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why is `int test {}` a function definition in C language BNF

I'm interested in the famous The syntax of C in Backus-Naur Form and studied for a while, what confuse me is that some syntax looks wrong to me but is considered right according to the BNF.

For example, int test {}, what's this? I think this is a ill syntax in C, but the truth is the BNF considered this a function definition: 

int -> type_const -> type_spec -> decl_specs
test-> id -> direct_declarator -> declarator
'{' '}' -> compound_stat
decl_specs declarator compound_stat -> function_definition

I tried this with bison, it considered the input int test {} is a right form, but I tried this on a C compiler, it will not compile.

So got questions:

  1. int test {} a right syntax or not?
  2. If it is a right syntax, what is that mean and why compiler do not recognized it?
  3. If it is an ill syntax, can I say the BNF is not rigorous？ And does that mean modern C compiler does not stick with this BNF?
Solution

  • The grammar is necessary but not sufficient to describe a valid C program. For that you need constraints from the standard too. A simpler example of this would be 0++, which follows the syntax of a C expression, but certainly isn't a valid program fragment...

    C11 6.9.1p2:

    1. The identifier declared in a function definition (which is the name of the function) shall have a function type, as specified by the declarator portion of the function definition. [162]

    The footnote 162 explains that the intent of the constraint is that a typedef cannot be used, i.e. that 

    typedef int F(void);
F f { /* ... */ }

    will not be valid, even though such a typedef could be used for a function declaration, i.e. 

    F f;

    would declare the function

    int f(void);

    But mere existence of this constraint also proves that the BNF grammar in itself is not sufficient in this case. Hence you are correct in that the grammar would consider such a fragment a function definition.