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(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[hash (#+ Hash)]
[monad (#+ do)]
["." predicate]
[\\specification
["$." equivalence]
["$." hash]]]
[data
["." bit ("#\." equivalence)]
[collection
["." set]
["." list ("#\." mix)]]]
[math
["." random (#+ Random)]
[number
["n" nat]]]]]
[\\library
["." /]])
(def: count
(Random Nat)
(\ random.monad map (|>> (n.% 10) ++) random.nat))
(def: .public (random size hash count element)
(All [a] (-> Nat (Hash a) (Random Nat) (Random a) (Random (/.Set a))))
(do {! random.monad}
[elements (random.set hash size element)
element_counts (random.list size ..count)]
(in (list\mix (function (_ [count element] set)
(/.has count element set))
(/.empty hash)
(list.zipped/2 element_counts
(set.list elements))))))
(def: signature
Test
(do {! random.monad}
[diversity (\ ! map (n.% 10) random.nat)]
($_ _.and
(_.for [/.equivalence]
($equivalence.spec /.equivalence (..random diversity n.hash ..count random.nat)))
(_.for [/.hash]
(|> random.nat
(\ random.monad map (function (_ single)
(/.has 1 single (/.empty n.hash))))
($hash.spec /.hash)))
)))
(def: composition
Test
(do {! random.monad}
[diversity (\ ! map (n.% 10) random.nat)
sample (..random diversity n.hash ..count random.nat)
another (..random diversity n.hash ..count random.nat)]
(`` ($_ _.and
(~~ (template [<name> <composition>]
[(_.cover [<name>]
(let [|sample| (/.support sample)
|another| (/.support another)
sample_only (set.difference |another| |sample|)
another_only (set.difference |sample| |another|)
common (set.intersection |sample| |another|)
composed (<name> sample another)
no_left_changes! (list.every? (function (_ member)
(n.= (/.multiplicity sample member)
(/.multiplicity composed member)))
(set.list sample_only))
no_right_changes! (list.every? (function (_ member)
(n.= (/.multiplicity another member)
(/.multiplicity composed member)))
(set.list another_only))
common_changes! (list.every? (function (_ member)
(n.= (<composition> (/.multiplicity sample member)
(/.multiplicity another member))
(/.multiplicity composed member)))
(set.list common))]
(and no_left_changes!
no_right_changes!
common_changes!)))]
[/.sum n.+]
[/.union n.max]
))
(_.cover [/.intersection]
(let [|sample| (/.support sample)
|another| (/.support another)
sample_only (set.difference |another| |sample|)
another_only (set.difference |sample| |another|)
common (set.intersection |sample| |another|)
composed (/.intersection sample another)
left_removals! (list.every? (|>> (/.member? composed) not)
(set.list sample_only))
right_removals! (list.every? (|>> (/.member? composed) not)
(set.list another_only))
common_changes! (list.every? (function (_ member)
(n.= (n.min (/.multiplicity sample member)
(/.multiplicity another member))
(/.multiplicity composed member)))
(set.list common))]
(and left_removals!
right_removals!
common_changes!)))
))))
(def: .public test
Test
(<| (_.covering /._)
(_.for [/.Set])
(do {! random.monad}
[diversity (\ ! map (n.% 10) random.nat)
sample (..random diversity n.hash ..count random.nat)
non_member (random.only (predicate.complement (set.member? (/.support sample)))
random.nat)
addition_count ..count
partial_removal_count (\ ! map (n.% addition_count) random.nat)
another (..random diversity n.hash ..count random.nat)]
($_ _.and
(_.cover [/.list /.of_list]
(|> sample
/.list
(/.of_list n.hash)
(\ /.equivalence = sample)))
(_.cover [/.size]
(n.= (list.size (/.list sample))
(/.size sample)))
(_.cover [/.empty?]
(bit\= (/.empty? sample)
(n.= 0 (/.size sample))))
(_.cover [/.empty]
(/.empty? (/.empty n.hash)))
(_.cover [/.support]
(list.every? (set.member? (/.support sample))
(/.list sample)))
(_.cover [/.member?]
(let [non_member_is_not_identified!
(not (/.member? sample non_member))
all_members_are_identified!
(list.every? (/.member? sample)
(/.list sample))]
(and non_member_is_not_identified!
all_members_are_identified!)))
(_.cover [/.multiplicity]
(let [non_members_have_0_multiplicity!
(n.= 0 (/.multiplicity sample non_member))
every_member_has_positive_multiplicity!
(list.every? (|>> (/.multiplicity sample) (n.> 0))
(/.list sample))]
(and non_members_have_0_multiplicity!
every_member_has_positive_multiplicity!)))
(_.cover [/.has]
(let [null_scenario!
(|> sample
(/.has 0 non_member)
(\ /.equivalence = sample))
normal_scenario!
(let [sample+ (/.has addition_count non_member sample)]
(and (not (/.member? sample non_member))
(/.member? sample+ non_member)
(n.= addition_count (/.multiplicity sample+ non_member))))]
(and null_scenario!
normal_scenario!)))
(_.cover [/.lacks]
(let [null_scenario!
(\ /.equivalence =
(|> sample
(/.has addition_count non_member))
(|> sample
(/.has addition_count non_member)
(/.lacks 0 non_member)))
partial_scenario!
(let [sample* (|> sample
(/.has addition_count non_member)
(/.lacks partial_removal_count non_member))]
(and (/.member? sample* non_member)
(n.= (n.- partial_removal_count
addition_count)
(/.multiplicity sample* non_member))))
total_scenario!
(|> sample
(/.has addition_count non_member)
(/.lacks addition_count non_member)
(\ /.equivalence = sample))]
(and null_scenario!
partial_scenario!
total_scenario!)))
(_.cover [/.of_set]
(let [unary (|> sample /.support /.of_set)]
(list.every? (|>> (/.multiplicity unary) (n.= 1))
(/.list unary))))
(_.cover [/.sub?]
(let [unary (|> sample /.support /.of_set)]
(and (/.sub? sample unary)
(or (not (/.sub? unary sample))
(\ /.equivalence = sample unary)))))
(_.cover [/.super?]
(let [unary (|> sample /.support /.of_set)]
(and (/.super? unary sample)
(or (not (/.super? sample unary))
(\ /.equivalence = sample unary)))))
(_.cover [/.difference]
(let [|sample| (/.support sample)
|another| (/.support another)
sample_only (set.difference |another| |sample|)
another_only (set.difference |sample| |another|)
common (set.intersection |sample| |another|)
composed (/.difference sample another)
ommissions! (list.every? (|>> (/.member? composed) not)
(set.list sample_only))
intact! (list.every? (function (_ member)
(n.= (/.multiplicity another member)
(/.multiplicity composed member)))
(set.list another_only))
subtractions! (list.every? (function (_ member)
(let [sample_multiplicity (/.multiplicity sample member)
another_multiplicity (/.multiplicity another member)]
(n.= (if (n.> another_multiplicity sample_multiplicity)
0
(n.- sample_multiplicity
another_multiplicity))
(/.multiplicity composed member))))
(set.list common))]
(and ommissions!
intact!
subtractions!)))
..signature
..composition
))))
|
