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interval-algebra-2.1.2: test/IntervalAlgebra/IntervalUtilitiesSpec.hs

{-# LANGUAGE FlexibleContexts  #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeApplications  #-}
{- HLINT ignore -}
module IntervalAlgebra.IntervalUtilitiesSpec
  ( spec
  ) where

import           Control.Monad                     (liftM2)
import           Data.List                         (sort)
import           Data.Maybe                        (fromJust, isJust, isNothing)
import           Data.Set                          (Set, difference, fromList,
                                                    member, toList)
import qualified Data.Set                          (null)
import           Data.Time                         (Day, UTCTime)
import           IntervalAlgebra                   (Interval,
                                                    IntervalCombinable (..),
                                                    IntervalRelation (..),
                                                    IntervalSizeable,
                                                    Intervallic (..),
                                                    beginerval, complement,
                                                    converse, disjointRelations,
                                                    duration, intervalRelations,
                                                    moment, predicate,
                                                    rangeInterval, safeInterval,
                                                    starts,
                                                    strictWithinRelations,
                                                    withinRelations)
import           IntervalAlgebra.Arbitrary         (arbitraryWithRelation)
import           IntervalAlgebra.IntervalUtilities (clip, combineIntervals,
                                                    combineIntervalsFromSorted,
                                                    durations, filterAfter,
                                                    filterBefore, filterConcur,
                                                    filterContains,
                                                    filterDisjoint,
                                                    filterDuring,
                                                    filterEnclosedBy,
                                                    filterEncloses,
                                                    filterEquals,
                                                    filterFinishedBy,
                                                    filterFinishes, filterMeets,
                                                    filterMetBy,
                                                    filterNotDisjoint,
                                                    filterOverlappedBy,
                                                    filterOverlaps,
                                                    filterStartedBy,
                                                    filterStarts, filterWithin,
                                                    foldMeetingSafe,
                                                    formMeetingSequence, gaps,
                                                    gapsL, gapsWithin,
                                                    intersect, nothingIfAll,
                                                    nothingIfAny, nothingIfNone,
                                                    relationsL)
import           IntervalAlgebra.PairedInterval    (PairedInterval, getPairData,
                                                    makePairedInterval,
                                                    trivialize)
import           Test.Hspec                        (Spec, describe, it,
                                                    shouldBe)
import           Test.Hspec.QuickCheck             (modifyMaxDiscardRatio,
                                                    modifyMaxSuccess)
import           Test.QuickCheck                   (Arbitrary (arbitrary, shrink),
                                                    Arbitrary1 (liftArbitrary),
                                                    Property,
                                                    Testable (property),
                                                    elements, listOf,
                                                    orderedList, resize,
                                                    sublistOf, suchThat, (===),
                                                    (==>))
import           Witherable                        (Filterable)

-- Types for testing

-- SmallInterval is just to test properties for which events of interest are so
-- rare QuickCheck gives up, e.g. filterEquals
newtype SmallInterval
  = SmallInterval { unSmall :: Interval Int }
  deriving (Eq, Show)

instance Arbitrary SmallInterval where
  arbitrary = SmallInterval . beginerval 0 <$> elements [0 .. 10]

-- A "state" here is just used test formMeetingSequence
newtype Events a
  = Events { getEvents :: [StateEvent a] }
  deriving (Eq, Ord, Show)

newtype State
  = State [Bool]
  deriving (Eq, Show)

instance Semigroup State where
  State x <> State y = State $ zipWith (||) x y

instance Monoid State where
  mempty = State [False, False, False]

newtype StateEvent a = MkEvent { getEvent :: PairedInterval State a }
   deriving (Eq, Ord, Show)

unEvents :: [StateEvent a] -> [PairedInterval State a]
unEvents = fmap getEvent

-- Type for checking arbitraryWithRelation
-- A target and reference pair, where targetInterval satisfies at least one of
-- refRelations relative to refInterval
data IntervalReferenced = IntervalReferenced
  { refInterval    :: Interval Int
  , refRelations   :: Set IntervalRelation
  , targetInterval :: Maybe (Interval Int)
  }
  deriving (Eq, Show)


mkEv :: IntervalSizeable a a => (a, a) -> b -> PairedInterval b a
mkEv i s = makePairedInterval s (safeInterval i)

instance Arbitrary State where
  arbitrary = State <$> suchThat (listOf arbitrary) (\x -> length x == 3)

