(.module:
  [lux #*
   data/text/format
   ["r" math/random (#+ Random)]
   ["_" test (#+ Test)]
   [abstract/monad (#+ do)]
   [abstract
    [equivalence (#+)]
    [functor (#+)]]
   [data
    ["." bit ("#@." equivalence)]
    [number
     ["." nat]]
    [collection
     ["." list]]]]
  {1
   ["." /]})

(def: #export test
  Test
  (<| (_.context (%name (name-of /._)))
      (do r.monad
        [x r.nat
         y r.nat]
        ($_ _.and
            (_.test "Can automatically select first-order structures."
                    (let [(^open "list@.") (list.equivalence nat.equivalence)]
                      (and (bit@= (:: nat.equivalence = x y)
                                  (/.::: = x y))
                           (list@= (list.n/range 1 10)
                                   (/.::: map inc (list.n/range 0 9)))
                           )))
            (_.test "Can automatically select second-order structures."
                    (/.::: =
                      (list.n/range 1 10)
                      (list.n/range 1 10)))
            (_.test "Can automatically select third-order structures."
                    (let [lln (/.::: map (list.n/range 1)
                                (list.n/range 1 10))]
                      (/.::: = lln lln)))
            ))))