> there have been a number of formal specification tools that have been developed in recent years which use programming-language-like notation, such as FizzBee, P, PlusCal, and Quint. I think these notations are more approachable for programmers than the more set-theoretic notation of TLA+.

This statement may make it seem like the design of those other languages is a later development than TLA+, while the opposite is the case. Programming-language-like specification languages have existed continuously since the 70s and 80s (VDM, Estelle, SMV, Spin/PROMELLA - they were about as known to practising programmers at the time as the newer ones are known today...), as well as model-checkable programming languages similar to P (Esterel). The new incarnations are very similar to those from more than four decades ago.

TLA+ was the newer development, designed as a reaction to the old programming-like approach, which, Leslie Lamport felt, wasn't simple and succinct enough, didn't allow for specification at arbitrary levels of detail, and didn't allow for easy manipulation and substitution (e.g. that `x = 2` might mean something different from `x + 3 = 5` is not just added complexity, but makes it hard to describe the relationship between specifications of the same system at different levels of detail).

Lamport decided to ditch the older style in favour of one based almost solely on simple mathematics (there were some earlier attempts, but they were still more programming-like than TLA+). He didn't expect that mathematics at the level taught in an introductory, first-semester university course would be so unapproachable to programmers.

What's your recommendation on how to rapidly learn TLA+? I spent some time staring at references and the UI a few months ago and came away very defeated. But I'd like to actually level up here.