Hi Paul, Yes, you've got the idea. The following document shows one such attempt to construct a system of traits for algebraic concepts: http://www.cs.rpi.edu/~schupp/entries/SOFTWARE/simpl/doc/AlgCpp.pdf also, more information is available starting at: http://www.cs.rpi.edu/~schupp/entries/SOFTWARE/simpl/ Cheers, Jeremy On Jul 7, 2004, at 7:32 PM, Paul C. Leopardi wrote:

Jeremy, Dave, I think I get it. See below. Best regards On Thursday 08 July 2004 02:25, David Abrahams wrote:

...

  Jeremy Graham Siek <jsiek@osl.iu.edu> writes:   > group_traits<T>::is_commutative       is_commutative_group<T>::type       is_commutative_group<T>::type::value

OK, for a type where you have one operation (a group). For a two operation type, I suppose you would then want

is_ring<T>::type is_ring<T>::type::value

is_commutative_ring<T>::type is_commutative_ring<T>::type::value

Along these lines, you could build a header file called arithmetic_traits.hpp or something similar. The object of this file would be to describe some of the semantics of operator+, operator* and possibly other operators when used with various types. Eg. you could have say

is_algebra< framed_multi<T,L,H>, T>::type is_algebra< framed_multi<T,L,H>, T>::scalar_type

This header would also be used to define the zero element of addition and the identity element of multiplication, if it exists.

Once this header is established, you could build template libraries which perform arithmetic according to the axioms embodied in the traits. Such a library would not eg. assume that multiplication is commutative, it would check this at compile time.

Note that there would also need to be a distinction between approximate and exact arithmetic. This especially affects associativity, where eg. addition of real numbers behaves differently from addition of floating point numbers due to loss of precision. eg. http://h18009.www1.hp.com/fortran/docs/vf-html/pg/pg1round.htm http://www.ibiblio.org/pub/languages/fortran/ch4-6.html

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_______________________________________________ Jeremy Siek <jsiek@osl.iu.edu> http://www.osl.iu.edu/~jsiek Ph.D. Candidate, Indiana University Bloomington C++ Booster (http://www.boost.org) _______________________________________________