PARSER_BEGIN(Q2)

class Q2 {


  /** Standard code to call the parser
   */
  public static void main(String args[]) {

    Q2 parser;

    System.out.println("Reading from standard input . . .");
    parser = new Q2(System.in);
    try {
      boolean res = parser.s();
      System.out.println("The answer is: "+res);
     } catch (ParseException e) {
      System.out.println("Encountered errors during parse.");
    }
  }   /* End of function "main" */


}

PARSER_END(Q2)



/******************/
/***** TOKENS *****/
/******************/

SKIP : /* WHITE SPACE */
{
  " " 
| "\t"
| "\n"
| "\r"
| "\f"
}

TOKEN : 
{
  < AND : "and" >
| < IMPLIES : "=>" >
| < TRUE : "true" >
| < FALSE : "false" >
| < LBR : "(" >
| < RBR : ")" >
}
 

/*************************/
/***** GRAMMAR RULES *****/
/*************************/

boolean s() :
{
  boolean b;
}
{
  b=e() <EOF> { return b; }
}

boolean e() : 
{
  boolean b1, b2;
}
{
  b1=t() (<AND> b2=t() { b1 = b1 & b2; } )* { return b1; }
}
    
boolean t() : 
{
  boolean b1, b2;
}
{
  b1=f() (<IMPLIES> b2=f() { b1 = !(b1 & !b2); } )* { return b1; }
}


boolean f() :
{
  boolean b;
}
{
  <TRUE> { return true; }
| <FALSE> { return false; }
| <LBR> b=e() <RBR> { return b; }
}