SDD for Type Checking 

   Production Rule       Semantic Rule
   ================      ==================
   E -> E_1 + T          E_1.type == T.type  // semantic constraint 
   E -> T                E.type = T.type
   T -> R                T.type = R 
   T -> W                T.type = W
   R -> num.num          // defined in lexer          
   W -> num              // defined in lexer  
   num -> [0..9]+        // defined in lexer

  Example. 5 + 3 + 2. Annotated Syntax Tree and Parse Tree.  

             E.type==T.type? YES                      E
            /           |    \                      / | \
   E.type==T.type? YES  +     T.type=W            E   +  T
       /   |   \                |               / | \    |
  E.type=W +   T.type=W         W              E  +  T   W
     |         |                             /       |
     T         W                            T        W
     |                                      |
     W                                      W