Page:AIM-453.djvu/27

 Here we have envisioned the value of (CONS α β) as a vector of two elements, with zero-origin indexing. However, this definition of CONS makes use of the primitive operator =. We can define the "primitive operators" CONS, CAR, and CDR without using another primitive operator at all! Following [Church], we write:

Rather than using 0 and 1 (i.e. data objects) as selectors, we instead use (LAMBDA (A D) A) and (LAMBDA (A D) D) (i.e. procedures).

We can think of the LAMBDA-expression which appears as the body of the definition of DERIVATIVE or of CONS as a for new procedures. When DERIVATIVE or CONS is called, this prototype is instantiated as a closure, with certain variables free to the prototype bound to the arguments given to the constructor.

At this point it looks like we have solved all our problems. We started with a referentially transparent but expressively weak language. We augmented it with procedural objects and a notation for them in order to capture certain notions of abstraction and modularity. In doing this we lost the referential transparency. We have now regained it, and in the process uncovered even more powerful abstraction capabilities.

"The Three Laws of Thermodynamics: 1. You can't win. 2. You can't break even. 3. You can't get out of the game." — Unknown

There is no free lunch. We have ignored a necessary change to the top level driver loop. We have changed the format of &PROCEDURE-objects. DRIVER-LOOP-1 constructs &PROCEDURE-objects; it must be rewritten to accommodate the change. We must include an environment in each such object. The obvious fix is shown in Figure 8.