We illuminate important aspects of the semantics of higher-order
functions that are common in the presence of local state, exceptions,
names and type abstraction via a series of examples that add to those
given by Stark.  Most importantly we show that any of these language
features gives rise to the phenomenon that certain behaviour of
higher-order functions can only be observed by providing them with
arguments which internally call the functions again.  Other examples
show the need for the observer to accumulate values received from the
program and generate new names.  This provides evidence for the
necessity of complex conditions for functions in the definition of
environmental bisimulation, which deviates in each of these ways from
that of applicative bisimulation.