CC: Functional dependencies question

[Ashley Yakeley]

In article <200305130355.h4D3ttcB013484@adric.fnmoc.navy.mil>,
 oleg@pobox.com wrote:

> Just for the record: yet another way to introduce negative numbers is
> through an explicit constructor Neg. For example:
> 	http://pobox.com/~oleg/ftp/Computation/type-arithmetics.html
> (sorry, the code uses C++ templates. The idea is just the same
> however: a mere Prolog in a more verbose notation).  The above example
> demonstrates division of signed Peano numbers. The Neg constructor
> becomes quite handy then.

I prefer NegativeSucc, i.e. -(n+1) or -n-1. My integer types are thus T 
or NegativeSucc T for any natural type T, and the two don't overlap.

Another trick is to use the same class for addition and subtraction:

  class Add a b ab | a b -> ab, ab a -> b;

I found you can't build the instances if you have all three possible 
fundeps (because of overlaps), but you can with two.

<http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/hbase/Source/HBase/TypeCa
lc/>.

As for dimensions, what would be most interesting would be to allow the 
user to add their own "basis" units, so for instance:

  module MyModule where
  import PhysicalUnits

  -- new basis unit
  type Cost = [whatever]

  dollar :: Cost
  dollar = [whatever]

  goldValue :: (Div Mass Cost t) => t
  goldValue = ...

...but that may be hard and/or messy.

-- 
Ashley Yakeley, Seattle WA