667:≐ * ( 1 + 3 )$ SHIFT $ ⋖ T ≐ * ⋖ ( 1 + 3 )$ SHIFT $ ⋖ T ≐ * ⋖ ( ⋖ 1 + 3 )$ SHIFT $ ⋖ T ≐ * ⋖ ( ⋖ 1 ⋗ + 3 )$ REDUCE 4× (F -> num) (T -> F) (T' -> T) (E ->T ') $ ⋖ T ≐ * ⋖ ( ⋖ E ≐ + 3 )$ SHIFT $ ⋖ T ≐ * ⋖ ( ⋖ E ≐ + ⋖ 3 )$ SHIFT $ ⋖ T ≐ * ⋖ ( ⋖ E ≐ + < 3 ⋗ )$ REDUCE 3× (F -> num) (T -> F) (T' -> T) $ ⋖ T ≐ * ⋖ ( ⋖ E ≐ + ≐ T ⋗ )$ REDUCE 2× (E -> E + T) (E' -> E) $ ⋖ T ≐ * ⋖ ( ≐ E' ≐ )$ SHIFT $ ⋖ T ≐ * ⋖ ( ≐ E' ≐ ) ⋗ $ REDUCE (F -> ( E' )) $ ⋖ T ≐ * ≐ F ⋗ $ REDUCE (T -> T * F) $ ⋖ T ⋗ $ REDUCE 2× (T' -> T) (E -> T') $ ⋖ E $ ACCEPT
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STACK PRECEDENCE INPUT ACTION $ ⋖ 2 * ( 1 + 3 )$ SHIFT $ ⋖ 2 ⋗ * ( 1 + 3 )$ REDUCE (F -> num) $ ⋖ F ⋗ * ( 1 + 3 )$ REDUCE (T -> F) $ ⋖ T
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Search the table for the relationship between the nonterminal from the production and first symbol in the stack (Starting from top)
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Given following language, which can parse arithmetic expressions with the multiplication and addition operations:
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E --> E + T' | T' T' --> T T --> T * F | F F --> ( E' ) | num E' --> E
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Search the table for the relationship between Top(stack) and NextToken(Input)
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Find the topmost ⋖ in the stack; this and all the symbols above it are the
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The implementation of the parser is quite similar to the generic
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125:. The symbols ⋖, ≐ and ⋗ are used to identify the
237:Find the production of the grammar which has the
171:Until Stack equals "$ S" and Input equals "$ "
43:but its sources remain unclear because it lacks
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694:The Theory and Practice of Compiler Writing
692:Jean-Paul Tremblay, P. G. Sorenson (1985).
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687:Compiler construction: Theory and Practice
685:William A. Barrett, John D. Couch (1979).
150:table for a grammar with initial symbol S.
676:Alfred V. Aho, Jeffrey D. Ullman (1977).
74:Learn how and when to remove this message
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271:represents an arithmetic expression,
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148:Wirth–Weber precedence relationship
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226:SearchProductionToReduce (Stack)
1098:Programming language topic stubs
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940:History of compiler construction
20:
945:Comparison of parser generators
209:Remove the Pivot from the Stack
206:SearchProductionToReduce(Stack)
164:$ to the string being parsed (
682:. 1st Edition. Addison–Wesley.
177:if the relationship is ⋖ or ≐
1:
689:. Science Research Associate.
679:Principles of Compiler Design
189:Push(Stack, NextToken(Input))
113:. A stack is used to store a
1041:. You can help Knowledge by
984:. You can help Knowledge by
153:Initialize a stack with the
950:Operator-precedence grammar
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104:simple precedence grammars
218:Push(Stack, Non terminal)
215:Push(Stack, relationship)
197:if the relationship is ⋗
186:Push(Stack, relationship)
102:that can be used only by
92:simple precedence parser
29:This article includes a
893:Definite clause grammar
282:and the Parsing table:
259:is a terminal, and the
58:more precise citations.
1093:Computer science stubs
1037:-related article is a
192:RemoveNextToken(Input)
129:, and to know when to
898:Deterministic parsing
263:parse any integer as
100:context-free grammars
1035:programming-language
123:rightmost derivation
935:Scannerless parsing
903:Dynamic programming
1088:Parsing algorithms
731:Parsing algorithms
241:as its right side.
31:list of references
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841:Shift-reduce
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146:Compute the
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50:Please help
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908:Memoization
873:Statistical
867:Left corner
824:Generalized
781:Precedence
133:or when to
56:introducing
1082:Categories
925:Parse tree
857:Combinator
814:Look-ahead
671:References
160:Append an
64:March 2023
819:Canonical
774:Bottom-up
790:Operator
739:Top-down
246:Example
121:from a
52:improve
809:Simple
785:Simple
747:Earley
201:Reduce
135:Reduce
1033:This
976:This
862:Chart
261:lexer
239:Pivot
232:Pivot
181:Shift
166:Input
131:Shift
127:pivot
117:of a
37:, or
1039:stub
982:stub
918:LALR
601:num
98:for
90:, a
930:AST
888:PEG
831:CYK
632:$
413:T'
354:E'
320:$
317:num
265:num
257:num
157:$ .
86:In
1084::
804:LR
752:LL
627:⋗
596:⋗
570:)
536:(
506:*
474:+
469:⋗
443:F
438:⋗
408:⋗
382:T
325:E
299:T'
293:E'
267:;
168:).
137:.
106:.
41:,
33:,
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1063:t
1056:v
1045:.
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1006:t
999:v
988:.
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709:v
658:⋖
653:⋖
646:⋖
643:⋖
640:⋖
635:⋖
622:⋗
617:⋗
614:⋗
591:⋗
586:⋗
583:⋗
563:⋖
558:⋖
551:⋖
548:⋖
545:⋖
542:≐
539:⋖
529:⋖
524:⋖
517:≐
499:⋖
494:⋖
487:⋖
484:≐
481:⋖
464:⋗
459:⋗
456:⋗
433:⋗
426:⋗
403:⋗
398:≐
395:⋗
373:≐
345:⋗
338:≐
314:)
311:(
308:*
305:+
302:F
296:T
290:E
277:F
273:T
269:E
234:.
203::
183::
77:)
71:(
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62:(
48:.
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