Re: Concepts and CopyConstructible

===================================== MODERATOR'S COMMENT:

===================================== END OF MODERATOR'S COMMENT
On 3 Mai, 18:26, Douglas Gregor <doug.gre...@gmail.com> wrote:


Hmmh, I assume you mean something along the lines
of this (from N2193, sect. 7.6.1.4):

concept CopyConstructible<typename T> {
  T::T(const T&);
  axiom CopyEquivalence(T x) {
    T(x) == x; // okay, uses implicit ==
  }
}

I must say that I have problems understanding
the meaning of == and != in axioms, even if
the rules are specified in 7.6.1.4/2:

"Within the body of an axiom-definition, equality (==)
and inequality (!=) operators are available for each
concept type parameter and associated type T.[..]"

How does this work, if T is *not* EqualityComparable?

I would understand, if we would (a) define a proper
concept for EquivalenceRelation, e.g. using the
well-known triad of reflexivity, symmmetry, and
transititvity, e.g.

concept EquivalenceRelation<typename Op, typename T> {
  bool operator()(Op, T, T);
  axiom Reflexivity(Op op, T x) { op(x, x); }
  axiom Symmetry(Op op, T x, T y) { op(x, y) == op(y, x); }
  axiom Transitivity(Op op, T x, T y, T z) {
    if (op(x, y) && op(y, z)) op(x, z) == true;
  }
}

and (b) would use this concept inside the definition
of CopyConstructible. Regrettably, the following is
probably invalid Concept C++:

concept CopyConstructible<typename T> {
  T::T(const T&);
  template <typename Op>
  requires EquivalenceRelation<Op, T>
  axiom CopyEquivalence(T x, Op rel) {
    rel(T(x), x);
  }
}

To repair that I could simply create a valid analogon
by *generalizing* CopyConstructible in this way:

concept CopyConstructible<typename T, typename Op> {
  T::T(const T&);
  requires EquivalenceRelation<Op, T>;
  axiom CopyEquivalence(T x, Op rel) { rel(T(x), x); }
}

or in that one:

concept CopyConstructible<typename T> {
  T::T(const T&);
  typename equivalence_relation;
  requires EquivalenceRelation<equivalence_relation, T>;
  axiom CopyEquivalence(T x, equivalence_relation rel) {
    rel(T(x), x);
  }
}

but both solutions require that we provide an
associated equivalence relation with the actual
type.

What have I misunderstood here?

Another point: Assume that we define above
mentioned concept EquivalenceRelation, could
or should we add a *fourth* axiom Identity in the
following way:

concept EquivalenceRelation<typename Op, typename T> {
  ... // As before
  axiom Identity(Op op, T x, T y) { if (&x == &y) op(x, y) == true; }
}

?

I assume thate there is a problem because the axiom might
not be generally valid if we consider some possible user-defined
types e.g.

class UnAddressable {
  void operator&(); // private and *not* defined
  void operator&() const; // private and *not* defined
}

Is it possible to put a further condition in the signature of
an axiom? Consider:

auto concept Addressable<typename T> { ... }

concept EquivalenceRelation<typename Op, typename T> {
  ... // As before
  axiom Identity(Op op, Addressable<T> x, Addressable<T> y) { // Not
legal!
    if (&x == &y) op(x, y) == true;
  }
}

So how do we say: An axiom is valid, *iff* a further requirement
applies?

Greetings from Bremen,

Daniel

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