Template parameters and template argument_template argument for template type parameter must

Note from https://en.cppreference.com/w/cpp/language/template_parameters
C++ C++ language Templates
Template parameters
Every template is parameterized by one or more template parameters, indicated in the parameter-list of the template declaration syntax:

template < parameter-list > declaration
Each parameter in parameter-list may be:

a non-type template parameter;
a type template parameter;
a template template parameter.
Non-type template parameter
type name(optional) (1)
type name(optional) = default (2)
type … name(optional) (3) (since C++11)
placeholder name (4) (since C++17)

1. A non-type template parameter with an optional name.
2. A non-type template parameter with an optional name and a default value.
3. A non-type template parameter pack with an optional name.
4. A non-type template parameter with a placeholder type. placeholder may be any type that includes the placeholder auto (such as plain auto, auto ** or auto &), a placeholder for a deduced class type (since C++20), or decltype(auto).
   A non-type template parameter must have a structural type, which is one of the following types (optionally cv-qualified, the qualifiers are ignored):

lvalue reference type (to object or to function);
an integral type;
a pointer type (to object or to function);
a pointer to member type (to member object or to member function);
an enumeration type;
std::nullptr_t;
(since C++11)
a floating-point type;
a literal class type with the following properties:
all base classes and non-static data members are public and non-mutable and
the types of all base classes and non-static data members are structural types or (possibly multi-dimensional) array thereof.
(since C++20)
Array and function types may be written in a template declaration, but they are automatically replaced by pointer to object and pointer to function as appropriate.

When the name of a non-type template parameter is used in an expression within the body of the class template, it is an unmodifiable prvalue unless its type was an lvalue reference type, or unless its type is a class type (since C++20).

A template parameter of the form class Foo is not an unnamed non-type template parameter of type Foo, even if otherwise class Foo is an elaborated type specifier and class Foo x; declares x to be of type Foo.

The type of a non-type template parameter may be deduced if it includes a placeholder type (auto, a placeholder for a deduced class type (since C++20), or decltype(auto)). The deduction is performed as if by deducing the type of the variable x in the invented declaration T x = template-argument;, where T is the declared type of the template parameter. If the deduced type is not permitted for a non-type template parameter, the program is ill-formed.

template struct B { /* … */ };
B<5> b1; // OK: non-type template parameter type is int
B<‘a’> b2; // OK: non-type template parameter type is char
B<2.5> b3; // error (until C++20): non-type template parameter type cannot be double
For non-type template parameter packs whose type uses a placeholder type, the type is independently deduced for each template argument and need not match:

template<auto…> struct C {};
C<‘C’, 0, 2L, nullptr> x; // OK
(since C++17)
An identifier that names a non-type template parameter of class type T denotes a static storage duration object of type const T, called a template parameter object, whose value is that of the corresponding template argument after it has been converted to the type of the template parameter. All such template parameters in the program of the same type with the same value denote the same template parameter object. A template parameter object shall have constant destruction.

struct A { friend bool operator==(const A&, const A&) = default; };
template void f() {
&a; // OK
const A& ra = a, &rb = a; // Both bound to the same template parameter object
assert(&ra == &rb); // passes
}
(since C++20)
Type template parameter
type-parameter-key name(optional) (1)
type-parameter-key name(optional) = default (2)
type-parameter-key … name(optional) (3) (since C++11)
type-constraint name(optional) (4) (since C++20)
type-constraint name(optional) = default (5) (since C++20)
type-constraint … name(optional) (6) (since C++20)
type-constraint - either the name of a concept or the name of a concept followed by a list of template arguments (in angle brackets). Either way, the concept name may be optionally qualified
type-parameter-key is either typename or class. There is no difference between these keywords in a type template parameter declaration.

1. A type template parameter without a default.
   template
   class My_vector { /* … */ };
2. A type template parameter with a default.
   template
   struct My_op_functor { /* … */ };
3. A type template parameter pack.
   template<typename… Ts>
   class My_tuple { /* … */ };
   This section is incomplete
   Reason: Exposition of cases 4-6 needed.

The name of the parameter is optional:

// Declarations of the templates shown above:
template class My_vector;
template<class = void> struct My_op_functor;
template<typename…> class My_tuple;
In the body of the template declaration, the name of a type parameter is a typedef-name which aliases the type supplied when the template is instantiated.