-- SmallInterval again to address issue of generating from too large a possible
-- range of intervals
instance Arbitrary (StateEvent Int) where
  arbitrary = liftM2 (\x y -> MkEvent $ makePairedInterval x y)
                     arbitrary
                     (unSmall <$> arbitrary)

instance Arbitrary (Events Int) where
  arbitrary = Events <$> orderedList

-- restricted refIv to decrease rareness causing quickcheck to quit
instance Arbitrary IntervalReferenced where
  arbitrary = do
    refIv <- liftM2 beginerval (elements [1 .. 3]) (elements [0 .. 3])
    rels  <- fromList <$> sublistOf (toList intervalRelations)
    iv    <- arbitraryWithRelation refIv rels
    pure $ IntervalReferenced refIv rels iv

-- Testing functions
checkSeqStates :: (Intervallic i) => [i Int] -> Bool
checkSeqStates x = (length x > 1) || all (== Meets) (relationsL x)

-- Creation functions
iv :: Int -> Int -> Interval Int
iv = beginerval

evpi :: Int -> Int -> [Bool] -> StateEvent Int
evpi i j s = MkEvent $ makePairedInterval (State s) (beginerval i j)

-- Test cases
containmentInt :: Interval Int
containmentInt = iv (10 :: Int) (0 :: Int)

noncontainmentInt :: Interval Int
noncontainmentInt = iv 6 4

anotherInt :: Interval Int
anotherInt = iv 5 (15 :: Int)

gapInt :: Interval Int
gapInt = iv 5 (10 :: Int)

meets1 :: [Interval Int]
meets1 = [iv 2 0, iv 2 2]

meets2 :: [Interval Int]
meets2 = [iv 2 0, iv 2 2, iv 10 4, iv 2 14]

meets3 :: [PairedInterval Int Int]
meets3 = map (uncurry makePairedInterval)
             [(5, iv 2 0), (5, iv 2 2), (9, iv 10 4), (10, iv 2 14)]

meets3eq :: [PairedInterval Int Int]
meets3eq =
  map (uncurry makePairedInterval) [(5, iv 4 0), (9, iv 10 4), (10, iv 2 14)]

c0in :: [StateEvent Int]
c0in =
  [ evpi 9 1 [True, False, False]
  , evpi 8 2 [True, False, False]
  , evpi 3 5 [False, True, False]
  , evpi 3 6 [False, True, False]
  ]
c0out :: [StateEvent Int]
c0out =
  [ evpi 4 1 [True, False, False]
  , evpi 4 5 [True, True, False]
  , evpi 1 9 [True, False, False]
  ]

c1in :: [StateEvent Int]
c1in = [evpi 4 1 [True, False, False], evpi 4 6 [False, True, False]]
c1out :: [StateEvent Int]
c1out =
  [ evpi 4 1 [True, False, False]
  , evpi 1 5 [False, False, False]
  , evpi 4 6 [False, True, False]
  ]

c2in :: [StateEvent Int]
c2in = [evpi 4 1 [True, False, False], evpi 5 5 [False, True, False]]
c2out :: [StateEvent Int]
c2out = [evpi 4 1 [True, False, False], evpi 5 5 [False, True, False]]

c3in :: [StateEvent Int]
c3in = [evpi 4 1 [True, False, False], evpi 6 4 [False, True, False]]
c3out :: [StateEvent Int]
c3out =
  [ evpi 3 1 [True, False, False]
  , evpi 1 4 [True, True, False]
  , evpi 5 5 [False, True, False]
  ]

c4in :: [StateEvent Int]
c4in =
  [ evpi 1 (-1) [True, True, False]
  , evpi 1 3    [True, False, True]
  , evpi 1 3    [False, False, False]
  ]
c4out :: [StateEvent Int]
c4out =
  [ evpi 1 (-1) [True, True, False]
  , evpi 3 0    [False, False, False]
  , evpi 1 3    [True, False, True]
  ]



