Re-implement the parser using a parser combinator library

[exarkun]

The ad hoc parser currently in use includes a lot of redundancy and is difficult to reason about. For example, it uses int(s) in many places where it means "a positive integer". This could be fixed by replacing all uses of int with some API which addresses the problem of negative and 0 values being accepted but leaves all of the redundancy so similar future changes again have to fix N different call sites.

A parser combinator library makes it easy to avoid this kind of duplication.

Additionally, parser combinators are familiar to at least some people. The completely custom parser currently in use is familiar to approximately no one.