201506 CSE340 Lecture 15

CSE340 - Principles of
Programming Languages
Lecture 15:
Parsing Techniques III
Javier Gonzalez-Sanchez
javiergs@asu.edu
BYENG M1-38
Office Hours: By appointment

Javier Gonzalez-Sanchez | CSE340 | Summer 2015 | 2
Parser | Error Recovery
PROGRAM
Line N: expected {
Line N: expected }
currentToken++;
Searching for
FIRST(BODY) or }

Parser | Error Recovery
Rule FIRST set FOLLOW set
PROGRAM { EOF
BODY FIRST (PRINT) U FIRST (ASIGNMENT) U FIRST(VARIABLE) U FIRST
(WHILE) U FIRST(IF) U FIRST (RETURN)
}
PRINT print ;
ASSIGNMENT identifier ;
VARIABLE int, float, boolean, void, char, string ;
WHILE while } U FIRST(BODY)
IF if } U FIRST(BODY)
RETURN return ;
EXPRESSION FIRST(X) ), ;
X FIRST(Y) | U FOLLOW(EXPRESSION)
Y ! U FIRST(R) & U FOLLOW(X)
R FIRST(E) FOLLOW(Y)
E FIRST (A) !=, ==, >, < U FOLLOW(R)
A FIRST (B) -, + U FOLLOW(E)
B - U FIRST (C) *, /, U FOLLOW(A)
C integer, octal, hexadecimal, binary, true, false, string, char, float, identifier, ( FOLLOW(B)

Calculating the First Set

FIRST set
Definition
FIRST (a) is the set of tokens that can begin the construction a.
Example
<E> → <A> {+ <A>}
<A> → {* }
 → -<C> | <C>
<C> → integer
FIRST(E) = {-, integer}
FIRST(A) = {-, integer}
FIRST(B) = {-, integer}
FIRST(C) = {integer}

FIRST set
Define FIRST (BODY)
FIRST(BODY) =
FIRST (PRINT) U FIRST (ASSIGNMENT) U FIRST(VARIABLE) U FIRST(WHILE) U
FIRST(IF) U FIRST(RETURN)

FIRST set
Define FIRST (C)

FIRST set
Define FIRST (A)
Define FIRST (B)

FIRST set
<S> → <A><C>
<S> → <F>
<A> → <E><F>d
<A> → a
 → ab
 → ε
<C> → c<C>
<C> → d
<E> → e<E>
<E> → <F>
<F> → <F>f
<F> → ε

Calculate the FIRST set
1.  FIRST(X) = {X}
if X is a terminal
2. FIRST(ε) = {ε}.
note that this is not covered by the first rule because
ε is not a terminal.
3.  If A → Xα, add FIRST(X) − {ε} to FIRST(A)
4.  If A → A1A2A3 ...AiAi+1 ... Ak and
ε ∈ F IRST (A1) and ε ∈ FIRST (A2) and . . . and ε ∈ FIRST (Ai),
then add FIRST (Ai+1) − {ε} to FIRST (A).
5.  If A → A1A2A3 ...Ak and
ε ∈ FIRST(A1) and ε ∈ FIRST(A2) and... and ε ∈ FIRST(Ak),
then add ε to FIRST(A).

Calculate the FIRST set
loop

FIRST set
S → ABC
S → F
A → EFd
A → a
B → aBb
B → ε
C → cC
C → d
E → eE
E → F
F → Ff
F → ε
rule
FIRST set -‐‑ evolution
S
ø {a, ε} {a, ε, e, f} {a, ε, e, f, d}
A
ø {a} {a, e} {a, e, f, d}
B
ø {a, ε}
C
ø {c, d}
E
ø {e} {e, ε} {e, ε, f}
F
ø {ε} {ε, f}

<X> → <A>
<X> → <A> a
<A> → 
<A> → b
 → <C><D><E>
 → c d e
 → <C> c <D> d <E> e
<C> → one
<D> → two
<E> → three
OPTION 1:
FIRST(X) = {c, one}
FIRST(A) = {c, one}
FIRST(B) = {c, one}
FIRST(C) = {one}
FIRST(D) = {two}
FIRST(E) = {three}
OPTION 2:
FIRST(X) = {c, one, ε}
FIRST(A) = {b, c, one}
FIRST(B) = {c, one}
FIRST(C) = {one}
FIRST(D) = {two}
FIRST(E) = {three}

