Van: to...@tuxteam.de Verzonden: maandag 9 december 2024 21:38 Aan: Mikael Djurfeldt CC: Stefan Schmiedl; guile-user@gnu.org Onderwerp: Re: sorted?
>On Mon, Dec 09, 2024 at 08:45:33PM +0100, Mikael Djurfeldt wrote: >> On Mon, Dec 9, 2024 at 8:23 PM <to...@tuxteam.de> wrote: >> >> > (lambda (p1 p2) (< (car p1) (car p2))) >> > >> > Then you'd need a corresponding equal, because otherwise you >> > end up with things which are neither less nor equal nor greater, >> > i.e. the ordering isn't total, which is bad for sorting :) >> > >> >> `sort' assumes that the elements belong to a "strict total order", which >> means that the connectedness-axiom is true, which means that a = b is >> *equivalent to* not (a < b or a > b). So, we don't need equal. > >I think we need one of = or >, which we both don't have. We just have <, which is one too few. You do have >, ‘a > b’ is the same as ‘b < a’. This usually isn’t mentioned in the axioms of orderings because it’s simply notation – whenever you mirror the symbol of a binary relation, that is simply notation for swapping the arguments (in logic those would be called terms I think) (a < b = b > a). >From ‘<’, you have ‘=’, by the equivalence mentioned above. Just because it’s not passed explicitly, doesn’t mean you don’t have it – you can derive ‘=’ from the axioms and some logic. Did you see my previous mail, where I said pretty much the same as what Tomas is writing (except about sorted? instead of sort)? Best regards, Maxime Devos
