Great write up, particularly building up towards parsing simple expressions. One benefit - hinted at, but not explicitly said - between this approach and parse

Great write up, particularly building up towards parsing simple expressions. One benefit - hinted at, but not explicitly said - between this approach and parser generators is that all of the user's parsing code lives in the same place. An ANTLR grammar that solved this problem would take about the same amount of lines - but that wouldn't be enough. You would still need to write the Java code that takes actions on the grammar rules, and that code will live in a separate place. Add in the complexity of setting up your build to deal with generated source code, and you won't want to go the ANTLR (or other parser generator) approach unless you really have to. I only compare against parser generators because the other solutions are, to me, in different classes. Regular expressions are not arbitrarily flexible, so they're not a full solution. And rolling your own recursive descent parser is not using an existing library, but going the "hammer and tongs" route (as my compilers professor used to say).