[Axiom-developer] Re: Dimensions as types...

[Ralf Hemmecke]

Hi Cliff,

> Looking ahead to units:

> Let's say I multiply meters:Length and seconds:Time together.  I want
> to end up with meters*seconds:Length*Time, which is both a new unit and
> a new dimensional type.

What do you think the code

main(): () == {
        a: Length := 2 centimeter;
        b: Time := 3 hour;
        c: (Length * Time) := a * b;
        import from Length * Time * Time;
        d := c * 3 second;
        stdout << "a = " << a << newline;
        stdout << "b = " << b << newline;
        stdout << "c = " << c << newline;
        stdout << "d = " << d << newline;
}

that I sent before represents?

Look at the line

       c: (Length * Time) := a * b;

It constructs a type Length*Time and imports the operations from that 
NEW domain. Only after that import it is clear what the * on the right 
hand side actually is. The * on the left and the * on the right hand 
side are terribly different. The first is of type

(Dimension, Dimension) -> Dimension

and the second of type

(Length, Time) -> Length*Time;

And my code is unable to do something like

Integer * String

because neither Integer nor String is of type Dimension, so the (first) 
* cannot apply.

Take your time and study my code in detail. At each step you should 
understand what it is doing.

For example, do you know why I could simply write

        a: Length := 2 centimeter;

? There is only a space between 2 and centimeter.

Ralf