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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]
[\\spec
[functor
["$." contravariant]]]]
[data
["." bit ("#\." equivalence)]]
[math
["." random (#+ Random)]
[number
["n" nat]]]]]
[\\library
["." /
[//
[equivalence (#+ Equivalence)]]]])
(def: #export test
Test
(<| (_.covering /._)
(do random.monad
[left random.nat
right (|> random.nat (random.filter (|>> (n.= left) not)))
#let [equivalence (: (Equivalence (/.Order Nat))
(implementation
(def: (= leftO rightO)
(and (bit\= (\ leftO < left left)
(\ rightO < left left))
(bit\= (\ leftO < right right)
(\ rightO < right right))
(bit\= (\ leftO < left right)
(\ rightO < left right))))))]])
($_ _.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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