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Tying the knot in Clojure

From: andrew cooke <andrew@...>

Date: Wed, 18 Jul 2012 23:41:56 -0400

(defn stream [seed]
  (defn helper
    ([slow] (helper (first slow) seed (rest slow)))
    ([c fast slow]
      (let [fast (seq fast)]
        (if fast
          (lazy-seq (cons (str c (first fast)) (helper c (rest fast) slow)))
          (helper slow)))))
  (declare delayed)
  (let [slow (cons "" (lazy-seq delayed))]
    (def delayed (helper slow))
    delayed))

(take 5 (stream ["a" "b" "c"]))
("a" "b" "c" "aa" "ab" "ac" "ba" "bb" "bc" "ca" "cb" "cc" "aaa" 
"aab" "aac" "abb" "abc" "aca" "acb" "acc" "baa" "bab" "bac" "bba")

From http://stackoverflow.com/a/11553140/181772

The idea is pretty simple: I take the output from the sequence and feed it
back on itself. For each value in the output (which is also the input), I
generate a new output by appending each of the letters in the seed
sequence. Since this is circular it just keeps on going.

The process of feeding the output into the input is called "tying the knot" in
a fairly famous paper for Haskell. But it's harder to do in Clojure because
it's an eager language (and even lazy sequences aren't "lazy enough") - the
only solution I could find was that mess with def (I suspect someone might do
better with delay and force, but I had no luck).

https://github.com/andrewcooke/clojure-lab/blob/master/src/org/acooke/lab/perms.clj

Andrew

Improved Code

From: andrew cooke <andrew@...>

Date: Thu, 19 Jul 2012 15:13:14 -0400

(defn stream [seed]
      (defn helper [slow]
        (concat (map #(str (first slow) %) seed) (lazy-seq (helper (rest
      slow)))))
      (declare delayed)
      (let [slow (cons "" (lazy-seq delayed))]
        (def delayed (helper slow))
        delayed))
    
    (take 25 (stream ["a" "b" "c"]))
    ("a" "b" "c" "aa" "ab" "ac" "ba" "bb" "bc" "ca" "cb" "cc" "aaa" "aab"
    "aac" "aba" "abb" "abc" "aca" "acb" "acc" "baa" "bab" "bac" "bba")

Also: http://stackoverflow.com/questions/11567625/tying-the-knot-in-clojure

Andrew

PS And I had a typo in teh earlier code - should have been "take 25".

iterate

From: Javier Neira Sanchez <atreyu.bbb@...>

Date: Thu, 19 Jul 2012 23:11:05 +0200

I think tying the knot is about corecursion and the more elegant to
make it in clojure is with iterate

(def abc (map str (map char (range 65 91))))
    (defn cols [seed]
      (let [next #(for [x %] (for [y seed] (str x y)))]
        (->> (iterate #(apply concat (next %)) seed)
             (mapcat identity))))

    (time (first (drop 475254 (cols abc))))
    "Elapsed time: 356.879148 msecs"
    "AAAAA"

    (doc iterate)
    -------------------------
    clojure.core/iterate
    ([f x])
      Returns a lazy sequence of x, (f x), (f (f x)) etc. f must be
free of side-effects

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