Constrained traversals

[adamgundry]

See discussion starting from https://discord.com/channels/701454007775920128/855385315942203433/855825282833711115

type TraversalC c s t = (forall a b. c a b => p a b) -> p s t

This allows traversing structures containing multiple different types, satisfying a constraint. Pick c ~ Equals a b where class (a1 ~ a, b1 ~ b) => Equals a b a1 b1 to recover existing traversals.

Can/should we generalise optics to support this?

[phadej]

That discussion link needs login.

[phadej]

You have a typo, missing p:

type TraversalC p c s t = (forall a b. c a b => p a b) -> p s t

It would be more correct to speak about constrained optics:

type OpticC p c s t = (forall a b. c a b => p a b) -> p s t

then constrainted traversal would be

type TraversalC c s t = forall p. Traversing p => OpticC p c s t

and similarly constrained lens, prisms, setters, ...

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Can/should we generalise optics to support this?

Can: probably yes.
Should: I'd rather see someone else try this first.