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(.module:
[lux #*
[abstract
[monoid (#+ Monoid)]
[equivalence (#+ Equivalence)]
hash
[codec (#+ Codec)]]
[control
["." function]]])
(structure: #export equivalence
(Equivalence Bit)
(def: (= x y)
(if x
y
(not y))))
(structure: #export hash
(Hash Bit)
(def: &equivalence ..equivalence)
(def: (hash value)
(case value
#1 1
#0 0)))
(template [<name> <identity> <op>]
[(structure: #export <name>
(Monoid Bit)
(def: identity <identity>)
(def: (compose x y) (<op> x y)))]
[disjunction #0 or]
[conjunction #1 and]
)
(structure: #export codec (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."))))
(def: #export complement
{#.doc (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)))
(function.compose not))
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