I need to do a parser for propositional logic. I pretend to do it by hand implemented like a recursive descent parser in java.
My question is about the lexer, is it really needed for this job? I mean to define a finite state machine to recognize tokens etc. I have seen some examples about simple parsers for arithmetic and they handle all in a "single parser" relying only on the grammar rules. It doesn't look like they care about a separate independent lexer which provides the tokens for the parser.
Since i want to do this in the most correct way, i ask for advice for this job. Any link to related info is welcome.