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Interesting approach. Maybe it is even better to first start with a back-tracking parser. Although back-tracking has the reputation of being slow, there is a rather straightforward mapping from grammar to functions. Although it is slower than traditional parsing techniques, it is fast enough for many practical applications.

One easy trick to optimize back-tracking is memoization.

Another is the left-recursion into right-recursion trick, which is also rather straightforward to apply.

These two tricks are used in IParse Studio [0] which is an interpreting parser that parses a grammar and uses that grammar to parse some input. I also can help you with rewriting the grammar using the described approach.

[0] https://fransfaase.github.io/MCH2022ParserWorkshop/IParseStu...

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def parse_Expr(self): # parse_ExprInner parses CanBeLhsOfAssignExpr or CanNotBeLhsOfAssignExpr cases result = self.parse_ExprInner() if self.peekToken() == TOKEN_ASSIGN: if result.is_CanBeLhsOfAssignExpr: token = self.skipToken() # assignment is right-associative rhs = self.parse_Expr() result = self.make_AssignExpr(token, result, rhs) else: self.raiseParseError("{} can't be target of assignment", result) return result