Each constrained parameter P whose type-constraint is Q designating the concept C introduces a constraint-expression E according to the following rules:

if Q is C (without an argument list),
if P is not a parameter pack, E is simply C

otherwise, P is a parameter pack, E is a fold-expression (C

&& …)
if Q is C<A1,A2…,AN>, then E is C<P,A1,A2,…AN> or (C<P,A1,A2,…AN> && …), respectively.
template concept C1 = true;
template<typename… Ts> concept C2 = true; // variadic concept
template<typename T, typename U> concept C3 = true;

template struct s1; // constraint-expression is C1
template<C1… T> struct s2; // constraint-expression is (C1 && …)
template<C2… T> struct s3; // constraint-expression is (C2 && …)
template<C3 T> struct s4; // constraint-expression is C3<T, int>
template<C3… T> struct s5; // constraint-expression is (C3<T, int> && …)
(since C++20)
Template template parameter
template < parameter-list > typename(C++17)|class name(optional) (1)
template < parameter-list > typename(C++17)|class name(optional) = default (2)
template < parameter-list > typename(C++17)|class … name(optional) (3) (since C++11)

1. A template template parameter with an optional name.
2. A template template parameter with an optional name and a default.
3. A template template parameter pack with an optional name.
   Unlike type template parameter declaration, template template parameter declaration can only use the keyword class and not typename.

(until C++17)
In the body of the template declaration, the name of this parameter is a template-name (and needs arguments to be instantiated).

template class my_array {};

// two type template parameters and one template template parameter:
template<typename K, typename V, template typename C = my_array>
class Map
{
C key;
C value;
};
Name resolution for template parameters
The name of a template parameter is not allowed to be redeclared within its scope (including nested scopes). A template parameter is not allowed to have the same name as the template name.

template<class T, int N>
class Y {
int T; // error: template parameter redeclared
void f()
{
char T; // error: template parameter redeclared
}
};

template class X; // error: template parameter redeclared
In the definition of a member of a class template that appears outside of the class template definition, the name of a member of the class template hides the name of a template parameter of any enclosing class templates, but not a template parameter of the member if the member is a class or function template.

template
struct A {
struct B {};
typedef void C;
void f();
template void g(U);
};

template
void A::f()
{
B b; // A’s B, not the template parameter
}

template
template
void A::g©
{
B b; // A’s B, not the template parameter
C c; // the template parameter C, not A’s C
}
In the definition of a member of a class template that appears outside of the namespace containing the class template definition, the name of a template parameter hides the name of a member of this namespace.

namespace N {
class C {};
template
class B {
void f(T);
};
}
template
void N::B::f©
{
C b; // C is the template parameter, not N::C
}
In the definition of a class template or in the definition of a member of such a template that appears outside of the template definition, for each non-dependent base class, if the name of the base class or the name of a member of the base class is the same as the name of a template parameter, the base class name or member name hides the template parameter name.

struct A {
struct B {};
int C;
int Y;
};

template<class B, class C>
struct X : A {
B b; // A’s B
C b; // error: A’s C isn’t a type name
};
Template arguments
In order for a template to be instantiated, every template parameter (type, non-type, or template) must be replaced by a corresponding template argument. For class templates, the arguments are either explicitly provided, deduced from the initializer, (since C++17) or defaulted. For function templates, the arguments are explicitly provided, deduced from the context, or defaulted.

If an argument can be interpreted as both a type-id and an expression, it is always interpreted as a type-id, even if the corresponding template parameter is non-type:

template void f(); // #1
template void f(); // #2
void g() {
f<int()>(); // “int()” is both a type and an expression,
// calls #1 because it is interpreted as a type
}
Template non-type arguments
The following limitations apply when instantiating templates that have non-type template parameters:

For integral and arithmetic types, the template argument provided during instantiation must be a converted constant expression of the template parameter’s type (so certain implicit conversion applies).
For pointers to objects, the template arguments have to designate the address of a complete object with static storage duration and a linkage (either internal or external), or a constant expression that evaluates to the appropriate null pointer or std::nullptr_t value.
For pointers to functions, the valid arguments are pointers to functions with linkage (or constant expressions that evaluate to null pointer values).
For lvalue reference parameters, the argument provided at instantiation cannot be a temporary, an unnamed lvalue, or a named lvalue with no linkage (in other words, the argument must have linkage).
For pointers to members, the argument has to be a pointer to member expressed as &Class::Member or a constant expression that evaluates to null pointer or std::nullptr_t value.
In particular, this implies that string literals, addresses of array elements, and addresses of non-static members cannot be used as template arguments to instantiate templates whose corresponding non-type template parameters are pointers to objects.

