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

1

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

2

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

3

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

4

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

5


non-terminal to expand

One dimension for next token

Table entry contains one production

6


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

production

7

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

8

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

9

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

10

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.

11

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.

12

Predictive ParsersPredictive ParsersPredictive ParsersPredictive Parsers

a + b $

Predictive parser

stackXYZ$

Parsing table M

input

output

13

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

14

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 $.

15


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

16


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

17


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

There are three possibilities.

18


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

There are three possibilities.

19


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

20


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

21


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

22


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).

23

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.

24


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

25


Example:

Let’s parse the input string

id+ididusing the nonrecursive LL(1) parser

26

id

E

+ id id

$

$

stack Parsing Table M

27

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 )

28

id

E

+ id id

$

$


E →T E'

29

id + id id

$

$


T →

TE'

F T'

30

T'

id + id id

$

$


→

E'

F

F id

31

T'

id + id id

$

$


E'

id

32

T'

+ id id

$

$


→

E'

T'

id

33

+ id id

$

$

stack Parsing Table M→

E'

E' +

id

E'T

34

+ id id

$

$


E'

+

id

T

35

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'

36

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

37

Stack Input Ouput

$E' T' $ $E' $ T' →$ $ E' →

38

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

39

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

40

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

41


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

Always expand the leftmost non-terminal

42

id+idid

E

T E'

F

id

T'

E'T+

and so on ....

43

E

T E'

F

id

T'

E'T+

The leaves at any point form a stringA

44

E

T E'

F

id

T'

E'T+

only contains terminals

45

E

T E'

F

id

T'

+ E'Tid + id id b

input string is bThe prefix matchesNext token is b

46

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

47

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

48


1. b belongs to an expansion of A

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

49


1. b belongs to an expansion of A

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

50


In this case we say that b FIRST()

51


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

52


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

53


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

54


We say that b FOLLOW(A)

55


Any A → can be used if expands to

We say that FIRST(A) in this case

56

ComputingComputing FIRST FIRST Sets SetsComputingComputing FIRST FIRST Sets Sets

DefinitionFIRST(X) =

{ b | X → ba }

{ | X → }

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

Documents

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