On 2006-12-13, Tom Lane <[EMAIL PROTECTED]> wrote: > I wrote: >>>> Right offhand I cannot see a reason why there should be different >>>> equality operators with the same sortops. (If anyone can come up with >>>> a plausible scenario for that, stop me here...) > > BTW, I think it's possible to prove that there need never be two for the > case of both sides the same datatype. If we have a sortop "A < B" on a > single datatype, then its commutator is well defined: "A > B" if and > only if "B < A". And by the trichotomy law, "A = B" must be true in > exactly those cases for which neither "A < B" nor "A > B". So there is > only one possible behavior for an equality operator that is consistent > with the sortop.

Counterexample even for a single data type: define an operator x =* y which is true when 2x = y. This is mergejoinable using the following operators: SORT1 = <, SORT2 = <, LTCMP = (2x < y), RTCMP = (2x > y) (which is of course the same sortops as for regular =). The LTCMP and GTCMP operators imply a unique join operator due to trichotomy, but this is not true for the sortops. While the above is a bit contrived, I think non-contrived examples could be found too. -- Andrew, Supernews http://www.supernews.com - individual and corporate NNTP services ---------------------------(end of broadcast)--------------------------- TIP 1: if posting/reading through Usenet, please send an appropriate subscribe-nomail command to [EMAIL PROTECTED] so that your message can get through to the mailing list cleanly