(until C++17)
The template argument that can be used with a non-type template parameter can be any converted constant expression of the type of the template parameter.

template<const int* pci> struct X {};
int ai[10];
X xi; // ok: array to pointer conversion and cv-qualification conversion

struct Y {};
template<const Y& b> struct Z {};
Y y;
Z z; // ok: no conversion

template<int (&pa)[5]> struct W {};
int b[5];
W w; // ok: no conversion

void f(char);
void f(int);
template<void (*pf)(int)> struct A {};
A<&f> a; // ok: overload resolution selects f(int)
The only exceptions are that non-type template parameters of reference or pointer type and non-static data members of reference or pointer type in a non-type template parameter of class type and its subobjects (since C++20) cannot refer to/be the address of

a subobject (including non-static class member, base subobject, or array element);
a temporary object (including one created during reference initialization);
a string literal;
the result of typeid;
or the predefined variable func.
template<class T, const char* p> class X {};
X<int, “Studebaker”> x1; // error: string literal as template-argument

template<int* p> class X {};
int a[10];
struct S
{
int m;
static int s;
} s;
X<&a[2]> x3; // error: address of array element
X<&s.m> x4; // error: address of non-static member
X<&s.s> x5; // ok: address of static member
X<&S::s> x6; // ok: address of static member

template<const int& CRI> struct B {};
B<1> b2; // error: temporary would be required for template argument
int c = 1;
B b1; // ok
(since C++17)
Template type arguments
A template argument for a type template parameter must be a type-id, which may name an incomplete type:

template class X {}; // class template

struct A; // incomplete type
typedef struct {} B; // type alias to an unnamed type

int main()
{
X x1; // ok: ‘A’ names a type
X<A*> x2; // ok: ‘A*’ names a type
X x3; // ok: ‘B’ names a type
}
Template template arguments
A template argument for a template template parameter must be an id-expression which names a class template or a template alias.

When the argument is a class template, only the primary template is considered when matching the parameter. The partial specializations, if any, are only considered when a specialization based on this template template parameter happens to be instantiated.

template class A { int x; }; // primary template
template class A<T*> { long x; }; // partial specialization

// class template with a template template parameter V
template<template class V> class C
{
V y; // uses the primary template
V<int*> z; // uses the partial specialization
};

C c; // c.y.x has type int, c.z.x has type long
To match a template template argument A to a template template parameter P, each of the template parameters of A must match corresponding template parameters of P exactly (until C++17) P must be at least as specialized as A (since C++17). If P’s parameter list includes a parameter pack, zero or more template parameters (or parameter packs) from A’s template parameter list are matched by it.

template struct eval; // primary template

template<template<typename, typename…> class TT, typename T1, typename… Rest>
struct eval<TT<T1, Rest…>> {}; // partial specialization of eval

template struct A;
template<typename T1, typename T2> struct B;
template struct C;
template<typename T1, int N> struct D;
template<typename T1, typename T2, int N = 17> struct E;

eval<A> eA; // ok: matches partial specialization of eval
eval<B<int, float>> eB; // ok: matches partial specialization of eval
eval<C<17>> eC; // error: C does not match TT in partial specialization because
// TT’s first parameter is a type template parameter,
// while 17 does not name a type
eval<D<int, 17>> eD; // error: D does not match TT in partial specialization
// because TT’s second parameter is a type parameter pack,
// while 17 does not name a type
eval<E<int, float>> eE; // error: E does not match TT in partial specialization
// because E’s third (default) parameter is a non-type
template class A { /* … / };
template<class T, class U = T> class B { / … / };
template <class …Types> class C { / … */ };

template<template class P> class X { /* … */ };
X xa; // OK
X xb; // OK in C++17 after CWG 150
// Error earlier: not an exact match
X xc; // OK in C++17 after CWG 150
// Error earlier: not an exact match

template<template<class …> class Q> class Y { /* … */ };
Y ya; // OK
Y yb; // OK
Y yc; // OK

template class D { /* … / }; // note: C++17
template<template class R> class Z { / … */ };
Z zd; // OK

template struct SI { /* … */ };
template <template class> void FA(); // note: C++17
FA(); // Error
Formally, a template template-parameter P is at least as specialized as a template template argument A if, given the following rewrite to two function templates, the function template corresponding to P is at least as specialized as the function template corresponding to A according to the partial ordering rules for function templates. Given an invented class template X with the template parameter list of A (including default arguments):

Each of the two function templates has the same template parameters, respectively, as P or A.
Each function template has a single function parameter whose type is a specialization of X with template arguments corresponding to the template parameters from the respective function template where, for each template parameter PP in the template parameter list of the function template, a corresponding template argument AA is formed. If PP declares a parameter pack, then AA is the pack expansion PP…; otherwise, AA is the id-expression PP.
If the rewrite produces an invalid type, then P is not at least as specialized as A.

