On Sun, 2009-01-25 at 07:11 -0800, Jonathan Cast wrote:
On Sun, 2009-01-25 at 10:46 +0100, Thomas Davie wrote:
On 25 Jan 2009, at 10:08, Daniel Fischer wrote:
Am Sonntag, 25. Januar 2009 00:55 schrieb Conal Elliott:
It's obvious because () is a defined value, while bottom is not - per definitionem.
I wonder if this argument is circular.
I'm not aware of "defined" and "not defined" as more than informal terms.
They are informal. I could've written one is a terminating computation while the other is not.
Is that a problem when trying to find the least defined element of a set of terminating computations?
Yes. If you've got a set of terminating computations, and it has multiple distinct elements, it generally doesn't *have* a least element. The P in CPO stands for Partial.
Yes, "partial" as in "partial order" (v. total order or preorder) not as in partiality. It's actually the "complete" part that indicates the existence of a least element, pretty much by definition. A cpo is a dcpo (directed complete partial order) with a least element, though sometimes "cpo" is used for "dcpo" in which case a least element is not guaranteed.