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|
(.using
[library
[lux (.except)
[abstract
[equivalence (.only Equivalence)]
[order (.only Order)]
[monoid (.only Monoid)]
[codec (.only Codec)]
[monad (.only do)]]
[control
["[0]" try (.only Try)]
["[0]" exception (.only exception:)]
["<>" parser (.only)
["<[0]>" code]]]
[data
["[0]" product]
["[0]" text (.open: "[1]#[0]" monoid)
["<[1]>" \\parser (.only Parser)]]]
[macro
["[0]" code]]
[math
[number
["i" int (.open: "[1]#[0]" decimal)]]]
[type
[primitive (.except)]]]]
["[0]" //
["[1]" modulus (.only Modulus)]])
(primitive .public (Mod m)
(Record
[#modulus (Modulus m)
#value Int])
(def .public (modular modulus value)
(All (_ %) (-> (Modulus %) Int (Mod %)))
(abstraction [#modulus modulus
#value (i.mod (//.divisor modulus) value)]))
(with_template [<name> <type> <side>]
[(def .public <name>
(All (_ %) (-> (Mod %) <type>))
(|>> representation <side>))]
[modulus (Modulus %) product.left]
[value Int product.right]
)
(exception: .public [%] (incorrect_modulus [modulus (Modulus %)
parsed Int])
(exception.report
"Expected" (i#encoded (//.divisor modulus))
"Actual" (i#encoded parsed)))
(def separator
" mod ")
(def intL
(Parser Int)
(<>.codec i.decimal
(<text>.and (<text>.one_of "-+") (<text>.many <text>.decimal))))
(def .public (codec expected)
(All (_ %) (-> (Modulus %) (Codec Text (Mod %))))
(implementation
(def (encoded modular)
(let [[_ value] (representation modular)]
(all text#composite
(i#encoded value)
..separator
(i#encoded (//.divisor expected)))))
(def decoded
(<text>.result
(do <>.monad
[[value _ actual] (all <>.and intL (<text>.this ..separator) intL)
_ (<>.assertion (exception.error ..incorrect_modulus [expected actual])
(i.= (//.divisor expected) actual))]
(in (..modular expected value)))))))
(with_template [<name> <op>]
[(def .public (<name> reference subject)
(All (_ %) (-> (Mod %) (Mod %) Bit))
(let [[_ reference] (representation reference)
[_ subject] (representation subject)]
(<op> reference subject)))]
[= i.=]
[< i.<]
[<= i.<=]
[> i.>]
[>= i.>=]
)
(def .public equivalence
(All (_ %) (Equivalence (Mod %)))
(implementation
(def = ..=)))
(def .public order
(All (_ %) (Order (Mod %)))
(implementation
(def equivalence ..equivalence)
(def < ..<)))
(with_template [<name> <op>]
[(def .public (<name> param subject)
(All (_ %) (-> (Mod %) (Mod %) (Mod %)))
(let [[modulus param] (representation param)
[_ subject] (representation subject)]
(abstraction [#modulus modulus
#value (|> subject
(<op> param)
(i.mod (//.divisor modulus)))])))]
[+ i.+]
[- i.-]
[* i.*]
)
(with_template [<composition> <identity> <monoid>]
[(def .public (<monoid> modulus)
(All (_ %) (-> (Modulus %) (Monoid (Mod %))))
(implementation
(def identity
(..modular modulus <identity>))
(def composite
<composition>)))]
[..+ +0 addition]
[..* +1 multiplication]
)
(def .public (inverse modular)
(All (_ %) (-> (Mod %) (Maybe (Mod %))))
(let [[modulus value] (representation modular)
[[vk mk] gcd] (i.extended_gcd value (//.divisor modulus))]
(case gcd
+1 {.#Some (..modular modulus vk)}
_ {.#None})))
)
(exception: .public [r% s%] (moduli_are_not_equal [reference (Modulus r%)
subject (Modulus s%)])
(exception.report
"Reference" (i#encoded (//.divisor reference))
"Subject" (i#encoded (//.divisor subject))))
(def .public (adapter reference subject)
(All (_ r% s%)
(-> (Modulus r%) (Modulus s%)
(Try (-> (Mod s%) (Mod r%)))))
(if (//.= reference subject)
{try.#Success (|>> ..value
(..modular reference))}
(exception.except ..moduli_are_not_equal [reference subject])))
|
