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(.module:
[lux #*
[control
[monoid (#+ Monoid)]
[equivalence (#+ Equivalence)]
hash
[codec (#+ Codec)]]
function])
## [Structures]
(structure: #export _ (Equivalence Bit)
(def: (= x y)
(if x
y
(not y))))
(structure: #export _ (Hash Bit)
(def: eq Equivalence<Bit>)
(def: (hash value)
(case value
#1 +1
#0 +0)))
(do-template [<name> <identity> <op>]
[(structure: #export <name> (Monoid Bit)
(def: identity <identity>)
(def: (compose x y)
(<op> x y)))]
[ Or@Monoid<Bit> #0 or]
[And@Monoid<Bit> #1 and]
)
(structure: #export _ (Codec Text Bit)
(def: (encode x)
(if x
"#1"
"#0"))
(def: (decode input)
(case input
"#1" (#.Right #1)
"#0" (#.Right #0)
_ (#.Left "Wrong syntax for Bit."))))
## [Values]
(def: #export complement
{#.doc "Generates the complement of a predicate.
That is a predicate that returns the oposite of the original predicate."}
(All [a] (-> (-> a Bit) (-> a Bit)))
(compose not))
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