lecture 9 - predictive parsing

8/12/2019 Lecture 9 - Predictive Parsing

1/24

Predictive

Parsing

Robb T.Koether

The ParseTable Entries

The Parse

Table

PredictiveParsing

Assignment

Predictive ParsingLecture 9

Section 4.4

Robb T. Koether

Hampden-Sydney College

Wed, Feb 11, 2009
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Outline

1 The Parse Table Entries

2 The Parse Table

3 Predictive Parsing

4 Assignment
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Nullability and FIRST for Strings

The parse table has

One row for each nonterminal,One column for each terminal and $.

$is the end-of-file marker.

Each cell in the table represents a combination (A, a) ofa nonterminal Aand a terminal a.
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment


We need to extend the definitions of nullable andFIRST tostringsof grammar symbols.

is nullable.Let = X1X2. . .Xn be a string of grammar symbols.Then is nullable if each Xi is nullable.
http://find/


5/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment


By definition, FIRST() = .

For the string = X1X2 . . . Xn,

Let kbe the largest integer for which X1, X2, . . . , and Xkare nullable.Then

FIRST() = FIRST(X1) . . . FIRST(Xk+1).

We will not need FOLLOW for strings.
http://goforward/http://find/http://goback/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Parse Table Entries

Each table entry is a production A .

Rules for entering A

in the table:For every rule A and for every a FIRST(), writeA in cell (A, a).For every that is nullable and for every rule A andfor every a FOLLOW(A), write A in cell (A, a).

Write error in all cells that do not contain a production.
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Parse Table Entries

The interpretation of A in cell (A, a) is that if Ais on

top of the stack and we encounter ain the input, thenwe should replace Aby on the stack.

Push the symbols of onto the stack inreverse order,

from right to left, so that the first (leftmost) symbol is on

the top of the stack.


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example

Example (Parse Table)

Let the grammar be

E T E

E + T E |

T F T

T

*F T

| F (E)| id| num
http://find/http://goback/


9/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example


Recall

Nonterminal Nullable FIRST FOLLOWE No {(, id, num} {$, )}

E Yes {+} {$, )}

T No {(, id, num} {$, ),+}

T Yes

{} {$, ),

+}F No {(, id, num} {, $, ),+}
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example


Consider the production E T E.FIRST(TE) = FIRST(T) = {(, num, id}.Therefore, enter E T E in cells (E, (), (E, num), and(E, id).T E

is not nullable.
http://find/


11/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example


Consider the production E .FIRST() = .

is nullable and FOLLOW(E) = {$, )}.

Therefore, enter E in cells (E, $) and (E, )).


12/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example


Handle the other productions similarly.

In which cells do we enter E + T E?

In which cells do we enter T F T?

In which cells do we enter T * F T?

In which cells do we enter T ?

In which cells do we enter F

(E)

?In which cells do we enter F id?

In which cells do we enter F num?
http://find/


13/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Example


+ * ( ) num id $

E E T E E T E E T E

E

E + T E E E

T T F T T F T T F T

T

T T * F T

T

T

F F (E) F num F id
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Predictive Parsing

Definition (LL(1) Grammar)

AnLL(1) grammaris a grammar whose predictive parsetable does not contain any multiple entries.

A multiple entry would indicate that we could not decide

which production to apply.
http://find/


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Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment

Predictive Parsing Algorithm

The predictive parsing algorithm usesThe parse table,An input buffer containing a sequence of tokens,A stack of grammar symbols.
http://find/


16/24

Predictive

Parsing

Robb T.Koether


The Parse

Table

PredictiveParsing

Assignment


The Parsing AlgorithmInitialize the input buffer to the input followed by $.

Initialize the stack to $and S, with Son the top.


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Predictive

Parsing

Robb T.Koether


The Parse

TablePredictiveParsing

Assignment


The Parsing Algorithm

Consider the top stack symbol X.There are three possibilities.

Xis a terminal.Xis a nonterminal.X is $.


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Predictive

Parsing

Robb T.Koether


The Parse


Assignment



If Xis a terminal, thenIf Xmatches the current token,

Pop Xfrom the stack.

Advance to the next token.

Otherwise, it is an error.
http://find/


19/24

PredictiveParsing

Robb T.Koether


The Parse


Assignment



If Xis a nonterminal, then

Use Xtogether with the current token to get the entryfrom the parse table.If the entry is a production,

Pop Xfrom the stack.

Push the symbols on the right-hand side of the

production, from right to left, onto the stack.

Otherwise, it is an error.


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PredictiveParsing

Robb T.Koether


The ParseTable

PredictiveParsing

Assignment

Example

Example (Predictive Parsing)

Parse the string (id + num)* id.
http://find/


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PredictiveParsing

Robb T.Koether


The ParseTable

PredictiveParsing

Assignment

Example


Stack Input

$ E ( id + num )* id $

$ E T ( id + num )* id $

$ E

T

F ( id + num )* id $$ E T ) E) ( id + num )* id $

$ E T ) E id + num )* id $

$ E T ) E T id + num )* id $

$ E T ) E T F id + num )* id $

$ E

T

) E

T

id id + num )* id $$ E T ) E T + num )* id $

$ E T ) E + num )* id $

$ E T ) E T + + num )* id $

$ E T ) E T num )* id $


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PredictiveParsing

Robb T.Koether


The ParseTable

PredictiveParsing

Assignment

Example


Stack Input

$ E T ) E T F num )* id $

$ E T ) E T num num )* id $

$ E

T

) E

T

)* id $$ E T ) E )* id $

$ E T ) )* id $

$ E T * id $

$ E T F * * id $

$ E

T

F id $$ E T id id $

$ E T $

$ E $

$ $
http://find/


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PredictiveParsing

Robb T.Koether


The ParseTable

PredictiveParsing

Assignment

Assignment

Homework

The grammar

R R R| RR| R* | (R)| a| b

generates all regular expressions on the alphabet

= {a, b}.

Using FIRST and FOLLOW from the exercise of the

previous lecture, construct a parse table for thisgrammar.

Parse the expression ab*(a b).
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lecture 9 - predictive parsing

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