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|
(.require
[library
[lux (.except)
["_" test (.only Test)]
[abstract
[monad (.only do)]
[order (.only Order)]
[\\specification
["$[0]" equivalence]]]
[data
["[0]" bit (.use "[1]#[0]" equivalence)]
[collection
["[0]" list]]]
[math
["[0]" random (.only Random) (.use "[1]#[0]" monad)]
[number
["n" nat]]]]]
[\\library
["[0]" / (.only Set)
["[0]" //]]])
(def size
(random.Random Nat)
(at random.monad each (n.% 100) random.nat))
(def .public (random size order gen_value)
(All (_ a) (-> Nat (Order a) (Random a) (Random (Set a))))
(case size
0
(random#in (/.empty order))
_
(do random.monad
[partial (random (-- size) order gen_value)
value (random.only (|>> (/.member? partial) not)
gen_value)]
(in (/.has value partial)))))
(def .public test
Test
(<| (_.covering /._)
(_.for [/.Set])
(do [! random.monad]
[sizeL ..size
sizeR ..size
usetL (random.set n.hash sizeL random.nat)
non_memberL (random.only (|>> (//.member? usetL) not)
random.nat)
.let [listL (//.list usetL)]
listR (|> (random.set n.hash sizeR random.nat) (at ! each //.list))
.let [(open "/#[0]") /.equivalence
setL (/.of_list n.order listL)
setR (/.of_list n.order listR)
empty (/.empty n.order)]]
(`` (all _.and
(_.for [/.equivalence]
($equivalence.spec /.equivalence (..random sizeL n.order random.nat)))
(_.coverage [/.size]
(n.= sizeL (/.size setL)))
(_.coverage [/.empty?]
(bit#= (n.= 0 (/.size setL))
(/.empty? setL)))
(_.coverage [/.empty]
(/.empty? (/.empty n.order)))
(_.coverage [/.list]
(at (list.equivalence n.equivalence) =
(/.list (/.of_list n.order listL))
(list.sorted (at n.order <) listL)))
(_.coverage [/.of_list]
(|> setL
/.list (/.of_list n.order)
(/#= setL)))
(~~ (with_template [<coverage> <comparison>]
[(_.coverage [<coverage>]
(case (<coverage> setL)
{.#Some value}
(|> setL /.list (list.every? (<comparison> value)))
{.#None}
(/.empty? setL)))]
[/.min n.>=]
[/.max n.<=]
))
(_.coverage [/.member?]
(let [members_are_identified!
(list.every? (/.member? setL) (/.list setL))
non_members_are_not_identified!
(not (/.member? setL non_memberL))]
(and members_are_identified!
non_members_are_not_identified!)))
(_.coverage [/.has]
(let [setL+ (/.has non_memberL setL)]
(and (not (/.member? setL non_memberL))
(/.member? setL+ non_memberL)
(n.= (++ (/.size setL))
(/.size setL+)))))
(_.coverage [/.lacks]
(|> setL
(/.has non_memberL)
(/.lacks non_memberL)
(at /.equivalence = setL)))
(_.coverage [/.sub?]
(let [self!
(/.sub? setL setL)
empty!
(/.sub? setL empty)]
(and self!
empty!)))
(_.coverage [/.super?]
(let [self!
(/.super? setL setL)
empty!
(/.super? empty setL)
symmetry!
(bit#= (/.super? setL setR)
(/.sub? setR setL))]
(and self!
empty!
symmetry!)))
(~~ (with_template [<coverage> <relation> <empty?>]
[(_.coverage [<coverage>]
(let [self!
(at /.equivalence =
setL
(<coverage> setL setL))
super!
(and (<relation> (<coverage> setL setR) setL)
(<relation> (<coverage> setL setR) setR))
empty!
(at /.equivalence =
(if <empty?> empty setL)
(<coverage> setL empty))
idempotence!
(at /.equivalence =
(<coverage> setL (<coverage> setL setR))
(<coverage> setR (<coverage> setL setR)))]
(and self!
super!
empty!
idempotence!)))]
[/.union /.sub? false]
[/.intersection /.super? true]
))
(_.coverage [/.difference]
(let [self!
(|> setL
(/.difference setL)
(at /.equivalence = empty))
empty!
(|> setL
(/.difference empty)
(at /.equivalence = setL))
difference!
(not (list.any? (/.member? (/.difference setL setR))
(/.list setL)))
idempotence!
(at /.equivalence =
(/.difference setL setR)
(/.difference setL (/.difference setL setR)))]
(and self!
empty!
difference!
idempotence!)))
)))))
|
