Extending Gg Odel for Expressing Restricted Quantiications and Arrays

The expressiveness of the declarative language G odel can be improved by adding to it bounded quanti cations, i.e., quanti cations over nite domains, and arrays. Many problems can be expressed more concisely using bounded quanti cations than using recursion. Arrays are natural for many applications, e.g., in scienti c computing, and are conveniently used in bounded quanti cations. Treating bounded quanti cations di erently from other quanti cations also reduces oundering, allows e cient sequential execution and enables e cient parallel execution on various architectures. In extending Godel to allow bounded quanti cations, the niteness condition would be di cult to implement. Thus the extension de ned in this paper allows restricted quanti cations where the domain can be restricted, but not necessarily nite.