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From: rosen@enst.fr (Jean-Pierre Rosen)
Newsgroups: comp.lang.ada
Subject: Re: Types with physical dimension
Date: 5 Oct 1994 09:38:05 +0100
Organization: Ecole Nationale Superieure des Telecommunications, Paris France
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References: <GRAHAM.94Sep27181841@canopus.clsi.COM>
 <SAL714.94Oct3133110@rs710.gsfc.nasa.gov>
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Date: 1994-10-05T09:38:05+01:00
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In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov>, sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:
> I run robots with Ada, so I deal with real dimensions all the time. Very early
> on, I started to write a package that enforced dimensionality; I defined 
> METERS, METERS_PER_SECOND, etc. I quickly discovered that even simple equations
> need up to cubic dimensions, in all combinations of length, mass and time.
> Defining all these types and the associated operators was far too
> time-consuming to be worth it. So now I rely on code reviews and careful
> testing.
> 
> The moral; strong typing is nice, but is no substitute for careful design
> and thorough testing.
> 
There is another solution: run-time checking of dimensionality. You define a
type like:
   type Physical is
      record
         Length : Dimension;
         Time   : Dimension;
         Mass   : Dimension;
         Charge : Dimension;
         Value  : Float;
      end record;
 (Dimension being some Integer type).
You redefine operators so that "+" and "-" operate only if the dimensions are
the same (and raise Dimension_error otherwise), and "*" and "/" add 
(or subtract) dimensions.
Note that if you are concerned about efficiency, you use this type for 
debugging, and then change it to:
   type Physical is new Float;
for the working version (assuming a Value_of function to access the value).

Alternatively, you can make the dimensions discriminants; this will improve
safety and allow you to define nice subtypes like:
   subtype Meters is Physical(1, 0, 0, 0);
but will make moving to plane Floats more difficult.

Acknowledgements:
  I saw this idea in a paper long ago. As far as I recall, it was by
  N. Cohen. Norm, are you listening?