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|
(.using
[library
[lux (.except)
["_" test (.only Test)]
[abstract
[monad (.only do)]
[\\specification
["$[0]" equivalence]
["$[0]" hash]
["$[0]" order]
["$[0]" enum]
["$[0]" interval]
["$[0]" monoid]
["$[0]" codec]]]
[data
["[0]" bit (.open: "[1]#[0]" equivalence)]]
[math
["[0]" random]]]]
[\\library
["[0]" / (.only)
[//
["f" frac]]]])
(def: signature
Test
(`` (all _.and
(_.for [/.equivalence /.=]
($equivalence.spec /.equivalence random.nat))
(_.for [/.hash]
($hash.spec /.hash random.nat))
(_.for [/.order /.<]
($order.spec /.order random.nat))
(_.for [/.enum]
($enum.spec /.enum random.nat))
(_.for [/.interval]
($interval.spec /.interval random.nat))
(~~ (template [<composite> <monoid>]
[(_.for [<monoid> <composite>]
($monoid.spec /.equivalence <monoid> random.nat))]
[/.+ /.addition]
[/.* /.multiplication]
[/.min /.minimum]
[/.max /.maximum]
))
(~~ (template [<codec>]
[(_.for [<codec>]
($codec.spec /.equivalence <codec> random.nat))]
[/.binary] [/.octal] [/.decimal] [/.hex]
))
)))
(def: predicate
Test
(do [! random.monad]
[sample random.nat]
(all _.and
(_.coverage [/.even? /.odd?]
(bit#= (/.even? sample)
(not (/.odd? sample))))
)))
(def: .public test
Test
(<| (_.covering /._)
(_.for [.Nat])
(all _.and
(do random.monad
[sample random.nat]
(all _.and
(_.coverage [/.-]
(and (/.= 0 (/.- sample sample))
(/.= sample (/.- 0 sample))))
(_.coverage [/./]
(and (/.= 1 (/./ sample sample))
(/.= sample (/./ 1 sample))))
))
(do random.monad
[left random.nat
right random.nat]
(all _.and
(_.coverage [/.>]
(bit#= (/.> left right)
(/.< right left)))
(_.coverage [/.<= /.>=]
(bit#= (/.<= left right)
(/.>= right left)))
))
(do random.monad
[left (random.only (|>> (/.= 0) not)
random.nat)
right random.nat]
(all _.and
(_.coverage [/.%]
(let [rem (/.% left right)
div (|> right (/.- rem) (/./ left))]
(/.= right
(|> div (/.* left) (/.+ rem)))))
(_.coverage [/./%]
(let [[div rem] (/./% left right)]
(and (/.= div (/./ left right))
(/.= rem (/.% left right)))))
))
(do [! random.monad]
[.let [random (# ! each (|>> (/.% 1,000) ++) random.nat)]
left random
right random]
(all _.and
(_.coverage [/.gcd]
(let [gcd (/.gcd left right)]
(and (/.= 0 (/.% gcd left))
(/.= 0 (/.% gcd right)))))
(_.coverage [/.co_prime?]
(bit#= (/.= 1 (/.gcd left right))
(/.co_prime? left right)))
(_.coverage [/.lcm]
(let [lcm (/.lcm left right)]
(and (/.= 0 (/.% left lcm))
(/.= 0 (/.% right lcm)))))
))
(do [! random.monad]
[expected (# ! each (/.% 1,000,000) random.nat)
sample random.nat]
(_.coverage [/.frac]
(and (|> expected /.frac f.nat (/.= expected))
(f.number? (/.frac sample)))))
..predicate
..signature
)))
|
