Hello all, I'm reading N3351: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3351.pdf It's a bottom-up approach to define concepts starting from what's needed by STL algorithms. So far so good--I like it probably more than C++0x concept proposals--N331 is simpler :) However, N3351 STL design is not fully compatible with the current STL specifications--maybe N3351 is better, more mathematically sound? In N3351, concepts are boolean constants: ``We can define concepts as simple (constant) Boolean expressions. This is useful when building constraints predicated on non-syntactic and non-semantics properties of types.`` So I can implement concepts in C++11 as boolean meta-functions using expression SFINAE to check the requirements and enable_if to disable generic algorithms when the instantiated types don't model the concepts (i.e., the concept's boolean meta-function is false). For example, that's the case for the bool{a== b} and bool{a!=b} expressions of the EqualityComparable concept below. However, N3351 says that axioms should not be checked by the compiler... ``Axioms express the semantics of a concept’s required syntax; they are assumed to be true and must not be checked by the compiler beyond conformance to the C++ syntax. Any additional checking is beyond the scope of the compiler’s translation requirements. The compiler must not generate code that evaluates axioms as preconditions, either. This could lead to program errors if the evaluated assertions have side effects. For example, asserting that distance(first, last) > 1 when the type of those iterators is istream_iterator will consume the first element of the range, causing the assertion to pass, but the algorithm to have undefined behavior.'' So what am I supposed to do with axioms? Do nothing? Axioms are just "comments" that document the semantic? For example: `` concept EqualityComparable<typename T> = requires (T a, T b, T c) { bool { a == b }; bool { a != b }; axiom { a == b <=> eq(a, b); } // true equality axiom { a == a; // reflexive a == b => b == a; // symmetric a == b && b == c => a == c; // transitive } axiom { a != b <=> !(a == b); } // complement }; So, EqualityComparable<T> is true if T 1. has == and != with result types that can be converted to bool 2. == compares for true equality 3. == is reflexive, symmetric, and transitive 4. != is the complement of == However, the compiler can only check the first of these conditions. The rest must be verified through other means (i.e. manually). '' Thanks, --Lorenzo