interval-algebra-1.4.0: src/IntervalAlgebra/IntervalUtilities.hs
{-|
Module : Interval Algebra Utilities
Description : Functions for operating on containers of Intervals.
Copyright : (c) NoviSci, Inc 2020
License : BSD3
Maintainer : bsaul@novisci.com
Stability : experimental
In the examples below, @iv@ is a synonym for 'beginerval' used to save space.
-}
{-# LANGUAGE Safe #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE FlexibleInstances #-}
module IntervalAlgebra.IntervalUtilities
(
-- * Fold over sequential intervals
combineIntervals
, combineIntervalsL
, gaps
, gapsL
, gapsWithin
-- * Operations on Meeting sequences of paired intervals
, foldMeetingSafe
, formMeetingSequence
-- * Withering functions
-- ** Clear containers based on predicate
, nothingIf
, nothingIfNone
, nothingIfAny
, nothingIfAll
-- ** Filter containers based on predicate
, filterBefore
, filterMeets
, filterOverlaps
, filterFinishedBy
, filterContains
, filterStarts
, filterEquals
, filterStartedBy
, filterDuring
, filterFinishes
, filterOverlappedBy
, filterMetBy
, filterAfter
, filterDisjoint
, filterNotDisjoint
, filterConcur
, filterWithin
, filterEnclose
, filterEnclosedBy
-- * Misc utilities
, relations
, relationsL
, intersect
, clip
, durations
) where
import safe Control.Applicative ( (<*>)
, Applicative(pure)
)
import qualified Control.Foldl as L
import safe Control.Monad ( Functor(fmap) )
import safe Data.Bool ( (&&)
, Bool
, not
, otherwise
, (||)
)
import safe Data.Eq ( Eq((==)) )
import safe Data.Foldable ( Foldable(foldl', null, toList)
, all
, any
, or
)
import safe Data.Function ( ($)
, (.)
, flip
)
import safe Data.Maybe ( Maybe(..)
, maybe
, maybeToList
)
import safe Data.Monoid ( Monoid(mempty) )
import safe Data.Ord ( Ord(max, min) )
import safe Data.Semigroup ( Semigroup((<>)) )
import safe Data.Traversable ( Traversable(sequenceA) )
import safe Data.Tuple ( fst )
import safe GHC.Int ( Int )
import safe GHC.Show ( Show )
import safe IntervalAlgebra.Core ( (<|>)
, ComparativePredicateOf1
, ComparativePredicateOf2
, Interval
, IntervalCombinable
( (<+>)
, (><)
)
, IntervalRelation(..)
, IntervalSizeable
( diff
, duration
)
, Intervallic(..)
, after
, before
, begin
, beginerval
, beginervalFromEnd
, concur
, contains
, disjoint
, during
, enclose
, enclosedBy
, end
, enderval
, endervalFromBegin
, equals
, extenterval
, finishedBy
, finishes
, meets
, metBy
, notDisjoint
, overlappedBy
, overlaps
, relate
, startedBy
, starts
, within
)
import safe IntervalAlgebra.PairedInterval ( PairedInterval
, equalPairData
, getPairData
, makePairedInterval
)
import safe Safe ( headMay
, initSafe
, lastMay
, tailSafe
)
import safe Witherable ( Filterable(filter)
, Witherable(..)
, catMaybes
, mapMaybe
)
-------------------------------------------------
-- Unexported utilties used in functions below --
-------------------------------------------------
-- Just a synonym used to examples to save typing
iv :: Int -> Int -> Interval Int
iv = beginerval
-- An internal utility function for creating a @Fold@ that maps over a structure
-- by consecutive pairs into a new structure.
makeFolder :: (Monoid (m b), Applicative m) => (a -> a -> b) -> L.Fold a (m b)
makeFolder f = L.Fold step begin done
where
begin = (mempty, Nothing)
step (fs, Nothing) y = (fs, Just y)
step (fs, Just x ) y = (fs <> pure (f x y), Just y)
done (fs, _) = fs
-- Used to combine two lists by combining the last element of @x@ and the first
-- element of @y@ by @f@. The combining function @f@ will generally return a
-- singleton list in the case that the last of x and head of y can be combined
-- or a two element list in the case they cannot.
listCombiner
:: (Maybe a -> Maybe a -> [a]) -- ^ f
-> [a] -- ^ x
-> [a] -- ^ y
-> [a]
listCombiner f x y = initSafe x <> f (lastMay x) (headMay y) <> tailSafe y
{-# INLINABLE listCombiner #-}
-- | Returns a list of the 'IntervalRelation' between each consecutive pair
-- of intervals. This is just a specialized 'relations' which returns a list.
