The project is a CFGI (Context Free Grammar Interpreter)

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Create a tree-like structure that would allow the interpreter to translate the regular language generated by user.

I will use Antlr4 to get the job done. I have used it earlier to generate parsing rules for symbolic differentiation rules in my app on app store(SymbolArc on Microsoft store & "step-by-step diffentiation" on google play store. I can generate code in C# or JAVA. ANTLR4 already follows rules of CFG as specified in your file. Also, it is not possible to write generic programs that accept any CFG on the run. There is separate program to parse for each CFG. Yes, you can provide any number of input strings to test your string acceptance against defined CFG.