this post was submitted on 28 Mar 2024
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It's because most of the hard questions and theorems can be phrased over the Booleans. Lawvere's fixed-point theorem, which has Turing's theorem and Rice's theorem as special cases (see also Yanofsky 2003), applies to Boolean values just as well as to natural numbers.
That said, you're right to feel like there should be more explanation. Far too many parser papers are written with only recognition in mind, and the actual execution of parsing rules can be a serious engineering challenge. It would be nice if parser formalisms were described in terms of AST constructors and not mere verifiers.