ordered_monoid_concept.h

// Description: Ordered additive monoid concept
// Documentation: algebra.txt

#ifndef PASTELSYS_ORDERED_MONOID_CONCEPT_H
#define PASTELSYS_ORDERED_MONOID_CONCEPT_H

#include "pastel/sys/algebra/ordered_semigroup_concept.h"
#include "pastel/sys/algebra/monoid_concept.h"

#include "pastel/sys/algebra/native_ordered_monoid.h"

namespace Pastel 
{

    //! An ordered additive monoid.
    /*! 
   An ordered monoid (X, +, 0) is an additive monoid (X, +, 0)
   which is also an ordered additive semigroup.
   */
    struct Ordered_Additive_Monoid_Concept
    : Refines<
        Ordered_Additive_SemiGroup_Concept,
        Additive_Monoid_Concept>
    {
        template <typename Type>
        auto requires_(Type&& t) -> decltype
        (
            conceptCheck(
                //! Returns whether 'that' > 0.
                Concept::convertsTo<bool>(positive(t)),
                //! Returns whether 'that' < 0.
                Concept::convertsTo<bool>(negative(t)),
                //! Returns the absolute value of 'that'.
                Concept::convertsTo<Type>(abs(t))
            )
        );
    };

}

#endif