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|
(.require
[library
[lux (.except)
["_" test (.only Test)]
[abstract
[monad (.only do)]
[\\specification
["$[0]" equivalence]
["$[0]" order]
["$[0]" monoid]
["$[0]" codec]]]
[control
["[0]" maybe (.use "[1]#[0]" functor)]]
[data
["[0]" bit (.use "[1]#[0]" equivalence)]]
[math
["[0]" random (.only Random)]]]]
[\\library
["[0]" / (.only)
[//
["n" nat (.use "[1]#[0]" equivalence)]]]])
(def part
(Random Nat)
(at random.monad each
(|>> (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])
(`` (all _.and
(_.for [/.equivalence /.=]
($equivalence.spec /.equivalence ..random))
(_.for [/.order /.<]
($order.spec /.order ..random))
(~~ (with_template [<composite> <monoid>]
[(_.for [<monoid> <composite>]
($monoid.spec /.equivalence <monoid> ..random))]
[/.+ /.addition]
[/.* /.multiplication]
))
(_.for [/.codec]
($codec.spec /.equivalence /.codec ..random))
(do random.monad
[.let [(open "#[0]") /.equivalence]
denom/0 ..part
denom/1 ..part]
(_.coverage [/.ratio]
(#= (/.ratio 0 denom/0)
(/.ratio 0 denom/1))))
(do random.monad
[numerator ..part
denominator (random.only (|>> (n#= 1) not)
..part)]
(_.coverage [/.nat]
(let [only_numerator!
(|> (/.ratio numerator)
/.nat
(maybe#each (n#= numerator))
(maybe.else false))
denominator_1!
(|> (/.ratio numerator 1)
/.nat
(maybe#each (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]
(all _.and
(_.coverage [/.-]
(and (/.= (/.ratio 0) (/.- sample sample))
(/.= sample (/.- (/.ratio 0) sample))))
(_.coverage [/./]
(and (/.= (/.ratio 1) (/./ sample sample))
(/.= sample (/./ (/.ratio 1) sample))))
(_.coverage [/.reciprocal]
(/.= (/.ratio 1)
(/.* sample (/.reciprocal sample))))
))
(do random.monad
[left (random.only (|>> (/.= (/.ratio 0)) not)
..random)
right ..random]
(_.coverage [/.%]
(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]
(all _.and
(_.coverage [/.>]
(bit#= (/.> left right)
(/.< right left)))
(_.coverage [/.<= /.>=]
(bit#= (/.<= left right)
(/.>= right left)))
))
))))
|
