Exercise 4.79: When we implemented the Lisp
evaluator in 4.1, we saw how to use local environments to avoid
name conflicts between the parameters of procedures.  For example, in
evaluating


(define (square x) 
  (* x x))

(define (sum-of-squares x y)
  (+ (square x) (square y)))

(sum-of-squares 3 4)

there is no confusion between the x in square and the x in
sum-of-squares, because we evaluate the body of each procedure in an
environment that is specially constructed to contain bindings for the local
variables.  In the query system, we used a different strategy to avoid name
conflicts in applying rules.  Each time we apply a rule we rename the variables
with new names that are guaranteed to be unique.  The analogous strategy for
the Lisp evaluator would be to do away with local environments and simply
rename the variables in the body of a procedure each time we apply the
procedure.

Implement for the query language a rule-application method that uses
environments rather than renaming.  See if you can build on your environment
structure to create constructs in the query language for dealing with large
systems, such as the rule analog of block-structured procedures.  Can you
relate any of this to the problem of making deductions in a context (e.g., “If
I supposed that 
  P
 were true, then I would be able to deduce 
  A
 and

  B
.”) as a method of problem solving?  (This problem is open-ended.  A good
answer is probably worth a Ph.D.)