloading works on typed values, not "valueless" types. In some programming languages (like Python), class are values too, but why implement `a * MyClass` when you can write `MyClass(a)` which is 100% clearer on the intent?

Using operator overloading for types to implement casting is just black magic.

> expressions which look like maths don’t necessarily have a corresponding mathematical representation

Programming languages and the whole field of Computer Science is a branch of mathematics. They are not a natural language like english or german. They are an extension of maths.

> An equals infix operator in maths is a statement, establishing an immutable fact.

An operator only has meaning within the theory you use it.

For example:

  `Matrix_A * Matrix_B` is not the same `*` as `Number_A * Number_B`
  `1 + 2` is not the same `+` as `1 + 2 + 3 + ...`
  `a = 3` in a math theorem is ont the same `=` as `a = 3` in a programming language (and that depends on the programming language)

As long as the theory defines the operators and the rules on how to use them, it does not matter which symbol you use. I can write a language where you have `<-` instead of `=`, and the mathematical rules (precedence, associativity, commutativity, ...) will be the same.

> Reacting as if it’s impossibly absurd that someone might read 1 * time.Seconds * time.Seconds as anything other than 1 * 1s * 1s is just snobbery.

First, that's not what I said. You should read that as `scalar * constant * constant` because reading that as `scalar * unit * unit` does not make sense nor in math, nor in any programming language.

If caring about readability and consistency is snobbery, then so be it.

> Not knowing Go, I focused on the syntax and the explicit values, and tried to build a syntax tree on top of it.

And the syntax is pretty explicit, because it's the same as math or any programming language: `scalar * constant * constant`. This is why using math as a point of reference is useful, you can easily make sense of what you're reading, no matter the syntax.

> I am a fan of lisps, so my mental syntax model was (* (* 1 time.Seconds) time.Seconds))

I still read this as `(* (* scalar constant) constant))`. And I expect your compiler/interpreter to throw an error if `time.Seconds` is anything without a clear value to evaluate the expression properly.

And I would expect to read `(* (* 1 (seconds 1) (seconds 1)))` as `scalar * quantity * quantity`, and I would expect to get square seconds as an output.

Anything else would not be correct and have little to no use.