Proving syntactic ambiguity of type declaration grammar

Question

Given a grammar to achieve C-style type declarations:

Declaration ::= Type Declarator ;

       Type ::= int | char

 Declarator ::= * Declarator

              | Declarator [ num ]

              | Declarator ( Type )

              | ( Declarator )

              | name

I must prove syntactic ambiguity. I am having difficulty identifying cases it which it is ambiguous. Here are all of the following cases I have come up with that satisfy the grammar:

• int * Declarator;
• char * Declarator;
• int Declarator[num];
• char Declarator[num];
• int Declarator(type);
• char Declarator(type);
• int Declarator;
• char Declarator;
• int name;
• char name;

What am I not seeing here?

Answer 1

Is int *something[3] an array of three pointers or a pointer to an array of three ints? How about int **something[3]?

A simplified C grammar from the C standard's Appendix A includes:

(Many productions omitted)
declarator: pointeropt direct-declarator
pointer: '*'
       | '*' pointer
direct-declarator: identifier
                   '(' declarator ')'
                   direct-declarator '[' assignment-expressionopt ']'

How does that resolve the above ambiguity?

Also, consider the expression *a[3] and the declaration int *a[3]. In the expression, the postfix qualifier [3] takes precedence over the prefix qualifier *, which is the normal pattern for expressions. How does that compare with the syntax of the declaration? Why was that decision taken?