In this assignment you will make some small modifications to the explicit-control evaluator presented in Chapter 5 of the text, and experiment with enabling and disabling tail-recursion.

The assignment is not easy and will take you a fair amount of time. But please note that of the 5 problems, the last 3 are very straightforward and probably won't take very much time at all. You can do these problems in any order.

Start by copying your hw8/regsim.scm file into a new hw9 directory. Then copy all the files in ~offner/cs450/hw9  into that directory as well. You may end up making edits to any of these files (with the exception of load-eceval.scm; you won't need to make any changes to that file). I will collect them all. I will also collect a file notes.txt, as usual.

Remember that you invoke the explicit-control evaluator by loading load-eceval.scm. For instance, from the Unix prompt you can just type

       scheme load-eceval.scm

       (start eceval)

1. The footnote on page 549 points out that the dispatch could be written in data-directed style, as we did in s450.scm. Implement this.

   Some hints: conceptually this is really very similar to what we did in s450.scm. You create a table to manage the special forms, just as you did for s450.scm. The difference is this: In s450.scm the cdr of each pair was the lambda expression that implemented the special form. But now the cdr of each pair is the label in eceval.scm at which the code implementing that special form is found. So install-special-form wants to be called like this, in eceval-support.scm:

          (install-special-form 'quote 'ev-quoted)
          (install-special-form 'set! 'ev-assignment)
   

   and so on.

   eceval.scm will need to use a built-in operation (i.e., a machine "operation", or what I have been calling a "machine primitive") type-of, which is just as trivially simple as it was in s450.scm. You will also need to check to see if a "bare symbol" is a special form name, so you will probably also need a built-in operation in eceval.scm for this purpose. Don't be surprised if you end up having two jumps to the same location; at least, that's what happened when I implemented this.

   When I implemented this, I found it necessary to allow instructions in eceval.scm of the form

          (assign val (label (reg val)))
   

   That is, in the expression (label xxx), xxx must be able to be a register reference rather than a literal. To do this you have to add some code to regsim.scm. This happens in make-elementary-exp. (Note: if you don't need to do this, that's perfectly fine. I'm curious to see how different people do this. I just wanted to warn you of something that might come up and how to deal with it.)

2. Exercise 5.24 (page 560). This exercise asks you to add support for the special form cond. In the previous Exercise 5.23 (which I am not asking you to do), the book suggests you "cheat" and use the syntax transformer cond->if in syntax.scm. I don't want you to do this. And I don't want you to use expand-clauses, either. Make cond a special form with its own machine code in eceval.scm and its own label ev-cond. You will of course need some of the selectors such as cond-clauses from syntax.scm as built-in operators; just remember to add them to the list of built-in operators in the machine. You may want to add some more selectors of your own; feel free to do this.

   You will want to be careful about considering which registers need to be saved and restored when implementing this. Present your reasoning in notes.txt.

3. Exercise 5.26 (page 564). For clarity, call this function (which the book calls factorial) fact-i (the "i" for "iterative"). Be sure to answer the questions in parts a and b.

   Note that this exercise does not involve writing any code. You just have to experiment with the machine.

4. Exercise 5.27 (page 564). For clarity, call this function (which the book also calls factorial) fact-r (the "r" for "recursive").

   Like the last exercise, this exercise does not involve writing any code. In both exercises, you should collect data at least for values of n from 1 through 5.

5. Exercise 5.28 (page 565). This requires changing some of the code in eceval.scm, but the book shows you exactly what to do. Add the code anywhere you want, just so long as it won't be "fallen into", and just leave the label ev-sequence for the new code commented out. Then to try the new code for this exercise, comment out the old label ev-sequence and uncomment the new one.

   Please note that this problem is similar to the two previous ones combined, so you will need to report just as much data and just as many formulas as in those two problems combined.

Some more information about problems 3, 4 and 5:

• You are asked to write some simple formulas. You have all taken algebra (and calculus, for that matter) and you should all know how to write a simple formula cleanly. For instance, suppose you come up with some expression such as

      2(n-3) + 11
  

  This is not what you want to write. You want to simplify this, so you write

      2n + 5
  

  And you do not write

      2*n + 5   !!! WRONG !!!
  

  That's not mathematical notation. That is what you might write if you were writing code in some computer language. But you are not writing code in some computer language. You are writing an algebraic expression.

  Please be careful about this.

• The point of producing all these tables (there should be four of them) and formulas (there should actually be eight of them) is to learn something, not just produce some meaningless expressions. What do you observe from these results? Put your answers in notes.txt.