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

[Ralf Hemmecke]

> I just wanted to point out that you can give the Aldor Category "Dimension" an
> algebraic structure. This is in fact one of the main advantages of Aldor over
> SPAD.
>
> The code will read roughly as follows:
>
> Scalar: Dimension with {
>         scalar: %;
> } == AuxiliaryDimension add {
>         scalar: % == [1, ""];
> }
>
> DimensionThing: Group == add {
>         Rep == Dimension;
>         1: % == per ConstantDimension;
>         (x: %) * (y: %): % == per(x * y);
>         (x: %) / (y: %): % == ...
> }

Yep, that is exactly what I called a wrapper domain in my previous mail. 
And note that the line

(x: %) * (y: %): % == per(x * y);

is wrong. It should read "per(rep x * rep y)" on the right hand side.
And note also that the * on the right hand side is the _domain 
constructor_ that I defined in the file dimension.as.

The main point is that one defines the various dimension domains like 
Length, Time, etc. on the top level with basically no relation to each 
other. In order to work with these things one creates another domain 
that has domains like Length, Time, Mass, etc as elements.

Ralf

PS: Martin probably wanted Scalar = ConstantDimension. No?