Predictive Parsing and LL(1) - Compiler Design - Dr. D. P. Sharma - NITK Surathkal by wahid311

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Nonrecursive Predictive Nonrecursive Predictive ParsingParsingNonrecursive Predictive Nonrecursive Predictive ParsingParsing It is possible to build a

nonrecursive predictive parser

This is done by maintaining an explicit stack

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Nonrecursive Predictive Nonrecursive Predictive ParsingParsingNonrecursive Predictive Nonrecursive Predictive ParsingParsing It is possible to build a

nonrecursive predictive parser

This is done by maintaining an explicit stack

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Table-driven ParsersTable-driven ParsersTable-driven ParsersTable-driven Parsers The nonrecursive LL(1)

parser looks up the production to apply by looking up a parsing table

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Table-driven ParsersTable-driven ParsersTable-driven ParsersTable-driven ParsersLL(1) table: One dimension for current

non-terminal to expand One dimension for next token Table entry contains one

production

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Table-driven ParsersTable-driven ParsersTable-driven ParsersTable-driven ParsersLL(1) table: One dimension for current

non-terminal to expand

One dimension for next token

Table entry contains one production

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Table-driven ParsersTable-driven ParsersTable-driven ParsersTable-driven ParsersLL(1) table: One dimension for current

non-terminal to expand One dimension for next token Table entry contains one

production

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Consider the expression grammar

1 E → T E' 2 E' → + T E' 3 | 4 T → F T' 5 T' → * F T' 6 | 7 F → ( E )8 | id

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Predictive Parsing TablePredictive Parsing TablePredictive Parsing TablePredictive Parsing Tableid + * ( ) $

E E →TE' E →TE'

E' E' → +TE'

E' → E' →

T T →FT' T →FT'

T' T' → T →*FT' T' → T' →

F F → id F →(E )

Rows for current non-terminal to expandColumns for next token

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Predictive Parsing TablePredictive Parsing TablePredictive Parsing TablePredictive Parsing Tableid + * ( ) $

E E →TE' E →TE'

E' E' → +TE'

E' → E' →

T T →FT' T →FT'

T' T' → T →*FT' T' → T' →

F F → id F →(E )

Table entries are productionsBlank entries are errors

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Predictive ParsersPredictive ParsersPredictive ParsersPredictive Parsers The predictive parser uses

an explicit stack to keep track of pending non-terminals

It can thus be implemented without recursion.

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Predictive ParsersPredictive ParsersPredictive ParsersPredictive Parsers The predictive parser uses

an explicit stack to keep track of pending non-terminals

It can thus be implemented without recursion.

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Predictive ParsersPredictive ParsersPredictive ParsersPredictive Parsers

a + b $

Predictive parser

stackXYZ$

Parsing table M

input

output

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm The input buffer contains

the string to be parsed; $ is the end-of-input marker

The stack contains a sequence of grammar symbols

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

Initially, the stack contains the start symbol of the grammar on the top of $.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

The parser is controlled by a program that behaves as follows:

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

The program considers X, the symbol on top of the stack, and a, the current input symbol.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

These two symbols, X and a determine the action of the parser.

There are three possibilities.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

These two symbols, X and a determine the action of the parser.

There are three possibilities.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

1. X a $, the parser halts and annouces successful completion.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

2. X a $the parser pops X off the stack and advances input pointer to next input symbol

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

3. If X is a nonterminal, the program consults entry M[X,a] of parsing table M.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

If the entry is a production M[X,a] = {X → UVW }the parser replaces X on top of the stack by WVU (with U on top).

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmAs output, the parser just prints the production used: X → UVW

However, any other code could be executed here.

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

If M[X,a] =error, the parser calls an error recovery routine

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm

Example:

Let’s parse the input string

id+ididusing the nonrecursive LL(1) parser

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id

E

+ id id

$

$

stack Parsing Table M

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Predictive Parsing TablePredictive Parsing TablePredictive Parsing TablePredictive Parsing Table

id + * ( ) $

E E →TE' E →TE'

E' E' → +TE'

E' → E' →

T T →FT' T →FT'

T' T' → T →*FT' T' → T' →

F F → id F →(E )

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id

E

+ id id

$

$

stack Parsing Table M

E →T E'

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id + id id

$

$

stack Parsing Table M

T →

TE'

F T'

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T'

id + id id

$

$

stack Parsing Table M

→

E'

F

F id

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T'

id + id id

$

$

stack Parsing Table M

E'

id

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T'

+ id id

$

$

stack Parsing Table M

→

E'

T'

id

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+ id id

$

$

stack Parsing Table M→

E'

E' +

id

E'T

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+ id id

$

$

stack Parsing Table M

E'

+

id

T

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Stack Input Ouput$E id+idid$

$E' T id+idid$ E →TE'

$E' T' F id+idid$ T →FT'$E'T' id id+idid$ F → id

$E' T' +idid$$E' +idid$ T' →$E' T + +idid$ E' → +TE'

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Stack Input Ouput$E' T idid$ $E' T' F idid$ T →FT'$E' T' id idid$ F → id$E' T' id$$E' T' F id$ T → FT'$E' T' F id$$E'T' id id$ F → id

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Stack Input Ouput

$E' T' $ $E' $ T' →$ $ E' →

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm Note that productions output

are tracing out a lefmost derivation

The grammar symbols on the stack make up left-sentential forms

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LL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing AlgorithmLL(1) Parsing Algorithm Note that productions output

are tracing out a lefmost derivation

The grammar symbols on the stack make up left-sentential forms

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

Top-down parsing expands a parse tree from the start symbol to the leaves

Always expand the leftmost non-terminal

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

Top-down parsing expands a parse tree from the start symbol to the leaves

Always expand the leftmost non-terminal

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id+idid

E

T E'

F

id

T'

E'T+

and so on ....

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E

T E'

F

id

T'

E'T+

The leaves at any point form a stringA

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E

T E'

F

id

T'

E'T+

only contains terminals

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E

T E'

F

id

T'

+ E'Tid + id id b

input string is bThe prefix matchesNext token is b

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction Consider the state

S → Awith b the next token and we are trying to match b

There are two possibilities

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction Consider the state

S → Awith b the next token and we are trying to match b

There are two possibilities

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

1. b belongs to an expansion of A

Any A → can be used if b can start a string derived from

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

1. b belongs to an expansion of A

Any A → can be used if b can start a string derived from

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

In this case we say that b FIRST()

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

2. b does not belong to an expansion of A

Expansion of A is empty, i.e.,

A → and b belongs an expansion of , e.g., b

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

2. b does not belong to an expansion of A

Expansion of A is empty, i.e.,

A → and b belongs an expansion of , e.g., b

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

which means that b can appear after A in a derivation of the form S → Ab

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

We say that b FOLLOW(A)

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LL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table ConstructionLL(1) Table Construction

Any A → can be used if expands to

We say that FIRST(A) in this case

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ComputingComputing FIRST FIRST Sets SetsComputingComputing FIRST FIRST Sets Sets

DefinitionFIRST(X) =

{ b | X → ba }

{ | X → }