Something I'm trying to wrap my head around is why this concept of a DSL is different from say a library or APIs? Like for example, PyTorch as a library can go ahead and abstract away from a lot of the tasks of writing network layers and also making sure computation on GPU is fast with CUDA. But then, is PyTorch a DSL? Even Halide makes it seem like these are just more advanced APIs that are tailored to the task but I'm curious what the distinctions are to be made for these.

I also find it hard to distinguish between languages and APIs since we refer to Halide as a language but I'm pretty sure Kayvon said that it's technically just a C++ API with operator overloading. My guess maybe we refer to it as a language if its syntax/way it works is sufficiently different from the language it was written in? I've never used PyTorch but after googling "PyTorch code" I see the syntax looks almost identical to Python so maybe that's why it's a "library" and not a "language". Of course in this slide we're only considering "programming system" which I'm assuming could include both APIs and languages so the distinction might not matter that much after all.