Syntax Semantics

1
Syntax -- Semantics
Grammar
Determines ??
Help??
Determines
Ambiguities
2
Ambiguity in English
I saw an airplane with a telescope.
I saw a girl with her boyfriend.
I saw a scout with a telescope on the mountain
top.
I saw a pretty girl with a telescope on the
mountain top.
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Ambiguity in Programming Languages
if (a 2) if (b 1) b else
a
Dangling else
if (a 2) if (b 1) b else a
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Three Equivalent Grammars
G1 - a b c
G2 -
a b c
G3 -
a b c
They are equivalent! (what does that mean?)
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Parse a-b-c using G1
G1 - a b c


-


-


a
-


-


c
b
c
a
b
G1 is an ambiguous grammar
6
Left and Right Association rules
Right associative rule a-b-c-d a (b-(c-d))
Left associative rule a-b-c-d ((ab)-c)-d
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G2 and G3 Grammars
G2 -
a b c G3
- a b c
Right associative rule
Left associative rule a-b-c-d ((ab)-c)-d
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A grammar for Arithmetic Expressions

( ) a
b c
Example ((ab)c)
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What is the meaning of abc




c

a

b
c
a
b
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An unambiguous grammar for Arithmetic Expressions


( )
a b c




a
Example abc

b
c
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An unambiguous grammar for Arithmetic Expressions


( )
a b c




a

Example abc

Right association
b
abc a(bc)
c
12
Alter the order


( )
a b c




( )
Example (ab)c
c

a
b
13
An unambiguous left associative grammar for
Arithmetic Exp.
No such thing called left associative grammar

Better way to say this A grammar for left
associative arithmetic exp.


( )
a b c




c
Example abc

b
a
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Dangling else
s1 s2 if
then else if
then e1 e2
if e1 then if e2 then s1 else s2
if (a 2) if (b 1) b else
a
if (a 2) if (b 1) b else a
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if (a 2) if (b 1) b else a
if (a 2) if (b 1) b else
a
Most languages else goes withnearest then
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Eliminating The Ambiguity
s1 s2 if
then else
if then e1 e2
then-else are all matched
s1 s2
if then else
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A Parse Tree for if-stmt
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Languages That Dont Dangle

• Algol then part cant be another if (a block is
  allowed)
• Ada if statement must be terminated with an end
  if

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Options

• Rewrite grammar to eliminate ambiguity
• Leave ambiguity but explain in accompanying text
  how things like associativity, precedence, and
  the dangling else should be parsed
• Do both in separate grammars

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Abstract Syntax Tree

• Abbreviated version of the parse tree
• Details are implementation-dependent
• Usually, there is a node for every operation,
  with a subtree for every operand

Most systems construct an AST instead
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parse tree
abstract syntax tree
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Operators

• Special symbols for frequently-used simple
  operations like addition, subtraction,
  multiplication and division
• Usually predefined, but not always
• Usually a single token, but not always

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Operands

• Operands are the inputs to an operator, like 1
  and 2 in the expression 12
• Unary operators take one operand -1
• Binary operators take two 12
• Ternary operators take three a?bc

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Operator Position

• infix a b
• prefix a b
• postfix a b

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Operator Precedence

• Most languages put at a higher precedence level
  than .
• abc a(bc)

(sign, as unary operators)
-

/
-

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Precedence Examples in C
a b c
a b a 27
Some conclusions from the textbook
with (my view)

• Grammars define syntax, and more (more?)
• They define not just a set of legal programs, but
  the (a) parse tree for each program
• The structure of a parse tree corresponds to the
  order (entity) in which different parts of the
  program are to be executed (as an entity)
• Thus, grammars contribute (a little) to the
  definition of semantics