 The natural semantics was to find a set "D" isomorphic to the function space "D" → "D", of functions on itself.However, no nontrivial such "D" can exist, by cardinality constraints because the set of all functions from "D" to "D" has greater cardinality than "D", unless "D" is a singleton set.In the 1970s, Dana Scott showed that, if only continuous functions were considered, a set or domain "D" with the required property could be found, thus providing a model for the lambda calculus.