<X> → <A>
<X> → <A> a
<A> → 
<A> → b
 → <C><D><E>
 → c d e
 → <C> c <D> d <E> e
<C> → one
<C> → ε
<D> → two
<D> → ε
<E> → three
FIRST(X) = {c, one, three, two}
FIRST(A) = {c, one, three, two}
FIRST(B) = {c, one, three, two}
FIRST(C) = {one, ε}
FIRST(D) = {two, ε}
FIRST(E) = {three}

Calculating the Follow Set

FOLLOW set
Definition
FOLLOW (a) is the set of tokens that can follow the construction a.
Example
<E> → <A> {+ <A>}
<A> → {* }
 → -<C> | <C>
<C> → integer
5 + 4 + -7 * 12 + 75
5 + 4 + ((-7) * 12) + 75
What follows <C> ?
What follows <A> ?
What follows <E> ?

FOLLOW set
Definition
FOLLOW (a) is the set of tokens that can follow the construction a.
Example
<E> → <A> {+ <A>}
<A> → {* }
 → <C> | <C>
<C> → integer
FOLLOW(E) = {$} // $ represents end of input, i.e., EOF
FOLLOW(A) = {+, $}
FOLLOW(B) = {*, +, $}
FOLLOW(C) = {*, +, $}

FOLLOW set
Define FOLLOW (BODY)
FIRST(BODY) = }

FOLLOW set
Define FOLLOW (C)

FOLLOW set
<S> → <A><C>
<S> → <F>
<A> → <E><F>d
<A> → a
 → ab
 → ε
<C> → c<C>
<C> → d
<E> → e<E>
<E> → <F>
<F> → <F>f
<F> → ε

Calculate the FOLLOW set
1.  First put $ (the end of input marker) in Follow(S) (S is the start
symbol)
2.  If there is a production A → aBb,
(where a can be a whole string)
then everything in FIRST(b) except for ε is placed in FOLLOW(B).
(apply the rule 4 in calculate FIRST set)
3.  If there is a production A → aB,
then add FOLLOW(A) to FOLLOW(B)
4.  If there is a production A → aBb,
where FIRST(b) contains ε,
then add FOLLOW(A) to FOLLOW(B)

Calculate the FOLLOW set

FOLLOW set
S → ABC
S → F
A → EFd
A → a
B → aBb
B → ε
C → cC
C → d
E → eE
E → F
F → Ff
F → ε
rule
FOLLOW set -‐‑ evolution
S
{eof}
A
{a} {a, c, d}
B
{c, d} {c, d, b}
C
{eof}
E
{f} {f, d}
F
{eof} {eof, d} {eof, d, f}
FIRST sets:
S={a,ε,e,f,d}
A={a, e, f, d}
B={a, ε}
C= {c, d}
E={e, ε, f}
F={ε,f}

Another Example
<E> → <T> {+<T>}
<T> → <F> {*<F>}
<F> → (<E>) | integer
FIRST (E) = {(, integer}
FIRST (T) = {(, integer}
FIRST (F) = {(, integer}
FOLLOW(E) = {$, )}
FOLLOW(T) = {$, ),+ }
FOLLOW(F) = {$, ),+, * }

Prediction Rules

Prediction Rules
Rule 1.
It should always be possible to choose among several
alternatives in a grammar rule.
FIRST(R1) FIRST(R2) FIRST(R3)... FIRST(Rn) = Ø
BODY

Prediction Rules
Rule 1.1
The FIRST sets of any two choices in one rule must not
have tokens in common in order to implement a single-
symbol look ahead predictive parser.

Prediction Rules
Rule 2.
For any optional part, no token beginning the optional part
can also come after the optional part.
FIRST(RULE) != FOLLOW(RULE)
BODY PROGRAM

Homework
Programming Assignment #2

CSE340 - Principles of Programming Languages
Javier Gonzalez-Sanchez
javiergs@asu.edu
Summer 2015
Disclaimer. These slides can only be used as study material for the class CSE340 at ASU. They cannot be distributed or used for another purpose.

201506 CSE340 Lecture 15

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201506 CSE340 Lecture 15