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We clearly need to develop a proposal on how to fix up the Function
data-type. Probably Function is the union of Function-Name and
Function-Object, where the things that qualify for each of these
sub-classes are carefully enumerated. Certainly a concept like
Compiled-Function has to be defined as something (we don't need to
specify what) that the compiler produces and that we can test for. We
need to replace the old wording about "suitable for use by APPLY" or
whatever, and the correctness and well-formedness of the function should
play no part in the type decision.
If anyone wants to try to produce a comprehensive proposal on this, feel
free: if not, I'll get to it sometime soon.