(.module:
  [library
   [lux "*"
    ["_" test {"+" [Test]}]
    [abstract
     [monad {"+" [do]}]
     [\\specification
      ["$[0]" equivalence]
      ["$[0]" hash]
      ["$[0]" monoid]
      ["$[0]" codec]]]
    [control
     ["[0]" function]]
    [math
     ["[0]" random]]]]
  [\\library
   ["[0]" /]])

(def: .public test
  Test
  (<| (_.covering /._)
      (do random.monad
        [value random.bit]
        ($_ _.and
            (_.for [/.equivalence]
                   ($equivalence.spec /.equivalence random.bit))
            (_.for [/.hash]
                   ($hash.spec /.hash random.bit))
            (_.for [/.disjunction]
                   ($monoid.spec /.equivalence /.disjunction random.bit))
            (_.for [/.conjunction]
                   ($monoid.spec /.equivalence /.conjunction random.bit))
            (_.for [/.codec]
                   ($codec.spec /.equivalence /.codec random.bit))
            
            (_.cover [/.no /.yes]
                     (and (\ /.equivalence = false /.no)
                          (\ /.equivalence = true /.yes)))
            (_.cover [/.off /.on]
                     (and (\ /.equivalence = false /.off)
                          (\ /.equivalence = true /.on)))
            (_.cover [/.complement]
                     (and (not (\ /.equivalence = value ((/.complement function.identity) value)))
                          (\ /.equivalence = value ((/.complement not) value))))
            ))))