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(.module:
[lux #*
["_" test (#+ Test)]
["." function]
[control
[monad (#+ do)]
{[0 #test]
[/
["." equivalence]
["." codec]]}]
data/text/format
[math
["r" random]]]
{1
["." /]})
(def: #export test
Test
(<| (_.context (%name (name-of .Bit)))
(do r.monad
[value r.bit]
($_ _.and
(_.test "A value cannot be true and false at the same time."
(not (and value (not value))))
(_.test "A value must be either true or false at any time."
(or value (not value)))
(_.test "Can create the complement of a predicate."
(and (not (:: /.equivalence = value ((/.complement function.identity) value)))
(:: /.equivalence = value ((/.complement not) value))))
(equivalence.test /.equivalence r.bit)
(codec.test /.codec /.equivalence r.bit)
(_.test "Or/disjunction monoid."
(and (not (:: /.or-monoid identity))
(:: /.or-monoid compose value (not value))))
(_.test "And/conjunction monoid."
(and (:: /.and-monoid identity)
(not (:: /.and-monoid compose value (not value)))))
))))
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