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(.module:
[library
[lux #*
["." meta]
[abstract
[monad (#+ do)]]
[control
["." try (#+ Try)]
["." exception (#+ exception:)]
[parser
["<.>" code]]]
[macro
[syntax (#+ syntax:)]
["." code]]
[math
[number
["i" int]]]
[type
abstract]]])
(exception: #export zero_cannot_be_a_modulus)
(abstract: #export (Modulus %)
Int
{#.doc (doc "A number used as a modulus in modular arithmetic."
"It cannot be 0.")}
(def: #export (modulus value)
(Ex [%] (-> Int (Try (Modulus %))))
(if (i.= +0 value)
(exception.except ..zero_cannot_be_a_modulus [])
(#try.Success (:abstraction value))))
(def: #export divisor
(All [%] (-> (Modulus %) Int))
(|>> :representation))
(def: #export (= reference subject)
(All [%r %s] (-> (Modulus %r) (Modulus %s) Bit))
(i.= (:representation reference)
(:representation subject)))
(def: #export (congruent? modulus reference subject)
(All [%] (-> (Modulus %) Int Int Bit))
(|> subject
(i.- reference)
(i.% (:representation modulus))
(i.= +0)))
)
(syntax: #export (literal {divisor <code>.int})
{#.doc (doc "Success!"
(literal 123)
"Failure!"
(literal 0))}
(meta.lift
(do try.monad
[_ (..modulus divisor)]
(in (list (` ((~! try.assumed) (..modulus (~ (code.int divisor))))))))))
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