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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]
[\\specification
["$." monoid]]]
[math
["." random]
[number
["r" rev]]]]]
[\\library
["." /]])
(def: .public test
Test
(<| (_.covering /._)
(do random.monad
[left random.rev
mid random.rev
right random.rev]
(`` ($_ _.and
(~~ (template [<monoid>]
[(_.for [<monoid>]
($monoid.spec r.= <monoid> random.rev))]
[/.disjunction]
[/.conjunction]
))
(_.cover [/.true /.false]
(let [true=max!
(r.= /.false (++ /.true))
false=min!
(r.= /.true (-- /.false))]
(and true=max!
false=min!)))
(_.cover [/.or]
(let [identity!
(r.= left (/.or /.false left))
annihilation!
(r.= /.true (/.or /.true left))
idempotence!
(r.= left (/.or left left))
associativity!
(r.= ($_ /.or left mid right)
(_$ /.or left mid right))]
(and identity!
annihilation!
idempotence!
associativity!
(let [l|r (/.or left right)]
(and (r.>= left l|r)
(r.>= right l|r))))))
(_.cover [/.and]
(let [identity!
(r.= left (/.and /.true left))
annihilation!
(r.= /.false (/.and /.false left))
idempotence!
(r.= left (/.and left left))
associativity!
(r.= ($_ /.and left mid right)
(_$ /.and left mid right))]
(and identity!
annihilation!
idempotence!
associativity!
(let [l&r (/.and left right)]
(and (r.<= left l&r)
(r.<= right l&r))))))
(_.cover [/.not]
(let [inverses!
(and (r.= /.false (/.not /.true))
(r.= /.true (/.not /.false)))
double_negation!
(r.= left (/.not (/.not left)))
de_morgan!
(and (r.= (/.not (/.or left right))
(/.and (/.not left) (/.not right)))
(r.= (/.not (/.and left right))
(/.or (/.not left) (/.not right))))]
(and inverses!
double_negation!
de_morgan!)))
(_.cover [/.implies]
(let [modus_tollens!
(r.= (/.implies right left)
(/.implies (/.not left) (/.not right)))]
(and modus_tollens!)))
(_.cover [/.=]
(let [trivial!
(and (r.= /.true (/.= /.true /.true))
(r.= /.true (/.= /.false /.false))
(r.= /.false (/.= /.true /.false)))
common!
(and (r.>= left
(/.= left left))
(r.>= right
(/.= right right)))]
(and trivial!
common!)))
)))))
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