(.using
 [library
  [lux "*"
   ["_" test {"+" Test}]
   [abstract
    [monad {"+" do}]]
   [control
    ["[0]" maybe]]
   [data
    [collection
     ["[0]" list]]]
   [math
    ["[0]" random]
    [number
     ["n" nat]]]]]
 [\\library
  ["[0]" / {"+" Functor}]])

(def: .public test
  Test
  (do random.monad
    [left random.nat
     right random.nat
     shift random.nat]
    (<| (_.covering /._)
        (all _.and
             (_.cover [/.Or /.sum]
                      (and (case (# (/.sum maybe.functor list.functor) each
                                    (n.+ shift)
                                    {.#Left {.#Some left}})
                             {.#Left {.#Some actual}}
                             (n.= (n.+ shift left) actual)

                             _
                             false)
                           (case (# (/.sum maybe.functor list.functor) each
                                    (n.+ shift)
                                    {.#Right (list right)})
                             (pattern {.#Right (list actual)})
                             (n.= (n.+ shift right) actual)

                             _
                             false)))
             (_.cover [/.And /.product]
                      (case (# (/.product maybe.functor list.functor) each
                               (n.+ shift)
                               [{.#Some left} (list right)])
                        (pattern [{.#Some actualL} (list actualR)])
                        (and (n.= (n.+ shift left) actualL)
                             (n.= (n.+ shift right) actualR))

                        _
                        false))
             (_.cover [/.Then /.composite]
                      (case (# (/.composite maybe.functor list.functor) each
                               (n.+ shift)
                               {.#Some (list left)})
                        (pattern {.#Some (list actual)})
                        (n.= (n.+ shift left) actual)

                        _
                        false))
             ))))