[Haskell-cafe] Feeding a monad into itself

[Jake]

Very interesting! What do you mean by a "better" unfold?

On Fri, Jul 21, 2017, 13:06 MarLinn <monkleyon at gmail.com> wrote:

> On 2017-07-21 17:57, Kim-Ee Yeoh wrote:
>
> Another perfectly cromulent definition is:
>
> untilNothing f = fromJust . last . takeWhile isJust . iterate (f =<<) .
> Just
>
> This has 2 advantages:
>
> 1. It illustrates the haskellism that "A list is a loop is a list."
> 2. It composes much-beloved list combinators into a reasonable pipeline.
>
> Note that
>
> 	fromJust . last . takeWhile isJust . iterate (f =<<) . Just
> 	≡
> 	last . catMaybes . takeWhile isJust . iterate (f =<<) . Just
>
> Note further that that with duplicate x = (x,x),
>
> 	\initialElement -> catMaybes . takeWhile isJust . iterate (f =<<) . Just $ initialElement
> 	≡
> 	\initialElement -> initialElement: unfoldr (fmap duplicate . f) initialElement
>
> In other words, the pipeline is basically equivalent to a simple unfoldr
> modulo the first step. Therefore,
>
> 	untilNothing f initialElement = last $ initialElement : unfoldr (fmap duplicate . f) initialElement
>
> Which reveals the relation to anamorphisms and makes it possible to drop
> two of the three pain-inducing functions (isJust and fromJust).
>
> This further hints at the fact that loops are a combination of
> anamorphisms/unfolds (here: unfoldr) and catamorphisms/folds (here: last).
> As last can easily be replaced with better options like foldMap Last, the
> search for a "better" implementation should basically consist of a search
> for a more suitable unfold. A simple hoogle seems to reveal several options.
>
>
> Cheers,
> MarLinn
>
> PS: The relation to lists still remains in my version, but it may be
> easier to see that the "haskellism" is just an unfortunate result of both
> their prominence in the standard libraries and the specialised syntax we
> have for them. That's why it's a "haskellism", and not a universal relation.
>
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