Tags SICP

Exercise 4.32

As the authors themselves note, the lazy car permits us to implicitly delay both elements of a cons cell. This allows us to construct arbitrary data structures from lists that are completely lazy. One good example is trees.

Recall why lazyness is useful in the first place. One of its chief advantages is the ability to seamlessly handle infinite data structures. So having a lazy car as well as a lazy cdr will allows us to manipulate infinite trees without worrying. Infinite trees can be useful in artificial intelligence, for instance, where they represent all possible positions a game can reach – and this is used to evaluate potential moves in games like chess.

Exercise 4.33

First of all, let’s recall that our evaluator doesn’t know how to handle the quote symbol ' at the moment. In a real Lisp interpreter, the ' symbol is translated by the reader1 to (quote ...), which is what the evaluator sees. We haven’t yet implemented a reader for our evaluator, so we’ll have to stick to an explicit (quote ...).

Therefore, instead of:

(car '(a b c))

We’ll be dealin with:

(car (quote (a b c)))

Also, up until now we’ve had cons, car and cdr “borrowed” from the host language as primitive procedures. Now we’ll implement them, as shown:

(interpret
  '(define (cons x y)
    (lambda (m) (m x y))))

(interpret
  '(define (car z)
    (z (lambda (p q) p))))

(interpret
  '(define (cdr z)
    (z (lambda (p q) q))))

And replace text-of-quotation with:

(defun text-of-quotation (exp env) 
  (let ((quote-operand (cadr exp)))
    (if (consp quote-operand)
      (eval. (make-lazy-list (cadr exp)) env)
      quote-operand)))

(defun make-lazy-list (elems)
  (if (null elems)
    '()
    (list
      'cons
      (car elems)
      (make-lazy-list (cdr elems)))))

Note that now env must be passed to text-of-quotation. For this reason, the main dispatching cond in eval. must be slightly modified.

Exercise 4.34

Here’s an outline of the solution:

1. At the moment, lazy lists are applications of cons. We have to mark them specially, some kind of lazy-list-application.

2. When the printer meets an expression of type lazy-list-application, it follows the list links for some pre-specified amount of elements, say 20, and prints them out. After the 20th element, it prints … to avoid trying to print infinite lists.

1 The first stage of the read-eval-print loop (REPL).


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