A rule-application method that uses environments

When we implemented the Lisp evaluator in section 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.)

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