bottom up parsing - compiler design - dr. d. p. sharma - nit surathkal by wahid311

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing Bottom-up parsing is more

general than top-down parsing

Bottom-up parsers handle a large class of grammars.

Preferred method in practice

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing Bottom-up parsing is more

general than top-down parsing

Bottom-up parsers handle a large class of grammars.

Preferred method in practice

3

Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing Bottom-up parsing is more

general than top-down parsing

Bottom-up parsers handle a large class of grammars.

Preferred method in practice

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingAlso called LR parsing L means that tokens are

read left to right R means that the parser

constructs a rightmost derivation.

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingAlso called LR parsing L means that tokens are

read left to right R means that the parser

constructs a rightmost derivation.

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingAlso called LR parsing L means that tokens are

read left to right R means that the parser

constructs a rightmost derivation.

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing LR parsers donot need

left-factored grammars LR parsers can handle

left-recursive grammars

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing LR parsers donot need

left-factored grammars LR parsers can handle

left-recursive grammars

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing

LR parsing reduces a string to the start symbol by inverting productions.

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing A derivation consists of a

series of rewrite steps

S 0 1 ... n-1 n sentence

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingS 0 ... n sentence

Each i is a sentential form if contains only terminals,

is a sentence in L(G) If contains 1

nonterminals, is a sentential form

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingS 0 ... n sentence

Each i is a sentential form if contains only terminals,

is a sentence in L(G) If contains 1

nonterminals, is a sentential form

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up ParsingS 0 ... n sentence

Each i is a sentential form if contains only terminals,

is a sentence in L(G) If contains 1

nonterminals, is a sentential form

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing A bottom-up parser builds a

derivation by working from input sentence back towards the start symbol S

S 0 ... n sentence

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing Consider the grammar

S → aABeA → Abc | bB → d

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing The sentence abbcde can be

reduced to S:abbcdeaAbcdeaAdeaABeS

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing The sentence abbcde can be

reduced to S:abbcdeaAbcdeaAdeaABeS

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing The sentence abbcde can be

reduced to S:abbcdeaAbcdeaAdeaABeS

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing The sentence abbcde can be

reduced to S:abbcdeaAbcdeaAdeaABeS

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing The sentence abbcde can be

reduced to S:abbcdeaAbcdeaAdeaABeS

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing These reductions, in fact,

trace out the following right-most derivation in reverse: S aABe

aAde aAbcde abbcde

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S By y xy rmrm rm

xx y

B

S

rule: B →

Terminals only

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing

Consider the grammar

1. E → E + (E) 2. | int

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing

Consider bottom-up parse of the string

int + (int) + (int)

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int + (int) + (int)

int+ ( int )int + ( )

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int + (int) + (int)

E + (int) + (int)

int+ ( int )int + ( )

E

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int + (int) + (int)

E + (int) + (int)

E + (E) + (int)

int+ ( int )int + ( )

E E

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int + (int) + (int)

E + (int) + (int)

E + (E) + (int)E + (int)

int+ ( int )int + ( )

E E

E

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int + (int) + (int)

E + (int) + (int)E + (E) + (int)E + (int)E + (E)

int+ ( int )int + ( )

E E E

E

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int + (int) + (int)

E + (int) + (int)E + (E) + (int)E + (int)E + (E)E

int+ ( int )int + ( )

E E E

E

EA rightmost derivation in reverse

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Bottom-up ParsingBottom-up ParsingBottom-up ParsingBottom-up Parsing

An LR parser traces a rightmost derivation in reverse

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ConsequenceConsequenceConsequenceConsequence Let be a step of a

bottom-up parse Assume that next reduction

is A → Then is a string of

terminals!

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ConsequenceConsequenceConsequenceConsequence Let be a step of a

bottom-up parse Assume that next reduction

is A → Then is a string of

terminals!

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ConsequenceConsequenceConsequenceConsequence Let be a step of a

bottom-up parse Assume that next reduction

is A → Then is a string of

terminals!

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ConsequenceConsequenceConsequenceConsequenceWhy? Because A → is a

step in a rightmost derivation

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NotationNotationNotationNotation

Idea: Split the string into two

substrings

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NotationNotationNotationNotation Right substring (a string of

terminals) is as yet unexamined by parser

Left substring has terminals and non-terminals

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NotationNotationNotationNotation Right substring (a string of

terminals) is as yet unexamined by parser

Left substring has terminals and non-terminals

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NotationNotationNotationNotation The dividing point is marked

by a ►

• The ► is not part of the string

Initially, all input is unexamined: ►x1 x1 . . . xn

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Shift-Reduce ParsingShift-Reduce ParsingShift-Reduce ParsingShift-Reduce Parsing

Bottom-up parsing uses only two kinds of actions:

1. Shift2. Reduce

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ShiftShiftShiftShiftMove ► one place to the rightshifts a terminal to the left string

E + (► int) E + (int ►)

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ReduceReduceReduceReduceApply an inverse production at the right end of the left string. If E → E + (E) is a production, then E + ( E+(E)►) E + ( E ►)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

►int + (int) + (int) $

shift

int ► + (int) + (int) $

reduce E → int

E ► + (int) + (int) $

shift 3 times

E + (int ►) + (int) $

reduce E → int

E + (E ►) + (int) $ shift

E + (E) ► + (int) $ reduce E → E+(E)

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Shift-Reduce ExampleShift-Reduce ExampleShift-Reduce ExampleShift-Reduce Example

E ► + (int) $ shift 3 times

E + (int ►) $ reduce E → int

E + (E ►) $ shift

E + (E) ► $ red E → E+(E)E ► $ accept