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(.module:
[lux #*
[abstract
[equivalence (#+ Equivalence)]
[order (#+ Order)]]
[data
[collection
["." list ("#\." fold)]
[dictionary
["/" ordered]]]]
[type
abstract]])
(abstract: #export (Set a)
(/.Dictionary a a)
(def: #export new
(All [a] (-> (Order a) (Set a)))
(|>> /.new :abstraction))
(def: #export (member? set elem)
(All [a] (-> (Set a) a Bit))
(/.key? (:representation set) elem))
(template [<type> <name> <alias>]
[(def: #export <name>
(All [a] (-> (Set a) <type>))
(|>> :representation <alias>))]
[(Maybe a) min /.min]
[(Maybe a) max /.max]
[Nat size /.size]
[Bit empty? /.empty?]
)
(def: #export (add elem set)
(All [a] (-> a (Set a) (Set a)))
(|> set :representation (/.put elem elem) :abstraction))
(def: #export (remove elem set)
(All [a] (-> a (Set a) (Set a)))
(|> set :representation (/.remove elem) :abstraction))
(def: #export to-list
(All [a] (-> (Set a) (List a)))
(|>> :representation /.keys))
(def: #export (from-list &order list)
(All [a] (-> (Order a) (List a) (Set a)))
(list\fold add (..new &order) list))
(def: #export (union left right)
(All [a] (-> (Set a) (Set a) (Set a)))
(list\fold ..add right (..to-list left)))
(def: #export (intersection left right)
(All [a] (-> (Set a) (Set a) (Set a)))
(|> (..to-list right)
(list.filter (..member? left))
(..from-list (get@ #/.&order (:representation right)))))
(def: #export (difference param subject)
(All [a] (-> (Set a) (Set a) (Set a)))
(|> (..to-list subject)
(list.filter (|>> (..member? param) not))
(..from-list (get@ #/.&order (:representation subject)))))
(structure: #export equivalence
(All [a] (Equivalence (Set a)))
(def: (= reference sample)
(\ (list.equivalence (\ (:representation reference) &equivalence))
= (..to-list reference) (..to-list sample))))
)
(def: #export (sub? super sub)
(All [a] (-> (Set a) (Set a) Bit))
(|> sub
..to-list
(list.every? (..member? super))))
(def: #export (super? sub super)
(All [a] (-> (Set a) (Set a) Bit))
(sub? super sub))
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