Consider adding `converge` and friends.

[Andreas Abel]

Here are some related functions for fixpoint computation:

 
http://hackage.haskell.org/package/Agda-2.6.1/docs/Agda-Utils-Function.html

On 2020-08-20 18:36, Ignat Insarov wrote:
> Hello…
> 
> This function first appeared _(to my knowledge)_ in [a Stack Overflow
> answer][1]. I found it useful several times, and eventually [I extended it to a
> family of 4 derived functions][2]: `converge`, `convergeBy`, `fixp` and
> `fixpBy`.
> 
> * `convergeBy` is like `takeWhile` but with a binary predicate.
> * `converge` cuts a list at a point where it starts to repeat itself.
> * `fixp` takes the last element.
> 
> These operations are useful in many practical cases. For example, the
> Newton-Raphson approximation method:
> 
>      λ r a = \x -> (x + a/x) / 2
>      λ fixp (r 2) 1
>      1.414213562373095
> 
> Or let us compute the alternating group A₄:
> 
>      λ import qualified Data.List as List
>      λ xs */ ys = fmap (xs !!) ys
>      λ generate1 gens elems = List.union elems [ elem */ gen | elem <-
> elems, gen <- gens ]
>      λ ε = [0.. 3]
>      λ rota3 = [1, 2, 0, 3]
>      λ rota3' = [0, 2, 3, 1]
>      λ length $ fixp (generate1 [rota3, rota3']) [ε]
>      12
> 
> I propose adding these functions to `Data.List`.
> 
> [1]: https://stackoverflow.com/a/7443379
> [2]: https://stackoverflow.com/q/48353457
> _______________________________________________
> Libraries mailing list
> Libraries at haskell.org
> http://mail.haskell.org/cgi-bin/mailman/listinfo/libraries
>