Streams as Lazy Lists

Streams Revisited

In section Lesson 11, we showed how to implement streams as delayed lists. We introduced special forms delay and cons-stream, which allowed us to construct a "promise" to compute the cdr of a stream, without actually fulfilling that promise until later. We could use this general technique of introducing special forms whenever we need more control over the evaluation process, but this is awkward. For one thing, a special form is not a first-class object like a procedure, so we cannot use it together with higher-order procedures. Additionally, we were forced to create streams as a new kind of data object similar but not identical to lists, and this required us to reimplement many ordinary list operations (map, append, and so on) for use with streams.

Streams in Lazy Evaluator

With lazy evaluation, streams and lists can be identical, so there is no need for special forms or for separate list and stream operations. All we need to do is to arrange matters so that cons is non-strict. One way to accomplish this is to extend the lazy evaluator to allow for non-strict primitives, and to implement cons as one of these. An easier way is to recall Lesson 4 that there is no fundamental need to implement cons as a primitive at all. Instead, we can represent pairs as procedures

(define (cons x y)
  (lambda (m) (m x y)))
(define (car z)
  (z (lambda (p q) p)))
(define (cdr z)
  (z (lambda (p q) q)))

In terms of these basic operations, the standard definitions of the list operations will work with infinite lists (streams) as well as finite ones, and the stream operations can be implemented as list operations. Here are some examples:

(define (list-ref items n)
  (if (= n 0)
      (car items)
      (list-ref (cdr items) (- n 1))))

(define (map proc items)
  (if (null? items)
      (cons (proc (car items))
            (map proc (cdr items)))))
(define (scale-list items factor)
  (map (lambda (x) (* x factor))
(define (add-lists list1 list2)
  (cond ((null? list1) list2)
        ((null? list2) list1)
        (else (cons (+ (car list1) (car list2))
                    (add-lists (cdr list1) (cdr list2))))))
(define ones (cons 1 ones))
(define integers (cons 1 (add-lists ones integers)))
;;; L-Eval input:
(list-ref integers 17)
;;; L-Eval value:

Note that these lazy lists are even lazier than the streams of Lesson 11: The car of the list, as well as the cdr, is delayed. In fact, even accessing the car or cdr of a lazy pair need not force the value of a list element. The value will be forced only when it is really needed -- e.g., for use as the argument of a primitive, or to be printed as an answer.