c5in :: [PairedInterval State Int]
c5in =
  [ mkEv (-63, 21) (State [False, True, True])
  , mkEv (-56, 20) (State [True, True, True])
  , mkEv (1  , 41) (State [False, True, False])
  , mkEv (11 , 34) (State [True, False, True])
  , mkEv (27 , 28) (State [False, True, True])
  ]

c5out :: [PairedInterval State Int]
c5out =
  [ mkEv (-63, -56) (State [False, True, True])
  , mkEv (-56, 34)  (State [True, True, True])
  , mkEv (34 , 41)  (State [False, True, False])
  ]

-- Properties

-- arbitraryWithRelation props
-- 'tautology' because this repeats the logic of arbitraryWithRelation
prop_withRelation_tautology :: IntervalReferenced -> Bool
prop_withRelation_tautology ir
  | isEnclose && isMom = isNothing iv
  | otherwise          = isJust iv && predicate rels refIv (fromJust iv)
 where
  refIv = refInterval ir
  iv    = targetInterval ir
  rels  = refRelations ir
  isEnclose =
    Data.Set.null $ Data.Set.difference rels (converse strictWithinRelations)
  isMom = duration refIv == moment @Int


-- Check that the only relation remaining after applying a function is Before
prop_before
  :: (Ord a) => ([Interval a] -> [Interval a]) -> [Interval a] -> Property
prop_before f x = relationsL ci === replicate (length ci - 1) Before
  where ci = f (sort x)

prop_combineIntervals1 :: (Ord a, Show a, Eq a) => [Interval a] -> Property
prop_combineIntervals1 = prop_before combineIntervals

prop_gaps1 :: (Ord a) => [Interval a] -> Property
prop_gaps1 = prop_before gapsL

-- In the case that that the input is not null, then
-- * all relationsL should be `Meets` after formMeetingSequence
prop_formMeetingSequence0 :: Events Int -> Property
prop_formMeetingSequence0 x =
  not (null es)
    ==> all (== Meets) (relationsL $ formMeetingSequence (unEvents es))
    === True
  where es = getEvents x

-- In the case that the input has
-- *     at least one Before relation between consequent pairs
-- * AND does not have any empty states
--
-- THEN the number empty states in the output should smaller than or equal to
--      the number before relationsL in the output
prop_formMeetingSequence1 :: Events Int -> Property
prop_formMeetingSequence1 x =
  (beforeCount > 0 && not
      (any (\x -> getPairData x == State [False, False, False])
           (unEvents $ getEvents x)
      )
    )
    ==> beforeCount
    >=  emptyCount
 where
  res         = formMeetingSequence (unEvents $ getEvents x)
  beforeCount = lengthWhen (== Before) (relationsL (unEvents $ getEvents x))
  emptyCount  = lengthWhen (\x -> getPairData x == mempty) res
  lengthWhen f = length . filter f

-- Check that formMeetingSequence doesn't return an empty list unless input is
-- empty.
prop_formMeetingSequence2 :: Events Int -> Property
prop_formMeetingSequence2 x = not (null $ getEvents x) ==> not $ null res
  where res = formMeetingSequence (unEvents $ getEvents x)

class ( Ord a ) => FiltrationProperties a  where
   prop_filtration ::
      (Interval a ->  [Interval a] -> [Interval a])
      -> Set IntervalRelation
      -> Interval a
      -> [Interval a]
      -> Property
   prop_filtration fltr s x l =
      not (null res) ==> and (fmap (predicate s x) res) === True
     where res = fltr x l

   prop_filterOverlaps :: Interval a
      -> [Interval a]
      -> Property
   prop_filterOverlaps = prop_filtration filterOverlaps (fromList [Overlaps])

   prop_filterOverlappedBy :: Interval a
      -> [Interval a]
      -> Property
   prop_filterOverlappedBy = prop_filtration filterOverlappedBy (fromList [OverlappedBy])

   prop_filterBefore :: Interval a
      -> [Interval a]
      -> Property
   prop_filterBefore = prop_filtration filterBefore (fromList [Before])

