Boolean expressions

Boolean expressions have two primary purposes. They are used for computing the logical values. They are also used as conditional expression using if-then-else or while-do.

Consider the grammar

1. E  →  E OR E  
2. E  →  E AND E  
3. E  →  NOT E   
4. E  →  (E)  
5. E →  id relop id  
6. E  →  TRUE  
7. E  →  FALSE  

The relop is denoted by <, >, <, >.

The AND and OR are left associated. NOT has the higher precedence then AND and lastly OR.

Production rule	Semantic actions
E → E1 OR E2	{E.place = newtemp(); Emit (E.place ':=' E1.place 'OR' E2.place) }
E → E1 + E2	{E.place = newtemp(); Emit (E.place ':=' E1.place 'AND' E2.place) }
E → NOT E1	{E.place = newtemp();  Emit (E.place ':=' 'NOT' E1.place) }
E → (E1)	{E.place = E1.place}
E → id relop id2	{E.place = newtemp();  Emit ('if' id1.place relop.op id2.place 'goto'  nextstar + 3);  EMIT (E.place ':=' '0')  EMIT ('goto' nextstat + 2)  EMIT (E.place ':=' '1') }
E → TRUE	{E.place := newtemp();  Emit (E.place ':=' '1') }
E → FALSE	{E.place := newtemp();  Emit (E.place ':=' '0') }

The EMIT function is used to generate the three address code and the newtemp( ) function is used to generate the temporary variables.

The E → id relop id2 contains the next_state and it gives the index of next three address statements in the output sequence.

Here is the example which generates the three address code using the above translation scheme:

1. p>q AND r<s OR u>r  
2. 
   
3.      100: if p>q goto 103  
4.      101: t1:=0  
5.      102: goto 104  
6.      103: t1:=1  
7.      104: if r<s goto 107  
8.      105: t2:=0  
9.      106: goto 108  
10.      107: t2:=1  
11.      108: if u>v goto 111  
12.      109: t3:=0  
13.      110: goto 112  
14.      111: t3:= 1  
15.      112: t4:= t1 AND t2  
16.      113: t5:= t4 OR t3