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|
(.module:
[library
[lux #*
["_" test (#+ Test)]
[abstract
[equivalence (#+ Equivalence)]
[monad (#+ do)]
[\\specification
[functor
["$." contravariant]]]]
[data
["." bit ("#\." equivalence)]
[collection
["." list]
["." set]]]
[math
["." random (#+ Random)]
[number
["n" nat]
["r" rev]]]]]
[\\library
["." / (#+ Fuzzy)
["/#" // #_
["#" continuous]]]])
(def: trivial
Test
(do random.monad
[sample random.rev]
($_ _.and
(_.cover [/.empty]
(r.= //.false (/.empty sample)))
(_.cover [/.full]
(r.= //.true (/.full sample)))
)))
(def: simple
Test
(do {! random.monad}
[sample random.rev
threshold_0 (\ ! each (r.% .5)
random.rev)
threshold_1 (\ ! each (|>> (r.% .5) (r.+ .5))
random.rev)
.let [bottom (r.min threshold_0 threshold_1)
top (r.max threshold_0 threshold_1)]]
($_ _.and
(_.cover [/.gradient]
(let [ascending!
(let [set (/.gradient bottom top)]
(and (r.= //.false (set bottom))
(r.= //.true (set top))
(let [membership (set sample)]
(cond (r.<= bottom sample)
(r.= //.false membership)
(r.>= top sample)
(r.= //.true membership)
(r.> //.false membership)))))
descending!
(let [set (/.gradient top bottom)]
(and (r.= //.true (set bottom))
(r.= //.false (set top))
(let [membership (set sample)]
(cond (r.<= bottom sample)
(r.= //.true membership)
(r.>= top sample)
(r.= //.false membership)
(r.> //.false membership)))))]
(and ascending!
descending!)))
(_.cover [/.membership]
(let [set (/.gradient bottom top)]
(r.= (set sample)
(/.membership set sample))))
)))
(def: composition
Test
(do {! random.monad}
[sample random.rev
[bottom middle_bottom middle_top top]
(|> random.rev
(random.set r.hash 4)
(\ ! each (|>> set.list (list.sorted r.<)))
(random.one (function (_ thresholds)
(case thresholds
(^ (list threshold_0 threshold_1 threshold_2 threshold_3))
(#.Some [threshold_0 threshold_1 threshold_2 threshold_3])
_
#.None))))
.let [bottom_set (/.gradient bottom middle_bottom)
top_set (/.gradient middle_top top)]]
($_ _.and
(_.cover [/.union]
(let [set (/.gradient bottom top)]
(and (r.= (/.membership set sample)
(/.membership (/.union /.empty set) sample))
(r.= (/.membership /.full sample)
(/.membership (/.union /.full set) sample))
(r.>= (/.membership bottom_set sample)
(/.membership (/.union bottom_set top_set) sample))
(r.>= (/.membership top_set sample)
(/.membership (/.union bottom_set top_set) sample)))))
(_.cover [/.intersection]
(let [set (/.gradient bottom top)]
(and (r.= (/.membership /.empty sample)
(/.membership (/.intersection /.empty set) sample))
(r.= (/.membership set sample)
(/.membership (/.intersection /.full set) sample))
(r.<= (/.membership bottom_set sample)
(/.membership (/.intersection bottom_set top_set) sample))
(r.<= (/.membership top_set sample)
(/.membership (/.intersection bottom_set top_set) sample)))))
(_.cover [/.complement]
(let [set (/.gradient bottom top)
trivial!
(and (r.= (/.membership /.full sample)
(/.membership (/.complement /.empty) sample))
(r.= (/.membership /.empty sample)
(/.membership (/.complement /.full) sample)))
common!
(and (r.>= (/.membership set sample)
(/.membership (/.union set (/.complement set)) sample))
(r.<= (/.membership set sample)
(/.membership (/.intersection set (/.complement set)) sample)))
de_morgan!
(and (r.= (/.membership (/.complement (/.union bottom_set top_set))
sample)
(/.membership (/.intersection (/.complement bottom_set) (/.complement top_set))
sample))
(r.= (/.membership (/.complement (/.intersection bottom_set top_set))
sample)
(/.membership (/.union (/.complement bottom_set) (/.complement top_set))
sample)))]
(and trivial!
common!
de_morgan!)))
(_.cover [/.difference]
(let [set (/.gradient bottom top)]
(and (r.= (/.membership set sample)
(/.membership (/.difference /.empty set) sample))
(r.= (/.membership /.empty sample)
(/.membership (/.difference /.full set) sample))
(r.<= (/.membership top_set sample)
(/.membership (/.difference bottom_set top_set) sample))
(r.<= (/.membership bottom_set sample)
(/.membership (/.difference bottom_set top_set) sample)))))
)))
(def: geometric
Test
(<| (_.covering /._)
(_.for [/.Fuzzy])
(do {! random.monad}
[sample random.rev
[bottom middle_bottom middle_top top]
(|> random.rev
(random.set r.hash 4)
(\ ! each (|>> set.list (list.sorted r.<)))
(random.one (function (_ thresholds)
(case thresholds
(^ (list threshold_0 threshold_1 threshold_2 threshold_3))
(#.Some [threshold_0 threshold_1 threshold_2 threshold_3])
_
#.None))))]
($_ _.and
(_.cover [/.triangle]
(let [reference (/.triangle bottom middle_bottom top)
irrelevant_order!
