On Friday 20 May 2005 08:11, "TSa (Thomas Sandlaß)" wrote:
> John Macdonald wrote:
> > ... (and there may be additional
> > operator attributes that make sense there too, although none
> > come immediately to mind).
>
> Well, I wonder why people neglect the fact that the
> neutral/identity element is not a property of the operator
> alone?! Besides the associativity and commutativity of the
> operator the inverse element---or the left and right
> one---with respect to the underlying representation come at
> least to my mind :)
Yes, a number of operators have an inverse on Boolean 0 and 1
only.
> This would give an "axiomatic" type system:
>
> class Num does Group[Num,+,0] {...}
> class Num does Field[Num,+,0,*,1] {...}
> class Str does Monoid[Str,~,''] {...}
>
> class Complex does Field[Array[2] of Num,+,[0,0],*,[1,0]]
> {...}
>
> class 3DVector does VectorSpace[Array[3] of Num,+,[0,0,0]]
> {...}
>
> And it provides valuable information to the optimizer.
--
Edward Cherlin
Generalist & activist--Linux, languages, literacy and more
"A knot! Oh, do let me help to undo it!"
--Alice in Wonderland
http://cherlin.blogspot.com
