Diagonalization/ dupe for monads and tuples?

[Carter Schonwald]

Rob,
1) your foldEither is way better and I love it.

2) this is a way more pleasing Avenue of design for the tuple and either
combinators ! Thank you for sharing this great little exposition.

On Wed, Sep 23, 2020 at 8:20 AM Rob Rix via Libraries <libraries at haskell.org>
wrote:

> TL;DR: maybe we can think of this as combining disjoint empty & non-empty
> cases of folds.
>
> Every time I’ve wanted to define something like this I’ve found myself
> dissatisfied because of this asymmetry.
>
> Looking at it from another angle, I frequently encounter a vaguely similar
> situation with folds: given some collection which can be empty or non-, I
> want to fold over it with a function if non-empty, or return a default
> value if empty:
>
> foldr1OrDefault :: Foldable t => (a -> a -> a) -> a -> t a -> a
> foldr1OrDefault f z t
>   | null t    = z
>   | otherwise = foldr1 f t
>
>
> This is a bit like Control.Lens.Fold.foldBy in lens, except that the
> combining function f does not receive z at any point. Quite useful when you
> have a Semigroup but not a Monoid, or when you otherwise want to treat the
> empty case specially.
>
> fromMaybe is a special case of this function, without the conceit of
> pretending that Maybe can hold multiple values. I’ve sometimes involved
> Maybe in this construction for just that reason when e.g. a is a Semigroup:
>
> fold1Maybe :: (Foldable t, Semigroup a) => t a -> Maybe a
> fold1Maybe = foldMap Just
>
> fold1OrDefault :: (Foldable t, Semigroup a) => a -> t a -> a
> fold1OrDefault z = fromMaybe z . foldMap Just
>
>
> (All of these names are intentionally bad because I don’t want to propose
> adding these functions anywhere just yet.)
>
> For Either (and These for that matter), a full generalization also has to
> deal with the extra information in the null case, i.e. Either b a would
> need (b -> a) instead of a:
>
> fromEither :: (b -> a) -> Either b a -> a
> fromEither f = either f id
>
>
> I’m surprised about once every six months that this doesn’t exist (and
> then surprised again when consulting the types that fromLeft/fromRight
> aren’t either this *or* analogous to fromJust).
>
> All of which is to say, I think I would prefer to have the generality of
> this fromEither to the a -> Either a a -> a version, but it’d be nice to
> figure out a way to see it as a fold, too. Maybe the Bifoldable1 instance
> for Either has something to contribute here?
>
> Rob
>
> On Sep 17, 2020, at 1:13 PM, Philip Hazelden <philip.hazelden at gmail.com>
> wrote:
>
> On Thu, Sep 17, 2020 at 5:59 PM Jon Purdy <evincarofautumn at gmail.com>
> wrote:
>
>> { fromMaybe, fromLeft, fromRight, fromEither, fromThese, fromDynamic, … }
>> extracts “the” value out of a { Maybe, These, Dynamic, … } with a suitable
>> default if “it” isn’t present.
>>
>
> Hm. A weird thing about fromEither compared to (I think) all the rest of
> these, is that the type of the Either isn't fully general. That is,
> fromLeft and fromRight take an `Either a b`; fromThese takes a `These a b`.
> But the proposed `fromEither` takes an `Either a a`.
>
> This maybe isn't a big deal. Just seemed worth noting.
>
>
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