A restricted computation model on Scott domains and its partial primitive recursive functionals (Q1283120)

The paper builds on both a simple term system and a computation model on Scott domains via so-called parallel typed while programs (PTWP). The former provides a notion of partial primitive recursive functional on Scott domains, supporting a suitable concept of parallelism. Computability on Scott domains seems to entail that Kleene's Schema of higher-type simultaneous course-of-values recursion (SCVR) is not reducible to partial primitive recursion. So two extensions are studied and characterized that are closed under SCVR. Moreover, hierarchies of strictly increasing classes are built upon these extensions. Finally, SCVR is employed to define for each type the respective enumeration functional of all finite elements of its Scott domain.