   prop_filterAfter :: Interval a
      -> [Interval a]
      -> Property
   prop_filterAfter = prop_filtration filterAfter (fromList [After])

   prop_filterStarts :: Interval a
      -> [Interval a]
      -> Property
   prop_filterStarts = prop_filtration filterStarts (fromList [Starts])

   prop_filterStartedBy :: Interval a
      -> [Interval a]
      -> Property
   prop_filterStartedBy = prop_filtration filterStartedBy (fromList [StartedBy])

   prop_filterFinishes :: Interval a
      -> [Interval a]
      -> Property
   prop_filterFinishes = prop_filtration filterFinishes (fromList [Finishes])

   prop_filterFinishedBy :: Interval a
      -> [Interval a]
      -> Property
   prop_filterFinishedBy = prop_filtration filterFinishedBy (fromList [FinishedBy])

   prop_filterMeets :: Interval a
      -> [Interval a]
      -> Property
   prop_filterMeets = prop_filtration filterMeets (fromList [Meets])

   prop_filterMetBy :: Interval a
      -> [Interval a]
      -> Property
   prop_filterMetBy = prop_filtration filterMetBy (fromList [MetBy])

   prop_filterDuring :: Interval a
      -> [Interval a]
      -> Property
   prop_filterDuring = prop_filtration filterDuring (fromList [During])

   prop_filterContains :: Interval a
      -> [Interval a]
      -> Property
   prop_filterContains = prop_filtration filterContains (fromList [Contains])

   prop_filterEquals :: Interval a
      -> [Interval a]
      -> Property
   prop_filterEquals = prop_filtration filterEquals (fromList [Equals])

   prop_filterDisjoint :: Interval a
      -> [Interval a]
      -> Property
   prop_filterDisjoint = prop_filtration filterDisjoint disjointRelations

   prop_filterNotDisjoint :: Interval a
      -> [Interval a]
      -> Property
   prop_filterNotDisjoint = prop_filtration filterNotDisjoint (complement disjointRelations)

   prop_filterWithin :: Interval a
      -> [Interval a]
      -> Property
   prop_filterWithin = prop_filtration filterWithin withinRelations

   prop_filterEnclosedBy :: Interval a
      -> [Interval a]
      -> Property
   prop_filterEnclosedBy = prop_filtration filterEnclosedBy withinRelations

   prop_filterEncloses :: Interval a
      -> [Interval a]
      -> Property
   prop_filterEncloses = prop_filtration filterEncloses (converse withinRelations)

   prop_filterConcur :: Interval a
      -> [Interval a]
      -> Property
   prop_filterConcur = prop_filtration filterConcur (complement disjointRelations)

instance FiltrationProperties Int

prop_clip_intersect
  :: (Show a, Ord a, IntervalSizeable a b)
  => Interval a
  -> Interval a
  -> Property
prop_clip_intersect x y = clip x y === intersect (min x y) (max x y)

-- NOTE: use this instead of prop_filterEquals
prop_small_filterEquals :: SmallInterval -> [SmallInterval] -> Property
prop_small_filterEquals x l =
  not (null res) ==> and (fmap (predicate s i) res) === True
 where
  i   = unSmall x
  li  = map unSmall l
  res = filterEquals i li
  s   = fromList [Equals]

-- RUNNER

spec :: Spec
spec = do
  describe "gaps tests" $ modifyMaxSuccess (* 10) $ do
    it "no gaps in containmentInt and noncontainmentInt"
      $          gapsL [containmentInt, noncontainmentInt]
      `shouldBe` []
    it "no gaps in containmentInt" $ gapsL [containmentInt] `shouldBe` []
    it "single gap between containmentInt and anotherInt"
      $          gapsL [containmentInt, anotherInt]
      `shouldBe` [gapInt]
    it "after gaps, only relation should be Before" $ property (prop_gaps1 @Int)

  describe "durations unit tests" $ do
    it "durations of containmentInt is 10"
      $          durations [containmentInt]
      `shouldBe` [10]
    it "durations of empty list is empty list"
      $          durations ([] :: [Interval Int])
      `shouldBe` []
    it "durations of [containmentInt, anotherInt] is [10, 5]"
      $          durations [containmentInt, anotherInt]
      `shouldBe` [10, 5]

