lazy cat fibonacci

lazy-cat-fib.clj

;;So let’s work out the first couple of simple cases:

(take 1 head-fibo)
(take 1 (lazy-cat [0N 1N] (map + head-fibo (rest head-fibo))))
(take 1 (concat (lazy-seq [0N 1N])
                (lazy-seq (map + head-fibo (rest head-fibo)))))
;;since we’re taking 1, the 0N of the first lazy-seq suffices and
;;we don’t need to further evaluate
;; => (0N)

;;take 2 is similar, in that the first lazy-seq suffices by providing two values
;; => (0N 1N)

;;So now, to a more interesting case

(take 3 head-fibo)
(take 3 (lazy-cat [0N 1N] (map + head-fibo (read head-fibo))))
(take 3 (concat (lazy-seq [0N 1N])
                (lazy-seq (map + head-fibo (rest head-fibo)))))
;;now, the first lazy-seq only satisfies 2 out of the 3 values needed.
;;so we process the next lazy-seq
(take 3 (concat (lazy-seq [0N 1N])
                (lazy-seq (map +
                                (lazy-cat [0N 1N] (map + head-fibo (resd head-fibo)))
                                (rest (lazy-cat [0N 1N] (map + head-fibo (resd head-fibo))))))))

(take 3 (concat (lazy-seq [0N 1N])
                (lazy-seq (map +
                                (concat (lazy-seq [0N 1N]) (lazy-seq (map + head-fibo (rest head-fibo))))
                                (rest (concat (lazy-seq [0N 1N]) (lazy-seq (map + head-fibo (rest head-fibo)))))))))

;;since we need one more value, we map over the first value of each lazy-seq, namely 0N and 1N, giving:
(take 3 (concat (lazy-seq [0N 1N])
                (lazy-seq (map +
                               0N
                               1N))))
;; => (0N 1N 1N)