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(.using
 [library
  [lux "*"
   ["_" test {"+" Test}]
   [abstract
    [monad {"+" do}]
    [\\specification
     ["$[0]" equivalence]
     ["$[0]" functor {"+" Injection}]]]
   [control
    ["[0]" maybe]]
   [data
    ["[0]" bit ("[1]#[0]" equivalence)]]
   [math
    ["[0]" random]
    [number
     ["n" nat]]]]]
 [\\library
  ["[0]" /]])

(def: (injection value)
  (Injection /.Stack)
  (/.top value /.empty))

(def: .public test
  Test
  (<| (_.covering /._)
      (_.for [/.Stack])
      (do random.monad
        [size (# random.monad each (n.% 100) random.nat)
         sample (random.stack size random.nat)
         expected_top random.nat]
        (all _.and
             (_.for [/.equivalence]
                    ($equivalence.spec (/.equivalence n.equivalence) (random.stack size random.nat)))
             (_.for [/.functor]
                    ($functor.spec ..injection /.equivalence /.functor))
             
             (_.cover [/.size]
                      (n.= size (/.size sample)))
             (_.cover [/.empty?]
                      (bit#= (n.= 0 (/.size sample))
                             (/.empty? sample)))
             (_.cover [/.empty]
                      (/.empty? /.empty))
             (_.cover [/.value]
                      (case (/.value sample)
                        {.#None}
                        (/.empty? sample)
                        
                        {.#Some _}
                        (not (/.empty? sample))))
             (_.cover [/.next]
                      (case (/.next sample)
                        {.#None}
                        (/.empty? sample)
                        
                        {.#Some [top remaining]}
                        (# (/.equivalence n.equivalence) =
                           sample
                           (/.top top remaining))))
             (_.cover [/.top]
                      (case (/.next (/.top expected_top sample))
                        {.#Some [actual_top actual_sample]}
                        (and (same? expected_top actual_top)
                             (same? sample actual_sample))
                        
                        {.#None}
                        false))
             ))))