John Cowan wrote:

> = and < have to work together, and it does say that = must be transitive.

The above was clear to me in the SRFI, and is somewhat tangential to my
question, which is essentially: Are partial orders allowed?

> The whole point of comparators is to define a total order.

This answers that question.  It is probably a reasonable design choice,
and certainly the prerogative of the SRFI author.  However, it would be
very helpful if the SRFI were very explicit in this regard.

(Although there are a few mentions of total order in the draft, and they
do suggest that a required total order may be the intent, I did not read
them to specifically *require* a total order; rather, I read them to
require certain behavior *if* a total order exists.  In particular, the
other specific requirements, such as irreflexivity, transitivity, and
asymmetry do not imply a total order.  In any case, it seems to be an
important enough point to be made more prominent, and a single sentence
similar to the quoted one above placed early in the document would be
all that's needed to clarify things.

I will mention also that it may be useful to consider comparators that
reflect underlying partial (not total) orders.  A textbook use case
would be using a sorting library (that uses comparators) to sort plane
tickets that are only partially ordered by preference: x is better than
y if x is both a cheaper and a shorter flight than y.  (Of course, the
partial order can be mapped to a total order that is consistent with it,
but it seems like an artificial extra step in examples such as this
one.)

Regards,

-chaw