Difference Between LR

Q# Diferences between LR(0), LR(1) ,LR(k),LALR(1) and SLR(1): LR(0) and SLR(1): Both LR(0) and SLR(1) parsers are bottom-up, directional, predictive  parsers.  parsers. This means that  The parsers attempt to apply productions in reverse reverse to reduce the input sentence back to the start symbol (bottom-up ( bottom-up))  The parsers scan the input from from lefttori!ht (directional (directional))  The parsers attempt to predict "hat reductions to apply "ithout necessarily seein! all of the input ( predictive)  predictive) Both LR(0) and SLR(1) are shit/reduce arsers# meanin! that they process the tokens of the input stream by placin! them on a stack# and at each each point point either either shitin! a tok token by pushi pushin! n! it onto onto the the stac stack k or reducin! some se$uence of terminals and nonterminals atop the stack back to some nonterminal symbol. %t can be sho"n that any !rammar can be parsed bottomup usin! a shift&reduce parser# but that parser parser mi!ht mi!ht not be deterministic. deterministic. That is# the parser may have to '!uess' "hether to apply a shift or reduction# and may end up havin! to backtrack to realie that it made the "ron! choice. o matter ho" po"erful a deterministic shift&reduce parser you construct# it "ill never be able to parse all !rammars. *hen a deterministic shift&reduce parser is used to parse a !rammar shit/reduce that it cannot handle# it results in c"nicts or reduce/reduce c"nicts# "here the parser may enter a stat state e in "hic "hich h it cann cannot ot tell tell "hat "hat acti action on to take. take. %n a sh shif ift& t&rreduc educe e con+ict# it cannot tell "hether it should add another symbol to the stack or perform some reduction on the top symbols of the stack. %n a reduce&reduce con+ict# the parser kno"s that it needs to replace the top symbols of the stack "ith some nonterminal# but it can,t tell "hat reduction to use. •

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-n LR(0) parser is a shift&reduce parser that uses ero tokens of look ahead to determine "hat action to take (hence the 0). This means that in any con!urat uratiion of the pars arser# the pars arser must have ave an unambi!uous action to choose  either it shifts a specic symbol or applies a specic reduction. %f there are ever t"o or more choices to make# the parser fails and "e say that the !rammar is not LR(0). %n SLR(1)   ('Simp ('Simplie lied d LR(1)'),  the parser is allo"ed to look at one token of look ahead "hen decidin! "hether it should shift or reduce. %n particular# "hen the parser "ants to try reducin! somethin! of the form - / " (for nonterminal - and strin! ")# it looks at the net token of input. %f that token could le!ally appear after the nonterminal - in some some deri deriva vati tion on## the the pars parser er reduc educes es.. the ther" r"is ise# e# it does does not. not. The The

intuition here is that in some cases it makes no sense to attempt a reduction# because !iven the tokens "e,ve seen so far and the upcomin! token# there is no possible "ay that the reduction could ever be correct.  The only di2erence bet"een LR(0) and SLR(1) is this etra ability to help decide "hat action to take "hen there are con+icts. Because of  this# any !rammar that can be parsed by an LR(0) parser can be parsed by an SLR(1) parser. 3o"ever# SLR(1) parsers can parse a lar!er number of !rammars than LR(0). LR(k)

an LR(k) parser is a bottomup parser that "orks by maintainin! a stack of terminals an non terminals. The parser is controlled by a nite automaton that determines# based on the current state of the parser and the net k tokens of input# "hether to shift   a ne" token onto the stack or reduce the top symbols of the stack by applyin! a production in reverse. %n order to keep track of enou!h information to make a determination about "hether to shift or reduce# LR(k) parsers have each state correspond to a 'con!uratin! set#' a set of productions annotated "ith the follo"in! information4 3o" much of the production has been seen so far# and *hat tokens to epect after the production has been completed (the look ahead) $r"b%e& 5roblems arise in an LR(k) parser "hen there are con+icts about "hat the parser should do in a !iven state. ne type of con+ict# a shift/reduce conict # comes up "hen the parser is in a state "here a production has been completed# but the look ahead symbols for that production con+ict are also used by another uncompleted production in the state. This means that the parser can,t tell "hether to perform the reduction or not. - second type of con+ict is a reduce/reduce conict # "here the parser kno"s it has to do a reduction# but t"o or more reductions are possible and it can,t tell "hich to do. • •

LALR(1)

SLR(1) is still a fairly "eak parsin! method. 6ore commonly# you "ill see L-LR(1) ('Look ahead LR(1)') parsers bein! used. They too "ork by tryin! to resolve con+icts in an LR(0) parser# but the rules they use for resolvin! con+icts are far more precise than those used in SLR(1)# and conse$uently a much lar!er number of !rammars are L-LR(1) than are SLR(1). To be a bit more specic# SLR(1) parsers try to resolve con+icts by lookin! at the structure of the !rammar to learn more information

about "hen to shift and "hen to reduce. L-LR(1) parsers look at both the !rammar and the LR(0) parser to !et even more specic information about "hen to shift and "hen to reduce. Because L-LR(1) can look at the structure of the LR(0) parser# it can more precisely identify "hen certain con+icts are spurious. The Linu utilities yacc and bison# by default# produce L-LR(1) parsers. %n SLR(1) or L-LR(1)# the parser then makes the decision to shift or reduce based on the net token of look ahead.