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|
(.module:
[lux #*
["_" test (#+ Test)]
[abstract/monad (#+ do)]
[data
["." bit ("#@." equivalence)]
[number
["n" nat]
["i" int]]]
[math
["." random (#+ Random)]]]
{1
["." / (#+ Equivalence)]})
(def: #export test
Test
(do random.monad
[leftN random.nat
rightN random.nat
leftI random.int
rightI random.int
sample random.nat
different (|> random.nat (random.filter (|>> (n.= sample) not)))]
(<| (_.covering /._)
($_ _.and
(_.cover [/.sum]
(let [equivalence (/.sum n.equivalence i.equivalence)]
(and (bit@= (:: n.equivalence = leftN leftN)
(:: equivalence = (#.Left leftN) (#.Left leftN)))
(bit@= (:: n.equivalence = leftN rightN)
(:: equivalence = (#.Left leftN) (#.Left rightN)))
(bit@= (:: i.equivalence = leftI leftI)
(:: equivalence = (#.Right leftI) (#.Right leftI)))
(bit@= (:: i.equivalence = leftI rightI)
(:: equivalence = (#.Right leftI) (#.Right rightI))))))
(_.cover [/.product]
(let [equivalence (/.product n.equivalence i.equivalence)]
(and (bit@= (and (:: n.equivalence = leftN leftN)
(:: i.equivalence = leftI leftI))
(:: equivalence = [leftN leftI] [leftN leftI]))
(bit@= (and (:: n.equivalence = leftN rightN)
(:: i.equivalence = leftI rightI))
(:: equivalence = [leftN leftI] [rightN rightI])))))
(_.cover [/.rec]
(let [equivalence (: (Equivalence (List Nat))
(/.rec (function (_ equivalence)
(structure
(def: (= left right)
(case [left right]
[#.Nil #.Nil]
true
[(#.Cons leftH lefT) (#.Cons rightH rightT)]
(and (n.= leftH rightH)
(:: equivalence = lefT rightT))
_
false))))))]
(and (:: equivalence = (list sample sample) (list sample sample))
(not (:: equivalence = (list sample sample) (list sample)))
(not (:: equivalence = (list sample sample) (list different different))))))
))))
(def: #export (spec (^open "_@.") generator)
(All [a] (-> (Equivalence a) (Random a) Test))
(do random.monad
[left generator
right generator]
(<| (_.with-cover [/.Equivalence])
($_ _.and
(_.test "Reflexivity."
(_@= left left))
(_.test "Symmetry."
(if (_@= left right)
(_@= right left)
(not (_@= right left))))))))
|
