(.using
 [library
  [lux "*"
   ["_" test {"+" Test}]
   [abstract
    [monad {"+" do}]]
   [math
    ["[0]" random {"+" Random}]]]]
 [\\library
  ["[0]" /
   [//
    [equivalence {"+" Equivalence}]]]])

(def: .public (spec (open "_#[0]") (open "_#[0]") 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]
    (<| (_.for [/.Monoid])
        ($_ _.and
            (_.test "Left identity."
                    (_#= sample
                         (_#composite _#identity sample)))
            (_.test "Right identity."
                    (_#= sample
                         (_#composite sample _#identity)))
            (_.test "Associativity."
                    (_#= (_#composite left (_#composite mid right))
                         (_#composite (_#composite left mid) right)))
            ))))