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.