  describe "clip tests" $ do
    it "clip disjoint should be Nothing"
      $          clip containmentInt gapInt
      `shouldBe` Nothing
    it "clip Interval (4, 10) Interval (0, 10) should be Interval (4, 10)"
      $          clip noncontainmentInt containmentInt
      `shouldBe` Just (iv 6 4)
    it "clip x y === intersect sort x y " $ property (prop_clip_intersect @Int)

  describe "relationsL tests" $ do
    it
        "relationsL [(0, 10), (4, 10), (10, 15), (15, 20)] == [FinishedBy, Meets, Meets]"
      $ relationsL [containmentInt, noncontainmentInt, gapInt, anotherInt]
      `shouldBe` [FinishedBy, Meets, Meets]
    it "relationsL of [] shouldBe []"
      $          relationsL ([] :: [Interval Int])
      `shouldBe` []
    it "relationsL of singleton shouldBe []"
      $          relationsL [containmentInt]
      `shouldBe` []
    it "length of relationsL result should be 1 less then length of input"
      $ property
          (\x ->
            not (null x)
              ==> length (relationsL x)
              === length (x :: [Interval Int])
              -   1
          )

  describe "gapsWithin tests" $ do
    it "gapsWithin (1, 10) [(0,5), (7,9), (12,15)] should be [(5,7), (9,10)]"
      $          gapsWithin (iv 9 1) [iv 5 0, iv 2 7, iv 3 12]
      `shouldBe` Just [iv 2 5, iv 1 9]
    it "gapsWithin (1, 10) [(-1, 0), (12,15)] should be [(5,7), (9,10)]"
      $          gapsWithin (iv 9 1) [iv 1 (-1), iv 3 12]
      `shouldBe` Nothing
    it "gapsWithin (0, 455) [(0, 730), (731, 762), (763, 793)]"
      $ gapsWithin (safeInterval (0 :: Int, 455))
                   (fmap safeInterval [(0, 730), (731, 762), (763, 793)])
      `shouldBe` Just []
    it "gapsWithin (1, 10) [] should be []"
      $          gapsWithin (iv 9 1) ([] :: [Interval a])
      `shouldBe` Nothing

  describe "emptyIf tests" $ do
    it "emptyIfNone (starts (3, 5)) [(3,4), (5,6)] should be empty"
      $          nothingIfNone (starts (iv 2 3)) [iv 1 3, iv 1 5]
      `shouldBe` Nothing
    it "emptyIfNone (starts (3, 5)) [(3,6), (5,6)] shoiuld be input"
      $          nothingIfNone (starts (iv 2 3)) [iv 3 3, iv 1 5]
      `shouldBe` Just [iv 3 3, iv 1 5]

  describe "filtration tests" $ modifyMaxDiscardRatio (* 2) $ do
    it "disjoint filter should filter out noncontainment"
      $          filterDisjoint containmentInt [noncontainmentInt, anotherInt]
      `shouldBe` [anotherInt]
    it "notDisjoint filter should keep noncontainment"
      $ filterNotDisjoint containmentInt [noncontainmentInt, anotherInt]
      `shouldBe` [noncontainmentInt]
    it "filterBefore property" $ property (prop_filterBefore @Int)
    it "filterAfter property" $ property (prop_filterAfter @Int)
    it "filterOverlaps property" $ property (prop_filterOverlaps @Int)
    it "filterOverlappedBy property" $ property (prop_filterOverlappedBy @Int)
    it "filterStarts property" $ property (prop_filterStarts @Int)
    it "filterStartedBy property" $ property (prop_filterStartedBy @Int)
    it "filterFinishes property" $ property (prop_filterFinishes @Int)
    it "filterFinishedBy property" $ property (prop_filterFinishedBy @Int)
    it "filterMeets property" $ property (prop_filterMeets @Int)
    it "filterMetBy property" $ property (prop_filterMetBy @Int)
    it "filterDuring property" $ property (prop_filterDuring @Int)
    it "filterContains property" $ property (prop_filterContains @Int)
    it "filterEquals property" $ property prop_small_filterEquals
    it "filterDisjoint property" $ property (prop_filterDisjoint @Int)
    it "filterNotDisjoint property" $ property (prop_filterNotDisjoint @Int)
    it "filterWithin property" $ property (prop_filterWithin @Int)
    it "filterConcur property" $ property (prop_filterConcur @Int)
    it "filterEncloses property" $ property (prop_filterEncloses @Int)
    it "filterEnclosedBy property" $ property (prop_filterEnclosedBy @Int)

