Simple precedence parser
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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 grammars.
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. The symbols ⋖, ≐ and ⋗ are used to identify the pivot, and to know when to Shift or when to Reduce.
Implementation
- Compute the Wirth–Weber precedence relationship table for a grammar with initial symbol S.
- Initialize a stack with the starting marker $.
- Append an ending marker $ to the string being parsed (Input).
- Until Stack equals "$ S" and Input equals "$"
- Search the table for the relationship between Top(stack) and NextToken(Input)
- if the relationship is ⋖ or ≐
- Shift:
- Push(Stack, relationship)
- Push(Stack, NextToken(Input))
- RemoveNextToken(Input)
- if the relationship is ⋗
- Reduce:
- SearchProductionToReduce(Stack)
- Remove the Pivot from the Stack
- Search the table for the relationship between the nonterminal from the production and first symbol in the stack (Starting from top)
- Push(Stack, relationship)
- Push(Stack, Non terminal)
SearchProductionToReduce (Stack)
- Find the topmost ⋖ in the stack; this and all the symbols above it are the Pivot.
- Find the production of the grammar which has the Pivot as its right side.
Example
Given following language, which can parse arithmetic expressions with the multiplication and addition operations:
E --> E + T' | T' T' --> T T --> T * F | F F --> ( E' ) | num E' --> E
num is a terminal, and the lexer parse any integer as num; E represents an arithmetic expression, T is a term and F is a factor.
and the Parsing table:
E | E' | T | T' | F | + | * | ( | ) | num | $ | |
---|---|---|---|---|---|---|---|---|---|---|---|
E | ≐ | ⋗ | |||||||||
E' | ≐ | ||||||||||
T | ⋗ | ≐ | ⋗ | ⋗ | |||||||
T' | ⋗ | ⋗ | ⋗ | ||||||||
F | ⋗ | ⋗ | ⋗ | ⋗ | |||||||
+ | ⋖ | ≐ | ⋖ | ⋖ | ⋖ | ||||||
* | ≐ | ⋖ | ⋖ | ||||||||
( | ⋖ | ≐ | ⋖ | ⋖ | ⋖ | ⋖ | ⋖ | ||||
) | ⋗ | ⋗ | ⋗ | ⋗ | |||||||
num | ⋗ | ⋗ | ⋗ | ⋗ | |||||||
$ | ⋖ | ⋖ | ⋖ | ⋖ | ⋖ | ⋖ |
STACK PRECEDENCE INPUT ACTION $ ⋖ 2 * ( 1 + 3 )$ SHIFT $ ⋖ 2 ⋗ * ( 1 + 3 )$ REDUCE (F -> num) $ ⋖ F ⋗ * ( 1 + 3 )$ REDUCE (T -> F) $ ⋖ T ≐ * ( 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
References
- Alfred V. Aho, Jeffrey D. Ullman (1977). Principles of Compiler Design. 1st Edition. Addison–Wesley.
- William A. Barrett, John D. Couch (1979). Compiler construction: Theory and Practice. Science Research Associate.
- Jean-Paul Tremblay, P. G. Sorenson (1985). The Theory and Practice of Compiler Writing. McGraw–Hill.
![]() | Original source: https://en.wikipedia.org/wiki/Simple precedence parser.
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