--
-- >>> relationsL [iv 1 0, iv 1 1]
-- [Meets]
relationsL :: (Foldable f, Intervallic i a) => f (i a) -> [IntervalRelation]
relationsL = relations
-- | A generic form of 'relations' which can output any 'Applicative' and
-- 'Monoid' structure.
--
-- >>> (relations [iv 1 0, iv 1 1]) :: [IntervalRelation (Interval Int)]
-- [Meets]
--
relations
:: (Foldable f, Applicative m, Intervallic i a, Monoid (m IntervalRelation))
=> f (i a)
-> m IntervalRelation
relations = L.fold (makeFolder relate)
{-# INLINABLE relations #-}
-- | Forms a 'Just' new interval from the intersection of two intervals,
-- provided the intervals are not disjoint.
--
-- >>> intersect (iv 5 0) (iv 2 3)
-- Just (3, 5)
--
intersect
:: (Intervallic i a, IntervalSizeable a b) => i a -> i a -> Maybe (Interval a)
intersect x y | disjoint x y = Nothing
| otherwise = Just $ beginerval (diff e b) b
where
b = max (begin x) (begin y)
e = min (end x) (end y)
-- Internal function which folds over a structure by consecutive pairs, returing
-- gaps between each pair (@Nothing@ if no such gap exists).
gapsM
:: ( IntervalCombinable i a
, Traversable f
, Monoid (f (Maybe (Interval a)))
, Applicative f
)
=> f (i a)
-> f (Maybe (Interval a))
gapsM = L.fold (makeFolder (\i j -> getInterval i >< getInterval j))
{-# INLINABLE gapsM #-}
-- | Returns a @Maybe@ container of intervals consisting of the gaps
-- between intervals in the input. *To work properly, the input should be
-- sorted*. See 'gapsL' for a version that always returns a list.
--
-- >>> gaps [iv 4 1, iv 4 8, iv 3 11]
--
gaps
:: ( IntervalCombinable i a
, Traversable f
, Monoid (f (Maybe (Interval a)))
, Applicative f
)
=> f (i a)
-> Maybe (f (Interval a))
gaps = sequenceA . gapsM
{-# INLINABLE gaps #-}
-- | Returns a (possibly empty) list of intervals consisting of the gaps between
-- intervals in the input container. *To work properly, the input should be
-- sorted*. This version outputs a list. See 'gaps' for a version that lifts
-- the result to same input structure @f@.
gapsL
:: ( IntervalCombinable i a
, Applicative f
, Monoid (f (Maybe (Interval a)))
, Traversable f
)
=> f (i a)
-> [Interval a]
gapsL x = maybe [] toList (gaps x)
{-# INLINABLE gapsL #-}
-- | Returns the 'duration' of each 'Intervallic i a' in the 'Functor' @f@.
--
-- >>> durations [iv 9 1, iv 10 2, iv 1 5]
-- [9,10,1]
--
durations
:: (Functor f, Intervallic i a, IntervalSizeable a b) => f (i a) -> f b
durations = fmap duration
-- | In the case that x y are not disjoint, clips y to the extent of x.
--
-- >>> clip (iv 5 0) (iv 3 3)
-- Just (3, 5)
--
-- >>> clip (iv 3 0) (iv 2 4)
-- Nothing
--
clip
:: (Intervallic i0 a, Intervallic i1 a, IntervalSizeable a b)
=> i0 a
-> i1 a
-> Maybe (Interval a)
clip x y
| overlaps x y = Just $ enderval (diff (end x) (begin y)) (end x)
| overlappedBy x y = Just $ beginerval (diff (end y) (begin x)) (begin x)
| jx x y = Just (getInterval x)
| jy x y = Just (getInterval y)
| otherwise = Nothing {- disjoint x y case -}
where
jy = equals <|> startedBy <|> contains <|> finishedBy
jx = starts <|> during <|> finishes
{-# INLINABLE clip #-}
-- | Applies 'gaps' to all the non-disjoint intervals in @x@ that are *not* disjoint
-- from @i@. Intervals that 'overlaps' or are 'overlappedBy' @i@ are 'clip'ped
-- to @i@, so that all the intervals are 'within' @i@. If all of the input intervals
-- are disjoint from the focal interval or if the input is empty, then 'Nothing'
-- is returned. When there are no gaps among the concurring intervals, then
-- `Just mempty` (e.g. `Just []`) is returned.
