Re: Number/Algebraic concepts (was RE: [boost] RE: rational.hpp)

From: Doug Gregor (gregod_at_[hidden])
Date: 2001-01-16 14:22:37

On Monday 15 January 2001 10:51, you wrote:
> Good point. Ok, so I'm thinking about how to have the inheritance
> hierarchy, but also keep things simple... how about we do like the std
> iterators, define a hierarchy of simple tag classes, one tag for each
> algebra concept. This really has to be done anyways to allow for algorithm
> dispatching, and can also be used to check named conformance.

Perhaps something along the lines of:

----------------------
struct unknown_tag {};
template<typename Op> struct associative_tag {};
template<typename Op> struct commutative_tag {};
template<typename Op> struct identity_tag {};
template<typename Op> struct inverses_tag {};
// ...
template<typename Op> struct semigroup_tag : associative_tag<Op> {};
template<typename Op> struct commutative_semigroup_tag : semigroup_tag<Op> , 
commutative_tag<Op> {};
template<typename Op> struct monoid_tag : semigroup_tag<Op>, identity_tag<Op> 
{};
template<typename Op> struct abelian_monoid_tag : monoid_tag<Op>, 
commutative_tag<Op>, commutative_semigroup_tag<Op> {}
template<typename Op> struct group_tag : monoid_tag<Op>, inverses_tag<Op>
template<typename Op> struct abelian_group_tag : group_tag<Op>, 
commutative_tag<Op>, abelian_monoid_tag<Op> {}
// ...

template<typename Domain>
struct algebra_traits
{
  typedef unknown_tag category;
};

// ...
template<>
struct algebra_traits<float>
{
  typedef field_tag< std::plus<float>, std::mulitplies<float> > category;
};
-----------------------

All inheritance in the above should be public virtual, I'm just too lazy to 
type it out at the moment.

        Doug