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| In [[computer science]], a '''simple precedence parser''' is a type of [[bottom-up parser]] for [[context-free grammars]] that can be used only by [[simple precedence grammar]]s.
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| The implementation of the parser is quite similar to the generic [[bottom-up parser]]. A stack is used to store a [[viable prefix]] of a [[sentential form]] from a [[rightmost derivation]]. Symbols <math>\lessdot</math>, <math>\dot =</math> and <math>\gtrdot</math> are used to identify the '''pivot''', and to know when to '''Shift''' or when to '''Reduce'''.
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| ==Implementation==
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| * Compute the [[Wirth-Weber precedence relationship]] table.
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| * Start with a stack with only the '''starting marker''' $.
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| * Start with the string being parsed ('''Input''') ended with an '''ending marker''' $.
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| * While not (Stack equals to $S and Input equals to $) (S = Initial symbol of the grammar)
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| ** Search in the table the relationship between Top(stack) and NextToken(Input)
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| ** if the relationship is <Math> \dot =</math> or <Math>\lessdot</math>
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| *** '''Shift''':
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| *** Push(Stack, relationship)
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| *** Push(Stack, NextToken(Input))
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| *** RemoveNextToken(Input)
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| ** if the relationship is <Math>\gtrdot</math>
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| *** '''Reduce''':
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| *** SearchProductionToReduce(Stack)
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| *** RemovePivot(Stack)
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| *** Search in the table the relationship between the Non terminal from the production and first symbol in the stack (Starting from top)
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| *** Push(Stack, relationship)
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| *** Push(Stack, Non terminal)
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| SearchProductionToReduce (Stack)
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| * search the '''Pivot''' in the stack the nearest <Math>\lessdot</math> from the top
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| * search in the productions of the grammar which one have the same right side than the '''Pivot'''
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| ==Example==
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| <pre>
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| Given the language:
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| E --> E + T' | T'
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| T' --> T
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| T --> T * F | F
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| F --> ( E' ) | num
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| E' --> E
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| </pre>
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| '''num''' is a terminal, and the [[lexer (computer science)|lexer]] parse any integer as '''num'''.
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| and the Parsing table:
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| {|border="1" cellpadding="2"
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| | ||E|| E' || T || T' || F || + ||*||(||)||num || $
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| |-
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| | E || || || || || ||<math>\dot =</math>|| || ||<math>\gtrdot</math> || ||<math>\gtrdot</math>
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| |-
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| | E'|| || || || || || || || ||<math>\dot =</math>|| ||
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| |-
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| | T || || || || || ||<math>\gtrdot</math>||<math>\dot =</math>|| ||<math>\gtrdot</math>|| ||<math>\gtrdot</math>
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| |-
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| | T'|| || || || || ||<math>\gtrdot</math>|| || ||<math>\gtrdot</math>|| ||<math>\gtrdot</math>
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| |-
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| | F || || || || || ||<math>\gtrdot</math>||<math>\gtrdot</math>|| ||<math>\gtrdot</math>|| ||<math>\gtrdot</math>
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| |-
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| | + || || ||<math>\lessdot</math>||<math>\dot =</math>||<math>\lessdot</math>|| || ||<math>\lessdot</math>|| ||<math>\lessdot</math> ||
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| |-
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| | * || || || || ||<math>\dot =</math>|| || ||<math>\lessdot</math>|| ||<math>\lessdot</math> ||
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| |-
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| | ( ||<math>\lessdot</math>||<math>\dot =</math>||<math>\lessdot</math>||<math>\lessdot</math>||<math>\lessdot</math>|| || ||<math>\lessdot</math>|| ||<math>\lessdot</math> ||
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| |-
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| | ) || || || || || ||<math>\gtrdot</math>||<math>\gtrdot</math>|| ||<math>\gtrdot</math>|| ||<math>\gtrdot</math>
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| |-
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| | num|| || || || || ||<math>\gtrdot</math>||<math>\gtrdot</math>||||<math>\gtrdot</math>|| ||<math>\gtrdot</math>
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| |-
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| | $ ||<math>\lessdot</math>|| ||<math>\lessdot</math>||<math>\lessdot</math>||<math>\lessdot</math>|| || ||<math>\lessdot</math>|| ||<math>\lessdot</math> ||
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| |}
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| <pre>
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| STACK PRECEDENCE INPUT ACTION
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| $ < 2 * ( 1 + 3 )$ SHIFT
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| $ < 2 > * ( 1 + 3 )$ REDUCE (F -> num)
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| $ < F > * ( 1 + 3 )$ REDUCE (T -> F)
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| $ < T = * ( 1 + 3 )$ SHIFT
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| $ < T = * < ( 1 + 3 )$ SHIFT
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| $ < T = * < ( < 1 + 3 )$ SHIFT
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| $ < T = * < ( < 1 > + 3 )$ REDUCE 4 times (F -> num) (T -> F) (T' -> T) (E ->T ')
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| $ < T = * < ( < E = + 3 )$ SHIFT
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| $ < T = * < ( < E = + < 3 )$ SHIFT
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| $ < T = * < ( < E = + < 3 > )$ REDUCE 3 times (F -> num) (T -> F) (T' -> T)
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| $ < T = * < ( < E = + = T > )$ REDUCE 2 times (E -> E + T) (E' -> E)
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| $ < T = * < ( < E' = )$ SHIFT
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| $ < T = * < ( = E' = ) > $ REDUCE (F -> ( E' ))
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| $ < T = * = F > $ REDUCE (T -> T * F)
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| $ < T > $ REDUCE 2 times (T' -> T) (E -> T')
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| $ < E > $ ACCEPT
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| </pre>
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| ==References==
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| * Alfred V. Aho, Jeffrey D. Ullman (1977). ''Principles of Compiler Design''. 1st Edition. Addison-Wesley.
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| * William A. Barrett, John D. Couch (1979). ''Compiler construction: Theory and Practice''. Science Research Associate.
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| * Jean-Paul Tremblay, P. G. Sorenson (1985). ''The Theory and Practice of Compiler Writing''. McGraw-Hill.
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| {{DEFAULTSORT:Simple Precedence Parser}}
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| [[Category:Parsing algorithms]]
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| {{comp-sci-stub}}
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| {{Compu-lang-stub}}
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