--
-- >>> gapsWithin (iv 9 1) [iv 5 0, iv 2 7, iv 3 12]
-- Just [(5, 7),(9, 10)]
--
gapsWithin
:: ( Applicative f
, Witherable f
, Monoid (f (Interval a))
, Monoid (f (Maybe (Interval a)))
, IntervalSizeable a b
, Intervallic i0 a
, IntervalCombinable i1 a
)
=> i0 a -- ^ i
-> f (i1 a) -- ^ x
-> Maybe (f (Interval a))
gapsWithin i x | null ivs = Nothing
| otherwise = Just res
where
s = pure (endervalFromBegin 0 i)
e = pure (beginervalFromEnd 0 i)
ivs = mapMaybe (clip i) (filterNotDisjoint i x)
res = catMaybes $ gapsM (s <> ivs <> e)
{-# INLINABLE gapsWithin #-}
-- The Box is an internal type used to hold accumulated, combined intervals in
-- 'combineIntervalsL'.
newtype Box a = Box { unBox :: [a] }
packIntervalBoxes :: (Intervallic i a) => [i a] -> [Box (Interval a)]
packIntervalBoxes = fmap (\z -> Box [getInterval z])
instance (Ord a) => Semigroup (Box (Interval a)) where
Box x <> Box y = Box $ listCombiner (<->) x y
-- | Returns a container of intervals where any intervals that meet or share support
-- are combined into one interval. *To work properly, the input should
-- be sorted*. See 'combineIntervalsL' for a version that works only on lists.
--
-- >>> combineIntervals [iv 10 0, iv 5 2, iv 2 10, iv 2 13]
-- [(0, 12),(13, 15)]
--
combineIntervals
:: ( Applicative f
, Ord a
, Intervallic i a
, Monoid (f (Interval a))
, Foldable f
)
=> f (i a)
-> f (Interval a)
combineIntervals x =
foldl' (\x y -> x <> pure y) mempty (combineIntervalsL $ toList x)
-- TODO: surely combineIntervals and combineIntervalsL could be combined
{-# INLINABLE combineIntervals #-}
-- | Returns a list of intervals where any intervals that meet or share support
-- are combined into one interval. *To work properly, the input list should
-- be sorted*.
--
-- >>> combineIntervalsL [iv 10 0, iv 5 2, iv 2 10, iv 2 13]
-- [(0, 12),(13, 15)]
--
combineIntervalsL :: (Intervallic i a) => [i a] -> [Interval a]
combineIntervalsL l = unBox $ foldl' (<>) (Box []) (packIntervalBoxes l)
{-# INLINABLE combineIntervalsL #-}
-- Internal function for combining maybe intervals in the 'combineIntervalsL'
-- function
(<->) :: (IntervalCombinable i a) => Maybe (i a) -> Maybe (i a) -> [Interval a]
(<->) Nothing Nothing = []
(<->) Nothing (Just y) = [getInterval y]
(<->) (Just x) Nothing = [getInterval x]
(<->) (Just x) (Just y) = (<+>) (getInterval x) (getInterval y)
{-# INLINABLE (<->) #-}
-- | Given a predicate combinator, a predicate, and list of intervals, returns
-- the input unchanged if the predicate combinator is @True@. Otherwise, returns
-- an empty list. See 'nothingIfAny' and 'nothingIfNone' for examples.
nothingIf
:: (Monoid (f (i a)), Filterable f)
=> ((i a -> Bool) -> f (i a) -> Bool) -- ^ e.g. 'any' or 'all'
-> (i a -> Bool) -- ^ predicate to apply to each element of input list
-> f (i a)
-> Maybe (f (i a))
nothingIf quantifier predicate x =
if quantifier predicate x then Nothing else Just x
-- | Returns the 'Nothing' if *none* of the element of input satisfy
-- the predicate condition.
--
-- For example, the following returns 'Nothing' because none of the intervals
-- in the input list 'starts' (3, 5).
--
-- >>> nothingIfNone (starts (iv 2 3)) [iv 1 3, iv 1 5]
-- Nothing
--
-- In the following, (3, 5) 'starts' (3, 6), so 'Just' the input is returned.
--
-- >>> nothingIfNone (starts (iv 2 3)) [iv 3 3, iv 1 5]
-- Just [(3, 6),(5, 6)]
--
nothingIfNone
:: (Monoid (f (i a)), Foldable f, Filterable f)
=> (i a -> Bool) -- ^ predicate to apply to each element of input list
-> f (i a)
-> Maybe (f (i a))
nothingIfNone = nothingIf (\f x -> (not . any f) x)
-- | Returns 'Nothing' if *any* of the element of input satisfy the predicate condition.
