Twenty-Five Years of Domain Theory

Dana S Scott ( Hillman University Professor of Computer Science, Mathematical Logic and Philosophy, Carnegie Mellon University, Pittsburgh, Pennsylvania )

While visiting the late Christopher Strachey in Oxford during the fall of 1969, I tried to convince him that it made more sense to replace the formal -- and in my view, ad hoc -- interpretations of programming languages with which he was experimenting with a semantics based on appropriate mathematical models. The proposal was to take the cue from recursive function theory and the way partial recursive functionals had been treated. To make the argument convincing, a theory of models had to be set out that would provide all the necessary structures that the applications demanded. This was -- for me -- how domain theory was started. What was completely unexpected was: (i) how many domains would be found, (ii) how fairly simply models for the untyped lambda calculus would come out of the study, and (iii) how many difficulties would come to light. The lecture will review some of the basic definition, the subsequent history, and try to sketch something of the scope of work of the current, very active, world-wide research community.

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A written version of the lecture is being prepared for the Proceedings of the 10th International Conference of Logic, Methodology, and Philosophy of Science, August 1995, Florence, Italy.