I am not talking about operator precedence, that’s a separate thing. Consider the parsing of math expressions, where juxtaposition of terms denotes multiplication unless it can be interpreted as something else. So f(x+2) is function application, whereas 3(x+2) is multiplication. With a PEG, you just write a standard expression grammar with an additional choice at the end for the implicit multiplication. With a conventional parser, this is much more difficult – you have to explicitly list all the different ways that terms could be next to each other without meaning something else.