discussion: describe relation between Foldable and Unfoldable and there indexed versions

[safareli]

I had an idea:

What if instead of

Map.fromFoldable $ Map.toUnfoldable someMap

You could do:

unfoldWithIndex $ foldWithIndex someMap

where

foldWithIndex   ∷ ∀ g f idx a
    . Unfoldable g
    ⇒ FolableWithIndex idx f
    ⇒ f  idx   a
    → g (idx × a)
unfoldWithIndex ∷ ∀ g f idx a
    . Foldable g
    ⇒ UnfoldableWithIndex idx f
    ⇒ g (idx × a)
    → f  idx   a

p.s. names foldWithIndex and unfoldWithIndex are arbitrary just types meter

[safareli]

this two functions are describing relation between all 4 classes, we can derive a law
unfoldWithIndex <<< foldWithIndex === id

doing it the other way might be be an id (duplicate indexes in list for example)
unfoldWithIndex >>> foldWithIndex === id

[paf31]

I don't think you need a new UnfoldableWithIndex class, just unfold the index as you go.

[safareli]

yes but in that case you need special functions like Map.fromFoldable.
when Map could be an instance of UnfoldableWithIndex which means one could do unfoldrWithIndex and get as result a Map or any UnfoldableWithIndex.

[paf31]

Oh I see, you're unfolding with access to the key of the Map. There's something wrong with the kinds in your types though. f is applied to too many type arguments.

class UnfoldableWithIndex i f | f -> i where
  unfoldrWithIndex :: (s -> Maybe ({ value :: a, index :: i, next :: s }) -> s -> f a

Is that what you want?

That seems strange to me, since I can't write an UnfoldableWithIndex Int List instance, for example.

[safareli]

ah yes I was thinking index part was visible in types.
so they should be like this:

foldWithIndex ∷ ∀ g f idx a
    . Unfoldable g
    ⇒ FolableWithIndex idx f
    ⇒ f  a
    → g (idx × a)
unfoldWithIndex ∷ ∀ g f idx a
    . Foldable g
    ⇒ UnfoldableWithIndex idx f
    ⇒ g (idx × a)
    → f  a

That seems strange to me, since I can't write an UnfoldableWithIndex Int List instance, for example.

that's expected I think because linked-ness of List, I guss we can do:
UnfoldableWithIndex Int Array and UnfoldableWithIndex i (Map i)

[safareli]

actually we can name them fromFoldable and toUnfoldable:

fromFoldable ∷ ∀ g f idx a
    . Foldable g
    ⇒ UnfoldableWithIndex idx f
    ⇒ g (idx × a)
    → f a
toUnfoldable ∷ ∀ g f idx a
    . Unfoldable g
    ⇒ FolableWithIndex idx f
    ⇒ f a
    → g (idx × a)