I don't even know what this would entail. Reality is continuous and subjective; computers are not. And there's no reason that "legal APIs" would be any more cleaned up, consistent, simple or logical than our current legal system.

Wait until you hear about “case law”. Just because it’s not on the law books doesn’t mean it’s not legally binding. If a court rules something unconstitutional or whatever, the law sometimes remains on the books instead of being removed. “Why bother writing and passing a bill to repeal a law when the court said it’s unenforceable?”

So the government writes up a spec for how the legalese should map to code that engineers then implement? How is that different from what happens now?

Only the programmed end result in code would be legally binding. Lawmakers would have a big interst in making sure the code is correct and provide incentives/change procedures accordingly.

The inmates in this article would be released immediately after the code-law is implemented; you could apply new tax laws (i.e. as a config file) to your accounting software.

Why maintain an obfuscated legal text when you need it in software anyway?

The legal text is the specification. What you're suggesting is the equivalent of the classic "the spec is whatever the implementation does", and would erase the distinction between correct, incorrect, and undefined behaviour.

In other words: “it’s not a bug. it’s a feature!”