(since C++17)
Default template arguments
Default template arguments are specified in the parameter lists after the = sign. Defaults can be specified for any kind of template parameter (type, non-type, or template), but not to parameter packs.

If the default is specified for a template parameter of a primary class template, primary variable template, (since C++14) or alias template, each subsequent template parameter must have a default argument, except the very last one may be a template parameter pack. In a function template, there are no restrictions on the parameters that follow a default, and a parameter pack may be followed by more type parameters only if they have defaults or can be deduced from the function arguments.

Default parameters are not allowed

in the out-of-class definition of a member of a class template (they have to be provided in the declaration inside the class body). Note that member templates of non-template classes can use default parameters in their out-of-class definitions (see GCC bug 53856)
in friend class template declarations
in any function template declaration or definition
(until C++11)
On a friend function template declaration, default template arguments are allowed only if the declaration is a definition, and no other declarations of this function appear in this translation unit.

(since C++11)
Default template arguments that appear in the declarations and the definition are merged similarly to default function arguments:

template<typename T1, typename T2 = int> class A;
template class A;
// the above is the same as the following:
template class A;
But the same parameter cannot be given default arguments twice in the same scope

template class X;
template class X {}; // error
The template parameter lists of template template parameters can have their own default arguments, which are only in effect where the template template parameter itself is in scope:

// class template, with a type template parameter with a default
template struct B {};

// template template parameter T has a parameter list, which
// consists of one type template parameter with a default
template<template<typename = float> typename T> struct A
{
void f();
void g();
};

// out-of-body member function template definitions
template<template class T>
void A::f()
{
T<> t; // error: TT has no default in scope
}
template<template class T>
void A::g()
{
T<> t; // ok: t is T
}
Member access for the names used in a default template parameter is checked at the declaration, not at the point of use:

class B {};

template class C
{
protected:
typedef T TT;
};

template<typename U, typename V = typename U::TT> class D: public U {};

D<C>* d; // error: C::TT is protected
The default template argument is implicitly instantiated when the value of that default argument is needed, except if the template is used to name a function:

template<typename T, typename U = int> struct S { };
S* p; // The default argument for U is instantiated at this point
// the type of p is S<bool, int>*
(since C++14)
Template argument equivalence
Template argument equivalence is used to determine whether two template-ids are same.

Two values are template-argument-equivalent if they are of the same type and

they are of integral or enumeration type and their values are the same
or they are of pointer type and they have the same pointer value
or they are of pointer-to-member type and they refer to the same class member or are both the null member pointer value
or they are of lvalue reference type and they refer to the same object or function
or they are of type std::nullptr_t
(since C++11)
or they are of floating-point type and their values are identical
or they are of array type (in which case the arrays must be member objects of some class/union) and their corresponding elements are template-argument-equivalent
or they are of union type and either they both have no active member or they have the same active member and their active members are template-argument-equivalent
or they are of non-union class type and their corresponding direct subobjects and reference members are template-argument-equivalent
(since C++20)
Examples
Run this code
#include

// simple non-type template parameter
template
struct S { int a[N]; };

template<const char*>
struct S2 {};

// complicated non-type example
template
<
char c, // integral type
int (&ra)[5], // lvalue reference to object (of array type)
int (*pf)(int), // pointer to function
int (S<10>::*a)[10] // pointer to member object (of type int[10])

struct Complicated
{
// calls the function selected at compile time
// and stores the result in the array selected at compile time
void foo(char base)
{
ra[4] = pf(c - base);
}
};

S2<“fail”> s2; // error: string literal cannot be used
char okay[] = “okay”; // static object with linkage
S2< &okay[0] > s2; // error: array element has no linkage
S2 s2; // works

int a[5];
int f(int n) { return n; }

int main()
{
S<10> s; // s.a is an array of 10 int
s.a[9] = 4;

Complicated<'2', a, f, &S<10>::a> c;
c.foo('0');

std::cout << s.a[9] << a[4] << '\n';
1
2
3
4

}
Output:

42