[Haskell-cafe] and  = True; or  = False
ok at cs.otago.ac.nz
Mon Apr 26 19:16:16 EDT 2010
On Apr 27, 2010, at 12:15 AM, Bjorn Buckwalter wrote:
> Dear all,
> Does it make good sense that 'and ' returns 'True' and 'or '
> returns 'False'?
There is no other behaviour that would make sense.
You wouldn't expect sum  to return anything but 0, would you?
> What got me thinking about this was the apparently incorrect intuition
> that 'and xs' would imply 'or xs'.
Only if not (null xs).
See also Lisp and Scheme, where (AND) -> true, (OR) -> false,
and look up the behaviour of ∀ and ∃ in a logic book.
(∀x∈s)p(x) does NOT imply (∃x∈s)p(x) because s might be empty.
(This is where the modern ∀ and ∃ part company with Aristotelian
logic. In syllogisms, "all unicorns are white" does not count as
true unless there is at least one unicorn.)
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