(define $product
  (letrec 
    {[$subproduct (lambda [$xs $ys]
                    (match xs (List Something)
                      {[<nil> {}]
                       [<cons $z $zs> {@(map (lambda [$y] {z @y}) ys) @(subproduct zs ys)}]}))]}
    (lambda [$xs]
      (match xs (List Something)
        {[<nil> {}]
         [<cons $y <nil>> (map (lambda [$z] {z}) y)]
         [<cons $y $ys> (subproduct y (product ys))]}))))

(define $COC
  (lambda [$a $b] ;; a : collection-type   b : contents-type   see. an example below
    (type
      {[,$val []
        {[$tgt (match tgt (List (a b))
                 {[,val {[]}]
                  [_ {}]})]}]
       [<nil> [] ;; nil when some contents is nil
        {[$tgt (letrec
                 {[$helper (lambda [$xs]
                             (match xs (List Something)
                               {[<nil> {}]
                                [<cons $y $ys> (match y [(a b)]
                                                 {[<nil> {[]}]
                                                  [_ (helper ys)]})]}))]}
                 (helper tgt))]}]
       [<cons ,$xs _> [(COC a b)]
        {[$tgt (letrec
                 {[$helper (lambda [$xs $ys]
                             (match [xs ys] [(List Something) (List Something)]
                               {[[<nil> <nil>] {}]
                                [[<cons $x $xs> <cons $y $ys>] {(match-all y [(a b)] [<cons ,x $xs> xs]) @(helper xs ys)}]}))]}
                 (product (helper xs tgt)))]}]
       [<cons _ _> [(List b) (COC a b)]
        {[$tgt (letrec
                 {[$helper (lambda [$xs]
                             (match xs (List Something)
                               {[<nil> {}]
                                [<cons $y $ys> {(match-all y [(a b)] [<cons $z $zs> [z zs]]) @(helper ys)}]}))]
                  [$lt2tl (lambda [$xs]
                            (match xs (List [Something Something])
                              {[<nil> [{} {}]]
                               [<cons [$y $z] $ys> (let {[[$p $q] (lt2tl ys)]} [{y @p} {z @q}])]}))]}
                 (map lt2tl (product (helper tgt))))]}]
       [_ [Something]
        {[$tgt {tgt}]}]})))


;; (define $n-queen
;;   (lambda [$n]
;;    (match-all {(between 1 n) (between 2 (* 2 n)) (between (- 1 n) (- n 1))} (COC Multiset Integer)
;;      [(loop $l $i (between 1 n) <cons <cons $a_i ,{(+ a_i i) (- a_i i)}> l> <nil>)
;;       (loop $l $i (between 1 n) {a_i @l} {})])))