First I'd like to clarify my understanding of the situation you describe: The header contains (only) a static function declaration while the C file contains the definition, i.e. the function's source code. For example
some.h:
static void f();
// potentially more declarations
some.c:
#include "some.h"
static void f() { printf("Hello world\n"); }
// more code, some of it potentially using f()
If this is the situation you describe, I take issue with your remark
Since static functions have internal linkage we need to define it in every file we include the header file where the function is declared.
If you declare the function but do not use it in a given translation unit, I don't think you have to define it. gcc accepts that with a warning; the standard does not seem to forbid it, unless I missed something. This may be important in your scenario because translation units which do not use the function but include the header with its declaration don't have to provide an unused definition.
Now let's examine the questions:
- What is the problem of declaring static functions in header files?
It is somewhat unusual. Typically, static functions are functions needed in only one file. They are declared static to make that explicit by limiting their visibility. Declaring them in a header therefore is somewhat antithetical. If the function is indeed used in multiple files with identical definitions it should be made external, with a single definition. If only one translation unit actually uses it, the declaration does not belong in a header.
One possible scenario therefore is to ensure a uniform function signature for different implementations in the respective translation units. The common header leads to a compile time error for different return types in C (and C++); different parameter types would cause a compile time error only in C (but not in C++' because of function overloading).
- What are the risks?
I do not see risks in your scenario. (As opposed to also including the function definition in a header which may violate the encapsulation principle.)
- What the impact in compilation time?
A function declaration is small and its complexity is low, so the overhead of having additional function declarations in a header is likely negligible. But if you create and include an additional header for the declaration in many translation units the file handling overhead can be significant (i.e. the compiler idles a lot while it waits for the header I/O)
- Is there any risk in runtime?
I cannot see any.