<div dir="auto">dup and dedup? Just throwing out names. Not sure I'm a fan of diag/coding.</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Thu, Sep 17, 2020, 00:10 Emily Pillmore <<a href="mailto:emilypi@cohomolo.gy">emilypi@cohomolo.gy</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div><div><div style="display:none;border:0px;width:0px;height:0px;overflow:hidden"><img src="https://r.superhuman.com/3r14CnCTXU-TxCRPiwrkQu_w0cAF3YU9bv5_i65gk9voWtLnXhEx7uUH5nJscmv99rJ7HovTT1N9uHcCbXiNwxbV6V0wLMk5xh9QgslZauMhkMXYIazmUoCBJhMLUPUTA1M4i_1VsPNb0b6diXL8LsuOursIbiXXT7zwAx8P1l8sk_xOSD5EG80.gif" alt=" " width="1" height="0" style="display:none;border:0px;width:0px;height:0px;overflow:hidden"></div><div><div><div>Proposing the following names then to start, and we can talk about expanding this at a later date: <br><br>```</div><div>-- In Data.Tuple<br></div><div>diag :: a → (a,a)<br>diag a = (a, a)</div><div><br>-- In Data.Either<br>codiag :: Either a a → a<br>codiag = either id id</div><div>```<br></div><div><br></div><div>Thoughts?<br></div><div>Emily<br><br></div></div><br><div></div></div><br><div><div class="gmail_quote">On Thu, Sep 17, 2020 at 12:55 AM, Asad Saeeduddin <span dir="ltr"><<a href="mailto:masaeedu@gmail.com" target="_blank" rel="noreferrer">masaeedu@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="gmail_extra"><div class="gmail_quote" id="m_-8013011829333495463null"><p>`Either a a -> a` is another very handy operation. That and `a
-> (a, a)` together make up 90% of use cases for `duplicate ::
p x (t x x)`.<br>
</p>
<div>On 9/17/20 12:49 AM, Edward Kmett
wrote:<br>
</div>
<blockquote type="cite">
<div dir="ltr">For what it's worth, I'd just like to see a
no-nonsense
<div><br>
</div>
<div><font face="monospace">dup : a -> (a,a)</font></div>
<div><font face="monospace">dup a = (a,a)</font></div>
<div><br>
</div>
<div>in <font face="monospace">Data.Tuple</font>, where it is
out of the way, but right where you'd expect it to be when
looking for something for working with tuples.</div>
<div><br>
</div>
<div>Yes, <font face="monospace">bipure</font> and <font face="monospace">id &&& id</font> exist, and
generalize it on two incompatible axes, and if we had a proper
cartesian category we'd be able to supply this in full
generality, as a morphism to the diagonal functor, but all of
these require a level of rocket science to figure out.</div>
<div><br>
</div>
<div>I'd also happily support adding the equivalent in <font face="monospace">Data.Either</font> for <font face="monospace">Either a a -> a</font>, which invites
bikeshedding names.</div>
<div><br>
</div>
<div>-Edward</div>
</div>
<br>
<div class="gmail_quote">
<div class="gmail_attr" dir="ltr">On Wed, Sep 16, 2020 at 6:10
PM Emily Pillmore <<a href="mailto:emilypi@cohomolo.gy" rel="noopener noreferrer noreferrer" target="_blank">emilypi@cohomolo.gy</a>> wrote:<br>
</div>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote">
<div>
<div>
<div>
<div>
<div>
<div>Just to clarify, that's not the "real" diagonal
in the space, but it is a super useful translation
that I'd like for free :)</div>
</div>
<br>
</div>
<br>
<div>
<div class="gmail_quote">On Wed, Sep 16, 2020 at 9:08
PM, Emily Pillmore <span dir="ltr"><<a href="mailto:emilypi@cohomolo.gy" rel="noopener noreferrer noreferrer" target="_blank">emilypi@cohomolo.gy</a>></span>
wrote:<br>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote">
<div class="gmail_extra">
<div id="m_-8013011829333495463gmail-m_7220689800887981291null" class="gmail_quote">
<div>
<div>
<div>
<div>@Asad that's a perfectly reasonable
way to think about diagonal
operations: as the data of a cartesian
monoidal category, and the laws are
correct in this case. I think we can
get away with the additional
abstraction to `Biapplicative` in this
case, though.<br>
</div>
<div><br>
</div>
<blockquote>
<div style="text-decoration:none">
<div style="text-decoration:none">
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<p style="margin:0px">wouldn't
the existence of
appropriate
`forall a. a ->
t a a` and `forall
a. x -> Unit t`
functions
pigeonhole it into
being "the"
cartesian monoidal
structure on
`->` (and thus
naturally
isomorphic to
`(,)`)?<br>
</p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</blockquote>
<div>
<div><br>
</div>
<div>Only if you chose that particular
unit and that particular arrow. But
there are other places where having
a general `Biapplicative` contraint
would make it useful. For example,
