The document discusses non-recursive predictive parsing using a table-driven approach. It describes an algorithm that uses a parsing table to parse an input string according to a grammar. The algorithm initializes with the input string in a buffer and the start symbol on a stack. It then uses entries in the parsing table to pop symbols from the stack and advance through the input string, reporting errors if a valid parse cannot be found.

1. Non-recursive predictive parsing
Our recursive descent parser encodes state information in its run-time stack, or call stack.Using
recursive procedure calls to implement a stack abstraction may not be particularly efficient.
This suggests other implementation methods:
• Explicit stack, hand-coded parser
• Stack-based, table-driven parser
Algorithm: Table-driven predictive parsing.
INPUT: A string w and a parsing table M for grammar G.
OUTPUT: If w is in L(G), a leftmost derivation of w; otherwise, an
error indication.
METHOD: Initially, the parser is in a configuration with w$ in the input buffer and the
start symbol S of G on top of the stack, above $. The program in uses the predictive
parsing table M to produce a predictive parse for the input.
Set I p to point to the first symbol of w;
Set X to the top stack symbol;
W h i le (X $) {/* stack is not empty */
If (X is a) pop the stack and advance ip;

2. Else if (X is a terminal) error Q;
Else if (M[X, a] is an error entry) error Q;
Else if (M[X, a] = X -> Y1Y2 •••Yk) {
Set X to the top stack symbol;
}
Note that the sentential forms in this derivation correspond to the input that has already
been matched (in column M A T C H E D) followed by the stack contents. The matched
input is shown only to highlight the correspondence. For the same reason, the top of the
stack is to the left; when we consider bottom-up parsing, it will be more natural to show
the top of the stack to the right. The input pointer points to the leftmost symbol of the
string in the INPUT column.