Syntax != Semantics. Grammars. Help to. determine ??. Determine. Ambiguities. Ambiguity in English. I saw an airplane with a telescope. I saw a girl with her boyfriend. I saw a boy scout with a telescope on the mountain top.
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I saw an airplane with a telescope.
I saw a girl with her boyfriend.
I saw a boy scout with a telescope on the mountain top.
I saw a pretty girl with a telescope on the mountain top.
IT 327
if (a > 2)
if (b > 1)
b++;
else
a++;
Dangling else
if (a > 2)
if (b > 1)
b++;
else
a++;
IT 327
G1: <subexp> ::= <subexp>  <subexp>  a  b  c
G2: <subexp> ::= <var>  <subexp>  <var><var> ::= a  b  c
G3: <subexp> ::= <subexp>  <var>  <var><var> ::= a  b  c
They are equivalent! (what does that mean?)
IT 327
G1: <subexp> ::= <subexp>  <subexp>  a  b  c
<subexp>
<subexp>
<subexp>

<subexp>
<subexp>

<subexp>
a
<subexp>

<subexp>
<subexp>

<subexp>
c
b
c
a
b
G1 is an ambiguous grammar
IT 327
Right associative rule:
abcd = a–(b(cd))
Left associative rule:
abcd = ((a–b)c)d
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G3: <subexp> ::= <subexp>  <var>  <var><var> ::= a  b  c
G2: <subexp> ::= <var>  <subexp>  <var><var> ::= a  b  c
<subexp>
<subexp>
<subexp>

<var>
<var>

<subexp>
<subexp>

<var>
c
a
<var>

<subexp>
b
<var>
b
<var>
c
a
Right associative rule:
abc = a(bc)
Left associative rule:
abc = (ab)c
IT 327
<exp> ::= <exp> + <exp> 
<exp> * <exp> 
( <exp> ) 
a  b  c
Example: ((a+b)*c)
IT 327
We prefer this
Using leftmost derivation
<exp>
<exp>
<exp> + <exp>
<exp> * <exp>
c
a
<exp> * <exp>
<exp> + <exp>
b
c
a
b
Using rightmost derivation doesn’t help
IT 327
<exp>
<exp>
Call this a term
<exp> * <exp>
<exp> + <exp>
c
And term does not generate exp directly
<exp> + <exp>
a
<exp> * <exp>
a
b
b
c
Solution: restricting <exp> from generating * directly.
A term is an exp: a*bAn exp may not be a term: a+b
<exp> ::= <term>
<term> ::= <exp>
<term> ::= (<exp> )
IT 327
<exp>
<exp> ::= <term> + <exp>  <term>
<term> ::= <fact> * <term>  <fact>
<fact> ::=( <exp> ) 
a  b  c
<term> + <exp>
<fact>
<term>
<fact> * <term>
Example: a+b*c
a
<fact>
b
c
IT 327
<exp> ::= <term> + <exp>  <term>
<term> ::= <fact> * <term>  <fact>
<fact> ::=( <exp> ) 
a  b  c
<exp>
<term> + <exp>
<fact>
<term> + <exp>
<term>
a
<fact>
Example: a+b+c
<fact>
Right association
b
a+b+c = a+(b+c)
c
IT 327
<exp> ::= <term> + <exp>  <term>
<term> ::= <fact> * <term>  <fact>
<fact> ::=( <exp> ) 
a  b  c
<term> + <exp>
<term>
<fact>
<fact>
( <exp> )
Example: (a+b)+c
<term> + <exp>
c
a
b
IT 327
No such thing called left associative grammar
<exp>
A better way to say this:
A grammar for left associative arithmetic exp.
<exp> + <term>
<exp> ::= <exp> + <term>  <term>
<term> ::= <term> * <fact>  <fact>
<fact> ::=( <exp> ) 
a  b  c
<exp> + <term>
<fact>
<term>
<fact>
c
Example: a+b+c
<fact>
b
a
IT 327
Too much freedom to generate if statements from stmt
Dangling else<stmt> ::= <ifstmt>  s1  s2
<ifstmt> ::= if <expr> then <stmt> else <stmt>  if <expr> then <stmt>
<expr> ::= e1  e2
if e1 thenif e2 then s1 else s2
if (a > 2)
if (b > 1)
b++;
else
a++;
if (a > 2)
if (b > 1)
b++;
else
a++;
IT 327
if (b > 1)
b++;
else
a++;
if (a > 2)
if (b > 1)
b++;
else
a++;
Most languages: elsegoes withnearest then
IT 327
Numbers of then and else are the same
<stmt> ::= <ifstmt>  s1  s2
<ifstmt> ::= if <expr> then <fullstmt> else <stmt>  if <expr> then <stmt>
<expr> ::= e1  e2
<fullstmt> ::= <fullif>  s1  s2
<fullif> ::= if <expr> then <fullstmt> else <fullstmt>
IT 327
IT 327
Algol: then part can’t be another if (a block is allowed)
Ada: if statement must be terminated with an end if
IT 327
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Most systems construct an AST instead
IT 327
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IT 327
The priority in In the competition of getting operands.
Most languages put * at a higher precedence level than +.
a+b*c = a+(b*c)
(sign, as unary operators)
+ 
^
* / %
+ 
:=
IT 327
with (my view)
IT 327