CSc 453 Compilers and Systems Software. 6 : Top-Down Parsing I

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1 C 45 Compilers n ystems oftwre 6 : op-down Prsing I Christin Collberg Deprtment of Computer iene University of rizon ollberg@gmil.om Copyright 2009 Christin Collberg eptember 14, Overview 2 Compiler Phses soure Lexer tokens Prser errors We re here! errors Optimize IR Interm. Coe Gen emnti nlyser IR Mhine Coe Gen errors sm Grmmrs 4 Context ree Grmmrs CGs re use to esribe the syntx of progrmming lnguges. proution if then 1 else 2 in CG sys 1

2 If 1 n 2 re sttements n n expression then if then 1 else 2 is sttement. Notie tht this proution is reursive; it llows if-sttements to our within if-sttements. 5 Context ree Grmmrs... if then 1 else 2 if, then, n else re terminl symbols or tokens., 1, 2, n re non-terminls. hey re like vribles, tht represent the kins of strings tht the grmmr efines s sttements or expressions, respetively. 6 CG Nottion terminls:,b,,,+,-,,0,1,,if,o. nonterminls:,b,c,,,,expr,stmt. grmmr symbols: X, Y, Z, (either terminls or nonterminls). strings of terminls: u,v,w. strings of grmmr symbols: α, β, γ, (strings of terminls or nonterminls). proutions: α 1, α 2,, α k, or α 1 α 2 α k. 7 Derivtions Proutions s Rewrite Rules 1. trt with the strt symbol,. 2. Pik ny proution α, eg. :=.. We sy tht erives :=, or :=. := is sententil form erive from. 4. Repet: pik nonterminl from the sententil form, reple with the RH of proution α: := := + := + := +num. := +num. := if then + num 2

3 8 erminology grmmr is 4-tuple (non-terminls, terminls, proutions, strt-symbol) or (N,Σ,P,) proution is of the form α β where α,β re tken from N Σ. Re α β s rewrite α with β. Re s iretly erives. Re r s iretly erives using rule r. Re s erives in zero or more steps. 9 Derivtions... αβ αγβ if γ is proution, n α n β re strings of grmmr symbols. : Derives in one step. : Derives in 0 or more steps. + : Derives in 1 or more steps. lm: Leftmost erivtion. rm: Rightmost erivtion. L(G): he lnguge generte by grmmr G. his is the set of strings w, suh tht there is erivtion + w, where is G s strt-symbol. 10 Derivtions... he string of terminl symbols :=+num is generte by leftmost erivtion: lm := lm := + lm := + lm := +num + :=+num xmple Grmmr: := if then + num

4 11 Prse rees... If one step of our erivtion is X Y Z (i.e, we use the rule XY Z) then we ll get prse (sub-)tree..... X Y Z 12 Progrm BGIN tt ND ent := xpr "" Progrm BGIN tt ND BGIN ent := xpr ND BGIN "" := xpr ND BGIN "" := xpr + xpr ND BGIN "" := 5 + xpr ND BGIN "" := 5 + xpr * xpr ND BGIN "" := * xpr ND BGIN "" := * ND xpr 5 + xpr xpr * 4 xpr 1 op-down Prsing 14 op-down Bktrking Prser op-own prsing involves builing prse tree for the input string by strting t the root n ing noes in preorer. b 4

5 b 15 op-down Bktrking Prser... If bktrking top-own prser hooses the wrong proution rule to expn noe it bks up over the input, n unoes some of the prse tree onstrution: b oops! 16 Grmmr Rewriting 17 mbiguous Grmmrs grmmr is mbiguous if some string of tokens n proue two (or more) ifferent prse trees. ::= + * number * * * 5 + * * * * + * + 4 * * * Opertor Preeene he preeene of n opertor is mesure of its bining power, i.e. how strongly it ttrts its operns. 5

6 Usully hs higher preeene thn +: mens not (5 ), (4 + 5). We sy tht bins hrer thn Opertor ssoitivity he ssoitivity of n opertor esribes how opertors of equl preeene re groupe. + n re usully left ssoitive: mens not We sy tht + ssoites to the left. ^ ssoites to the right: (4 2) + = 5, 4 (2 + ) = 1. 2^^4 = 2^(^4). 20 xpression Grmmrs We must write unmbiguous expression grmmrs tht reflet the ssoitivity n preeene of ll opertors. he next sle gives the lgorithm for writing suh grmmrs. expr ::= expr + term term term ::= term * ftor ftor ftor ::= ( expr ) number Resulting xpression Grmmr: Crete one non-terminl for eh preeene level, for exmple p 1,p 2,,p n, where p n hs the highest preeene level. 2. or opertor op t preeene level i onstrut the following proution if the opertor is left ssoitive: p i ::= p i op p i+1 p i+1 right ssoitive: p i ::= p i+1 op p i p i+1 6

7 . Construt proution for nonterminl p n+1 whih represents primry expressions suh s entifiers, numbers, prenthesize expressions, et: p n+1 ::= (p 1 ) num 22 + * ::= + ::= * ::= number * * 5 + * * * + + * + * + * + 4 * + 4 * + 4 * * op-down Prsing 24 Reursive Desent Prsing PROCDUR (); I urr tok = if HN mth(if); (); mth(then); (); LI urr tok = HN := mth(); mth(:=); (); if then L syntx error NDI; PROCDUR (); + I urr tok = HN mth(); L I urr tok = num HN mth(num); L (); mth(+); (); NDI; num 25 Reursive Desent mll Problem 1 We my loop forever: PROCDUR (); I L (); mth(+); (); 7

8 26 Reursive Desent mll Problem 2 Wht bout proutions tht strt out similrly: if then if then else PROCDUR (); I urr tok = if HN mth(if); (); mth(then); (); LI urr tok = if HN mth(if); (); mth(then); (); mth(else); (); LI NDI 27 Reursive Desent mll Problem Wht if there re severl possible next tokens: prog el stt stt if () while el int rel PROCDUR prog (); I urr tok {if,, while} HN stt(); LI urr tok {int,rel} HN el() L syntx error NDI; ND; PROCDUR stt (); ND; PROCDUR el (); ND; 28 Left Reursion Removl Left reursion must be remove from the grmmr, by turning it into right reursion: xmple: α β β R α expr expr + term term expr term R R + term R 29 Left Reursion Removl... fter left reursion removl, our expression grmmr + * ( ) 8

9 turns into + * ( ) 0 Left toring top-own prser tht res input from left-to-right, n t hoose between proutions b n b. hese must be left ftore. α β 1 α β 2 α xmple: β 1 β 2 if then else if then if then else 1 op-down xpression Prser + * ( ) + * + * 2 op-down xpression Prser * + * 9

10 op-down xpression Prser * * + * + * 4 op-down xpression Prser... + * + * 5 Reings n Referenes Re Louen, pp Or, the Drgon Book: op-down Prsing rror Reovery Reursive Desent Prsing 40 55,