;; adapted from the Sudoku solver in `The Joy of Clojure 2nd Edition' 2014 by Michal Fogus and Chris Houser, Chater 16 Thinking Programs
(require '[clojure.core.logic :as l]         ;;the logic engine
         '[clojure.core.logic.fd :as fd])    ;;dealing with finite domains (integer numbers)

(defn latin-squares [n num-of-sols]                   ;; n - size of the square, num-fo-sols - number of solutions
  (let [tab (vec (repeatedly (* n n) l/lvar))         ;; n by n table of logic variables
        rows (partition n tab)                        ;; rows of the table
        cols (apply map vector rows)                  ;; columns of the table
        points  (fd/interval 0 (dec n))]              ;; valid entries
    (l/run num-of-sols [q]
      (l/everyg (fn [x] (fd/in x points)) tab)        ;; all entries are valid
      (l/everyg fd/distinct rows)                     ;; every row has distinct entries
      (l/everyg fd/distinct cols)                     ;; same for columns
      (l/== q tab))))                                 ;; unification