;; lib/minikanren/tests/latin.sx — 2x2 Latin square via ino + all-distincto.
;;
;; A 2x2 Latin square has 2 distinct fillings:
;;   ((1 2) (2 1))  and  ((2 1) (1 2)).
;; The 3x3 version has 12 fillings but takes minutes under naive search;
;; full CLP(FD) (Phase 6 proper) would handle it in milliseconds.

(define
  latin-2x2
  (fn
    (cells)
    (let
      ((c11 (nth cells 0))
        (c12 (nth cells 1))
        (c21 (nth cells 2))
        (c22 (nth cells 3))
        (dom (list 1 2)))
      (mk-conj
        (ino c11 dom)
        (ino c12 dom)
        (ino c21 dom)
        (ino c22 dom)
        (all-distincto (list c11 c12))
        (all-distincto (list c21 c22))
        (all-distincto (list c11 c21))
        (all-distincto (list c12 c22))))))   ;; col 2

(mk-test
  "latin-2x2-count"
  (let
    ((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
    (len squares))
  2)

(mk-test
  "latin-2x2-as-set"
  (let
    ((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
    (and
      (= (len squares) 2)
      (and
        (some
          (fn (s) (= s (list 1 2 2 1)))
          squares)
        (some
          (fn (s) (= s (list 2 1 1 2)))
          squares))))
  true)

(mk-test
  "latin-2x2-with-clue"
  (run*
    q
    (fresh
      (a b c d)
      (== a 1)
      (== q (list a b c d))
      (latin-2x2 (list a b c d))))
  (list (list 1 2 2 1)))

(mk-tests-run!)