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(.module:
[lux #*
["_" test (#+ Test)]
[abstract/monad (#+ do)]
[abstract
["." order]
{[0 #test]
[/
["$." equivalence]]}]
[control
[pipe (#+ case>)]]
[data
[number
["." nat]]
[text
format]
[collection
["." set]
["." list]]]
[math
["r" random (#+ Random)]]]
{1
["." / (#+ Interval) (",@." equivalence)]})
(template [<name> <cmp>]
[(def: #export <name>
(Random (Interval Nat))
(do r.monad
[bottom r.nat
top (|> r.nat (r.filter (|>> (n/= bottom) not)))]
(if (<cmp> top bottom)
(wrap (/.between nat.enum bottom top))
(wrap (/.between nat.enum top bottom)))))]
[inner n/<]
[outer n/>]
)
(def: #export singleton
(Random (Interval Nat))
(do r.monad
[point r.nat]
(wrap (/.singleton nat.enum point))))
(def: #export interval
(Random (Interval Nat))
($_ r.either
..inner
..outer
..singleton))
(def: boundaries
Test
(do r.monad
[bottom r.nat
top r.nat
#let [interval (/.between nat.enum bottom top)]]
($_ _.and
(_.test "A boundary value belongs to its interval."
(and (/.within? interval bottom)
(/.within? interval top)))
(_.test "An interval starts with its bottom."
(/.starts-with? bottom interval))
(_.test "An interval ends with its top."
(/.ends-with? top interval))
(_.test "The boundary values border the interval."
(and (/.borders? interval bottom)
(/.borders? interval top)))
)))
(def: union
Test
(do r.monad
[some-interval ..interval
left-inner ..inner
right-inner ..inner
left-singleton ..singleton
right-singleton ..singleton
left-outer ..outer
right-outer ..outer]
($_ _.and
(_.test "The union of an interval to itself yields the same interval."
(,@= some-interval (/.union some-interval some-interval)))
(_.test "The union of 2 inner intervals is another inner interval."
(/.inner? (/.union left-inner right-inner)))
(_.test "The union of 2 outer intervals yields an inner interval when their complements don't overlap, and an outer when they do."
(if (/.overlaps? (/.complement left-outer) (/.complement right-outer))
(/.outer? (/.union left-outer right-outer))
(/.inner? (/.union left-outer right-outer))))
)))
(def: intersection
Test
(do r.monad
[some-interval ..interval
left-inner ..inner
right-inner ..inner
left-singleton ..singleton
right-singleton ..singleton
left-outer ..outer
right-outer ..outer]
($_ _.and
(_.test "The intersection of an interval to itself yields the same interval."
(,@= some-interval (/.intersection some-interval some-interval)))
(_.test "The intersection of 2 inner intervals yields an inner interval when they overlap, and an outer when they don't."
(if (/.overlaps? left-inner right-inner)
(/.inner? (/.intersection left-inner right-inner))
(/.outer? (/.intersection left-inner right-inner))))
(_.test "The intersection of 2 outer intervals is another outer interval."
(/.outer? (/.intersection left-outer right-outer)))
)))
(def: complement
Test
(do r.monad
[some-interval ..interval]
($_ _.and
(_.test "The complement of a complement is the same as the original."
(,@= some-interval (|> some-interval /.complement /.complement)))
(_.test "The complement of an interval does not overlap it."
(not (/.overlaps? some-interval (/.complement some-interval))))
)))
(def: location
Test
(do r.monad
[[l m r] (|> (r.set nat.hash 3 r.nat)
(:: @ map (|>> set.to-list
(list.sort n/<)
(case> (^ (list b t1 t2))
[b t1 t2]
_
(undefined)))))
#let [left (/.singleton nat.enum l)
right (/.singleton nat.enum r)]]
($_ _.and
(_.test "'precedes?' and 'succeeds?' are symetric."
(and (/.precedes? right left)
(/.succeeds? left right)))
(_.test "Can check if an interval is before or after some element."
(and (/.before? m left)
(/.after? m right)))
)))
(def: touch
Test
(do r.monad
[[b t1 t2] (|> (r.set nat.hash 3 r.nat)
(:: @ map (|>> set.to-list
(list.sort n/<)
(case> (^ (list b t1 t2))
[b t1 t2]
_
(undefined)))))
#let [int-left (/.between nat.enum t1 t2)
int-right (/.between nat.enum b t1)]]
($_ _.and
(_.test "An interval meets another if its top is the other's bottom."
(/.meets? int-left int-right))
(_.test "Two intervals touch one another if any one meets the other."
(/.touches? int-left int-right))
(_.test "Can check if 2 intervals start together."
(/.starts? (/.between nat.enum b t2)
(/.between nat.enum b t1)))
(_.test "Can check if 2 intervals finish together."
(/.finishes? (/.between nat.enum b t2)
(/.between nat.enum t1 t2)))
)))
(def: overlap
Test
(do r.monad
[some-interval ..interval
[x0 x1 x2 x3] (|> (r.set nat.hash 4 r.nat)
(:: @ map (|>> set.to-list
(list.sort n/<)
(case> (^ (list x0 x1 x2 x3))
[x0 x1 x2 x3]
_
(undefined)))))]
($_ _.and
(_.test "Every interval is nested into itself."
(/.nested? some-interval some-interval))
(_.test "No interval overlaps with itself."
(not (/.overlaps? some-interval some-interval)))
(let [small-inner (/.between nat.enum x1 x2)
large-inner (/.between nat.enum x0 x3)]
(_.test "Inner intervals can be nested inside one another."
(and (/.nested? large-inner small-inner)
(not (/.nested? small-inner large-inner)))))
(let [left-inner (/.between nat.enum x0 x2)
right-inner (/.between nat.enum x1 x3)]
(_.test "Inner intervals can overlap one another."
(and (/.overlaps? left-inner right-inner)
(/.overlaps? right-inner left-inner))))
(let [small-outer (/.between nat.enum x2 x1)
large-outer (/.between nat.enum x3 x0)]
(_.test "Outer intervals can be nested inside one another."
(and (/.nested? small-outer large-outer)
(not (/.nested? large-outer small-outer)))))
(let [left-inner (/.between nat.enum x0 x1)
right-inner (/.between nat.enum x2 x3)
outer (/.between nat.enum x0 x3)]
(_.test "Inners can be nested inside outers."
(and (/.nested? outer left-inner)
(/.nested? outer right-inner))))
(let [left-inner (/.between nat.enum x0 x2)
right-inner (/.between nat.enum x1 x3)
outer (/.between nat.enum x1 x2)]
(_.test "Inners can overlap outers."
(and (/.overlaps? outer left-inner)
(/.overlaps? outer right-inner))))
)))
(def: #export test
Test
(<| (_.context (%name (name-of /.Interval)))
($_ _.and
($equivalence.spec /.equivalence ..interval)
(<| (_.context "Boundaries.")
..boundaries)
(<| (_.context "Union.")
..union)
(<| (_.context "Intersection.")
..intersection)
(<| (_.context "Complement.")
..complement)
(<| (_.context "Positioning/location.")
..location)
(<| (_.context "Touching intervals.")
..touch)
(<| (_.context "Nesting & overlap.")
..overlap)
)))
(def: #export (spec (^open ",@.") gen-sample)
(All [a] (-> (Interval a) (Random a) Test))
(<| (_.context (%name (name-of /.Interval)))
(do r.monad
[sample gen-sample]
($_ _.and
(_.test "No value is bigger than the top."
(,@< ,@top sample))
(_.test "No value is smaller than the bottom."
(order.> ,@&order ,@bottom sample))
))))
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