Talk:Domain theory

"Computations that have not yet returned a result" are *not* "The 'result' of a computation that never ends." Does the bottom in domain theory denote "insufficient information about a computation (that is guaranteed to terminate)" or "divergence, never ends."? These are completely different things. — Preceding unsigned comment added by 86.82.44.193 (talk) 22:00, 11 December 2016 (UTC)Reply

The lead of the article alludes to "special kinds of partially ordered sets (posets) commonly called domains", but the article never seems to specify what a "domain" is later on. There is a section about "motivation and intuition", followed by a "guide to formal definitions", but I can't see anywhere a clear explanation of what a domain is. On the other hand, Giez et al. give a definition on p. 54 (a domain is a dcpo that is continuous as a poset). I am not familiar with that field, but would like to get a better idea about it. Shouldn't there be a clear def of domain somewhere in the article? PatrickR2 (talk) 07:55, 31 August 2022 (UTC)Reply

I find the sentences “Such a model would formalize a link between the lambda calculus as a purely syntactic system and the lambda calculus as a notational system for manipulating concrete mathematical functions. The combinator calculus is such a model. However, the elements of the combinator calculus are functions from functions to functions; in order for the elements of a model of the lambda calculus to be of arbitrary domain and range, they could not be true functions, only partial functions.” to be impenetrable. Is LC’s need for a semantics any different from other formalisms like FOL? Can the CC be a model for LC? Why isn’t CC also a “purely syntactic system”? The last sentence is especially difficult, in that the part after the ; is not obviously related to the however part, and moreover makes statements (“could not be…would have to be…”) without explanation or justification. — Preceding unsigned comment added by 73.238.169.75 (talk) 02:58, 5 December 2022 (UTC)Reply

I would prefer this section to actually talk about the main requirement from Computations, namely that the functions involved be partial recursive, or recursive (when total). Also when are the sets recursively enumerable? Domain theory introduces many mathematical constructs, such as these "compact" elements which are not even finite. So explain the connection with recursion theory to actually connect with computations. RoyMWiki (talk) 17:00, 18 April 2023 (UTC)Reply