Lecture 4 Syntactic Analysis Part II Joey Paquet

Lecture 4 Syntactic Analysis Part II Joey Paquet, 2000, 2002, 2008, 2012, 2013 1

Part I Recursive Descent Predictive Parsers Joey Paquet, 2000, 2002, 2008, 2012, 2013 2

Method • Build FIRST and FOLLOW sets • For each non-terminal we have a corresponding function • In each function, for each possible right-hand-side of the corresponding productions, we have a possible path to follow. The choice is made according to the FIRST set of the right hand sides • If one of the alternatives is of the form A , the path is followed according to the FOLLOW set of the left-handside of the production • If no valid path is found, the function returns false • If any of the paths is followed without error, the function return true and does any appropriate computation Joey Paquet, 2000, 2002, 2008, 2012, 2013 3

Generating FIRST sets • If , where begins with a terminal symbol x, then x FIRST( ). • Algorithmic definition: FIRST(A) = 1. if ( (A T) (A is ) ) then FIRST(A) = {A} 2. if ( (A N) (A S 1 S 2…Sk R) | Si (N T) ) then FIRST(A) (FIRST(S 1) – { }) if, i < k ( FIRST(S 1), …, FIRST(Si) ) then FIRST(A) FIRST(Si+1) if ( FIRST(S 1), …, FIRST(Sk) ) then FIRST(A) { } • Or, generate the lookahead tree for A Joey Paquet, 2000, 2002, 2008, 2012, 2013 4

Example E TE E | +TE T FT T | FT F (E)|0|1 0 E TE’ FT’E’ 1 E’ +TE’ ( FIRST(E’) = { , +} FIRST(E) = {0, 1, (} 0 T FT’ T’ 1 FT’ ( FIRST(T’) = { , } FIRST(T) = {0, 1, (} 0 F 1 FIRST(F) = {0, 1, (} ( Joey Paquet, 2000, 2002, 2008, 2012, 2013 5

Generating the FOLLOW sets • FOLLOW(A) is the set of terminals that can come right after A in any sentential form derivable from the grammar of the language. • Algorithmic definition: FOLLOW( A | A N ) = 1. if ( A == S ) then ( FOLLOW(A) {$}) 2. if ( B A R ) then (FOLLOW(A) (FIRST( ) - { }) ) 3. if ( (B A R) ( ) then ( FOLLOW(A) FOLLOW(B) ) Joey Paquet, 2000, 2002, 2008, 2012, 2013 6

Constructing the Parser • Main parser function is: parse(){ lookahead = next. Token() if (start. Symbol() match(“$”) ) return(true) else return(false)} • function to match tokens with the lookahead symbol (next token in input): match(token){ if (lookahead == token) lookahead = next. Token(); return(true) else lookahead = next. Token(); return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 8

Constructing the Parser LHS(){ // LHS RHS 1 | RHS 2 | … | if (lookahead FIRST(RHS 1) ) if (non-terminals() match(terminals) ) write(“LHS RHS 1”) ; return(true) else return(false) else if (lookahead FIRST(RHS 2) ) if (non-terminals() match(terminals) ) write(“LHS RHS 2”) ; return(true) else return(false) else if … else if (lookahead FOLLOW(LHS) ) write(“LHS ”) ; return(true) else return(false)} // LHS RHS 1 // LHS RHS 2 // other right hand sides // only if LHS exists Joey Paquet, 2000, 2002, 2008, 2012, 2013 9

Example E(){ // E TE’ if (lookahead FIRST(TE’) ) if (T() E’() ) write(“E TE’ ”) ; return(true) else return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 10

Example E’(){ // E’ +TE’ | if (lookahead FIRST(+TE’) ) if ( match(‘+’) T() E’() ) write(“E’ +TE’ ”) ; return(true) else return(false) else if (lookahead FOLLOW(E’) ) write(“E’ ”) ; return(true) else return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 11

Example T(){ // T FT’ if (lookahead FIRST(FT’) ) if (F() T’() ) write(“T FT’ ”) ; return(true) else return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 12

Example T’(){ // T’ FT’ | if (lookahead FIRST( FT’) ) if ( match(‘ ’) F() T’() ) write(“T’ FT’ ”) ; return(true) else return(false) else if (lookahead FOLLOW(T’) ) write(“T’ ”) ; return(true) else return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 13

Example F(){ // F 0 | 1 | (E) if (lookahead FIRST(0) ) if ( match(‘ 0’) ) write(“F 0”) ; return(true) else return(false) else if (lookahead FIRST(1) ) if ( match(‘ 1’) ) write(“F 1”) ; return(true) else return(false) else if (lookahead FIRST(“(E)”) if ( match(‘(’) E() match(‘)’) ) write(“F (E)”) ; return(true) else return(false)} Joey Paquet, 2000, 2002, 2008, 2012, 2013 14

