[Haskell-cafe] Hyper-recursion?

[Anthony Clayden]

>> On 16 Jan 2017 04:43, "Lawrence Bottorff" <borgauf at
gmail.com> wrote:
>>
>> A while back I worked at an assessor's office, i.e., the
people responsible
>> for handling properties as land parcels. ...

Hi Lawrence, I too worked on land parcels -- a local
government rates billing 
and land valuation application.

>> ... how property changed hands, and especially how
property lines
>> changed due to properties either merging or being split
up. 
>> That is to say, how the parcel map changed over time.

I think the important aspect is that the a parcel
can be split, and one of the splits merged with another
parcel
that was not originally with it.

(I don't know how it was in your application. but in mine
 a legal parcel might consist of discontiguous areas of land
 -- for example a house in a terrace parcelled with a garage
amongst
 a block of garages at the end of the street,)

That is, looking over history you cannot group the parcels
into a
strict hierarchy of splits.

>> Somewhere in the functional paradigm, specifically
recursion,
>> would seem to be a model for this issue. 

No I'm not seeing anything specifically functional about
this.
It's a directed graph, where each node is an instance of
parcel ownership.

>> So in chapter 1 of any functional programming tutorial is
the factorial
>> calculation function done with recursion. We beginners
see the recursion
>> "going out" to the "last one," then "coming back," adding
up the results of
>> each stage as it returns . . . like a yo-yo winding out,
>> then winding up again.

Nice image, but there's no "last one" here (nor a "first
one"
that we could make sense of), There's no boundary
from where we could be "coming back".

Recursion does not apply [see more below]

>> David Turner dct25-561bs at mythic-beasts.com 
>> Mon Jan 16 07:47:41 UTC 2017
>>
>> I suspect you have stumbled onto the dual concept of
corecursion: ...

Nor corecursion.

a) because of the infinite and arbitrary potential for
splits/mergers;
b) because even if there was some time in the distant past
    when the whole country was a single parcel with a single
owner.
    (The Emperor? But even empires and countries split and
merge.
     Or no owner, only hunter-gatherers/nomads,
     which might as well be a single parcel.)
    We're never going to try to rebuild that history.
c) because there's never going to be a future end-state.
    Arbitrary splits/mergers will continue forever.
    We can't predict what might be the smallest parcels
    some area of land could be split into.
    (Note that one trick to prevent mineral exploitation
companies
     from buying up glorious scenery
     is to split it into $1-parcels and sell each to a
different owner.)


>> ... Haskell being the most pure functional language, is,
hence,
>> my starting point on this question. 

There's nothing specifically Haskell in this.
A better place to ask might be lambda-the-ultimate.


Anthony