;;;;;
;;;;;
;;;;; Order
;;;;;
;;;;;

(define $ordering
  (algebraic-data-matcher 
    {<less> <equal> <greater>}))

(define $compare
  (lambda [$m $n]
    (if (lt? m n)
        <Less>
        (if (eq? m n)
            <Equal>
            <Greater>))))

(define $min
  (lambda [$ns]
    (foldl' (lambda [$x $y] (if (lt? x y) x y)) (car ns) (cdr ns))))

(define $max
  (lambda [$ns]
    (foldl' (lambda [$x $y] (if (gt? x y) x y)) (car ns) (cdr ns))))

(define $min-and-max
  (lambda [$ns]
    (foldl' (lambda [$ret $x]
              (match ret [integer integer]
                {[[$min $max] (if (lt? x min) [x max]
                                (if (gt? x max) [min x]
                                  [min max]))]}))
           [(car ns) (car ns)]
           (cdr ns))))

(define $split-by-ordering (split-by-ordering/f compare $ $))

(define $split-by-ordering/f
  (lambda [$f $p $xs]
    (match xs (list something)
      {[<nil> [{} {} {}]]
       [<cons $x $rs>
        (let {[[$ys1 $ys2 $ys3] (split-by-ordering/f f p rs)]}
          (match (f x p) ordering
            {[<less> [{x @ys1} ys2 ys3]]
             [<equal> [ys1 {x @ys2} ys3]]
             [<greater> [ys1 ys2 {x @ys3}]]}))]})))

(define $qsort (qsort/f compare $))

(define $qsort/f
  (lambda [$f $xs]
    (match xs (list something)
      {[<nil> {}]
       [<cons $x <nil>> {x}]
       [_ (let {[$n (length xs)]}
            (let {[$p (nth (quotient n 2) xs)]}
              (let {[[$ys1 $ys2 $ys3] (split-by-ordering/f f p xs)]}
                {@(qsort/f f ys1) @ys2 @(qsort/f f ys3)})))]})))