In the programming-centric IBs I know of I have seen zero representation whatsoever of linguists. It's strange, considering the predominance of PLT. Now that I think of it, I haven't seen much talk about formal language theory either.
Is it that both fields have very little overlap?
Most of the discussion I've seen on programming languages revolves around the structure of languages and how they affect their use by people. I would like to see a sort of comparative approach between families of natural languages and those of programming languages.
I'm here, so there's at least one.
Natural languages and programming languages are different to the point that I don't like having to call them both languages. Yes, you can convey both instructions and information, but fundamentally, programming requires you to eliminate ambiguity and make the implicit explicit, whereas speech is basically shorthand. It's completely dependent on ambiguity, implicitness, and redundancy to achieve robust transmission through an unreliable, low-bandwidth medium. The whole point of digitization is bypassing those limitations.