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(.module:
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]
{[0 #spec]
[/
[functor
["$." contravariant]]]}]
[data
["." bit ("#@." equivalence)]
[number
["n" nat]]]
[math
["." random (#+ Random)]]]
{1
["." /
[//
[equivalence (#+ Equivalence)]]]})
(def: #export test
Test
(<| (_.covering /._)
(do random.monad
[left random.nat
right (|> random.nat (random.filter (|>> (n.= left) not)))
#let [equivalence (: (Equivalence (/.Order Nat))
(structure
(def: (= leftO rightO)
(and (bit@= (:: leftO < left left)
(:: rightO < left left))
(bit@= (:: leftO < right right)
(:: rightO < right right))
(bit@= (:: leftO < left right)
(:: rightO < left right))))))]])
($_ _.and
(_.with-cover [/.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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