Simple precedence parser

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. Symbols \lessdot, \dot = and \gtrdot are used to identify the pivot, and to know when to Shift or when to Reduce.

Implementation

SearchProductionToReduce (Stack)

Example

Given the language:

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.

and the Parsing table:

E E' T T' F + *()num $
E \dot = \gtrdot \gtrdot
E' \dot =
T \gtrdot\dot = \gtrdot \gtrdot
T' \gtrdot \gtrdot \gtrdot
F \gtrdot\gtrdot \gtrdot \gtrdot
+ \lessdot\dot =\lessdot \lessdot \lessdot
* \dot = \lessdot \lessdot
( \lessdot\dot =\lessdot\lessdot\lessdot \lessdot \lessdot
) \gtrdot\gtrdot \gtrdot \gtrdot
num \gtrdot\gtrdot\gtrdot \gtrdot
$ \lessdot \lessdot\lessdot\lessdot \lessdot \lessdot
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 times (F -> num) (T -> F) (T' -> T) (E ->T ') 
$ < T = * < ( < E            =        + 3 )$           SHIFT
$ < T = * < ( < E = +        <        3 )$             SHIFT
$ < T = * < ( < E = + < 3    >        )$               REDUCE 3 times (F -> num) (T -> F) (T' -> T) 
$ < T = * < ( < E = + = T    >        )$               REDUCE 2 times (E -> E + T) (E' -> E)
$ < T = * < ( < E'           =        )$               SHIFT
$ < T = * < ( = E' = )       >        $                REDUCE (F -> ( E' ))
$ < T = * = F                >        $                REDUCE (T -> T * F)
$ < T                        >        $                REDUCE 2 times (T' -> T) (E -> T')
$ < E                        >        $                ACCEPT

References


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