On the Representation of Stream Functions in Denotational Domains

Colin Riba (1, 2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages

We investigate the representation of functions on streams in some denota- tional domains. As expected, a total continuous stream function can always be represented by a Scott-continuous function, and moreover by a strongly stable map in the corresponding Hypercoherence. It seems however difficult to represent an arbitrary stream function by a monotone map on Scott domains such that the stream function is continuous if and only if its representant is Scott-continuous. The difficulty is that the set of Scott-approximants of an open subset of a not (topologically) compact set of streams may not be Scott-open. We show that this problem does not occur in the compact case.

Domaines: Logique en informatique [cs.LO]

Colin Riba. On the Representation of Stream Functions in Denotational Domains. 2011. ⟨hal-00617624⟩