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

The paper builds on both a simply typed term system PRω 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 Dρ 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 PRωe and PTWPe are studied that are closed under scvr. The twist are certain type 1 G¨odel recursors Rk for simultaneous partial primitive recursion. Formally, RkgHxi denotes a function fi ∈ Dι→ι, however, Rk is modelled such that fi is finite, or in other words, a partial sequence. As for PTWPe , the concept of type ι → ι writable variables is introduced, providing the possibility of creating and manipulating partial sequences. It is shown that the PTWPe -computable functionals coincide with those...

• Type: Journal
• Year: 1998
• Where: AML
• Authors: Karl-Heinz Niggl
• Keywords: AML 1998, Partial Primitive Recursion, Primitive Recursive Functional, PTWPe -computable Functionals