Does this grammar allow scope nesting?

Question

I'm only able to make functions inside the global scope. Scope nesting means being able make functions within functions, right? I'm not able to do that with this grammar. Is it possible?

/* C-Minus BNF Grammar */

%token ELSE
%token IF
%token INT
%token RETURN
%token VOID
%token WHILE

%token ID
%token NUM

%token LTE
%token GTE
%token EQUAL
%token NOTEQUAL
%%

program : declaration_list ;

declaration_list : declaration_list declaration | declaration ;

declaration : var_declaration | fun_declaration ;

var_declaration : type_specifier ID ';'
                | type_specifier ID '[' NUM ']' ';' ;

type_specifier : INT | VOID ;

fun_declaration : type_specifier ID '(' params ')' compound_stmt ;

params : param_list | VOID ;

param_list : param_list ',' param
           | param ;

param : type_specifier ID | type_specifier ID '[' ']' ;

compound_stmt : '{' local_declarations statement_list '}' ;

local_declarations : local_declarations var_declaration
                   | /* empty */ ;

statement_list : statement_list statement
               | /* empty */ ;

statement : expression_stmt
          | compound_stmt
          | selection_stmt
          | iteration_stmt
          | return_stmt ;

expression_stmt : expression ';'
                | ';' ;

selection_stmt : IF '(' expression ')' statement
               | IF '(' expression ')' statement ELSE statement ;

iteration_stmt : WHILE '(' expression ')' statement ;

return_stmt : RETURN ';' | RETURN expression ';' ;

expression : var '=' expression | simple_expression ;

var : ID | ID '[' expression ']' ;

simple_expression : additive_expression relop additive_expression
                  | additive_expression ;

relop : LTE | '<' | '>' | GTE | EQUAL | NOTEQUAL ;

additive_expression : additive_expression addop term | term ;

addop : '+' | '-' ;

term : term mulop factor | factor ;

mulop : '*' | '/' ;

factor : '(' expression ')' | var | call | NUM ;

call : ID '(' args ')' ;

args : arg_list | /* empty */ ;

arg_list : arg_list ',' expression | expression ;

Answer 1

Actually, a grammar doesn't imply a scope. It is how you deal with symbols semantically that determines scope.

Having said that, in this grammar there could be a global scope and a scope introduced by a compound statement. In the global scope you can declare variables and functions. In the compound statement scope, you can only declare variables.

If you want to support nested functions, change the grammar to allow function declarations within compound statements.