A simple C-based implementation to construct an Operator Precedence Table using grammar productions, helping visualize leading and trailing relationships between terminals and non-terminals.

To write a C program that constructs the Operator Precedence Table for a given grammar using the concepts of LEADING and TRAILING sets of non-terminals.

The program accepts a set of grammar productions in the form A=α, where A is a non-terminal and α is a combination of terminals and/or non-terminals.

1. Identify Terminals and Non-Terminals:
   Parses the input grammar to separate out terminals (lowercase/characters/symbols) and non-terminals (uppercase letters).

2. Compute LEADING and TRAILING Sets:

   • LEADING: First terminal symbols that can appear at the start of strings derived from non-terminals.
   • TRAILING: Last terminal symbols that can appear at the end of strings derived from non-terminals.

3. Precedence Rules:

   • a = b if a and b are adjacent terminals.
   • a < b if a is a terminal followed by a non-terminal that has b in its LEADING set.
   • a > b if a is a terminal preceded by a non-terminal that has a in its TRAILING set.
   • $ < leading(start symbol) and trailing(start symbol) > $ rules are also applied.

4. Output Tables:

   • LEADING Table
   • TRAILING Table
   • Precedence Table

Enter the number of productions: 3
Enter the productions:
E=E+T
T=TxV
V=a

LEADING Table:
LEADING(E) = a +
LEADING(T) = a
LEADING(V) = a

TRAILING Table:
TRAILING(E) = a
TRAILING(T) = a x
TRAILING(V) = a

Precedence Table:
+ x a $
. = - < -
x - = < -
a - > = >
$ < - < -

• Compiler Design: Used in syntax analysis and parsing to determine the correct order of operations.
• Expression Evaluation: Helps evaluate arithmetic/logical expressions where operator precedence affects the result.
• Parser Construction: Assists in building operator precedence parsers, a type of bottom-up parser.
• Programming Language Design: Ensures unambiguous grammar for operator handling in custom language design.