Allow the use of order-dependence to disambiguate symbol variants

[Enivex]

Let me first say: This is not a proposal to make symbol names order-dependent in general. Only variants where order is needed for disambiguation would be order-dependent.

Currently, ⪋ and ⪌ are lt.gt.equiv and gt.lt.equiv. However, the symbols ⪑ and ⪒ also exist, but have not yet been named. In order to name these in our current scheme, one would need to invent yet more unnatural modifiers.

With this proposal, we would be able to distinguish between

lt.equiv.gt ⪋
lt.gt.equiv ⪑
gt.equiv.lt ⪌
gt.lt.equiv ⪒

It would also enable #75 without abusing submodules, assuming we also get #94.

(Not to mention there are examples of current naming that could potentially be improved with this proposal, such as for arrows.)

[knuesel]

Thinking about what the alternatives would be, we could put these symbols under eq and add a modifier for the position of the equal sign:

eq.lt.gt ⪋
eq.lt.gt.bottom ⪑
eq.gt.lt ⪌
eq.gt.lt.bottom ⪒

though it's maybe not obvious what "bottom" applies to.

Edit: that doesn't make sense actually

[Enivex]

Thinking about what the alternatives would be, we could put these symbols under eq and add a modifier for the position of the equal sign:

eq.lt.gt ⪋
eq.lt.gt.bottom ⪑
eq.gt.lt ⪌
eq.gt.lt.bottom ⪒

though it's maybe not obvious what "bottom" applies to.

If all we care about is giving unique names, then yes, but this completely loses the meaning of each symbol.

[knuesel]

and it's just wrong, I mean eq.lt.gt and eq.gt.lt cannot both exist if order doesn't matter (I don't know what I was thinking).

[Enivex]

That too

[Enivex]

We could also use this to potentially get rid of neq, nequiv, napprox and ntilde.

As in lt.eq.not vs lt.not.eq

[MDLC01]

I don't think this would be a good idea. .neq is fine imo.

I think we should keep modifier order dependence to distinguish symbols that are constituted of multiple identical parts in different orders (e.g., ⪋ and ⪑). We shouldn't use it as a way for modifiers to modify other modifiers.