Question

Consider the following grammar (that admits a series of declarations, followed by expressions) and the associated syntax directed translation (SDT) actions, given as pseudo-code:

$P\to D^{\ast }{E}^{\ast }$

$D\to$ int ID {record that ID.|exeme is of type int}

$D\to$ bool ID {record that ID.|exeme is of type bool}

$E\to E_1+E_2\{\text{check that}{E}_1.\text{type=int; set E.type:=int}\}$

$E\to !E_1\{\text{check that}{E}_1.\text{type = bool; set E. type: = bool}\}$

$E\to ID$ {set E.type: = int}

With respect to the above grammar, which one of the following choices is correct?

• A. The actions can be used to type-check syntactically correct integer variable declarations and integer expressions.
• B. The actions will lead to an infinite loop.
• C. The actions can be used to type-check syntactically correct boolean variable declarations and boolean expressions.
• D. The actions can be used to correctly type-check any syntactically correct program.

Answer 1

The correct option is A The actions can be used to type-check syntactically correct integer variable declarations and integer expressions.

1. $P\to D^{\ast }{E}^{\ast }$
2. $D\to$ int ID {record that ID. lexeme is of type int}
3. $D\to$ bool ID {record that ID. lexeme is of type bool}
4. $E\to E_1+E_2\{\text{check that}{E}_1.type=E_2.type=\text{int; set E.type = int}\}$
5. $E\to !E_1\{\text{check that}{E}_1.\text{type = bool;set E.type = bool}\}$
6. $E\to ID$ {set E. type = int}

Rules 2 and 3 are used for entry into the symbol table. Rule 4 is used for type checking of the integer expression. But, in rule 6 only int type is set.

Hence answer is option (a).