How to define the partitions (factorizations w.r.t. concatenation) of a sequence as a lazy sequence of lazy sequences in Clojure

Question

I am new to Clojure and I want to define a function pt taking as arguments a number n and a sequence s and returning all the partitions of

Answer 1

The cons call in your split inline fn is the only place where eagerness is being introduced. You could replace that with something that lazily constructs a list, like concat:

(defn pt [n s]
  (lazy-seq
   (if (zero? n)
     (when (empty? s) [nil])
     ((fn split [a b]
        (concat
         (map (partial concat [a]) (pt (dec n) b))
         (when-let [[bf & br] (seq b)] (split (conj a bf) br))))
      [] s))))

(every? #(= clojure.lang.LazySeq (class %)) (pt 3 [0 1 2 3])) ;; => true

But, reading the code I feel like it's fairly unClojurey, and I think that's to do with the use of recursion. Often you'd use things like reductions, partition-by, split-at and so to do this sort of thing. I feel like there should also be a way to make this a transducer and separate out the lazyness from the processing (so you can use sequence to say you want it lazily), but I haven't got time to work that out right now. I'll try and come back with a more complete answer soon.