mathlib4

s it harder to learn the language (and, in particular, translate other ways of expressing mathematics into TLA+). I would love to see somebody who thinks deeply about PL syntax to make another language with the same semantics as TLA+, the same goals of looking like mathematics, but more familiar syntax. I don’t know what that would look like, but I’d love to see it. It seems like with the right library (see my mathlib point) and syntax, writing a TLA+ program should be no harder than writing a P program for the same behavior, but that’s not where we are right now. > The errors [types] catch are almost always quickly found by model checking. This hasn’t been my experience, and in fact a lot of the TLA+ programs I see contain partial implementations of arbitrary type checkers. I don’t think TLA+ needs a type system like Coq’s or Lean’s or Haskell’s, but I do think that some level of type enforcement would help avoid whole classes of common specification bugs (or even auto-generation of a type checking specification, which may be the way to go). > [A Coq-like type system] would put TLA+ beyond the ability of so many potential users that no proposal to add them should be taken seriously. I do think this is right, though. > This may turn out to be unnecessary if provers become smarter, which should be possible with the use of AI. Almost definitely will. This just seems like a no-brainer to bet on at this stage. See AlphaProof, moogle.ai, and many other similar examples. > A Unicode representation that can be automatically converted to the ascii version is the best alternative for now. Yes, please! Lean has a unicode representation, along with a nice UI for adding the Unicode operators in VSCode, and it’s awesome. The ASCII encoding is still something I trip over in TLA+, even after a decade of using it.