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LALR generators calculate lookahead sets by a more precise method based on exploring the graph of parser states and their transitions. This method considers the particular context of the current parser state. It customizes the handling of each grammar occurrence of some nonterminal S. See article
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As can be observed there is a shift-reduce conflict for state 1 and terminal '1'. This occurs because, when the action table for an LR(0) parser is created, reduce actions are inserted on a per-row basis. However, by using a follow set, reduce actions can be added with finer granularity. The follow
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for further details of this calculation. The lookahead sets calculated by LALR generators are a subset of (and hence better than) the approximate sets calculated by SLR generators. If a grammar has table conflicts when using SLR follow sets, but is conflict-free when using LALR follow sets, it is
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have identical methods and similar tables at parse time; they differ only in the mathematical grammar analysis algorithms used by the parser generator tool. SLR and LALR generators create tables of identical size and identical parser states. SLR generators accept fewer grammars than do LALR
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SLR generators calculate that lookahead by an easy approximation method based directly on the grammar, ignoring the details of individual parser states and transitions. This ignores the particular context of the current parser state. If some nonterminal symbol
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form requires more compromises and grammar hackery. So LALR generators have become much more widely used than SLR generators, despite being somewhat more complicated tools. SLR methods remain a useful learning step in college classes on compiler theory.
197:'s LR parser theory. The tables created for real grammars by full LR methods were impractically large, larger than most computer memories of that decade, with 100 times or more parser states than the SLR and LALR methods..
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uses Follow(S) as its LR(1) lookahead set. Such follow sets are also used by generators for LL top-down parsers. A grammar that has no shift/reduce or reduce/reduce conflicts when using follow sets is called an
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A reduce only needs to be added to a particular action column if that action is in the follow set associated with that reduce. This algorithm describes whether a reduce action must be added to an action column:
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To understand the differences between SLR and LALR, it is important to understand their many similarities and how they both make shift-reduce decisions. (See the article
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in a single left-to-right scan over the input stream, without guesswork or backtracking. The parser is mechanically generated from a formal grammar for the language.
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function mustBeAdded(reduceAction, action) { ruleNumber = reduceAction.value; ruleSymbol = rules.leftHandSide; return (action in followSet(ruleSymbol)) }
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The one difference between SLR and LALR is how their generators calculate the lookahead sets of input symbols that should appear next, whenever some completed
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is used in several places in the grammar, SLR treats those places in the same single way rather than handling them individually. The SLR generator works out
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and a relatively simple parser generator algorithm. As with other types of LR(1) parser, an SLR parser is quite efficient at finding the single correct
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Constructing the action and goto table as is done for LR(0) parsers would give the following item sets and tables:
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By using mustBeAdded on each reduce action in the action table, the result is a conflict-free action table:
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is false, because the left hand side of rule 2 is "E", and 1 is not in E's follow set. Contrariwise,
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A grammar that can be parsed by an SLR parser but not by an LR(0) parser is the following:
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now for that background, up through the section on reductions'
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466:is true, because "$ " is in E's follow set.
61:. Unsourced material may be challenged and
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236:. In the parse table, each reduction to
125:Learn how and when to remove this message
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189:SLR and LALR were both developed by
59:adding citations to reliable sources
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164:SLR and the more-general methods
824:History of compiler construction
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829:Comparison of parser generators
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819:Scannerless parsing
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170:Canonical LR parser
855:Parsing algorithms
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115:December 2012
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195:Donald Knuth
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53:Please help
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792:Memoization
757:Statistical
751:Left corner
708:Generalized
665:Precedence
579:SLR grammar
574:LALR parser
303:+ E → • 1 E
286:+ E → • 1 E
269:(1) E → 1 E
251:LALR parser
243:SLR grammar
183:SLR grammar
166:LALR parser
153:with small
809:Parse tree
741:Combinator
698:Look-ahead
436:following
319:Item set 3
311:Item set 2
294:Item set 1
280:Item set 0
147:SLR parser
85:newspapers
18:SLR parser
703:Canonical
658:Bottom-up
569:LL parser
564:LR parser
322:E → 1 E •
306:+ E → • 1
297:E → 1 • E
289:+ E → • 1
272:(2) E → 1
266:(0) S → E
230:Follow(S)
207:LR parser
151:LR parser
143:Simple LR
42:does not
849:Category
674:Operator
623:Top-down
558:See also
422:symbol
314:S → E •
300:E → 1 •
283:S → • E
258:Example
99:scholar
63:removed
48:sources
693:Simple
669:Simple
631:Earley
478:action
335:action
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746:Chart
490:state
445:1,$
378:s1/r2
347:state
179:Bison
106:JSTOR
92:books
802:LALR
483:goto
340:goto
177:and
175:yacc
168:and
141:, a
78:news
46:any
44:cite
814:AST
772:PEG
715:CYK
537:acc
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213:.)
145:or
137:In
57:by
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636:LL
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