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(.module:
[library
[lux "*"
["_" test {"+" Test}]
[abstract
[equivalence {"+" Equivalence}]
[monad {"+" do}]
[\\specification
["$[0]" monoid]
[functor
["$[0]" contravariant]]]]
[control
["[0]" function]]
[data
["[0]" bit ("[1]#[0]" equivalence)]
[collection
["[0]" list]]]
[math
["[0]" random {"+" Random}]
[number
["n" nat]]]]]
[\\library
["[0]" /]])
(def: (multiple? factor)
(-> Nat (/.Predicate Nat))
(case factor
0 (function.constant false)
_ (|>> (n.% factor) (n.= 0))))
(def: .public test
Test
(<| (_.covering /._)
(do [! random.monad]
[sample random.nat
samples (random.list 10 random.nat)
.let [equivalence (: (Equivalence (/.Predicate Nat))
(implementation
(def: (= left right)
(bit#= (left sample)
(right sample)))))]])
(_.for [/.Predicate])
($_ _.and
(_.for [/.functor]
($contravariant.spec equivalence (multiple? 2) /.functor))
(let [generator (: (Random (/.Predicate Nat))
(|> random.nat
(random.only (|>> (n.= 0) not))
(# ! each multiple?)))]
($_ _.and
(_.for [/.union]
($monoid.spec equivalence /.union generator))
(_.for [/.intersection]
($monoid.spec equivalence /.intersection generator))))
(_.cover [/.none]
(bit#= false (/.none sample)))
(_.cover [/.all]
(bit#= true (/.all sample)))
(_.cover [/.or]
(bit#= (/.all sample)
((/.or /.none /.all) sample)))
(_.cover [/.and]
(bit#= (/.none sample)
((/.and /.none /.all) sample)))
(_.cover [/.complement]
(and (not (bit#= (/.none sample)
((/.complement /.none) sample)))
(not (bit#= (/.all sample)
((/.complement /.all) sample)))))
(_.cover [/.difference]
(let [/2? (multiple? 2)
/3? (multiple? 3)]
(bit#= (and (/2? sample)
(not (/3? sample)))
((/.difference /3? /2?) sample))))
(_.cover [/.rec]
(let [even? (multiple? 2)
any_even? (: (/.Predicate (List Nat))
(/.rec (function (_ recur)
(function (_ values)
(case values
{.#End}
false
{.#Item head tail}
(or (even? head)
(recur tail)))))))]
(bit#= (list.any? even? samples)
(any_even? samples))))
)))
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