# Diagonalization/ dupe for monads and tuples?

Jon Purdy evincarofautumn at gmail.com
Thu Sep 17 17:20:04 UTC 2020

```I’m inclined against anything to do with higher tuples than pairs,
honestly. If there’s a real demand for it at some point, we can certainly
consider it, but pairs are vastly more common, and I’ve only ever wanted or
seen people wanting the ‘a → (a, a)’ version in practice.

Generally speaking, I see ≥3-tuples as a sign of a missing data type, and I
think I’m in likeminded company here.

If I really had my way, we’d make (,) a right-associative operator in both
values and types, so (a, b, c) = (a, (b, c)), and accessor functions could
work on any size of tuple.

I would also expect these functions to be called dup, dup3, dup4, &c. by
analogy with other tuple functions using that convention (e.g. zip, zip3).

On Thu, Sep 17, 2020, 10:03 AM David Feuer <david.feuer at gmail.com> wrote:

> Does dup come with trip, quadrup, etc.? It doesn't have to, but once you
> plug one hole the others nearby start to stand out.
>
> On Wed, Sep 16, 2020, 1:58 PM Carter Schonwald <carter.schonwald at gmail.com>
> wrote:
>
>> It was pointed out to me in a private communication that the tuple
>> function \x->(x,x) is actually a special case of a diagonalization for
>> biapplicative and some related structures monadicially.  Another example in
>> the same flavor is pure impl for the applicative instance for sized lists.
>>
>> diag x = bipure x x
>>
>> So framed a litttle differently, there’s definitely an abstraction or
>> common pattern lurking here. Perhaps folks can help Tease this out. One
>> person I chatted with this morning alluded to it being relevant to
>> computational flavors of adjunctions or some such ? It def matters in a
>> different way when doing computation resource aware programming in a
>> symmetric monoidal category.
>>
>> Let’s collect some ideas and patterns and get to the bottom of this!
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