Parsing algorithm

. The parser considers 'X' the symbol on top of stack, and 'a' the current input symbol

. These two symbols determine the action to be taken by the parser

. Assume that '$' is a special token that is at the bottom of the stack and terminates the input string

if X = a = $ then halt

if X = a ≠ $ then pop(x) and ip++

if X is a non terminal

then if M[X,a] = {X à UVW}

then begin pop(X); push(W,V,U)

end

else error

The parser is controlled by a program that behaves as follows. The program considers X , the symbol on top of the stack, and a , the current input symbol. These two symbols determine the action of the parser. Let us assume that a special symbol ' $ ' is at the bottom of the stack and terminates the input string. There are three possibilities:

1. If X = a = $, the parser halts and announces successful completion of parsing.

2. If X = a ≠ $, the parser pops X off the stack and advances the input pointer to the next input symbol.

3. If X is a nonterminal, the program consults entry M[X,a] of the parsing table M. This entry will be either an X-production of the grammar or an error entry. If, for example, M[X,a] = {X UVW}, the parser replaces X on top of the stack by UVW (with U on the top). If M[X,a] = error, the parser calls an error recovery routine.

The behavior of the parser can be described in terms of its configurations, which give the stack contents and the remaining input.