Compiler Design Chapter 3

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Compiler Design - Chapter 3
Parsing - Predictive Parsing
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Predicative Parsing

• Recursive decent simple algorithm easily
  parse some grammars
• Each production turns into a clause of recursive
  function

• Recursive Descent Parser for this grammar
• One function per non-terminal symbol
• One clause per production

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Predicative Parsing
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Predicative Parsing
Conflicts
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Recursive Descent

• Recursive Descent / Predictive Parsing
• Works only when first terminal symbol of each
  subexpression provides enough information to
  choose
• FIRST sets
• Parser generators rather use LR(1) parsing
  (later in course)
• Predictive parsing algorithm simple enough
  to construct parsers manually (without tools)

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FIRST sets
Let ? be a string with terminal and nonterminal
symbols FIRST(?) the set of all terminal
symbols that can begin any string derived from ?
? T F, FIRST(T F) id, num,
(
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Overlapping FIRST sets
Consider
X ? ?1
X ? ?2
If FIRST(?1) and FIRST(?2) overlaps, recursive-des
cent parsing cannot be used
If terminal symbol I is in FIRST(?1) and also
FIRST(?2), the function X() do not know what to
do (i.e., which production to use) given I.
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FIRST sets and nullable symbols
FIRST(X Y Z) not always the same as FIRST( X )

• Y produces empty string therefore
• X produces empty string therefore
• FIRST( X Y Z ) must include FIRST( Z )
• nullable symbols
• - Symbols that can produce empty string
• Must know what might follow nullable symbols

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nullable, FIRST and FOLLOW sets

• Let ? be a string with terminal and nonterminal
  symbols
• nullable(X) is true if X can derive empty string
• FIRST(?) the set of all terminal symbols that
  can begin any string derived from ?
• FOLLOW(X) the set of all terminal symbols that
  can immediately follow X.
• t ? FOLLOW(X) if there is any derivation
  containing Xt
• t ? FOLLOW(X) if derivation contains X Y Zt
  where Y and Z both derive e (empty string)

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Nullable, FIRST and FOLLOW sets
Smallest sets having the following properties
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Nullable, FIRST and FOLLOW sets Algorithm
Three relations do not need to be computed
simultaneously
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Example
Initially
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Example - First iteration
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Example Second iteration

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Generally
? is nullable if each symbol in ? is nullable
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Constructing a Predictive Parser
Can construct 2-dimnsinal predictive parsing
table indexed by nonterminals X and terminals T
to choose the right production for a input token
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Constructing a Predictive Parser

• Consider each X ? ?
• enter X ? ? in row X column T for each T ?
  FIRST(?)
• For Z ? d FIRST(d) d
• For Z ? X Y Z FIRST(X Y Z) a,c,d
• For Y ? c FIRST(c) c
• For X ? Y FIRST(Y) c
• For X ? a FIRST(a) a
• if ? is nullable, enter X ? ? in row X column T
  for each T ? FOLLOW(X)
• For Y ? FOLLOW(Y) a,c,d
• For X ? Y FOLLOW(X) a,c,d

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Duplicate entries in Predictive Parsing Table

• Predictive parser will not work if there are
  duplicate entries in the predictive parsing
  table.
• Grammar is ambiguous
• Sentence d more than one parsing table

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LL(1) Grammar

• Grammar with no duplicate entries in predictive
  parsing table LL(1) grammar
• Stands for
• Left-to-right parse,
• Left-most derivation,
• 1 symbol lookahead
• LL(k) parsing table rows are non-terminals,
  columns every sequence of k terminals
• Rarely done large tables
• No ambiguous grammar is LL(k) for any k

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Left Recursion

• cause duplicate entries since any tokenin
  FIRST(T) will also be in FIRST(ET)
• E appears as the first right-hand-side symbol in
  an E-production

• This is called left recursion
• Left-recursive grammars cannot be LL(1)

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Eliminating Left Recursion
Introduce a new nonterminal E and re-write using
right recursion
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Generally
a does not start with X
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Example
?1
?2
a1
Eliminate left-recursion
a1
?1
?2
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Nullable, FIRST FOLLOW
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Predictive Parser
enter X ? g in row X column T for each T ?
FIRST(g)
if g is nullable, enter X ? g in row X column T
for each T ? FOLLOW(X)

• For S?E FIRST(E ) ( id num
• For E?T E FIRST(T E) ( id num
• For E?TE FIRST(TE)
• For E?-TE FIRST(-TE) -

• For E? FOLLOW(E) )

etc.

• For T? FOLLOW(T) )-

-
etc.
E?-TE
T?
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Left Factoring

• When two productions for the same non-terminal
  symbols start with the same symbol
• Cause problems in predictive parsing

Left factor
take the allowable endings and make a new
nonterminal X
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Error Handling
Blank entry in table syntax error
T() does not expect to see other tokens
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Error Handling

• If an error is found can raise exception and
  quit parsing, which is not user friendly
• Error Recovery by deleting, replacing, or
  inserting tokens.
• Error Recovery by insertion pretend num token
  was found, print error message and return
  normally so that more errors can be found
• Cascading errors might cause infinite looping

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Error Handling

• Error Recovery by deletion skip tokens until a
  token in the FOLLOW set is reached

MINUS,
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Error Handling

• Recursive Descent error recovery must be
  adjusted to avoid a long cascade of error-repair
  messages