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Quoting @MatthewDaggitt
I too would like to do something about the ˘ syntax, even though I introduced it
I really hate it: it's difficult to type, it ruins the alignment of proofs and doesn't clearly convey symmetry to me.
Here are a few proposals to get the discussion going:
_↑≡⟨_⟩_
and_↓≡⟨_⟩_
, stolen from the categories library (at least they used to be there when I used it way back). The arrow indicates the direction in which we are applying the equality._↑⟨_⟩_
and_↓⟨_⟩_
as shorter alternatives.
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JacquesCarette commentedon Apr 3, 2020
I like the shorter alternatives. If we have to put in the relation wrt which we're working, I'm wondering about putting it in the other order, i.e.
_≡↑⟨_⟩_
.I think having these as aliases (or the current ones as aliases) could be an interesting experiment. Let a couple of versions go by, and see what people tend to use the most, then deprecate the other.
dylanede commentedon Apr 3, 2020
+1 for putting the direction indicator after the relation symbol.
Regarding the direction indicator, would horizontal arrows (of some style) make more sense or be more likely to be confused with the many other uses of horizontal arrows?
ajrouvoet commentedon Apr 4, 2020
Equality reasoning proves are usually code-set vertically. 🤷♂️
MatthewDaggitt commentedon Apr 26, 2020
I like the idea of vertical arrows. My only comment is that I also like having the angle brackets aligned on the page, which is one of things that I find very distressing about the current sym notation. This proposal would partially fix it as the sym and non-sym-ed versions would now align, but it still wouldn't align with other operators, e.g. inequalities:
Would people hate it if we moved the arrows inside the brackets? i.e.
_≡⟨↓_⟩_
and_≡⟨↑_⟩_
WolframKahl commentedon Apr 26, 2020
Yes. 😉
If you want them inside, you can also define
↓_ = ≡-sym
with appropriate low precedence.Having the arrows after the closing hint bracket looks more acceptable to me:
Or, even better: 😉
JacquesCarette commentedon Apr 26, 2020
I also would dislike the arrows inside the brackets. Having them after is better than inside [though not necessarily the best choice].
gallais commentedon Apr 26, 2020
A trailing character at the far right of the line is easy to miss. We dismissed
this possibility last time around for this reason.
What about a modified
≡
? I see⩧
("identical with dot above") exists.Or if we want to merge the idea of an arrow and an equality sign, we have the
pair
≙
and≚
that could play this role and still be only 1 character. I am nottoo happy about the fact that they are not derived from
≡
though. 😞Note that
⩪
exists! I could not find≈
with a dot but for some reasonthere's
⩯
and even weirder stuff such as⥵
⭊
. WTF unicode?!We do have
⩭
but that's not the blessed setoid symbol. :/ajrouvoet commentedon May 7, 2020
Yeah I think using different symbols to denote the same equality is more confusing than necessary.
It looks like we're mixing pragmatics and aesthetics. The pragmatics seem to be:
Additionally it would be nice if it is notation that is portable to other reasoning combinators?
ajrouvoet commentedon May 7, 2020
Oh, that is embarrassing, there is standard notation for this!
jamesmckinna commentedon Sep 20, 2022
A (perhaps mischievous) thought:
_≡⟩_⟩_
_≡⟨_⟩_
The tragedy is that it clashes with our existing conventions (sigh ;-)), but it has always seemed to me a cognitive overload to insist that
\langle,\rangle
function merely as parentheses, on top of which we then (discuss how best to) attempt to overlay an additional directional indicator: they're directional already!The tragedy is compounded by the choices for
_≤⟨_⟩_
etc., ... so my suggestion would be to (go against the tide ;-)) and invert theorderdirection of the above suggestions, and simply write_≡⟩_⟩_
for uses ofsym
... the point being to have it stick out, yet not violate the otherwise ambient typograhical/layout conventions.jamesmckinna commentedon Oct 26, 2022
On second thoughts, it seems that I prefer to reverse the 'bracket orientation':
_≡⟩_⟩_
for LHS to RHS appeal to an equation_≡⟨_⟨_
for thesym
direction...I'll fix this up when I'm not writing on my phone...
DONE. I was nearly there above, but now I think I'm happy. But we still won't make that change, alas... :-(
MatthewDaggitt commentedon Apr 26, 2023
I really like this suggestion 👍 The only one I've seen I'd be happy implementing! And it would be backwards compatible as we could leave the old names in place.
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