201506 CSE340 Lecture 09

CSE340 - Principles of
Programming Languages
Lecture 09:
Grammars 1
Javier Gonzalez-Sanchez
javiergs@asu.edu
BYENG M1-38
Office Hours: By appointment

Javier Gonzalez-Sanchez | CSE340 | Summer 2015 | 2
Ambiguity
•  A grammar is said to be ambiguous if there is at
least one string with two or more parse trees.
•  Note that ambiguity is a property of grammars, not
languages.

Ambiguity

Solution
•  If a grammar can be made unambiguous at all, it is
usually made unambiguous through layering.
•  Have exactly one way to build each piece of the
string.
•  Have exactly one way of combining pieces back
together.
•  Recursive constructions

Layering
Rule 1
Rule 2
Rule 3
Rule 4
Rule 5
. . . . .
Leaf (Terminals, i.e., Tokens)
Root
Start symbol
Layers

Layering
1
2
4
5
3
inputs:
§  1 + 2 + 3 < 4 * 5
§  1 * 2 + 3 + 4 < 5
§  1 < 2 + 3 + 4 * 5
§  1 + 2 < 3 * 4 + 5
§  1 + 2 * 3 < 4 + 5

Exercise
Provide a Grammar that is Not ambiguous
for arithmetic expressions
10 * 20 + 15
Precedence of operators and Associativity
þ (10 * 20) + 15
ý 10 * (20 + 15)

Exercise | Precedence
New Grammar:
<E> à <__> + <__>
< > à <__> - <__>
< > à <__> * <__>
< > à <__> / <__>
< > à - <__>
Original Grammar:
E à E OP E
E à integer
OPà + | - | * | /

Exercise | Hand written notes

<E> à <A> | <A> {'+' <A>} | <A> {'-' <A>}
<A> à | {'*' } | {'/' }
 à '-'<C> | <C>
<C> à integer

<E> à <A> {(’+'|'-’) <A>}
<A> à {('*'|'/') }
 à ['-'] <C>
<C> à integer

Syntax Diagrams
E
A
B
C

Exercise 1
Include rules for handling parenthesis into the previous
grammar. The grammar should accept as correct the
following expressions:
10 * 20 + 15
(10 * 20) + 15
10 * (20 + 15)
(10) * (20) + (15)
(10 * 20 + 15)
10 * (20) + 15

Exercise 1 | Hand written notes

Syntax Diagrams
E
A
B
C

Exercise 2
Include rules to accept variables names (identifiers) in
expressions. The grammar should accept as correct the
following expressions:
A * 20 + time
(x * y) + 15
10 * (ASU + cse340)
(10) * (20) + (15)
(hello * world + Arizona)
10 * (counter) + 15

Syntax Diagrams
E
A
B
C

Exercise 3
Provide a Grammar that is
Not ambiguous
with Precedence of operators and Associativity for this:
10 + 20 > 15 & -10 != 1 | 20 / ( 10 + 1) < 5

Exercise 3 | Note
Precedence of operators
|
&
!
< > == != <= >=
+ -
* /
-
( )

...

{ }
{ }
{ } { } { } { }...
{ } { }
{ } { }

Exercise 3
R
EXPRESSION
X
Y

Exercise 3
E
A
B
C

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 09

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201506 CSE340 Lecture 09