Re: [Haskell-cafe] Re: Laws and partial values

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 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 wrote:

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On 24 Jan 2009, at 22:19, Henning Thielemann wrote:

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On Sat, 24 Jan 2009, Thomas Davie wrote:

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On 24 Jan 2009, at 21:31, Dan Doel wrote:

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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

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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

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value in that type is (); bottom for pairs would be (_|_, _|_), as all

became the pairs

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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

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