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(.using
[library
[lux "*"
[abstract
[monoid (.only Monoid)]
[equivalence (.only Equivalence)]
[hash (.only Hash)]
[codec (.only Codec)]]
[control
["[0]" function]]]])
(template [<zero> <one>]
[(def: .public <zero> Bit #0)
(def: .public <one> Bit #1)]
[no yes]
[off on]
)
(implementation: .public equivalence
(Equivalence Bit)
(def: (= x y)
(if x
y
(not y))))
(implementation: .public hash
(Hash Bit)
(def: equivalence ..equivalence)
(def: (hash value)
(case value
#0 2
#1 3)))
(template [<name> <identity> <op>]
[(implementation: .public <name>
(Monoid Bit)
(def: identity <identity>)
(def: (composite x y) (<op> x y)))]
[disjunction #0 or]
[conjunction #1 and]
)
(implementation: .public codec
(Codec Text Bit)
(def: (encoded x)
(if x
"#1"
"#0"))
(def: (decoded input)
(case input
"#1" {.#Right #1}
"#0" {.#Right #0}
_ {.#Left "Wrong syntax for Bit."})))
(def: .public complement
(All (_ a) (-> (-> a Bit) (-> a Bit)))
(function.composite not))
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