That's why pow(3m, 2) = 9 m^2, and not `the value 9 of type meter`. Of course, you can define the type `square meter` as well, and define `pow -> meters -> positive integer -> square meters`. However this quickly becomes overwhelming once you start doing more complex expressions with multiple types. What is the type of `pow (3kg^2 * m/s, 3/2)`?
Edit to add: also, there is a simple fact that "sin(pi/2 kg)" is just not defined, in programming or math or physics or any other useful system. It's definitely not 1kg, just like sin ( (pi/2) * 2) is not sin (pi/2) * sin (2).
Isn't the "special constant" exactly "value 1, type meters", defined as equal to "value <...very large number...> type atoms" etc?
If not, then what would be the result of the multiplication of 3 with "m"?
> Of course, you can define the type `square meter` as well, and define `pow -> meters -> positive integer -> square meters`
As long as your power is an integer, you can reduce it to multiplication. So what you'd really want to define is the result of "<value1 of type meter> * <value2 of type meter>", "(<value1 of type meter> * <value2 of type meter>) * <value3 of type meter>" etc.
What this gets you in the end is a type algebra, but that is also not exactly a new concept.