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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[monad (#+ do)]
[\\specification
["$." equivalence]
["$." order]
["$." monoid]
["$." codec]]]
[control
["." maybe ("#\." functor)]]
[data
["." bit ("#\." equivalence)]]
[math
["." random (#+ Random)]]]]
[\\library
["." /
[//
["n" nat ("#\." equivalence)]]]])
(def: part
(Random Nat)
(\ random.monad map
(|>> (n.% 1,000,000) (n.max 1))
random.nat))
(def: .public random
(Random /.Ratio)
(do random.monad
[numerator ..part
denominator (random.only (|>> (n.= 0) not)
..part)]
(in (/.ratio numerator denominator))))
(def: .public test
Test
(<| (_.covering /._)
(_.for [/.Ratio])
(`` ($_ _.and
(_.for [/.equivalence /.=]
($equivalence.spec /.equivalence ..random))
(_.for [/.order /.<]
($order.spec /.order ..random))
(~~ (template [<compose> <monoid>]
[(_.for [<monoid> <compose>]
($monoid.spec /.equivalence <monoid> ..random))]
[/.+ /.addition]
[/.* /.multiplication]
))
(_.for [/.codec]
($codec.spec /.equivalence /.codec ..random))
(do random.monad
[.let [(^open "\.") /.equivalence]
denom/0 ..part
denom/1 ..part]
(_.cover [/.ratio]
(\= (/.ratio 0 denom/0)
(/.ratio 0 denom/1))))
(do random.monad
[numerator ..part
denominator (random.only (|>> (n\= 1) not)
..part)]
(_.cover [/.nat]
(let [only_numerator!
(|> (/.ratio numerator)
/.nat
(maybe\map (n\= numerator))
(maybe.else false))
denominator_1!
(|> (/.ratio numerator 1)
/.nat
(maybe\map (n\= numerator))
(maybe.else false))
with_denominator!
(case (/.nat (/.ratio numerator denominator))
(#.Some factor)
(and (n.= 0 (n.% denominator numerator))
(n.= numerator (n.* factor denominator)))
#.None
(not (n.= 0 (n.% denominator numerator))))]
(and only_numerator!
denominator_1!
with_denominator!))))
(do random.monad
[sample ..random]
($_ _.and
(_.cover [/.-]
(and (/.= (/.ratio 0) (/.- sample sample))
(/.= sample (/.- (/.ratio 0) sample))))
(_.cover [/./]
(and (/.= (/.ratio 1) (/./ sample sample))
(/.= sample (/./ (/.ratio 1) sample))))
(_.cover [/.reciprocal]
(/.= (/.ratio 1)
(/.* sample (/.reciprocal sample))))
))
(do random.monad
[left (random.only (|>> (/.= (/.ratio 0)) not)
..random)
right ..random]
(_.cover [/.%]
(let [rem (/.% left right)
div (|> right (/.- rem) (/./ left))]
(and (/.= right
(|> div (/.* left) (/.+ rem)))
(case (/.nat div)
(#.Some _) true
#.None false)))))
(do random.monad
[left ..random
right ..random]
($_ _.and
(_.cover [/.>]
(bit\= (/.> left right)
(/.< right left)))
(_.cover [/.<= /.>=]
(bit\= (/.<= left right)
(/.>= right left)))
))
))))
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