Writing about pratt parsing so I remember it

Could I suggest also looking at a sed-inspired parsing language (a DSL) which is called nom and is documented at http://www.nomlang.org An example script for parsing symbolic expressions is at http://www.nomlang.org/eg/maths.parse.pss and another which turns the expressions into LaTeX is /eg/maths.tolatex.pss

Nom may seem quite verbose. I have written another language (which compiles to nom) which I call Syntagma. The syntax of syntagma is much closer to EBNF but also has powerful additions, such as a "lookahead" syntax, a negated lookahead syntax (eg: "parse this as an expression if it is not followed by a multiply operator"). Also, Syntagma has a "condition" syntax, meaning that a parse rule will only reduce if the attributes of the parse tokens match certain conditions.

An example of an expression parser written in Syntagma is at http://www.nomlang.org/syntagma/eg/expr.sta This is much more succinct than the equivalent nom script. The script /syntagma/eg/expr.toforth.sta converts symbolic expressions (and assignments) into Forth.

Parsing is an interesting topic, but I feel that it is quite difficult or non-intuitive with some of the traditional tools and methods (at least for me).

Personally I never found the shunting yard algorithm very intuitive at all.

A recursive descent parser makes much more sense to me.