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(.using
[library
[lux "*"
["_" test {"+" Test}]
[abstract
[monad {"+" do}]
[\\specification
[functor
["$[0]" contravariant]]]]
[data
["[0]" bit ("[1]#[0]" equivalence)]]
[math
["[0]" random {"+" Random}]
[number
["n" nat]]]]]
[\\library
["[0]" /
[//
[equivalence {"+" Equivalence}]]]])
(def: .public test
Test
(<| (_.covering /._)
(do random.monad
[left random.nat
right (|> random.nat (random.only (|>> (n.= left) not)))
.let [equivalence (: (Equivalence (/.Order Nat))
(implementation
(def: (= leftO rightO)
(and (bit#= (# leftO < left left)
(# rightO < left left))
(bit#= (# leftO < right right)
(# rightO < right right))
(bit#= (# leftO < left right)
(# rightO < left right))))))]])
($_ _.and
(_.for [/.functor]
($contravariant.spec equivalence n.order /.functor))
(_.cover [/.Choice /.min /.max]
(n.< (/.max n.order left right)
(/.min n.order left right)))
(_.cover [/.Comparison /.>]
(not (bit#= (n.< left right)
(/.> n.order left right))))
(_.cover [/.<=]
(and (/.<= n.order left left)
(/.<= n.order right right)
(bit#= (# n.order < left right)
(/.<= n.order left right))))
(_.cover [/.>=]
(and (/.>= n.order left left)
(/.>= n.order right right)
(bit#= (/.> n.order left right)
(/.>= n.order left right))))
)))
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