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|
(.require
[library
[lux (.except has list)
[abstract
[equivalence (.only Equivalence)]
[order (.only Order)]]
[data
[collection
["[0]" list (.use "[1]#[0]" mix)]
[dictionary
["/" ordered]]]]
[type
[primitive (.except)]]]])
(primitive .public (Set a)
(/.Dictionary a a)
(def .public empty
(All (_ a) (-> (Order a) (Set a)))
(|>> /.empty abstraction))
(def .public (member? set elem)
(All (_ a) (-> (Set a) a Bit))
(/.key? (representation set) elem))
(with_template [<type> <name> <alias>]
[(def .public <name>
(All (_ a) (-> (Set a) <type>))
(|>> representation <alias>))]
[(Maybe a) min /.min]
[(Maybe a) max /.max]
[Nat size /.size]
[Bit empty? /.empty?]
)
(def .public (has elem set)
(All (_ a) (-> a (Set a) (Set a)))
(|> set representation (/.has elem elem) abstraction))
(def .public (lacks elem set)
(All (_ a) (-> a (Set a) (Set a)))
(|> set representation (/.lacks elem) abstraction))
(def .public list
(All (_ a) (-> (Set a) (List a)))
(|>> representation /.keys))
(def .public (of_list order list)
(All (_ a) (-> (Order a) (List a) (Set a)))
(list#mix has (..empty order) list))
(def .public (union left right)
(All (_ a) (-> (Set a) (Set a) (Set a)))
(list#mix ..has right (..list left)))
(def .public (intersection left right)
(All (_ a) (-> (Set a) (Set a) (Set a)))
(|> (..list right)
(list.only (..member? left))
(..of_list (the /.#order (representation right)))))
(def .public (difference param subject)
(All (_ a) (-> (Set a) (Set a) (Set a)))
(|> (..list subject)
(list.only (|>> (..member? param) not))
(..of_list (the /.#order (representation subject)))))
(def .public equivalence
(All (_ a) (Equivalence (Set a)))
(implementation
(def (= reference sample)
(at (list.equivalence (at (representation reference) equivalence))
= (..list reference) (..list sample)))))
)
(def .public (sub? super sub)
(All (_ a) (-> (Set a) (Set a) Bit))
(|> sub
..list
(list.every? (..member? super))))
(def .public (super? sub super)
(All (_ a) (-> (Set a) (Set a) Bit))
(sub? super sub))
|
