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(.module:
[lux #*
[control
[equivalence (#+ Equivalence)]
["." hash (#+ Hash)]
[predicate (#+ Predicate)]]
[data
[collection
["dict" dictionary (#+ Dictionary)]
["." list ("list/." fold)]]]
[type
abstract]])
(abstract: #export (Set a)
{}
(Dictionary a a)
(def: #export new
(All [a] (-> (Hash a) (Set a)))
(|>> dict.new :abstraction))
(def: #export size
(All [a] (-> (Set a) Nat))
(|>> :representation dict.size))
(def: #export (add elem set)
(All [a] (-> a (Set a) (Set a)))
(|> set :representation (dict.put elem elem) :abstraction))
(def: #export (remove elem set)
(All [a] (-> a (Set a) (Set a)))
(|> set :representation (dict.remove elem) :abstraction))
(def: #export (member? set elem)
(All [a] (-> (Set a) a Bit))
(|> set :representation (dict.contains? elem)))
(def: #export to-list
(All [a] (-> (Set a) (List a)))
(|>> :representation dict.keys))
(def: #export (union xs yx)
(All [a] (-> (Set a) (Set a) (Set a)))
(:abstraction (dict.merge (:representation xs) (:representation yx))))
(def: #export (difference sub base)
(All [a] (-> (Set a) (Set a) (Set a)))
(list/fold ..remove base (..to-list sub)))
(def: #export (intersection filter base)
(All [a] (-> (Set a) (Set a) (Set a)))
(:abstraction (dict.select (dict.keys (:representation filter))
(:representation base))))
(structure: #export equivalence (All [a] (Equivalence (Set a)))
(def: (= reference sample)
(let [[hash _] (:representation reference)]
(:: (list.equivalence (get@ #hash.&equivalence hash)) =
(..to-list reference) (..to-list sample)))))
(structure: #export hash (All [a] (Hash (Set a)))
(def: &equivalence ..equivalence)
(def: (hash set)
(let [[hash _] (:representation set)]
(list/fold (function (_ elem acc) (n/+ (:: hash hash elem) acc))
0
(..to-list set)))))
)
(def: #export empty?
(All [a] (-> (Set a) Bit))
(|>> ..size (n/= 0)))
(def: #export (from-list hash elements)
(All [a] (-> (Hash a) (List a) (Set a)))
(list/fold ..add (..new hash) elements))
(def: #export (sub? super sub)
(All [a] (-> (Set a) (Set a) Bit))
(list.every? (..member? super) (..to-list sub)))
(def: #export (super? sub super)
(All [a] (-> (Set a) (Set a) Bit))
(sub? super sub))
(def: #export predicate
(All [a] (-> (Set a) (Predicate a)))
..member?)
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