  describe "nothingIf unit tests" $ do
    it "nothing from nothingIfAll"
      $          nothingIfAll (starts (iv 2 3)) [iv 3 3, iv 4 3]
      `shouldBe` Nothing
    it "something from nothingIfAll"
      $          nothingIfAll (starts (iv 2 3)) [iv 3 0, iv 4 3]
      `shouldBe` Just [iv 3 0, iv 4 3]
    it "nothing from nothingIfAny"
      $          nothingIfAny (starts (iv 2 3)) [iv 3 3, iv 1 5]
      `shouldBe` Nothing
    it "something from nothingIfAny"
      $          nothingIfAny (starts (iv 2 3)) [iv 3 1, iv 1 5]
      `shouldBe` Just [iv 3 1, iv 1 5]

  describe "intersection tests" $ do
    it "intersection of (0, 2) (2, 4) should be Nothing"
      $          intersect (iv 2 0) (iv 2 2)
      `shouldBe` Nothing
    it "intersection of (0, 2) (3, 4) should be Nothing"
      $          intersect (iv 2 0) (iv 1 3)
      `shouldBe` Nothing
    it "intersection of (2, 4) (0, 2) should be Nothing"
      $          intersect (iv 2 2) (iv 2 0)
      `shouldBe` Nothing

  describe "intersection tests" $ do
    it "intersection of (0, 2) (2, 4) should be Nothing"
      $          intersect (iv 2 0) (iv 2 2)
      `shouldBe` Nothing
    it "intersection of (0, 2) (3, 4) should be Nothing"
      $          intersect (iv 2 0) (iv 1 3)
      `shouldBe` Nothing
    it "intersection of (2, 4) (0, 2) should be Nothing"
      $          intersect (iv 2 2) (iv 2 0)
      `shouldBe` Nothing
    it "intersection of (0, 2) (1, 3) should be Just (1, 2)"
      $          intersect (iv 2 0) (iv 2 1)
      `shouldBe` Just (iv 1 1)
    it "intersection of (0, 2) (-1, 3) should be Just (0, 2)"
      $          intersect (iv 2 0) (iv 4 (-1))
      `shouldBe` Just (iv 2 0)
    it "intersection of (0, 2) (0, 2) should be Just (0, 2)"
      $          intersect (iv 2 0) (iv 2 0)
      `shouldBe` Just (iv 2 0)
    it "intersection of (0, 2) (-1, 1) should be Just (0, 1)"
      $          intersect (iv 2 0) (iv 2 (-1))
      `shouldBe` Just (iv 1 0)
    it "intersection of (0, 3) (1, 2) should be Just (1, 2)"
      $          intersect (iv 3 0) (iv 1 1)
      `shouldBe` Just (iv 1 1)
  describe "rangeInterval unit tests" $ do
    it "range of empty list returns Nothing"
      $          rangeInterval ([] :: [Interval Int])
      `shouldBe` Nothing
    it "rangeInterval returns the containing interval"
      $          rangeInterval [beginerval 0 (1 :: Int), beginerval 3 (-1)]
      `shouldBe` (Just $ beginerval 3 (-1))
    it "disjoint intervals"
      $          rangeInterval [beginerval 10 (1 :: Int), beginerval 1 (-1)]
      `shouldBe` (Just $ beginerval 12 (-1))
    it "order of list does not matter"
      $          rangeInterval [beginerval 10 (1 :: Int), beginerval 1 (-1)]
      `shouldBe` rangeInterval [beginerval 1 (-1), beginerval 10 (1 :: Int)]
    it "works on Right"
      $          rangeInterval (Right $ beginerval 10 (1 :: Int))
      `shouldBe` (Just $ beginerval 10 (1 :: Int))
    it "Left variant returns Nothing"
      $          rangeInterval (Left $ beginerval 10 (1 :: Int))
      `shouldBe` (Nothing :: Maybe (Interval Int))
  describe "combineIntervals unit tests" $ do
    it "noncontainmentInt combined into containmentInt"
      $          combineIntervals [containmentInt, noncontainmentInt]
      `shouldBe` [containmentInt]
    it "noncontainmentInt combined into containmentInt; anotherInt unchanged"
      $ combineIntervals [containmentInt, noncontainmentInt, anotherInt]
      `shouldBe` [containmentInt, anotherInt]
    it "idempotency of containmentInt"
      $          combineIntervals [containmentInt]
      `shouldBe` [containmentInt]
    it "idempotency of noncontainmentInt"
      $          combineIntervals [noncontainmentInt]
      `shouldBe` [noncontainmentInt]
    it "combineIntervals [] should be []"
      $          combineIntervals ([] :: [Interval Int])
      `shouldBe` []
    it "combineIntervals works on sorted intervals"
      $          combineIntervals [iv 10 0, iv 5 2, iv 2 10, iv 2 13]
      `shouldBe` [iv 12 0, iv 2 13]
    it "combineIntervalsFromSorted works on sorted intervals"
      $          combineIntervalsFromSorted [iv 10 0, iv 5 2, iv 2 10, iv 2 13]
      `shouldBe` [iv 12 0, iv 2 13]
    it "combineIntervals works on unsorted intervals"
      $          combineIntervals [iv 2 13, iv 10 0, iv 2 10, iv 5 2]
      `shouldBe` [iv 12 0, iv 2 13]

