Categories for fixpoint semantics

A precise meaning is given to general recursive definitions of functionals of arbitrarily high type, including non-deterministic definitions. Domain equations involving products, sums, powers and functor domains are solved. The use of categories with ω-colimits as semantic domains is investigated and it is shown that such categories provide a general construction for power-domains and that no such construction can be obtained with partial orders. Initial fixpoints of continuous functors on such categories are defined and studied. They provide a meaning for recursive definitions of the type x:=f(x). The category of domains is defined and shown to possess ω-colimits. Initial fixpoints of continuous functors on the category of domains provide the solution to domain equations. The product, sum, power and functor domain of domains are defined and studied. Product, sum, power and functor domain are proved to be continuous functors in the category of domains