• Review: – How do we define a grammar (what are the

components in a grammar)?– What is a context free grammar?– What is the language defined by a grammar?– What is an ambiguous grammar?– Why we care about left or right derivation?

• Example:<PROGRAM> ->’program’ id ‘begin’ <stmt_list> ‘end’

<STMT_LIST> -> <STMT> ‘;’<STMT_LIST> | <STMT>

<STMT> -> id ‘=‘ <EXPR>

<EXPR> -><EXPR> <OP> <EXPR> | id

<OP> -> ‘+’ | ‘-’ | ‘*’ | ‘/’

program test

begin

t0 = t1 + t2;

t3 = t0 * t4

end

program testbegin t0 = t1+t2; t3 = t0*t4end

<PROGRAM> ==>*

• Parsing:– The process to determine whether the start

symbol can derive the program.• If successful, the program is a valid program.

• If failed, the program is invalid.

– Two approaches in general.• Expanding from the start symbol to the whole

program (top down)

• Reduction from the whole program to start symbol (bottom up).

• Parsing methods:– universal:

• There exists algorithms that can parse any context free grammar. These algorithms are too inefficient to be used anywhere.

• What is considered efficient? Scan the program (from left to right) once.

– Top-down parsing• build the parse tree from root to leave (using leftmost

derivation, why?).

• Recursive descent, and LL parser

– Bottom-up parsing• build the parse tree from leaves to root.

• Operator precedence parsing, LR (SLR, canonical LR, LALR).

– Recursive descent parsing associates a procedure with each nonterminal in the grammar, it may require backtracking of the input string.

– Example: <type>-><simple> | ^ id | array [<sample>] of <type>

<simple> ->integer | char | num dotdot numvoid type() {

if (lookahead == INTEGER || lookahead == CHAR || lookahead==NUM)

simple();

else if (lookahead == ‘^’) {

match (‘^’);

match(ID);

} else if (lookahead == ARRAY) {

match (ARRAY);

match(‘[‘);

simple();

match (‘]’);

match (OF);

type();

} else error();

}

– Example: <type>-><simple> | ^ id | array [<simple>] of <type>

<simple> ->integer | char | num dotdot numvoid simple() {

if (lookahead == INTEGER) match (INTEGER);

else if (lookahead == CHAR) match (CHAR);

else if (lookahead == NUM) {

match(NUM);

match(DOTDOT);

match(NUM);

} else error();

}

void match(token t) {

if (lookahead == t) {lookahead = nexttoken();}

else error();

}

– Recursive descent parsing may require backtracking of the input string

• try out all productions, backtrack if necessary.

• E.g S->cAd, A->ab | a

• input string cad

– A special case of recursive-descent parser that needs no backtracking is called a predictive parser.

• Look at the input string, must predict the right production every time to avoid backtracking.

• Needs to know what first symbols can be generated by the right side of a production only lookahead for one token)

– First(a) - the set of tokens that can appear as the first symbols of one or more strings generated from a. If a is empty string or can generate empty string, then empty string is also in First(a).

– Given productions A ->a | b, predictive (by looking at 1 token ahead) parsing requires First(a) and First(b) to be disjoint.

– Predictive parsing won’t work on some type of grammars:

• Left recursion: A->Aw (expanding A results in an infinite loop).

• Have common left factor: A->aB | aC (First(aB) and First(aC) is not disjoint).

– Eliminating Left Recursion• Immediate Left Recursion

– Replace A->Aa | b with A->bA’ and A’->aA’ | e

– Example: E->E+T | T

T->T*F | F

F->(E) | id

– In general,

Can be replaced bynmAAAA |...||||...|| 2121

|'|...|'|''

'|...|'|'

21

21

AAAA

AAAA

m

n

• Algorithm 4.1. Eliminating left recursion:Arrange the nonterminals in some order A1, A2, …,

An

for i = 1 to n do begin

for j = 1 to I-1 do begin

expand production of the form Ai ->Aj w

end for

eliminate the immediate left recursion among Ai productions.

End for

(the algorithm can fail if the grammar has a cycle (A==> A), or A->e)

Example 1:

S->Aa | b

A->Ac | Sd | e

Example 2:

X->YZ | a

Y->ZX |Xb

Z->XY | ZZ | a

– Left factoring (to produce a grammar suitable for predictive parsing)

• replace productions

by

mnA |...|||...|| 121

n

m

A

AA

|...|'

|...||'

1

1

Example: S->iEtS | iEtSeS|a E->b