"NEXT: infinite evaluation and errors"

((lambda (x) 1) some-infinite-calculation)

(define (some-infinite-calculation) (some-infinite-calculation))

((lambda (x) 1) (some-infinite-calculation))

((lambda (x) 1) 
   ((lambda (x) (x x)) (lambda (x) (x x))) )

((lambda (x) 1) (/ 5 0))

"NEXT: delay and force examples"

(delay (+ 5 6))

(force (delay (+ 5 6)))

(force 11)

(define pr (delay (+ 5 6)))

(+ 7 pr)

(+ 7 (force pr))

"NEXT: Streams stuff - prerequisites"

(define-syntax cons-stream
  (syntax-rules ()
    ((cons-stream x y)
     (cons x (delay y)))))

(define head car)

(define (tail stream) (force (cdr stream)))

(define empty-stream? null?)

(define the-empty-stream '())


(define (stream-section n stream)
  (cond ((= n 0) '())
        (else (cons (head stream)
              (stream-section 
                (- n 1)
               (tail stream))))))

(define (add-streams s1 s2)
 (let ((h1 (head s1))
       (h2 (head s2)))
   (cons-stream 
    (+ h1 h2)
    (add-streams (tail s1) (tail s2)))))

"NEXT: Stream examples"

(define ones (cons-stream 1 ones))

ones

(stream-section 7 ones)

(define (integers-starting-from n)
 (cons-stream n 
  (integers-starting-from (+ n 1))))

(define nat-nums
  (integers-starting-from 1))

nat-nums

(stream-section 10 nat-nums)

(define nat-nums 
 (cons-stream 1 
  (add-streams ones nat-nums)))

(stream-section 10 nat-nums)

(define fibs
  (cons-stream 0
    (cons-stream 1
      (add-streams (tail fibs) fibs))))

fibs

(stream-section 15 fibs)

"NEXT: The sieve of Eratosthenes"

(define (sieve stream)
   (cons-stream
     (head stream)
     (sieve 
       (filter-stream
         (lambda (x) (not (divisible? x (head stream))))
         (tail stream)))))

(define (divisible? x y)
  (= (remainder x y) 0))

(define (filter-stream p lst)
  (cond ((empty-stream? lst) the-empty-stream)
        ((p (head lst)) (cons-stream (head lst) (filter-stream p (tail lst))))
        (else (filter-stream p (tail lst)))))

(define primes (sieve (integers-starting-from 2)))

primes

(stream-section 100 primes)

"THE END"