i'd like to use this in `smash`
with `diag :: a → Smash a a`,
defining the adjoining of a point to
`a` and creating a diagonal in the
subcategory of pointed spaces in
Hask, so that I don't have to
redefine this as `diag' = quotSmash
. view _CanIso . diag . Just`. <br>
</div>
<div><br>
</div>
<div>Cheers,<br>
</div>
<div>Emily</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
</div>
<div><br>
</div>
</div>
<br>
</div>
<br>
<div>
<div class="gmail_quote">On Wed, Sep 16,
2020 at 6:35 PM, Asad Saeeduddin <span dir="ltr"><<a rel="noopener noreferrer noreferrer" href="mailto:masaeedu@gmail.com" target="_blank">masaeedu@gmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
<div class="gmail_extra">
<div class="gmail_quote" id="m_-8013011829333495463gmail-m_7220689800887981291null">
<p>Whoops, I just realized I've
been responding to Carter
specifically instead of to the
list.<br>
<br>
I was having some trouble
understanding the `unJoin` stuff
but I read it a few more times
and I think I understand it a
little better now.<br>
<br>
In my personal experience the
"abstracted version" of `x ->
(x, x)` I use most often looks
like this:<br>
<br>
```<br>
</p>
<pre>class SymmetricMonoidal t i p => CartesianMonoidal t i p</pre>
<pre> where</pre>
<pre> duplicate :: p x (x `t` x)</pre>
<pre> discard :: p x i
</pre>
<pre>-- Laws:</pre>
<pre>-- duplicate >>> first discard = fwd lunit</pre>
<pre>-- duplicate >>> second discard = fwd runit
</pre>
<pre>-- where</pre>
<pre>-- lunit :: Monoidal t i p => Iso p x (i `t` x)</pre>
<pre>-- runit :: Monoidal t i p => Iso p x (x `t` i)</pre>
<p>```<br>
<br>
i.e. adding a suitable duplicate
and discard to some symmetric
monoidal structure gives us a
cartesian monoidal structure.<br>
<br>
This doesn't really seem to be
relevant to what you folks are
looking for, but it does bring
up a question. If some
`Bifunctor` `t` happens to form
a monoidal structure on `->`,
wouldn't the existence of
appropriate `forall a. a -> t
a a` and `forall a. x -> Unit
t` functions pigeonhole it into
being "the" cartesian monoidal
structure on `->` (and thus
naturally isomorphic to `(,)`)?</p>
<div>On 9/16/20 5:26 PM, Emily
Pillmore wrote:<br>
</div>
<blockquote type="cite">
<div>
<div>
<div>
<div>
<div>Nice! <br>
<br>
That's kind of what I
was going for with
Carter earlier in the
day, thanks Matthew. </div>
<div><br>
</div>
<div>I think a
diagonalization
function and functor
are both very sensible
additions to
`bifunctors` and
`Data.Bifunctor`. The
theory behind this is
sound: The
diagonalization
functor Δ: Hask →
Hask^Hask, forms the
center of the adjoint
triple `colim -| Δ -|
lim : Hask →
Hask^Hask`. <br>
<br>
Certainly the function
`diag :: a → (a,a)` is
something I've seen
written in several
libraries, and should
be included in
`Data.Tuple` as a
`base` function. The
clear generalization
of this function is
`diag :: Biapplicative
f ⇒ a → f a a`. I'm in
favor of both existing
in their separate
capacities. </div>
<div><br>
</div>
<div>Thoughts? <br>
</div>
<div><br>
</div>
<div>Emily</div>
</div>
<br>
</div>
<br>
<div>
<div class="gmail_quote">On
Wed, Sep 16, 2020 at
3:49 PM, Carter
Schonwald <span dir="ltr"><<a href="mailto:carter.schonwald@gmail.com" rel="noopener noreferrer noreferrer" target="_blank">carter.schonwald@gmail.com</a>></span>
wrote:<br>
<blockquote style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex" class="gmail_quote">
<div class="gmail_extra">
<div id="m_-8013011829333495463gmail-m_7220689800887981291null" class="gmail_quote">
<div dir="auto">Is
the join bipure
definition
taking advantage
of the (a->)
monad instance?
Slick!</div>
<div dir="auto"><br>
</div>
<div dir="auto"><br>
</div>
<div>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On
Wed, Sep 16,
2020 at 3:39
PM Matthew
Farkas-Dyck
<<a rel="noopener noreferrer noreferrer" href="mailto:strake888@gmail.com" target="_blank">strake888@gmail.com</a>> wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">We also have<br>
<br>
<br>
<br>
diag = join
bipure<br>
<br>
<br>
<br>
and (in
pseudo-Haskell)<br>
<br>
<br>
<br>
diag = unJoin
. pure<br>
<br>
where<br>
<br>
newtype
Join f a =
Join { unJoin
:: f a a }
deriving
(Functor)<br>
<br>
deriving
instance
Biapplicative
f =>
Applicative
(Join f)<br>
<br>
<br>
<br>
The latter
seems on its
face
potentially
related to the
instance for<br>
<br>
lists of fixed
length, but i
am not sure
how deep the
connection may<br>
<br>
be.<br>
<br>
</blockquote>
</div>
</div>
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