3.4 · Time as a sequence

A stream reveals only the part you demand.

A stream keeps its first value now and delays the computation that can produce the rest of the sequence.

Guiding question

How can a finite run use a sequence with no final element?

Read a stream as a present value and a delayed tail
Follow demand through repeated stream-ref calls
Distinguish describing an infinite process from executing forever

integers-from can describe an unending sequence because cons-stream does not evaluate its tail immediately. Each tail is a promise for the next pair.

stream-ref forces exactly as many tails as it needs to reach the requested index. Asking for index 9 constructs a finite prefix and returns 10, so this particular run terminates.

Lispex · SICP sourceScheme-compatible SICP syntax executed by the Lispex SICP profile.

(letrec ((integers-from
          (lambda (n)
            (cons-stream n (integers-from (+ n 1)))))
         (stream-ref
          (lambda (stream n)
            (if (= n 0)
                (car stream)
                (stream-ref (force (cdr stream)) (- n 1))))))
  (stream-ref (integers-from 1) 9))

Lispex learning runtimeLispex SICP profile 1.0.0

Loading Lispex SICP runtime

Lispex · SICP source300 / 1,048,576 UTF-8 bytes

Examples

Result—

Output: —
Value: —
Diagnostic: —

Visible execution0 / 0 trace events

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Expected observation

The first program returns 10 after forcing nine stream tails.

Trace focus

Find the repeated force events. Each computed outcome exposes one more pair, while the unrequested remainder stays delayed.

Try it yourself

Change the program before you read the hint.

Change the requested index from 9 to 4. Predict the value and how many stream tails must be forced.

Show one hint

Index 0 uses the current car without forcing the cdr.