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copied!<p>I've used the most recent C++0x draft, <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2009/n2914.pdf" rel="noreferrer">N2914</a> (which still has concepts wording in it) as a reference for the following answer.</p> <p>1) Concepts are like interfaces in that. If your type supports a concept, it should also support all "base" concepts. Wikipedia statement you quote makes sense from the point of view of a type's client - if he knows that <code>T</code> satisfies concept <code>Derived<T></code>, then he also knows that it satisfies concept <code>Base<T></code>. From type author perspective, this naturally means that both have to be implemented. See 14.10.3/2.</p> <p>2) Yes, a concept with <code>typename</code> members can be <code>auto</code>. Such members can be automatically deduced if they are used in definitions of function members in the same concept. For example, <code>value_type</code> for iterator can be deduced as a return type of its <code>operator*</code>. However, if a type member is not used anywhere, it will not be deduced, and thus will not be implicitly defined. In your example, there's no way to deduce <code>SomeType<T>::Type</code> for either <code>Dummy</code> or <code>Dummy1</code>, as <code>Type</code> isn't used by other members of the concept, so neither class will map to the concept (and, in fact, no class could possibly auto-map to it). See 14.10.1.2/11 and 14.10.2.2/4.</p> <p>3) Axioms were a weak point of the spec, and they were being constantly updated to make some (more) sense. Just before concepts were pulled from the draft, there was a <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2009/n2887.pdf" rel="noreferrer">paper</a> that changed quite a bit - read it and see if it makes more sense to you, or you still have questions regarding it.</p> <p>For your specific example (accounting for syntactic difference), it would mean that compiler would be permitted to consider expression <code>(a*1)</code> to be the same as <code>(a*2)</code>, for the purpose of the "as-if" rule of the language (i.e. the compiler permitted to do any optimizations it wants, so long as the result behaves <em>as if</em> there were none). However, the compiler is not in any way required to validate the correctness of axioms (hence why they're called axioms!) - it just takes them for what they are.</p>

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