26 Apr
2010
26 Apr
'10
7:16 p.m.
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'?
YES! 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.)