Midterm Exam Solution

CS 536, Spring 2013

Question 1 (12 points)

Part (a) (6 points)

There are many possible ways to do this; here's one:

Part (b) (6 points)

There are many possible ways to do this; here are two:

cons* vowel (cons+ vowel)* cons*
cons* vowel (cons vowel | cons+)*

Question 2 (10 points)

stmt ::= FOR LPAREN forCond RPAREN LCURLY varDeclList stmtList RCURLY

forCond ::= ID ASSIGN exp COLON exp optFor

optFor ::= COLON exp
        |  /* epsilon */

Question 3 (27 points)

Part (a) (15 points)

exp → exp ? term  |  term
     
term → factor $ term  |  factor

factor → INTLIT  |  ( exp )

Part (b) (4 points)

        expr
       /  |  \
     /    |    \
 expr     ?    term
  |           /  |  \
 term    factor  $  term
  |        |         |
factor   INTLIT    factor
  |       (2)     /  |   \
INTLIT           (  expr  )
 (1)               / |  \
                expr ?  term
                 |       |
                term   factor
                 |       |
               factor  INTLIT
                 |      (4)
               INTLIT
                (3)

Part (c) (4 points)

exp → term exp'

exp' → ? term exp'  |  ε
     
term → factor $ term  |  factor

factor → INTLIT  |  ( exp )

Part (d) (4 points)

exp → term exp'

exp' → ? term exp'  |  ε

term → factor term'

term' → $ term  |  ε

factor → INTLIT  |  ( exp )

Question 4 (15 points)

Grammar rule	Translation rule
program → varDeclList stmtList	`program.trans = stmtList.trans`
varDeclList → varDeclList varDecl
varDeclList → varDecl
varDecl → type ID ;
type → INT
type → BOOL
stmtList → stmtList stmt	`stmtList₁.trans = union(stmtList₂.trans, stmt.trans)`
stmtList → stmt	`stmtList.trans = stmt.trans`
stmt → ID = exp ;	`stmt.trans = exp.trans`
stmt → IF ( exp ) { varDeclList stmtList }	`stmt.trans = union(exp.trans, stmtList.trans)`
exp → ID	`exp.trans = new List(ID.val)`
exp → INTLIT	`exp.trans = new List()`
exp → exp + exp	`exp₁.trans = union(exp₂.trans, exp₃.trans)`
exp → exp * exp	`exp₁.trans = union(exp₂.trans, exp₃.trans)`
exp → exp == exp	`exp₁.trans = union(exp₂.trans, exp₃.trans)`

Question 5 (36 points)

Part (a) (24 points)

Non-terminal X	FIRST(X)	FOLLOW(X)
block	LCURLY	EOF, ELSE, ID, IF, RETURN, RCURLY
declList	TYPE, ε	ID, IF, RETURN, RCURLY
stmtList	ID, IF, RETURN, ε	RCURLY
decl	TYPE	TYPE, ID, IF, RETURN, RCURLY
stmt	ID, IF, RETURN	ID, IF, RETURN, RCURLY
exp	ID, INT	SEMI, RPAREN

Part (b) (12 points)

Snapshot 1:

current stack


stmtList
 RCURLY
  EOF

Snapshot 2:

partial parse tree

               block
            __/ || \__
      _____/ __/  \__ \_____
     /      /        \      \
LCURLY  declList  stmtList  RCURLY
          /   \
         /     \
       decl  declList
      /  | \
     /   |  \
   TYPE ID  SEMI

Snapshot 3:

input: LCURLY RCURLY

current stack


stmtList
 RCURLY
  EOF