(.require
 [library
  [lux (.except)
   [abstract
    [monad (.only do)]]
   [math
    ["[0]" random (.only Random)]
    [number
     ["n" nat]]]
   [test
    ["_" property (.only Test)]]]]
 [\\library
  ["[0]" /]])

(def (within_boundaries? [min max] it)
  (-> [Nat Nat] Nat
      Bit)
  (and (n.<= max it)
       (n.>= min it)))

(def .public test
  Test
  (<| (_.covering /._)
      (do [! random.monad]
        [left random.nat
         right random.nat
         .let [max (n.max left right)
               min (n.min left right)]

         parameter (random.only (n.> 0) random.nat)
         subject random.nat])
      (all _.and
           (_.coverage [/.arithmetic]
             (let [boundaries_are_respected!
                   (let [(open "/#[0]") (/.arithmetic n.order [min max] n.arithmetic)]
                     (and (within_boundaries? [min max] (/#+ parameter subject))
                          (within_boundaries? [min max] (/#- parameter subject))
                          (within_boundaries? [min max] (/#* parameter subject))
                          (within_boundaries? [min max] (/#/ parameter subject))))

                   the_order_of_the_boundaries_does_not_matter!
                   (let [(open "/#[0]") (/.arithmetic n.order [max min] n.arithmetic)]
                     (and (within_boundaries? [min max] (/#+ parameter subject))
                          (within_boundaries? [min max] (/#- parameter subject))
                          (within_boundaries? [min max] (/#* parameter subject))
                          (within_boundaries? [min max] (/#/ parameter subject))))]
               (and boundaries_are_respected!
                    the_order_of_the_boundaries_does_not_matter!)))
           )))