On Fri, Dec 9, 2022 at 1:57 PM Marc Nieper-Wißkirchen <marc.nie...@gmail.com> wrote:
> \ > > I agree that the perfect terminology hasn't been found. > There is no such thing as perfect terminology: it is all arbitrary or imprecise or both. "The price of infinite precision is infinite verbosity." > one for setoids, one for totally ordered setoids, and one for setoids > with a hash function (with forgetful functors from the latter two to > the first). > I think this is the wrong analysis. If there is no equality predicate, then there is no meaningful comparator at all: it makes no sense to ask "Does electron A come before electron B?" given that electrons lack identity. So we have two properties and therefore four cases: neither orderable nor hashable, orderable but not hashable, hashable but not orderable, and both hashable and orderable. The reason for setting up the Comparator typeclass as I did is that most Scheme objects are both orderable and hashable (with the usual exceptions of procedures, ports, etc), although the order is not necessarily a semantically meaningful order. In many cases, such as B-trees, it doesn't matter what the order is as long as there is one. The same is true of hash functions mutatis mutandis. So all the cases except "orderable and hashable" are more or less degenerate. So ather than burdening users with the necessity of specifying an ordering predicate and/or a hash function that aren't going to be useful in their particular use cases, I allow them to specify simply #f and then throw an error if that is inadequate. I hope this is helpful.
