Exercise 2.85: This section mentioned a method
for “simplifying” a data object by lowering it in the tower of types as far
as possible.  Design a procedure drop that accomplishes this for the
tower described in Exercise 2.83.  The key is to decide, in some general
way, whether an object can be lowered.  For example, the complex number 

  
    1.5
    +
    0
    i
  
 can be lowered as far as real, the complex number 
  
    1
    +
    0
    i
  
 can
be lowered as far as integer, and the complex number 
  
    2
    +
    3
    i
  
 cannot
be lowered at all.  Here is a plan for determining whether an object can be
lowered: Begin by defining a generic operation project that “pushes”
an object down in the tower.  For example, projecting a complex number would
involve throwing away the imaginary part.  Then a number can be dropped if,
when we project it and raise the result back to the type we
started with, we end up with something equal to what we started with.  Show how
to implement this idea in detail, by writing a drop procedure that drops
an object as far as possible.  You will need to design the various projection
operations119 and
install project as a generic operation in the system.  You will also
need to make use of a generic equality predicate, such as described in
Exercise 2.79.  Finally, use drop to rewrite apply-generic
from Exercise 2.84 so that it “simplifies” its answers.