Why are pointers to inline functions allowed?

The inline keyword was originally a hint to the compiler that you the programmer think this function is a candidate for inlining - the compiler is not required to honor this.

In modern usage, it has little to nothing to do with inlining at all - modern compilers freely inline (or not) functions "behind you back", these form part of the optimization techniques.

Code transformations (including inlining) are done under the "as-if" rule in C++, which basically means that the compiler can transform the code as it wants to, so long as the execution is "as-if" the original code was executed as written. This rule fuels optimizations in C++.

That said, once an address is taken of a function, it is required to exist (i.e. the address is required to be valid). This may mean that it is no longer inlined, but could still be (the optimizer will apply the appropriate analysis).

So why can a pointer exist to a inline function, given that there is no fixed memory address of inline functions?

No, it is only a hint and largely relates to linkage and not actual inlining. This fuels, what is arguably the main current usage, defining functions in header files.

Should it not print different values of address of n each time func() is called?

It might, the n is a local variable, based on the stack location when the function executes. That said, the function inline, it relates to linkage, the linker will merge the functions over the translation units.

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As noted in the comments;

... that if the example is changed to static int n, then every call to the function must print a constant value (in a single program run of course) ... and that is true whether or not the code is inlined or not.

This is, again, the effect of the linkage requirement on the local variable n.

1) Why pointers to inline functions are allowed in c++?

Because inline functions are functions just like any other, and pointing to them is one of the things that you can do with functions. Inline functions just aren't special in this regard.

I have read that code of inline functions just get copied to the function calling statement and there is no compile time memory allocations in inline functions.

You (and perhaps the material you've read) have mixed two related and similarly named concepts.

An inline function is defined in all translation units that use it, while a non-inline function is defined in one translation unit only as required by the one definition rule. That is what an inline declaration of a function means; it relaxes the one definition rule, but also gives the additional requirement of being defined in all translation units that use it (which would not have been possible if the odr wasn't relaxed).

Inline expansion (or inlining) is an optimization, where a function call is avoided by copying the called function into the frame of the caller. A function call can be expanded inline, whether the function has been declared inline or not. And a function that has been declared inline is not necessarily expanded inline.

However, a function can not be expanded inline in a translation unit where it is not defined (unless link time optimization performs the expansion). Therefore the requirement of being defined in all TUs that the inline declaration allows, also makes possible the inline expansion of the function by allowing the function to be defined in all TUs that invoke it. But the optimization is not guaranteed.

2) Should it not print different values of address of n each time func() is called?

Inline expansion does cause the local variables to be located in the frame of the caller, yes. But their location will differ regardless of expansion if the calls originate from separate frames.

There is typically a regular non-expanded version generated of any function that has been expanded inline. If the address of a function is taken, it will point to that non-expanded function. If the compiler can prove that all calls to a function are inlined, the compiler might choose to not provide the non-expanded version at all. This requires that the function has internal linkage, and taking the address of the function typically makes such proof very difficult, or impossible.