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|
(.require
[library
[lux (.except)
[abstract
[equivalence (.only)]
[functor (.only)]
[monoid (.only)]
[monad (.only do)]
["[0]" enum]]
[data
["[0]" bit (.use "[1]#[0]" equivalence)]
[collection
["[0]" list]]]
[math
["[0]" random (.only Random)]
[number
["n" nat]]]
[test
["_" property (.only Test)]]]]
[\\library
["[0]" /]])
(/.implicitly n.multiplication)
(def .public test
Test
(<| (_.covering /._)
(do [! random.monad]
[.let [digit (at ! each (n.% 10) random.nat)]
left digit
right digit
.let [start (n.min left right)
end (n.max left right)]
left random.nat
right random.nat]
(all _.and
(_.coverage [/.a/an /.a /.an]
(let [first_order!
(let [(open "list#[0]") (list.equivalence n.equivalence)]
(and (bit#= (at n.equivalence = left right)
(/.a = left right))
(list#= (at list.functor each ++ (enum.range n.enum start end))
(/.an each ++ (enum.range n.enum start end)))))
second_order!
(/.a/an =
(enum.range n.enum start end)
(enum.range n.enum start end))
third_order!
(let [lln (/.a/an each (enum.range n.enum start)
(enum.range n.enum start end))]
(/.a/an = lln lln))]
(and first_order!
second_order!
third_order!)))
(_.coverage [/.with]
(/.with [n.addition]
(n.= (at n.addition composite left right)
(/.a/an composite left right))))
(_.coverage [/.implicitly]
(n.= (at n.multiplication composite left right)
(/.a/an composite left right)))
))))
|
