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(.require
[library
[lux (.except has list)
[abstract
[equivalence (.only Equivalence)]
[hash (.only Hash)]
[monoid (.only Monoid)]]
[control
[function
[predicate (.only Predicate)]]]
[data
[collection
["[0]" list (.use "[1]#[0]" mix)]]]
[math
[number
["n" nat]]]
[meta
[macro
["^" pattern]]]]]
["[0]" //
["[1]" dictionary (.only Dictionary)]])
(type .public (Set a)
(Dictionary a Any))
(def .public member_hash
(All (_ a) (-> (Set a) (Hash a)))
//.key_hash)
(def .public empty
(All (_ a) (-> (Hash a) (Set a)))
//.empty)
(def .public size
(All (_ a) (-> (Set a) Nat))
//.size)
(def .public (has elem set)
(All (_ a) (-> a (Set a) (Set a)))
(|> set (//.has elem [])))
(def .public lacks
(All (_ a) (-> a (Set a) (Set a)))
//.lacks)
(def .public member?
(All (_ a) (-> (Set a) a Bit))
//.key?)
(def .public list
(All (_ a) (-> (Set a) (List a)))
//.keys)
(def .public union
(All (_ a) (-> (Set a) (Set a) (Set a)))
//.composite)
(def .public (difference sub base)
(All (_ a) (-> (Set a) (Set a) (Set a)))
(list#mix ..lacks base (..list sub)))
(def .public (intersection filter base)
(All (_ a) (-> (Set a) (Set a) (Set a)))
(//.sub (//.keys filter)
base))
(def .public equivalence
(All (_ a) (Equivalence (Set a)))
(implementation
(def (= (^.let reference [hash _]) sample)
(and (n.= (..size reference)
(..size sample))
(list.every? (..member? reference)
(..list sample))))))
(def .public hash
(All (_ a) (Hash (Set a)))
(implementation
(def equivalence ..equivalence)
(def (hash set)
(|> set
..list
(at (list.hash (..member_hash set)) hash)))))
(def .public (monoid hash)
(All (_ a) (-> (Hash a) (Monoid (Set a))))
(implementation
(def identity (..empty hash))
(def composite ..union)))
(def .public empty?
(All (_ a) (-> (Set a) Bit))
(|>> ..size (n.= 0)))
(def .public (of_list hash elements)
(All (_ a) (-> (Hash a) (List a) (Set a)))
(list#mix ..has (..empty hash) elements))
(def .public (sub? super sub)
(All (_ a) (-> (Set a) (Set a) Bit))
(list.every? (..member? super) (..list sub)))
(def .public (super? sub super)
(All (_ a) (-> (Set a) (Set a) Bit))
(..sub? super sub))
(def .public predicate
(All (_ a) (-> (Set a) (Predicate a)))
..member?)
|
