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(.module:
[lux #*
[control
["ex" exception (#+ exception:)]
["p" parser]
[codec (#+ Codec)]
[monad (#+ do)]]
[data
["e" error (#+ Error)]
[number ("int/" Codec<Text,Int>)]
[text ("text/" Monoid<Text>)
["l" lexer (#+ Lexer)]]]
[type abstract]
[macro
[code]
["s" syntax (#+ syntax:)]]
[math]])
(exception: #export zero-cannot-be-a-modulus)
(abstract: #export (Modulus m)
{#.doc "A number used as a modulus in modular arithmetic.
It cannot be 0."}
Int
(def: #export (from-int value)
(Ex [m] (-> Int (Error (Modulus m))))
(if (i/= 0 value)
(ex.throw zero-cannot-be-a-modulus [])
(#e.Success (:abstraction value))))
(def: #export (to-int modulus)
(All [m] (-> (Modulus m) Int))
(|> modulus :representation))
)
(exception: #export [m] (incorrect-modulus {modulus (Modulus m)}
{parsed Int})
($_ text/compose
"Expected: " (int/encode (to-int modulus)) "\n"
" Actual: " (int/encode parsed) "\n"))
(exception: #export [rm sm] (cannot-equalize-moduli {reference (Modulus rm)}
{sample (Modulus sm)})
($_ text/compose
"Reference: " (int/encode (to-int reference)) "\n"
" Sample: " (int/encode (to-int sample)) "\n"))
(def: #export (congruent? modulus reference sample)
(All [m] (-> (Modulus m) Int Int Bool))
(|> sample
(i/- reference)
(i/% (to-int modulus))
(i/= 0)))
(syntax: #export (modulus {modulus s.int})
(case (from-int modulus)
(#e.Success _)
(wrap (list (` (e.assume (..from-int (~ (code.int modulus)))))))
(#e.Error error)
(p.fail error)))
(def: intL
(Lexer Int)
(p.codec number.Codec<Text,Int>
(p.either (l.seq (l.one-of "-") (l.many l.decimal))
(l.many l.decimal))))
(abstract: #export (Mod m)
{#.doc "A number under a modulus."}
{#remainder Int
#modulus (Modulus m)}
(def: #export (mod modulus)
(All [m] (-> (Modulus m) (-> Int (Mod m))))
(function (_ value)
(:abstraction {#remainder (i/mod (to-int modulus) value)
#modulus modulus})))
(def: #export (un-mod modular)
(All [m] (-> (Mod m) [Int (Modulus m)]))
(:representation modular))
(def: separator Text " mod ")
(structure: #export (Codec<Text,Mod> modulus)
(All [m] (-> (Modulus m) (Codec Text (Mod m))))
(def: (encode modular)
(let [[remainder modulus] (:representation modular)]
($_ text/compose
(int/encode remainder)
separator
(int/encode (to-int modulus)))))
(def: (decode text)
(<| (l.run text)
(do p.Monad<Parser>
[[remainder _ _modulus] ($_ p.seq intL (l.this separator) intL)
_ (p.assert (ex.construct incorrect-modulus [modulus _modulus])
(i/= (to-int modulus) _modulus))]
(wrap (mod modulus remainder))))))
(def: #export (equalize reference sample)
(All [r s] (-> (Mod r) (Mod s) (Error (Mod r))))
(let [[reference reference-modulus] (:representation reference)
[sample sample-modulus] (:representation sample)]
(if (i/= (to-int reference-modulus)
(to-int sample-modulus))
(#e.Success (:abstraction {#remainder sample
#modulus reference-modulus}))
(ex.throw cannot-equalize-moduli [reference-modulus sample-modulus]))))
(do-template [<name> <op>]
[(def: #export (<name> reference sample)
(All [m] (-> (Mod m) (Mod m) Bool))
(let [[reference _] (:representation reference)
[sample _] (:representation sample)]
(<op> reference sample)))]
[m/= i/=]
[m/< i/<]
[m/<= i/<=]
[m/> i/>]
[m/>= i/>=]
)
(do-template [<name> <op>]
[(def: #export (<name> param subject)
(All [m] (-> (Mod m) (Mod m) (Mod m)))
(let [[param modulus] (:representation param)
[subject _] (:representation subject)]
(:abstraction {#remainder (|> subject
(<op> param)
(i/mod (to-int modulus)))
#modulus modulus})))]
[m/+ i/+]
[m/- i/-]
[m/* i/*])
(def: (i/gcd+ a b)
(-> Int Int [Int Int Int])
(if (i/= 0 a)
[0 1 b]
(let [[ak bk gcd] (i/gcd+ (i/% a b) a)]
[(i/- (i/* ak
(i// a b))
bk)
ak
gcd])))
(def: #export (inverse modular)
(All [m] (-> (Mod m) (Maybe (Mod m))))
(let [[value modulus] (:representation modular)
_modulus (to-int modulus)
[vk mk gcd] (i/gcd+ value _modulus)
co-prime? (i/= 1 gcd)]
(if co-prime?
(#.Some (mod modulus vk))
#.None)))
)
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