On the Interpretation of Scott's Domain

The lattice-theoretic approach to the theory of computation, developed by D. Scott, is based on assumptions that the data spaces manipulated by a computation are complete lattice whose partial ordering represents a notion of approximation, and that the computable functions between such data spaces are continuous (in an appropriate sense). Since these assumptions lead to conclusions which are quite different from the concentional theory of computation, it is important to understand their intepretation in terms of actual computational process.