1 General LR Parsing. Bottom-Up Parsing

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1 ection - Bottom-Up Prsings: 1 Generl LR Prsing 1 Generl LR Prsing Bottom-Up Prsing Bottom-up prsing is more powerful nd preferle LR(1) exists for ny LR(k) (with end-mrkers) there re LR(1) tht do not hve equivlent LL(k) for ny k semntic nlysis is esier it is esier to generte intermedite code In ottom-up prsing, we pply the productions ckwrds nd finish when the strting symol is reched nd the input token string exhusted This corresponds to uilding the tree y plnting forest nd connecting pieces into tree This is reflected in more complex processing: the forest must e mnged Bottom-up prsing follows the rightmost derivtion (ckwrds since the input is scnned left to right) Bottom-up prsing procedure: strt with n empty stck; t ech stge if numer of elements on top of the stck mtch rhs of production, replce the elements with the lhs. uch elements form hndle nd the process is clled reduce lterntively, push the new token on the stck. This process is clled shift finish when stck contins only the strting symol nd the token string is exhusted In prctice, often egin nd end mrkers re used (sometimes needed to reduce k) Prolems: when mtch is hndle to e reduced shift-reduce conflict when more mtches of rhs, which to use s hndle? reduce-reduce conflict Exmple 1.1 Use the unmiguous expression grmmr nd stck to ottom-up prse id+id*id 2003 Cezry Z Jnikow 1

2 ection - Bottom-Up Prsings: 2 LL vs. LR 2 LL vs. LR Tle 1: LL vs. LR Attriute LL LR Power LL(k) doesnt exist for some LR(1) lwys exists CFG Derivtion Leftmost Rightmost Tree construction Root to leves Leves (forest) to root Tokens on the stck Predicted tokens Actul tokens Initil stck Empty uccess condition tck empty nd EOFtk next nd EOFtk next Production ppliction N -> α N <- α Conflicts Multiple productions for the Reduce-reduce nd reduce-shift sme nonterminl Conflict resolution First/Follow sets Decision Tle 3 Opertor-Precedence Prser Opertor-precedence is the simplest ottom-up prser. It pplies in limited circumstnces: There re never two consecutive nonterminls in the grmmr No two different nonterminls hve the sme rhs For ny two terminls, <, =, > hold, where the reltions relte to precedence There might e no empty productions Most often only expressions stisfy these properties then opertor-precedence prser cn e emedded in lrger predictive prser to prse expressions When stck is considered, < > etween stck terminls nd the incoming token mrk hndle If hndle is detected, reduction is pplied. Otherwise, shift is pplied For etter understnding, the reltion symols my e pushed etween n two terminls NOTE: grmmr should not specify ssocitivity, for it is explicit in the tle y mens of opertions. If expression grmmr is extended to specify ssocitivity, ll nonterminls should e treted with no distinction Cezry Z Jnikow 2

3 ection - Bottom-Up Prsings: 3 Opertor-Precedence Prser Exmple 3.1 Construct opertor-precedence tle for the epression grmmr used efore, nd use it to prse $ id+id*id $. Note tht +>+ indictes tht + is left ssocitive. For right Input +- */ ( ) id $ +- */ ( ) id $ ssocitivity, use +<+. > > > < < > < > < > < > < < < = < > > > > > > > > < < < < Empty entries indicte erroneous conditions they my e filled with pproprite error routines for ech cse. Rules for constructing the tle: If A ppers in production nd A *α then > ( is elow in the prse tree) If B ppers in production nd B *β then < ( is elow ) If nd pper in production seprted y single nonterminl then = (e.g., if C then else mens if=then nd then=else) A B α β A Alterntively, in expressions precedence cn e used directly if hs higher precedence thn then > nd < if nd (or ) hve the sme precedence, then for left ssocitivity > nd >; for right ssocitivity < nd < pired opertors like () re relted y =; this forces reductions inside for identifier id nd ny terminl tht cn leglly precede (follow) we hve id> (<id) end mrkers hve lower precedence thn ny other terminl 2003 Cezry Z Jnikow 3

4 ection - Bottom-Up Prsings: 4 LR Prsers 4 LR Prsers LR (red left to right, follow rightmost derivtion in reverse) prsers cn hndle cses tht opertor precedence or LL cnnot. Moreover, ny LR(k) grmmr cn e converted to LR(1) to fcilitte one-symol lookhed only. LR prsers re tle-driven, with tles similr to those of FA. Columns re seprted into ction prt (shift or reduce) for terminls nd go-to prt (sttes to enter fter reduction) for nonterminls. LR procedure uses stck to store sttes nd terminls. The ltter re optionl: Plce $ t the end of the token input nd push strting stte 0 Repet suppose q m is the current stte (tos); suppose i in the next token suppose cell (ction prt) [q m, i ] contins (uniquely) X when X=shift q n then (optionlly push i on the stck first) push q n when X=reduce n then reduce y mens of production #n; the hndle include k sttes (nd optionlly k symols), where k is length if rhs of rule #n; fter the lhs nonterminl A is pushed, push new stte from go-to prt, cell [q i,a], where q i is the stte on tos fter reduction is complete when X=ccept then prse is complete 2003 Cezry Z Jnikow 4

5 4 LR Prsers Exmple 4.1 Use the following grmmr nd tle to prse (i+i)/i. Use grmmr (1) E -> E+T (5) T -> T/F (2) E -> E-T (6) T -> F (3) E -> T (7) F -> (E) (4) T -> T*F (8) F -> i. t te TERMINAL NONTERM. i + - * / ( ) $ E T F 0 s5 s s6 s7 cc 2 r3 r3 s8 s9 r3 r3 3 r6 r6 r6 r6 r6 r6 4 s5 s r8 r8 r8 r8 r8 r8 6 s5 s s5 s s5 s s5 s s6 s7 s15 11 r1 r1 s8 s9 r1 r1 12 r2 r2 s8 s9 r2 r2 13 r4 r4 r4 r4 r4 r4 14 r5 r5 r5 r5 r5 r5 15 r7 r7 r7 r7 r7 r7 Lookhed might e used to ensure tht ech entry is single no conflicts. For prcticl resons, only one lookhed symol is used lookhed increse (up to exponentilly) the size of the tle rewriting the grmmr often increses its size nd reduces rediility imple LR (LR) is when no lookhed is needed; LR(0) When conflicts rise, ll sttes cn e expnded for different lookhed symols; cnonicl LR(1). Or, LR cn only expnd sttes tht hve conflicts; LALR(1) Progrmming Lnguge Processors 1999 Cezry Z. JnikowPge 5