Smoothing a lazy list of lazy lists in a Schema through a higher order accumulation procedure

Question

I am trying to find an implementation that smooths a lazy list of lazy lists using interleaveand lz-lst-accumulate, which are the procedures I wrote. This is the code so far:

(define lz-lst-accumulate
  (lambda (op initial lz)
    (if (empty? lz)
      initial
      (op (head lz)
        (lambda() (lz-lst-accumulate op initial (tail lz)))))))

(define interleave
  (lambda (lz1 lz2)
    (if (empty? lz1)
      (lz2)
      (cons (head lz1)
        (interleave (lz2) (lambda() (tail lz1)))))))

(define all-div-from-flattened
     (lambda (lower)
       (lz-lst-accumulate interleave '() (all-div-from lower))))

(define take
  (lambda (lz-lst n)
    (if (= n 0)
      (list)
      (cons (car lz-lst)
        (take (tail lz-lst) (sub1 n))))))

(define head
  (lambda (lz)
    (car lz)))

(define tail
  (lambda (lz-lst)
    ((cdr lz-lst))))

(define lz-lst-map
  (lambda (f lz)
    (if (empty? lz)
      lz
      (cons (f (head lz))
        (lambda () (lz-lst-map f (tail lz)))))))

; Signature: all-div-from (low)
; Type: [Number -> Lazy-list]
; Purpose: return a lazy-list of lazy-lists. The nested lazy-lists 
;          correspond to the integers greater than lower in an 
;          increasing order. Each nested lazy-list is the list of 
;          all integers divisible by i for some i>=lower.
; Pre-conditions: low is an integer
; Tests: > (define lz3 (all-div-from 7))
;        > (take lz3 3)
;        '((7 . #<procedure>) (8 . #<procedure>) (9 . #<procedure>))
;        > (take (head lz3) 3)
;        '(7 14 21)
;        > (take (head (tail lz3)) 3)
;        '(8 16 24)

(define all-div-from
    (lambda(lower)
      (cons (lz-lst-map (lambda(x) (* x lower)) (div-from 1 1))
            (lambda() (all-div-from (add1 lower))))))


; Signature: div-from (low int)
; Type: [[Number*Number]-> Lazy-list]
; Purpose: return the lazy-list of all integers that 
;          are larger than low and divisible by int
; Pre-conditions: int > low
; Tests: > (define lz1 (div-from 5 12))
;        > (take lz1 3)
;        '(12 24 36)
;        > (define lz2 (div-from 7 10))
;        > (take lz2 4)
;        '(10 20 30 40)
(define div-from
  (lambda (lower int)
    (lz-lst-filter (lambda(x) (> x (- lower 1))) 
      (lz-lst-map (lambda(x) (* x int)) (integers-from 1)))))

(define integers-from
  (lambda (n) (cons n
    (lambda () (integers-from (+ 1 n))))))

(define lz-lst-filter
  (lambda (p lz)
    (cond ((empty? lz) lz)
          ((p (head lz)) 
             (cons (head lz) 
               (lambda () (lz-lst-filter p (tail lz)))))
          (else (lz-lst-filter p (tail lz))))))

The procedure all-div-fromgets the lower bound lowand returns a lazy list of lazy lists. Each lazy list in it is made div-from, which receives a lower bound lowand an integer int > low, and returns a lazy list of all integers that are more than lowdivisible by int.

Example input and correct output:

 > (take (all-div-from-flattened 7) 10)
        '(7 8 14 9 21 16 28 10 35 24)

But when I try this line in the interpreter:

> (take (all-div-from-flattened 3) 3)

he gets into an endless cycle.

lz-lst-accumulate, interleave all-div-from-flattend.

, ?

Answer 1

interleave ; : cons , lambda. , cons 2- , :

(define interleave
  (lambda (lz1 dlz2)    ; "delayed" lz2
    (if (empty? lz1)
      (dlz2)
      (cons (head lz1)
            ; here:
            (interleave (dlz2) (lambda () (tail lz1)))))))

(define lz-lst-accumulate
  (lambda (op initial lz)
    (if (empty? lz)
      initial
      (op (head lz)
          (lambda () (lz-lst-accumulate op initial (tail lz)))))))

(all-div-from lower) , ( (lower . <proc1>) . <proc2> ), (lz-lst-accumulate interleave '() (all-div-from lower))

(interleave [lower . <proc1>]
            (lambda () (lz-lst-accumulate interleave '() (<proc2>))))

(cons lower 
      (interleave (lz-lst-accumulate interleave '() (<proc2>))
                  (lambda () (<proc1>))))

(cons lower 
      (lambda () (interleave ....)))

.

() lambda:

(define interleave
  (lambda (lz1 lz2)
    (if (empty? lz1)
      (lz2)
      (cons (head lz1)
            (lambda () (interleave (lz2) (lambda() (tail lz1))))))))

:

(take (all-div-from-flattened 7) 10)
, 12: (7 8 14 9 21 16 28 10 35 24)

---

,

(define integers-from-by
  (lambda (n d) (cons n
    (lambda () (integers-from (+ n d) d)))))

;(define div-from
;  (lambda (lower int)
;    (lz-lst-filter (lambda(x) (> x (- lower 1))) 
;      (lz-lst-map (lambda(x) (* x int)) (integers-from 1)))))

(define mults-from-of    ; n in [int, 2*int ..], n >= lower
  (lambda (lower int)
    (let ((x (* (quotient (+ lower (- int 1)) int) int)))
      (integers-from-by x int))))

(define mults-above-of   ; n in [int, 2*int ..], n > lower
  (lambda (lower int)
    (let ((x (* (+ (quotient lower int) 1) int)))
      (integers-from-by x int))))

; (define all-div-from
;    (lambda(lower)
;      (cons (lz-lst-map (lambda(x) (* x lower)) (div-from 1 1))
;            (lambda() (all-div-from (add1 lower))))))

(define all-mults-from
  (lambda (lower)
    (lz-lst-map (lambda (n) (mults-from-of n n))
                            ; or just (integers-from-by n n)
                (integers-from-by lower 1))))

interleave, mults-above-of all-mults-from, (lz-lst-accumulate interleave-ordered '() (all-mults-from-above 2)) , , , .

, Eratosthenes _{( "SiCp" )}.

: take , . .