gistfile1.clj

(def b1 '[3 - - - - 5 - 1 -
          - 7 - - - 6 - 3 -
          1 - - - 9 - - - -
          7 - 8 - - - - 9 -
          9 - - 4 - 8 - - 2
          - 6 - - - - 5 - 1
          - - - - 4 - - - 6
          - 4 - 7 - - - 2 -
          - 2 - 6 - - - - 3])


(defn rowify
  [board]
  (->> board
       (partition 9)
       (map vec)
       vec))

(defn colify
  [rows]
  (apply map vector rows))

(defn subgrid
  [rows]
  (partition 9 (for [row (range 0 9 3)
                     col (range 0 9 3)
                     x (range row (+ row 3))
                     y (range col (+ col 3))]
                 (get-in rows [x y]))))

(def logic-board #(repeatedly 81 logic/lvar))

(defn init
  [[lv & lvs] [cell & cells]]
  (if lv
    (fresh []
      (if (= '- cell)
        logic/succeed
        (== lv cell))
      (init lvs cells))
    logic/succeed))

(defn solve-logically
  [board]
  (let [legal-nums (fd/interval 1 9)
        lvars (logic-board)
        rows (rowify board)
        cols (colify rows)
        grids (subgrid rows)]
    (logic/run 1 [q]
      (init lvars board)
      (logic/everyg #(fd/in % legal-nums) lvars)
      (logic/everyg fd/distinct rows)
      (logic/everyg fd/distinct cols)
      (logic/everyg fd/distinct grids)
      (== q lvars))))