On the web, there's semantic HTML and Web Content Accessibility Guidelines which focus on making content for the Internet as broadly interoperable and accessible as possible. The former from a technical point of view, the latter from a human interaction point of view. They go together hand on hand.
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Concepts like Reactive programming are widely used in web/UI contexts. The problem of connecting a UI to an underlying data set is not trivial. Several frameworks deal with this.
As was already said, concerns like Accessibility are studied academically. They have more to do with user experience than the technology, so not sure if they match your question.
AFAIK, Halogen for Purescript is about as FP as it gets in the front-end world. It’s pretty complicated but Halogen takes advantage of “free monads”. Perhaps you are looking for something even more rigorous since you mentioned Idris but I figured I’d mention that one.
I’m learning it now and it has not been easy. I tried to port a simple vanilla JavaScript dynamic draggable table over to Halogen and it has not been fun at all. I got 80% of the way there then started to have to reach for FFI, unsafeCoerce, or build my own Purescript module to capture mousevents.
Maybe Elm? It was the result of Evan Czaplicki's thesis.