Understanding Predictive Parsing Preparing to Construct the Predictive Parsing

Table

Left Recursion Elimination

Left Factoring

LL(1) compatibility

Predictive Parsing

• The goal of predictive parsing is to construct a top-down parser that does not backtrack

• The lookahead symbol (token) unambiguously determines the production selected for each non-terminal

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Predictive Parsing and lookahead symbol

• The lookahead symbol is scanned from left to right

• The left recursive grammar always produces the same nonterminal and cannot be used to build predictive parsers

• The grammar rules are redefined

• These rules eliminate most common causes for backtracking

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Predictive Parsing

• Predictive parsing relies on information about what first symbols can be generated by the right side of a production

• We try collecting all terminals that could be generated first by all productions for a non terminal

• The decision making is based on the next lookahead and the selection of the rule is made based on the entries in the parsing table

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Predictive Parsing

• Let a rule be A α where α (alpha) is the sequence of terminal and non terminal variables at the RHS of the rule

• Define FIRST(α) as the set of terminals (tokens) that appear as the first symbols of one or more strings generated from α

• Follow-set of A, written as Follow(A), is defined as the set of terminals a such that there is a string of symbols αAaβ that can be derived from the start symbol.

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Example

Consider the grammar

S ASB

SaA | h

A cA | dB

B eA | fB |ε

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Verify the Input: cacdfed

FIRST(S)= {a,h,c,d}

FIRST(A)={c,d}

FIRST(B)={e,f, ε}

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Example: construct FIRST sets

Consider the grammar

S ABSB

SaA | h

A cA | dB |ε

B eA | fB

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FIRST(S)= {a,h,c,d,e,f}

FIRST(A)={c,d, ε}

FIRST(B)={e,f,} Parse strings

1. cf

2. ae

3. eac

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Example: construct FOLLOW sets

Consider the grammar

S ABS$

SaA | h

A cA | dB |ε

B eA | fB

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FOLLOW(S)= {$}

FOLLOW(A) = FIRST(B)

FOLLOW(B)= FIRST(S)

Parse the string

ecfh

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Predictive Parsing

The grammar rules are redefined with following aspects

1. Eliminate left recursion, and

2. Perform left factoring.

example : Compute FIRST(statement) <Statement> IF <condition> THEN <Statement>

<Statement> IF <condition> THEN <Statement> ELSE <Statement>

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Class assignment

• Parse the following input to verify whether the grammar is ambiguous

if E1 then S2 else if E2 then S2 else S3

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Left factored grammar

Can be left factored as

<Statement> IF <condition>THEN <Statement> <Elsepart>

<Elsepart> ε | ELSE <Statement >

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Parser

• The parser consists of

an input buffer,

a string from the grammar

a stack on which to store the terminals and non-terminals from the grammar yet to be parsed

a parsing table which tells it what (if any) grammar rule to apply given the symbols on top of its stack and the next input token

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Parser

• The parser applies the rule found in the table by matching the top-most symbol on the stack (row) with the current symbol in the input stream (column).

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Sample Parsing table

• Input : ( 1 + 1 )

• Parsing table for this grammar

( ) 1 + $

S 2 - 1 - -

F - - 3 - -

Grammar

1. S → F 2. S → ( S + F ) 3. F → 1

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