Propositional Logic Interpreter

A C++ interpreter for propositional logic expressions that lexes, parses, and evaluates boolean equations using recursive descent parsing.

Features

• Lexical Analysis: Tokenizes propositional logic expressions
• Syntax Analysis: Recursive descent parser that handles precedence
• Semantic Evaluation: Stack-based evaluation of boolean expressions
• Operator Support: NOT (~), AND (^), OR (v), IMPLIES (->)

Supported Grammar

The interpreter implements the following formal grammar:

B  → IT '.'
IT → OT IT'
IT' → '->' OT IT' | ε
OT → AT OT'
OT' → 'v' AT OT' | ε
AT → L AT'
AT' → '^' L AT' | ε
L  → '~' L | A
A  → 'T' | 'F' | '(' IT ')'

Building

Requires CMake 3.10+ and a minimum C++17 compiler.

mkdir build && cd build
cmake ..
make

This produces two executables:

• interpreter - Main interpreter binary
• test - Lexer testing

Usage

Currently configured for programmatic use. Modify main.cpp to evaluate different expressions:

std::string input = "TvF.";  // true OR false
lexer::Lex lex(input);

if (parser::B(lex)) {
    bool result = parser::getResult();
    std::cout << (result ? "True" : "False");
} 
else {
    std::cout << "Syntax invalid";
}

Example Expressions

Expression	Meaning	Result
T.	True	True
~F.	NOT False	True
T^F.	True AND False	False
TvF.	True OR False	True
F->T.	False IMPLIES True	True
T->(F->T).	Nested implication	True
~(T^F).	NOT (True AND False)	True