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(.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])
(all _.and
(_.property "Left identity."
(_#= sample
(_#composite _#identity sample)))
(_.property "Right identity."
(_#= sample
(_#composite sample _#identity)))
(_.property "Associativity."
(_#= (_#composite left (_#composite mid right))
(_#composite (_#composite left mid) right)))
))))
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