I've often wondered about this. I'm not looking for legal advice, just casual opinions ;)

If some company publishes an API on the web for their closed-source library, would it be legal for another party to release an open-source implementation of that API? Are function declarations considered source code?

Take GNU implementing the UNIX APIs, for example. The UNIX standard gives the following function declaration and defines its required behaviour in English:

char * mktemp(char *template);

Now, consider an API that lists and declares and describes several thousand (more much complex) functions, enums, etc.; an API which defines a solution to a non-trival set of problems. If an open-source project publishes C headers that copy (verbatim) the function definitions contained in the closed-source company's published API, doesn't that violate some sort copyright law?