13 Templates [temp]

13.5 Template constraints [temp.constr]

13.5.4 Constraint normalization [temp.constr.normal]

1
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The normal form of an expression E is a constraint that is defined as follows:
  • (1.1)
    The normal form of an expression ( E ) is the normal form of E.
  • (1.2)
    The normal form of an expression E1 || E2 is the disjunction of the normal forms of E1 and E2.
  • (1.3)
    The normal form of an expression E1 && E2 is the conjunction of the normal forms of E1 and E2.
  • (1.4)
    The normal form of a concept-id C<A, A, ..., A> is the normal form of the constraint-expression of C, after substituting A, A, ..., A for C's respective template parameters in the parameter mappings in each atomic constraint.
    If any such substitution results in an invalid type or expression, the program is ill-formed; no diagnostic is required.
    [Example 1: template<typename T> concept A = T::value || true; template<typename U> concept B = A<U*>; template<typename V> concept C = B<V&>;
    Normalization of B's constraint-expression is valid and results in T​::​value (with the mapping )  ∨  true (with an empty mapping), despite the expression T​::​value being ill-formed for a pointer type T.
    Normalization of C's constraint-expression results in the program being ill-formed, because it would form the invalid type V&* in the parameter mapping.
    — end example]
  • (1.5)
    The normal form of any other expression E is the atomic constraint whose expression is E and whose parameter mapping is the identity mapping.
2
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The process of obtaining the normal form of a constraint-expression is called normalization.
[Note 1: 
Normalization of constraint-expressions is performed when determining the associated constraints ([temp.constr.constr]) of a declaration and when evaluating the value of an id-expression that names a concept specialization ([expr.prim.id]).
— end note]
3
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[Example 2: template<typename T> concept C1 = sizeof(T) == 1; template<typename T> concept C2 = C1<T> && 1 == 2; template<typename T> concept C3 = requires { typename T::type; }; template<typename T> concept C4 = requires (T x) { ++x; }; template<C2 U> void f1(U); // #1 template<C3 U> void f2(U); // #2 template<C4 U> void f3(U); // #3
The associated constraints of #1 are sizeof(T) == 1 (with mapping )  ∧  1 == 2.

The associated constraints of #2 are requires { typename T​::​type; } (with mapping ).

The associated constraints of #3 are requires (T x) { ++x; } (with mapping ).
— end example]