;;;;;
;;;;;
;;;;; Number Library
;;;;;
;;;;;

;;;
;;; Integers
;;;
(define $integer
  (matcher
    {[,$n []
      {[$tgt (if (eq? tgt n)
                 {[]}
                 {})]}]
     [$ [something]
      {[$tgt {tgt}]}]
     }))

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

(define $between
  (lambda [$m $n]
    (match (compare-integer m n) ordering
      {[<less> {m @(between (+ m 1) n)}]
       [<equal> {n}]
       [<greater> {}]})))

(define $from
  (lambda [$m]
    {m @(from (+ m 1))}))

(define $min
  (lambda [$ns]
    (match ns (list integer)
      {[<cons $n <nil>> n]
       [<cons $n $rs>
        (let {[$r (min rs)]}
          (match (compare-integer n r) ordering
            {[<less> n]
             [_ r]}))]})))

(define $max
  (lambda [$ns]
    (match ns (list integer)
      {[<cons $n <nil>> n]
       [<cons $n $rs>
        (let {[$r (max rs)]}
          (match (compare-integer n r) ordering
            {[<greater> n]
             [_ r]}))]})))

(define $min-and-max
  (lambda [$ns]
    (match ns (list integer)
      {[<cons $n <nil>> [n n]]
       [<cons $n $rs>
        (let {[[$min-n $max-n] (min-and-max rs)]}
          (match (compare-integer n min-n) ordering
            {[<less> [n max-n]]
             [_ (match (compare-integer n max-n) ordering
                  {[<greater> [min-n n]]
                   [_ [min-n max-n]]})]}))]})))

(define $power
  (lambda [$x $n]
    (letrec {[$xs {x @xs}]}
      (foldl * 1 (take n xs)))))

(define $mod
  (lambda [$m]
    (matcher
      {[,$n []
        {[$tgt (if (eq? (modulo tgt m) (modulo n m))
                   {[]}
                   {})]}]
       [$ [something]
        {[$tgt {(modulo tgt m)}]}]
       })))

;;
;; Float Numbers
;;
(define $float
  (matcher
    {[,$d []
      {[$tgt (if (eq? tgt d) {[]} {})]}]
     [$ [something]
      {[$tgt {tgt}]}]
     }))

(define $compare-float
  (lambda [$d1 $d2]
    (if (lt? d1 d2)
        <Less>
        (if (eq? d1 d2)
            <Equal>
            <Greater>))))