lec22-fa06.pdfPages from Rudin-2.pdfPages from Rudin.pdfCS611 Lecture 22 Scott’s D∞Construction 20 October 2006Lecturer: Dexter KozenAs observed in Lecture 19, one of the problems with modeling the untyped λ-calculus is that we cannothave a nontrivial domain D isomorphic to its function space D → D be cause of c ardinality restrictions.However, Dana Scott showed that given any pointed CPO D, it is possible to embed D into a pointed CPOD∞that is isomorphic to its continuous function space [D∞→ D∞]. This construction allows us to give adenotational mo del of the untyped λ-calculus.The notes on the following pages give an overview of Scott’s construction. The notes are extracted fromLeonid Rudin, λ-Logic. Technical Report 4521, Computer Science Department, California Institute of Tech-nology, May
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