Questions

Using the syntax directed definition for does expression evaluation (see slides), draw and annotate the parse tree for the input: (4*7+1)*2

Draw and annotate a tree for input ((a)+(b)) assuming the rules below.

Production	Semantic Rule
E --> E + T	$$ = mknode("-",$1,$3)
E --> E - T	$$ = mknode("-",$1,$3)
E --> T	$$=$1;
T --> ( E )	$$ = $2;
T --> id	$$ = mkleaf(id,$1)
T --> num	$$ = mkleaf(num,$1)

All of the attributes are pointer to a given node type. Assume the lexer returns a string for both num and id. mkleaf creates a leaf node with a type (num or id) and an associated string (from the lexer). mknode(op,left,right) creates an operator node with the label op and two pointers: left and right

Let synthesized attribute val give the value of the binary number generated by S in the following grammar. For example, on input 101.101, S.val = 5.625

S --> L . L

S --> L

L --> L B

L --> B

B --> 0

B --> 1

Use synthesized attributes to determine S.val
The following grammar describes (at a high level) part of the syntax of a typical ALGOL-like language. (Notation: non-terminals are in CAPITALS and terminals are in lower case The details of ASSIGNMENT are uninteresting.)
```
PROGRAM      --> procedure STMT_LIST   
STMT_LIST    --> STMT STMT_LIST   
              |    STMT   
STMT         --> ASSIGNMENT   
              |     do var = constant to constant begin STMT_LIST end   
              |     if var then  STMT_LIST  else  STMT_LIST endif
```
As a first step toward understanding a program, it is interesting to understand the number of times that each statement in the program is executed. It is equally important to understand the total execution time. To estimate these numbers for the above language, we can use the following simple rules:
- the number of times that the body of a do-loop executes can be computed from the two constants that govern the range of its index variable;
- the then-part of an if statement executes half the time; similarly, the else-part executes half the time; and
- an ASSIGNMENT statement takes one unit of execution time.
1. Write a set of syntax--directed tranlation rules (using YACC--like notation or the notation in the text) that annotates each non--terminal node with the estimated cost (in terms of execution units) using the rules above. Be clear about what assumptions you are making with respect to how you compute these values and what attributes are associated with the different symbols.
2. Draw and annotate (with your attributes) this parse tree using your rules from part (a):
```
procedure
  do i = 1 to 100 begin
    if x then
      do j = 1 to 50 begin
        ASSIGNMENT
      end
    else
      ASSIGNMENT
    endif
    ASSIGNMENT
  end
```
Solutions