The problem at hand is not the notation of actual implemented languages, but rather the notation of programming language theory. In other words, when you read a

The problem at hand is not the notation of actual implemented languages, but rather the notation of programming language theory. In other words, when you read a paper published at a PL conference (POPL, PLDI, ICFP, SPLASH, etc.), the notation you are likely to encounter therein. There's like 50 years of notational history, and it can be wildly inconsistent. Some things are somewhat standardized, but there's no central location to look this stuff up. Probably one of the better resources is Benjamin Pierce's "Types and Programming Languages" (often referred to simply as TAPL), but I've seen even recent papers deviate from TAPL's treatment. So when new people are trying to break into the PL research sphere, there's a huge barrier to entry. Invariably, they'll need to ask other researchers to decipher some of the notation in whatever papers they read because the authors just assumed the notation was prevalent enough to not warrant explanation. This works fine for people privileged enough to already be working in PL research as undergrads, but it's much tougher if you're coming from a different background. The PL research community is fairly active on Twitter, but explanations of decades-old notation do not conform to 280-character text messages very well. It's a big issue that a lot of us younger PL researchers talk about often. I ask myself: how did I learn this stuff? Many meetings with my first PI as I had to bring up symbol after symbol from whatever papers I was trying to read. I took a graduate course in PL semantics which also helped, but then I've also seen deviations from that notation, so...??? And there's still notation I'm unfamiliar with. I was reading about substructural type systems recently (which are super cool, by the by) and encountered some symbols I didn't know and my current PI didn't know and none of my lab mates knew, so I resorted to a PL Discord server where some grad student at another university across the country was able to chime in with the answer. Such a headache.