(define $Suit
  (type
    {[$var-match (lambda [$tgt] {tgt})]
     [$inductive-match
      (destructor
        {[spade []
          {[<spade> {[]}]
           [_ {}]}]
         [heart []
          {[<heart> {[]}]
           [_ {}]}]
         [club []
          {[<club> {[]}]
           [_ {}]}]
         [diamond []
          {[<diamond> {[]}]
           [_ {}]}]})]
     [$equal?
      (lambda [$val $tgt]
        (match [val tgt] [Suit Suit]
          {[[<spade> <spade>] <true>]
           [[<heart> <heart>] <true>]
           [[<club> <club>] <true>]
           [[<diamond> <diamond>] <true>]
           [[_ _] <false>]}))]}))

(define $Mod
  (lambda [$m]
    (type
      {[$var-match (lambda [$tgt] {(mod tgt m)})]
       [$equal? (lambda [$val $tgt] (= (mod val m) (mod tgt m)))]})))

(define $Card
  (type
    {[$var-match (lambda [$tgt] {tgt})]
     [$inductive-match
      (destructor
        {[card [Suit (Mod 13)]
          {[<card $s $n> {[s n]}]}]})]
     [$equal? (lambda [$val $tgt]
                (match [val tgt] [Card Card]
                  {[[<card $s $n> <card ,s ,n>] <true>]
                   [[_ _] <false>]}))]}))

(define $poker-hands
  (lambda [$Cs]
    (match Cs (Multiset Card)
      {[<cons <card $S $n>
         <cons <card ,S ,(- n 1)>
          <cons <card ,S ,(- n 2)>
           <cons <card ,S ,(- n 3)>
            <cons <card ,S ,(- n 4)>
             !<nil>>>>>>
        <straight-flush>]
       [<cons <card _ $n>
         <cons <card _ ,n>
          !<cons <card _ ,n>
            !<cons <card _ ,n>
              !<cons _
                !<nil>>>>>>
        <four-of-kind>]
       [<cons <card _ $m>
         <cons <card _ ,m>
          <cons <card _ ,m>
           <cons <card _ $n>
            !<cons <card _ ,n>
              !<nil>>>>>>
        <full-house>]
       [<cons <card $S _>
         !<cons <card ,S _>
           !<cons <card ,S _>
             !<cons <card ,S _>
               !<cons <card ,S _>
                 !<nil>>>>>>
        <flush>]
       [<cons <card _ $n>
         <cons <card _ ,(- n 1)>
          <cons <card _ ,(- n 2)>
           <cons <card _ ,(- n 3)>
            <cons <card _ ,(- n 4)>
             !<nil>>>>>>
        <straight>]
       [<cons <card _ $n>
         <cons <card _ ,n>
          <cons <card _ ,n>
           <cons _
            <cons _
             !<nil>>>>>>
        <three-of-kind>]
       [<cons <card _ $m>
         <cons <card _ ,m>
          !<cons <card _ $n>
            <cons <card _ ,n>
             !<cons _
               !<nil>>>>>>
        <two-pair>]
       [<cons <card _ $n>
         <cons <card _ ,n>
          <cons _
           <cons _
            <cons _
             !<nil>>>>>>
        <one-pair>]
       [<cons _
         <cons _
          <cons _
           <cons _
            <cons _
             !<nil>>>>>>
        <nothing>]})))