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

The paper builds on both a simply typed 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 extensions and PTWP are studied that are closed under scvr. The twist are certain type 1 G?del recursors for simultaneous partial primitive recursion. Formally, denotes a function , however, is modelled such that is finite, or in other words, a partial sequence. As for PTWP, the concept of type writable variables is introduced, providing the possibility of creating and manipulating partial sequences. It is shown that the PTWP-computable functionals coincide with those definable in plus a constant for sequential minimisation. In particular, the functionals definable in denoted can be characterised by a subclass of PTWP-computable functionals denoted . Moreover, hierarchies of strictly increasing classes in the style of Heinermann and complexity classes are introduced such that . These results extend those for and PTWP Nig94]. Finally, scvr is employed to define for each type the enumeration functional of all finite elements of . Received January 30, 1996