I write a "hello world" program in C:
void main()
{ printf("Hello World\n"); }
Note that I haven't included any header file.
The program compiles with warning as
vikram@vikram-Studio-XPS-1645:~$ gcc hello.c
hello.c: In function ‘main’:
hello.c:2:2: warning: incompatible implicit declaration of built-in function ‘printf’
vikram@vikram-Studio-XPS-1645:~$ ./a.out
Hello World
vikram@vikram-Studio-XPS-1645:~$
How is this possible? How does the OS link a library without including any header?
The compiler builds your source file with a reference to a function called printf(), without knowing what arguments it actually takes or what its return type is. The generated assembly contains a push of the address of the string "Hello World" in the static data area of your program, followed by a call to printf.
When linking your object file into an executable, the linker sees a reference to printf and supplies the C standard library function printf(). By coincidence, the argument you have passed (const char*) is compatible with the declaration of the real printf(), so it functions correctly. However, note that the printf() that your program implicitly declares has return type int (I think), which the standard printf() also has; but if they differed, and you were to assign the result of calling printf() to a variable, you would be in the land of undefined behaviour and you would likely get an incorrect value.
Long story short: #include the correct headers to get the correct declarations for functions you use, because this kind of implicit declaration is deprecated, because it is error-prone.