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|
(.module:
[library
[lux #*
[abstract
[equivalence (#+ Equivalence)]
[order (#+ Order)]
[monoid (#+ Monoid)]
[codec (#+ Codec)]
[monad (#+ do)]]
[control
["." try (#+ Try)]
["." exception (#+ exception:)]
["<>" parser
["<.>" text (#+ Parser)]
["<.>" code]]]
[data
["." product]
["." text ("#\." monoid)]]
[macro
[syntax (#+ syntax:)]
["." code]]
[math
[number
["i" int ("#\." decimal)]]]
[type
abstract]]]
["." // #_
["#" modulus (#+ Modulus)]])
(abstract: .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)}))
(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))))
(implementation: .public (codec expected)
(All [%] (-> (Modulus %) (Codec Text (Mod %))))
(def: (encoded modular)
(let [[_ value] (:representation modular)]
($_ text\composite
(i\encoded value)
..separator
(i\encoded (//.divisor expected)))))
(def: decoded
(<text>.result
(do <>.monad
[[value _ actual] ($_ <>.and intL (<text>.this ..separator) intL)
_ (<>.assertion (exception.error ..incorrect_modulus [expected actual])
(i.= (//.divisor expected) actual))]
(in (..modular expected value))))))
(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.>=]
)
(implementation: .public equivalence
(All [%] (Equivalence (Mod %)))
(def: = ..=))
(implementation: .public order
(All [%] (Order (Mod %)))
(def: &equivalence ..equivalence)
(def: < ..<))
(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.*]
)
(template [<composition> <identity> <monoid>]
[(implementation: .public (<monoid> modulus)
(All [%] (-> (Modulus %) (Monoid (Mod %))))
(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])))
|
