>>> The notes d♯ to e♭ have different pitches in the staff notation
>>> system, which cannot express E12 enharmonic equivalents, so this
>>> is slur. So it should be a slur that looks like slur.
I disagree. For all practical purposes in standard classical music,
enharmonic equivalents *do* sound the same. What you are referring to
IMHO is a special case that might be controlled by a flag.
> I can think of special cases: Perhaps the tie and the slur are
> rendered slightly differently, say of different thickness, so in
> Werner's example it should be a tie in style. Somebody might want
> to indicate an E12 enharmonic equivalence, as in your example, even
> though it is not so in the staff notation system, and then it should
> be a tie in style.
As mentioned above: This might be controlled by a flag. Or maybe a
special “E12_tie_slur” engraver can handle this.
Werner