| **Definition:** | | This states that for any program (a non-function typed term in the typed lambda-calculus with constants) normal order reduction (outermost first) fails to terminate if and only if the standard semantics of the term is bottom. Moreover, if the reduction of program e1 terminates with some head normal form e2 then the standard semantics of e1 and e2 will be equal. This theorem is significant because it relates the operational notion of a reduction sequence and the denotational semantics of the input and output of a reduction sequence. |