Part II Table-Driven Predictive Parsers Joey Paquet, 2000, 2002, 2008, 2012, 2013 15

Method • Build FIRST and FOLLOW sets • Build the parser table • Implement the parser algorithm Joey Paquet, 2000, 2002, 2008, 2012, 2013 16

Building the Parser Table • Algorithm: 1. p : ( (p R) (p : A ) ) do steps 2 and 3 2. t : ( (t T) (t FIRST( )) ) add A to TT[A, t] 3. If ( FIRST( ) ) t : ((t T) (t FOLLOW(A)) ) add A to TT[A, t] 4. e : ( (e TT) (e == ) ) add “error” to e Joey Paquet, 2000, 2002, 2008, 2012, 2013 17

Building the Parser Table r 1: r 2: r 3: r 4: r 5: r 6: r 7: r 8: r 9: E TE’ E’ +TE’ E’ T FT’ T’ *FT’ T’ F 0 F 1 F (E) : : : : : FIRST(TE’) = {0, 1, (} FIRST(+TE’) = {+} FOLLOW(E’) = {$, )} FIRST(FT’) = {0, 1, (} FIRST(*FT’) = {*} FOLLOW(T’) = {+, $, )} FIRST(0) = {0} FIRST(1) = {1} FIRST( (E) ) = {(} : : : : : TT[E, 0][E, 1][E, (] TT[E’, +] TT[E’, $][E’, )] TT[T, 0][T, 1][T, (] TT[T’, *] TT[T’, +][T’, $][T’, )] TT[F, 0] TT[F, 1] TT[F, (] Joey Paquet, 2000, 2002, 2008, 2012, 2013 18

Building the Parser Table r 1: r 2: r 3: r 4: E E TE’ E’ +TE’ E’ T FT’ 0 1 ( r 1 r 1 E’ T r 4 r 7 r 8 T’ *FT’ T’ F 0 F 1 F (E) ) + r 3 r 2 r 6 * $ r 3 r 4 T’ F r 5: r 6: r 7: r 8: r 9: r 5 r 6 r 9 Joey Paquet, 2000, 2002, 2008, 2012, 2013 19

Parser Algorithm parse(){ push($) push(S) a = next. Token() while ( top() $ ) do x = top() if ( x T ) if ( x == a ) pop() ; a = next. Token() else skip. Errors() ; error = true else if ( TT[x, a] ‘error’ ) pop() ; inverse. Multiple. Push(TT[x, a]) else skip. Errors() ; error = true if ( ( a $ ) ( error == true ) ) return(false) else return(true)} *: skip. Errors() will be explained in lecture 5 Joey Paquet, 2000, 2002, 2008, 2012, 2013 20

Table Parsing Example Stack Input Production Derivation 1 $E (0+1)*0$ E 2 $E (0+1)*0$ r 1: E TE’ 3 $E’T (0+1)*0$ r 4: T FT’E’ 4 $E’T’F (0+1)*0$ r 9: F (E)T’E’ 5 $E’T’)E( (0+1)*0$ 6 $E’T’)E 0+1)*0$ r 1: E TE’ (TE’)T’E’ 7 $E’T’)E’T 0+1)*0$ r 4: T FT’ (FT’E’)T’E’ 8 $E’T’)E’T’F 0+1)*0$ r 7: F 0 (0 T’E’)T’E’ 9 $E’T’)E’T’ 0 0+1)*0$ 10 $E’T’)E’T’ +1)*0$ r 6: T’ (0 E’)T’E’ 11 $E’T’)E’ +1)*0$ r 2: E’ +TE’ (0+TE’)T’E’ 12 $E’T’)E’T+ +1)*0$ Joey Paquet, 2000, 2002, 2008, 2012, 2013 21

Table Parsing Example Stack Input Production Derivation 13 $E’T’)E’T 1)*0$ r 4: T FT’ (0+FT’E’)T’E’ 14 $E’T’)E’T’F 1)*0$ r 8: F 1 (0+1 T’E’)T’E’ 15 $E’T’)E’T’ 1 1)*0$ 16 $E’T’)E’T’ )*0$ r 6: T’ (0+1 E’)T’E’ 17 $E’T’)E’ )*0$ r 3: E’ (0+1)T’E’ 18 $E’T’) )*0$ 19 $E’T’ *0$ r 5: T’ *FT’ 20 $E’T’F* *0$ 21 $E’T’F 0$ r 7: F 0 22 $E’T’ 0 0$ 23 $E’T’ $ r 6: T’ (0+1)*0 E’ 24 $E’ $ r 3: E’ (0+1)*0 25 $ $ recognized Joey Paquet, 2000, 2002, 2008, 2012, 2013 (0+1)*FT’E’ (0+1)*0 T’E’ 22