如何使這個篩功能懶惰？

Question

下面是代碼：

;; Helper function for marking mutiples of a number as 0 
(defn mark 
    ([xs k m] (mark xs k m [])) 
    ([xs k m mark-vec] 
    (loop [[x & rest-xs] xs 
      k k 
      mark-vec mark-vec 
      ] 
    (cond 
     (and (nil? x) (nil? rest-xs)) mark-vec 
     (= k m) (recur rest-xs 1  (conj mark-vec 0)) 
     :else (recur rest-xs (inc k) (conj mark-vec x)) 
     )))) 

;; Sieve of Eratosthenes 
(defn sieve 
    ([xs] (sieve xs [])) 
    ([xs sieve-res] 
    (loop [[x & rest-xs] xs 
      sieve-res sieve-res] 
    (cond 
     (and (nil? x) (nil? rest-xs)) sieve-res 
     (= x 0) (recur rest-xs sieve-res) 
     :else (recur (mark rest-xs 1 x) (conj sieve-res x)))))) 

(take 10 (sieve (range 2 100))) 

我想使它收到類似(iterate inc 2)並生成素數的無限序列。

Answer 1

最好的方法是建立一個適當的功能增量篩，如Melissa E. O'Neill的The Genuine Sieve of Eratosthenes中所述。

Christophe Grand發佈了一些非常漂亮的增量篩實施here。