Haskell: FRP Reactive Parsec?

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Is there (or is it possible to have) a reactive Parsec (or any other pure functional parser) in Haskell?

Simply put, I want to feed parser myself char by char and get results as much as I feed enough to get output.

Or much simpler, how can I do it in foldr or at least map?

Do we need a different version of them to support such reactive behavior?

EDIT

My question is about FRP in particular. I used a parser as an example, which was the best I could think of to clarify my question and give big picture of what I need.

I believe FRP is not just about UI, right?

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