Is "inline" without "static" or "extern" ever useful in C99?

Question

When I try to build this code

inline void f() {}

int main()
{
    f();
}

using the command line

gcc -std=c99 -o a a.c

I get a linker error (undefined reference to f). The error vanishes if I use static inline or extern inline instead of just inline, or if I compile with -O (so the function is actually inlined).

This behaviour seems to be defined in paragraph 6.7.4 (6) of the C99 standard:

If all of the file scope declarations for a function in a translation unit include the inline function specifier without extern, then the definition in that translation unit is an inline definition. An inline definition does not provide an external definition for the function, and does not forbid an external definition in another translation unit. An inline definition provides an alternative to an external definition, which a translator may use to implement any call to the function in the same translation unit. It is unspecified whether a call to the function uses the inline definition or the external definition.

If I understand all this correctly, a compilation unit with a function defined inline as in the above example only compiles consistently if there is also an external function with the same name, and I never know if my own function or the external function is called.

Isn't this behaviour completely daft? Is it ever useful to define a function inline without static or extern in C99? Am I missing something?

Summary of answers

Of course I was missing something, and the behaviour isn't daft. :)

As Nemo explains, the idea is to put the definition of the function

inline void f() {}

in the header file and only a declaration

extern inline void f();

in the corresponding .c file. Only the extern declaration triggers the generation of externally visible binary code. And there is indeed no use of inline in a .c file -- it's only useful in headers.

As the rationale of the C99 committee quoted in Jonathan's answer explicates, inline is all about compiler optimisations that require the definition of a function to be visible at the site of a call. This can only be achieved by putting the definition in the header, and of course a definition in a header must not emit code everytime it is seen by the compiler. But since the compiler is not forced to actually inline a function, an external definition must exist somewhere.

Answer 1

Actually this excellent answer also answers your question, I think:

What does extern inline do?

The idea is that "inline" can be used in a header file, and then "extern inline" in a .c file. "extern inline" is just how you instruct the compiler which object file should contain the (externally visible) generated code.

[update, to elaborate]

I do not think there is any use for "inline" (without "static" or "extern") in a .c file. But in a header file it makes sense, and it requires a corresponding "extern inline" declaration in some .c file to actually generate the stand-alone code.