  describe "combineIntervals property tests" $ modifyMaxSuccess (* 10) $ do
    it "after combining, only relation should be Before"
      $ property (prop_combineIntervals1 @Int)
    it "after combining, only relation should be Before"
      $ property (prop_combineIntervals1 @Day)
    it "after combining, only relation should be Before"
      $ property (prop_combineIntervals1 @UTCTime)

  describe "foldMeets unit tests" $ do
    it "foldMeetingSafe meets1"
      $          foldMeetingSafe (trivialize meets1)
      `shouldBe` trivialize [iv 4 0]
    it "foldMeetingSafe meets2"
      $          foldMeetingSafe (trivialize meets2)
      `shouldBe` trivialize [iv 16 0]
    it "foldMeetingSafe meets3" $ foldMeetingSafe meets3 `shouldBe` meets3eq

  describe "formMeetingSequence unit tests" $ do
    it "formMeetingSequence unit test 0"
      $          formMeetingSequence (unEvents c0in)
      `shouldBe` unEvents c0out
    it "formMeetingSequence unit test 1"
      $          formMeetingSequence (unEvents c1in)
      `shouldBe` unEvents c1out
    it "formMeetingSequence unit test 2"
      $          formMeetingSequence (unEvents c2in)
      `shouldBe` unEvents c2out
    it "formMeetingSequence unit test 3"
      $          formMeetingSequence (unEvents c3in)
      `shouldBe` unEvents c3out
    it "formMeetingSequence unit test 4"
      $          formMeetingSequence (unEvents c4in)
      `shouldBe` unEvents c4out
    it "formMeetingSequence unit test 5"
      $          formMeetingSequence c5in
      `shouldBe` c5out
    it "formMeetingSequence unit test 6"
      $          formMeetingSequence ([] :: [PairedInterval State Int])
      `shouldBe` []

  describe "formMeetingSequence property tests" $ modifyMaxSuccess (* 2) $ do
    it "prop_formMeetingSequence0" $ property prop_formMeetingSequence0
     -- 2022-05-18 - BS
    -- Commmenting out this test as the execution of the test suite blows up
    -- when this property check is included.
    -- TODO: consider whether this check is worthwhile.
    -- it "prop_formMeetingSequence1" $ property prop_formMeetingSequence1
    it "prop_formMeetingSequence2" $ property prop_formMeetingSequence2

  -- describe "arbitraryWithRelation property tests" $ do
  --   it "prop_withRelation_tautology" $ property prop_withRelation_tautology