(list.every? (function (_ set)
(r.= (/.membership reference sample)
(/.membership set sample)))
(list (/.triangle bottom top middle_bottom)
(/.triangle middle_bottom bottom top)
(/.triangle middle_bottom top bottom)
(/.triangle top bottom middle_bottom)
(/.triangle top middle_bottom bottom)))
middle_maximum!
(r.= //.true (/.membership reference middle_bottom))
boundary_minima!
(and (r.= //.false (/.membership reference bottom))
(r.= //.false (/.membership reference top)))
inside_range!
(bit\= (r.> //.false (/.membership reference sample))
(and (r.> bottom sample)
(r.< top sample)))
outside_range!
(bit\= (r.= //.false (/.membership reference sample))
(or (r.<= bottom sample)
(r.>= top sample)))]
(and irrelevant_order!
middle_maximum!
boundary_minima!
inside_range!
outside_range!)))
(_.cover [/.trapezoid]
(let [reference (/.trapezoid bottom middle_bottom middle_top top)
irrelevant_order!
(list.every? (function (_ set)
(r.= (/.membership reference sample)
(/.membership set sample)))
(let [r0 bottom
r1 middle_bottom
r2 middle_top
r3 top]
(list (/.trapezoid r0 r1 r2 r3)
(/.trapezoid r0 r1 r3 r2)
(/.trapezoid r0 r2 r1 r3)
(/.trapezoid r0 r2 r3 r1)
(/.trapezoid r0 r3 r1 r2)
(/.trapezoid r0 r3 r2 r1)
(/.trapezoid r1 r0 r2 r3)
(/.trapezoid r1 r0 r3 r2)
(/.trapezoid r1 r2 r0 r3)
(/.trapezoid r1 r2 r3 r0)
(/.trapezoid r1 r3 r0 r2)
(/.trapezoid r1 r3 r2 r0)
(/.trapezoid r2 r0 r1 r3)
(/.trapezoid r2 r0 r3 r1)
(/.trapezoid r2 r1 r0 r3)
(/.trapezoid r2 r1 r3 r0)
(/.trapezoid r2 r3 r0 r1)
(/.trapezoid r2 r3 r1 r0)
(/.trapezoid r3 r0 r1 r2)
(/.trapezoid r3 r0 r2 r1)
(/.trapezoid r3 r1 r0 r2)
(/.trapezoid r3 r1 r2 r0)
(/.trapezoid r3 r2 r0 r1)
(/.trapezoid r3 r2 r1 r0)
)))
middle_maxima!
(and (r.= //.true (/.membership reference middle_bottom))
(r.= //.true (/.membership reference middle_top)))
boundary_minima!
(and (r.= //.false (/.membership reference bottom))
(r.= //.false (/.membership reference top)))
inside_range!
(bit\= (r.> //.false (/.membership reference sample))
(and (r.> bottom sample)
(r.< top sample)))
outside_range!
(bit\= (r.= //.false (/.membership reference sample))
(or (r.<= bottom sample)
(r.>= top sample)))
inside_inner_range!
(bit\= (r.= //.true (/.membership reference sample))
(and (r.<= middle_top sample)
(r.>= middle_bottom sample)))]
(and irrelevant_order!
middle_maxima!
boundary_minima!
inside_range!
outside_range!
inside_inner_range!)))
))))
(def: discrete
Test
(do random.monad
[threshold random.nat
.let [under? (n.< threshold)
set (set.of_list n.hash (list threshold))]
sample random.nat]
($_ _.and
(_.cover [/.of_predicate]
(bit\= (r.= //.true (/.membership (/.of_predicate under?) sample))
(under? sample)))
(_.cover [/.of_set]
(and (r.= //.true (/.membership (/.of_set set) threshold))
(bit\= (r.= //.true (/.membership (/.of_set set) sample))
(set.member? set sample))))
)))
(def: gradient
(Random [[Rev Rev] (Fuzzy Rev)])
(do random.monad
[sample random.rev
threshold_0 random.rev
threshold_1 random.rev
.let [bottom (r.min threshold_0 threshold_1)
top (r.max threshold_0 threshold_1)]]
(in [[bottom top]
(/.gradient bottom top)])))
(def: threshold
Test
(do random.monad
[[_ set] ..gradient
threshold random.rev
sample random.rev]
($_ _.and
(_.cover [/.predicate]
(bit\= (not ((/.predicate threshold set) sample))
(r.< threshold (/.membership set sample))))
(_.cover [/.cut]
(bit\= (r.= //.false (/.membership (/.cut threshold set) sample))
(r.< threshold (/.membership set sample))))
)))
(def: .public test
Test
(<| (_.covering /._)
(_.for [/.Fuzzy])
(do random.monad
[sample random.rev
[_ fuzzy] ..gradient
.let [equivalence (: (Equivalence (/.Fuzzy Rev))
(implementation
(def: (= left right)
(r.= (left sample)
(right sample)))))]]
($_ _.and
(_.for [/.functor]
($contravariant.spec equivalence fuzzy /.functor))
..trivial
..simple
..composition
..geometric
..discrete
..threshold
))))
|
