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## https://en.wikipedia.org/wiki/Multiset
(.module:
[lux #*
[control
[equivalence (#+ Equivalence)]
[hash (#+ Hash)]]
["." function]
[type (#+ :share)
abstract]]
[////
["." maybe]]
[///
["." list ("list/." Fold<List>)]
["." dictionary (#+ Dictionary)]]
["." //])
(abstract: #export (Set a)
{}
(Dictionary a Nat)
(def: #export new
(All [a] (-> (Hash a) (Set a)))
(|>> dictionary.new :abstraction))
(def: #export size
(All [a] (-> (Set a) Nat))
(|>> :representation dictionary.values (list/fold n/+ +0)))
(def: #export (add/* count elem set)
(All [a] (-> Nat a (Set a) (Set a)))
(|> set :representation (dictionary.update~ elem +0 (n/+ count)) :abstraction))
(def: #export add/1
(All [a] (-> a (Set a) (Set a)))
(add/* +1))
(def: #export (remove/* count elem set)
(All [a] (-> Nat a (Set a) (Set a)))
(case (dictionary.get elem (:representation set))
(#.Some current)
(let [transform (:share [a]
{(Set a)
set}
{(-> (Dictionary a Nat) (Dictionary a Nat))
(if (n/> count current)
(dictionary.update elem (n/- count))
(dictionary.remove elem))})]
(|> set :representation transform :abstraction))
#.None
set))
(def: #export remove/1
(All [a] (-> a (Set a) (Set a)))
(remove/* +1))
(def: #export (multiplicity elem set)
(All [a] (-> a (Set a) Nat))
(|> set :representation (dictionary.get elem) (maybe.default +0)))
(def: #export to-list
(All [a] (-> (Set a) (List a)))
(let [append (: (All [a] (-> a Nat (List a) (List a)))
(function (append elem count output)
(case count
+0 output
_ (|> output (#.Cons elem) (append elem (dec count))))))]
(|>> :representation
dictionary.entries
(list/fold (function (_ [elem count] output)
(append elem count output))
#.Nil))))
(def: #export (union parameter subject)
(All [a] (-> (Set a) (Set a) (Set a)))
(:abstraction (dictionary.merge-with n/+ (:representation parameter) (:representation subject))))
(def: #export (difference parameter subject)
(All [a] (-> (Set a) (Set a) (Set a)))
(|> parameter
:representation
dictionary.entries
(list/fold (function (_ [elem count] output)
(remove/* count elem output))
subject)))
(def: #export (intersection parameter subject)
(All [a] (-> (Set a) (Set a) (Set a)))
(|> parameter
:representation
dictionary.entries
(list/fold (function (_ [elem count] (^:representation output))
(:abstraction (if (dictionary.contains? elem output)
(dictionary.update elem (n/min count) output)
output)))
subject)))
(def: #export (sub? reference subject)
(All [a] (-> (Set a) (Set a) Bit))
(|> subject
:representation
dictionary.entries
(list.every? (function (_ [elem count])
(|> reference
:representation
(dictionary.get elem)
(maybe.default +0)
(n/>= count))))))
(def: #export (support set)
(All [a] (-> (Set a) (//.Set a)))
(let [(^@ set [Hash<a> _]) (:representation set)]
(|> set
dictionary.keys
(//.from-list Hash<a>))))
(structure: #export Equivalence<Set> (All [a] (Equivalence (Set a)))
(def: (= (^:representation reference) (^:representation sample))
(and (n/= (dictionary.size reference)
(dictionary.size sample))
(|> reference
dictionary.entries
(list.every? (function (_ [elem count])
(|> sample
(dictionary.get elem)
(maybe.default +0)
(n/= count))))))))
(structure: #export Hash<Set> (All [a] (Hash (Set a)))
(def: eq ..Equivalence<Set>)
(def: (hash (^:representation set))
(let [[Hash<a> _] set]
(list/fold (function (_ [elem count] acc)
(|> elem (:: Hash<a> hash) (n/* count) (n/+ acc)))
+0
(dictionary.entries set)))))
)
(def: #export (member? set elem)
(All [a] (-> (Set a) a Bit))
(|> set (..multiplicity elem) (n/> +0)))
(def: #export empty?
(All [a] (-> (Set a) Bit))
(|>> ..size (n/= +0)))
(def: #export (from-list Hash<a> subject)
(All [a] (-> (Hash a) (List a) (Set a)))
(list/fold ..add/1 (..new Hash<a>) subject))
(def: #export super?
(All [a] (-> (Set a) (Set a) Bit))
(function.flip sub?))
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