A constraint is a sequence of logical operations and
operands that specifies requirements on template arguments.

The operands of a logical operation are constraints.

There are three different kinds of constraints:

In order for a constrained template to be instantiated ([temp.spec]),
its associated constraints
shall be satisfied as described in the following subclauses.

[Note 1: *end note*]

Forming the name of a specialization of
a class template,
a variable template, or
an alias template ([temp.names])
requires the satisfaction of its constraints.

Overload resolution
requires the satisfaction of constraints
on functions and function templates.

— There are two binary logical operations on constraints: conjunction
and disjunction.

A conjunction is a constraint taking two
operands.

If that is not satisfied, the conjunction is not satisfied.

Otherwise, the conjunction is satisfied if and only if the second
operand is satisfied.

A disjunction is a constraint taking two
operands.

If that is satisfied, the disjunction is satisfied.

Otherwise, the disjunction is satisfied if and only if the second
operand is satisfied.

[Example 1: template<typename T>
constexpr bool get_value() { return T::value; }
template<typename T>
requires (sizeof(T) > 1) && (get_value<T>())
void f(T); // has associated constraint sizeof(T) > 1 ∧ get_value<T>()
void f(int);
f('a'); // OK: calls f(int)
*end example*]

In the satisfaction of the associated constraints
of f, the constraint sizeof(char) > 1 is not satisfied;
the second operand is not checked for satisfaction.

— [Note 2: *end note*]

A logical negation expression ([expr.unary.op]) is an atomic constraint;
the negation operator is not treated as a logical operation on constraints.

As a result, distinct negation constraint-expressions
that are equivalent under [temp.over.link]
do not subsume one another under [temp.constr.order].

Furthermore, if substitution to determine
whether an atomic constraint is satisfied ([temp.constr.atomic])
encounters a substitution failure, the constraint is not satisfied,
regardless of the presence of a negation operator.

[Example 2: template <class T> concept sad = false;
template <class T> int f1(T) requires (!sad<T>);
template <class T> int f1(T) requires (!sad<T>) && true;
int i1 = f1(42); // ambiguous, !sad<T> atomic constraint expressions ([temp.constr.atomic])
// are not formed from the same expression
template <class T> concept not_sad = !sad<T>;
template <class T> int f2(T) requires not_sad<T>;
template <class T> int f2(T) requires not_sad<T> && true;
int i2 = f2(42); // OK, !sad<T> atomic constraint expressions both come from not_sad
template <class T> int f3(T) requires (!sad<typename T::type>);
int i3 = f3(42); // error: associated constraints not satisfied due to substitution failure
template <class T> concept sad_nested_type = sad<typename T::type>;
template <class T> int f4(T) requires (!sad_nested_type<T>);
int i4 = f4(42); // OK, substitution failure contained within sad_nested_type
*end example*]

—
Here,
requires (!sad<typename T::type>) requires
that there is a nested type that is not sad,
whereas
requires (!sad_nested_type<T>) requires
that there is no sad nested type.

— An atomic constraint is formed from
an expression E
and a mapping from the template parameters
that appear within E to
template arguments that are formed via substitution during constraint normalization
in the declaration of a constrained entity (and, therefore, can involve the
unsubstituted template parameters of the constrained entity),
called the parameter mapping ([temp.constr.decl]).

Two atomic constraints, and , are
identical
if they are formed from the same appearance of the same
expression
and if, given a hypothetical template A
whose template-parameter-list consists of
template-parameters corresponding and equivalent ([temp.over.link]) to
those mapped by the parameter mappings of the expression,
a template-id naming A
whose template-arguments are
the targets of the parameter mapping of
is the same ([temp.type]) as
a template-id naming A
whose template-arguments are
the targets of the parameter mapping of .

[Note 2: *end note*]

The comparison of parameter mappings of atomic constraints
operates in a manner similar to that of declaration matching
with alias template substitution ([temp.alias]).

[Example 1: template <unsigned N> constexpr bool Atomic = true;
template <unsigned N> concept C = Atomic<N>;
template <unsigned N> concept Add1 = C<N + 1>;
template <unsigned N> concept AddOne = C<N + 1>;
template <unsigned M> void f()
requires Add1<2 * M>;
template <unsigned M> int f()
requires AddOne<2 * M> && true;
int x = f<0>(); // OK, the atomic constraints from concept C in both fs are Atomic<N>
// with mapping similar to
template <unsigned N> struct WrapN;
template <unsigned N> using Add1Ty = WrapN<N + 1>;
template <unsigned N> using AddOneTy = WrapN<N + 1>;
template <unsigned M> void g(Add1Ty<2 * M> *);
template <unsigned M> void g(AddOneTy<2 * M> *);
void h() {
g<0>(nullptr); // OK, there is only one g
}
— *end example*]

This similarity includes the situation where a program is ill-formed, no diagnostic required,
when the meaning of the program depends on whether two constructs are equivalent,
and they are functionally equivalent but not equivalent.

[Example 2: template <unsigned N> void f2()
requires Add1<2 * N>;
template <unsigned N> int f2()
requires Add1<N * 2> && true;
void h2() {
f2<0>(); // ill-formed, no diagnostic required:
// requires determination of subsumption between atomic constraints that are
// functionally equivalent but not equivalent
}
— *end example*]

— To determine if an atomic constraint is
satisfied,
the parameter mapping and template arguments are
first substituted into its expression.

If substitution results in an invalid type or expression,
the constraint is not satisfied.

Otherwise, the lvalue-to-rvalue conversion
is performed if necessary,
and E shall be a constant expression of type bool.

If, at different points in the program, the satisfaction result is different
for identical atomic constraints and template arguments,
the program is ill-formed, no diagnostic required.

[Example 3: template<typename T> concept C =
sizeof(T) == 4 && !true; // requires atomic constraints sizeof(T) == 4 and !true
template<typename T> struct S {
constexpr operator bool() const { return true; }
};
template<typename T> requires (S<T>{})
void f(T); // #1
void f(int); // #2
void g() {
f(0); // error: expression S<int>{} does not have type bool
} // while checking satisfaction of deduced arguments of #1;
// call is ill-formed even though #2 is a better match
— *end example*]