luhn.clj

(defn map-every-nth [f coll n]
  (map-indexed #(if (zero? (mod (inc %1) n)) (f %2) %2) coll))

(defn convert-to-number-seq [num-string]
  (map #(Integer/parseInt %) (re-seq #"\d" num-string)))

(defn double-every-second-digit [coll]
  (map-every-nth #(* 2 %) (reverse coll) 2))

(defn subtract-high-digits [coll]
  (map-every-nth #(if (> % 9) (- % 9) %) coll 2))

(defn sum [coll]
  (reduce + coll))

(defn divisible-by-10? [n]
  (= (mod n 10) 0))

(defn invalid-chars? [num-string]
  (not (empty? (re-find #"[^\d.\s]" num-string))))

(defn invalid-count? [num-string]
  (<= (count (convert-to-number-seq num-string)) 1))

(defn invalid? [num-string]
  (or (invalid-chars? num-string) 
      (invalid-count? num-string)))

(defn valid? [num-string]
  (if (invalid? num-string) false
      (-> num-string      
          convert-to-number-seq 
          double-every-second-digit
          subtract-high-digits
          sum
          divisible-by-10?)))