Compiler Design Chapter 3

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Compiler Design - Chapter 3
Parsing Context-Free Grammars
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Syntax
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Symbols representing regular expressions

• Abbreviation
• digits 0-9
• sum (digits)digits
• Defines sums of the form
• 283019

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Balanced Parentheses

• digits 0-9
• sum exprexpr
• expr (sum)digits
• defines
• (10923)
• 61
• (1(2503))
• Automaton cannot recognize balanced parentheses
  a machine with N states cannot remember
  parenthesis-nesting greater than N

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How does a lexical analyzer implement regular
expression abbreviations?
digits 0-9
RHS 0-9 substituted for digits before
translation to finite automaton not possible
for sum-and-expr
Mutually Recursive
Recursion - Important
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Alternation at top level
can be re-written as
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Elimination of alternation
can be re-written as
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Kleene closure unnecessary
can be re-written as
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Grammars

• Regular expressions describe the structure of
  lexical tokens
• Grammars define syntactic structure declaratively
• Need a more powerful tool than finite automata to
  parse languages described by grammars
• Grammars can be used to describe the structure of
  lexical tokens but regular expressions are
  adequate and more concise

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Context-free Grammars

• Language set of strings
• Each string finite set symbols taken from a
  finitealphabet
• PARSING
• Strings source programs
• Symbols lexical tokens
• Alphabet set of token types returned by
  lexicalanalyzer

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Context-free Grammars

• Context-free grammar describes a language
• A grammar has a set of productions of the form

Zero or more symbols on RHS

• Symbol can be
• Terminal token from the alphabet of stringsin
  the language
• token can not appear on LHS
• Non-terminal appears on LHS of some production
• can appear on RHS also

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Context-free grammar example
A syntax for straight-line programs
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Context-free grammar example
Sentence (statement) in this language
From source language (before lexical analysis)
Token- types (terminal symbols) id, num, , etc
Names (a, b, c, d) Numbers (7, 5, 6)
semantic values associated with tokens
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Derivation

• Derivation to show this sentence is in the
  language of the grammar
• Start with the start symbol
• Repeatedly replace any non-terminal by its RHS
• Leftmost always expand leftmost non-terminal
  first
• Rightmost always expand rightmost non-terminal
  first
• Neither leftmost or rightmost

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Left-most derivation
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Parse tree

• Parse tree
• Connecting each symbol in derivation to the
  one from which it was derived
• Two different derivations can have the same
  parse tree

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Ambiguous Grammars
Grammar ambiguous if the same sentence can be
derived with two different parse trees
Two parse trees for the same sentence
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Another Ambiguous Grammar
Grammar 3.5
-4
2
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Another Ambiguous Grammar
Grammar 3.5
9
7
Different semantics!
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Ambiguous Grammars

• Problematic for compiling
• Need unambiguous grammars
• Ambiguous grammars can often be transformed to
  unambiguous grammars

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Transforming an Ambiguous Grammar

• has higher precedence (bind tighter) than
• Each operator associates to the left (1-2)-3 not
  1-(2-3)
• Introduce new non-terminal symbols
• E expression
• T term (things you add)
• F factor (things you multiply)

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Unambiguous Grammar
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Associate to the right
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Ambiguous Languages

• Ambiguity can usually be eliminated
• Some languages, howeveronly ambiguous grammars
• These languages are problematic as programming
  languages
• Syntactic ambiguity problems in
  writing/understanding programs

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EOF Marker
Start symbol
Augmented Grammar Added
EOF Marker