(.module:
  [lux #*
   ["_" test (#+ Test)]
   [abstract
    [monad (#+ do)]]
   [math
    ["." random (#+ Random)]]]
  {1
   ["." /
    [//
     [equivalence (#+ Equivalence)]]]})

(def: #export (spec (^open "@//.") (^open "@//.") gen-sample)
  (All [a] (-> (Equivalence a) (/.Monoid a) (Random a) Test))
  (do random.monad
    [sample gen-sample
     left gen-sample
     mid gen-sample
     right gen-sample]
    (<| (_.with-cover [/.Monoid])
        ($_ _.and
            (_.test "Left identity."
                    (@//= sample
                          (@//compose @//identity sample)))
            (_.test "Right identity."
                    (@//= sample
                          (@//compose sample @//identity)))
            (_.test "Associativity."
                    (@//= (@//compose left (@//compose mid right))
                          (@//compose (@//compose left mid) right)))
            ))))