A variant on UIs I'd like to try:
data UI model = UI
{ view :: model -> DOM
, update :: Δmodel -> model -> ΔDOM
}
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i.e. you have a view function, but also the derivative of the view function. Instead of diffing the virtual dom, you diff the model.
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It helps to add a model->viewmodel indirection. Then structure viewmodel such that vm diff +- isomorphic to imperative widget toolkit calls.
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In my case viewmodel is a nested Erlang map, with diffs expressed in terms of key "paths". Keeps JS code minimal.
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Stumbling around til I find the light switch :) Started reading "Theory of Changes". This smells a lot like CCC AD:
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The rules for app and abs D(\x->t ) => \(x,dx) -> D(t), D(s t) => D(s) (t, D(t)) look like "dual number" representations from autodiff.
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Yes! That's how I implement it in my purescript-incremental library actually. There is also a section in the Compiling to Categories paper.