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are functions from functions to functions; in order for the elements of a model of the lambda calculus to be of arbitrary domain and range, they could not be true functions, only partial functions.” to be impenetrable. Is LC’s need for a semantics any different from other formalisms like FOL? Can the CC be a model for LC? Why isn’t CC also a “purely syntactic system”? The last sentence is especially difficult, in that the part after the ; is not obviously related to the however part, and moreover makes statements (“could not be…would have to be…”) without explanation or justification.
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Computations, namely that the functions involved be partial recursive, or recursive (when total). Also when are the sets recursively enumerable? Domain theory introduces many mathematical constructs, such as these "compact"
216:"Computations that have not yet returned a result" are *not* "The 'result' of a computation that never ends." Does the bottom in domain theory denote "insufficient information about a computation (that is guaranteed to terminate)" or "divergence, never ends."? These are completely different things.
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elements which are not even finite. So explain the connection with recursion theory to actually connect with computations.
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