Hm. Isn't _|_ simply, by definition, the bottom (least) element in an ordering? I see merit in Haskell's choice that () /= _|_, but so far I'm not persuaded that it's the only possible choice.
On Sat, Jan 24, 2009 at 1:47 PM, Lennart Augustsson <lenn...@augustsson.net>wrote: > You can dream up any semantics you like about bottom, like it has to > be () for the unit type. > But it's simply not true. I suggest you do some cursory study of > denotational semantics and domain theory. > Ordinary programming languages include non-termination, so that has to > be captured somehow in the semantics. > And that's what bottom does. > > -- Lennart > > On Sat, Jan 24, 2009 at 9:31 PM, Thomas Davie <tom.da...@gmail.com> wrote: > > > > On 24 Jan 2009, at 22:19, Henning Thielemann wrote: > > > >> > >> On Sat, 24 Jan 2009, Thomas Davie wrote: > >> > >>> On 24 Jan 2009, at 21:31, Dan Doel wrote: > >>> > >>>> For integers, is _|_ equal to 0? 1? 2? ... > >>> > >>> Hypothetically (as it's already been pointed out that this is not the > >>> case in Haskell), _|_ in the integers would not be known, until it > became > >>> more defined. I'm coming at this from the point of view that bottom > would > >>> contain all the information we could possibly know about a value while > >>> still being the least value in the set. > >>> > >>> In such a scheme, bottom for Unit would be (), as we always know that > the > >>> value in that type is (); bottom for pairs would be (_|_, _|_), as all > pairs > >>> look like that (this incidentally would allow fmap and second to be > equal on > >>> pairs); bottom for integers would contain no information, etc. > >> > >> Zero- and one-constructor data types would then significantly differ > from > >> two- and more-constructor data types, wouldn't they? > > > > Yes, they would, but not in any way that's defined, or written in, the > fact > > that they have a nice property of being able to tell something about what > > bottom looks like is rather nice actually. > > > > Bob > > _______________________________________________ > > Haskell-Cafe mailing list > > Haskell-Cafe@haskell.org > > http://www.haskell.org/mailman/listinfo/haskell-cafe > > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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