<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto"><div></div><div><div><span style="background-color: rgba(255, 255, 255, 0);">Genuinely curious: can people point to specific examples in their (or others') code where the ((,) a) instance for Foldable is really helpful and difficult to replace?</span></div><div><span style="background-color: rgba(255, 255, 255, 0);"><br></span></div><div><span style="background-color: rgba(255, 255, 255, 0);">Tom</span></div></div><div><span style="background-color: rgba(255, 255, 255, 0);"><br></span></div><div><br>El 9 abr 2017, a las 09:29, Benno Fünfstück <<a href="mailto:benno.fuenfstueck@gmail.com">benno.fuenfstueck@gmail.com</a>> escribió:<br><br></div><blockquote type="cite"><div><div dir="ltr">Correct me I I'm wrong but I believe Tony Morris is saying the following:<div><br></div><div>* not every operation defined for the integers "makes sense" for all integers. Example: '/' does not make sense in the case of 'x / 0'</div><div>* yet, we still include '0' in the integers even though not every operation makes sense for '0'</div><div>* -> not every operation in Foldable makes sense for `(,) a`</div><div>* -> but we also include `0` in the integers, so "not every operation makes sense" is not an argument to exclude `(,) a` from being foldable,</div><div> just as `0` is not excluded from the integers.</div><div><br></div><div>Kind regards,</div><div>Benno</div></div><br><div class="gmail_quote"><div dir="ltr">Tony Morris <<a href="mailto:tonymorris@gmail.com">tonymorris@gmail.com</a>> schrieb am So., 9. Apr. 2017 um 14:26 Uhr:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">These two things are true:<br class="gmail_msg">
<br class="gmail_msg">
* 0 is in the set of integers<br class="gmail_msg">
* ∀ a. ((,) a) is Foldable, and as one of many consequences, the length<br class="gmail_msg">
of all values in the set ∀ a. ((,) a) is 1.<br class="gmail_msg">
<br class="gmail_msg">
There are four possible positions to take on these claims:<br class="gmail_msg">
<br class="gmail_msg">
1. Both are true.<br class="gmail_msg">
2. Both are false.<br class="gmail_msg">
3. The first true and second false.<br class="gmail_msg">
4. The second true and the first false.<br class="gmail_msg">
<br class="gmail_msg">
I respect arguments 1 and 2. If I chose 1 and you chose 2, I'd say "well<br class="gmail_msg">
rightio then mate and cheers to that", we'd clink glasses and move on.<br class="gmail_msg">
Same if it were vice versa.<br class="gmail_msg">
<br class="gmail_msg">
I do not have the same respect for positions 3 and 4.<br class="gmail_msg">
<br class="gmail_msg">
On 09/04/17 19:48, Jon Fairbairn wrote:<br class="gmail_msg">
> Tony Morris <<a href="mailto:tonymorris@gmail.com" class="gmail_msg" target="_blank">tonymorris@gmail.com</a>> writes:<br class="gmail_msg">
><br class="gmail_msg">
>> I don't think it is the "appropriate" set. It's an example. 0 is in the<br class="gmail_msg">
>> set of integers. The value 0 is in many sets.<br class="gmail_msg">
> OK, so I clearly do not understand your argument. The<br class="gmail_msg">
> implication I took from “and 0 is not an integer” is that the<br class="gmail_msg">
> foldable instance for ((,) a) should be present because it is<br class="gmail_msg">
> the zero case of something that has integers as its domain, and<br class="gmail_msg">
> I wanted to know what that something is. If this was not the<br class="gmail_msg">
> intention of your argument, what was?<br class="gmail_msg">
><br class="gmail_msg">
<br class="gmail_msg">
<br class="gmail_msg">
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