--
-- >>> nothingIfAny (starts (iv 2 3)) [iv 3 3, iv 1 5]
-- Just [(3, 6),(5, 6)]
--
-- >>> nothingIfAny (starts (iv 2 3)) [iv 3 3, iv 1 5]
-- Nothing
--
nothingIfAny
:: (Monoid (f (i a)), Foldable f, Filterable f)
=> (i a -> Bool) -- ^ predicate to apply to each element of input list
-> f (i a)
-> Maybe (f (i a))
nothingIfAny = nothingIf any
-- | Returns 'Nothing' if *all* of the element of input satisfy the predicate condition.
--
-- >>> nothingIfAll (starts (iv 2 3)) [iv 3 3, iv 4 3]
-- Nothing
--
nothingIfAll
:: (Monoid (f (i a)), Foldable f, Filterable f)
=> (i a -> Bool) -- ^ predicate to apply to each element of input list
-> f (i a)
-> Maybe (f (i a))
nothingIfAll = nothingIf all
-- | Creates a function for filtering a 'Witherable.Filterable' of @i1 a@s
-- by comparing the @Interval a@s that of an @i0 a@.
makeFilter
:: (Filterable f, Intervallic i0 a, Intervallic i1 a)
=> ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a
-> (f (i1 a) -> f (i1 a))
makeFilter f p = Witherable.filter (f p)
{- |
Filter 'Witherable.Filterable' containers of one @'Intervallic'@ type based by comparing to
a (potentially different) 'Intervallic' type using the corresponding interval
predicate function.
-}
filterOverlaps, filterOverlappedBy, filterBefore, filterAfter, filterStarts, filterStartedBy, filterFinishes, filterFinishedBy, filterMeets, filterMetBy, filterDuring, filterContains, filterEquals, filterDisjoint, filterNotDisjoint, filterConcur, filterWithin, filterEnclose, filterEnclosedBy
:: (Filterable f, Intervallic i0 a, Intervallic i1 a)
=> i0 a
-> f (i1 a)
-> f (i1 a)
filterOverlaps = makeFilter overlaps
filterOverlappedBy = makeFilter overlappedBy
filterBefore = makeFilter before
filterAfter = makeFilter after
filterStarts = makeFilter starts
filterStartedBy = makeFilter startedBy
filterFinishes = makeFilter finishes
filterFinishedBy = makeFilter finishedBy
filterMeets = makeFilter meets
filterMetBy = makeFilter metBy
filterDuring = makeFilter during
filterContains = makeFilter contains
filterEquals = makeFilter equals
filterDisjoint = makeFilter disjoint
filterNotDisjoint = makeFilter notDisjoint
filterConcur = makeFilter concur
filterWithin = makeFilter within
filterEnclose = makeFilter enclose
filterEnclosedBy = makeFilter enclosedBy
-- | Folds over a list of Paired Intervals and in the case that the 'getPairData'
-- is equal between two sequential meeting intervals, these two intervals are
-- combined into one. This function is "safe" in the sense that if the input is
-- invalid and contains any sequential pairs of intervals with an @IntervalRelation@,
-- other than 'Meets', then the function returns an empty list.
foldMeetingSafe
:: (Eq b, Ord a, Show a)
=> [PairedInterval b a] -- ^ Be sure this only contains intervals
-- that sequentially 'meets'.
-> [PairedInterval b a]
foldMeetingSafe l = maybe [] (getMeeting . foldMeeting) (parseMeeting l)
-- | Folds over a list of Meeting Paired Intervals and in the case that the 'getPairData'
-- is equal between two sequential meeting intervals, these two intervals are
-- combined into one.
foldMeeting
:: (Eq b, Ord a, Show a)
=> Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a]
foldMeeting (Meeting l) =
foldl' joinMeetingPairedInterval (Meeting []) (packMeeting l)
-- This type identifies that @a@ contains intervals that sequentially meet one
-- another.
newtype Meeting a = Meeting { getMeeting :: a } deriving (Eq, Show)
-- Box up Meeting.
packMeeting :: [a] -> [Meeting [a]]
packMeeting = fmap (\z -> Meeting [z])
-- Test a list of intervals to be sure they all meet; if not return Nothing.
parseMeeting :: Intervallic i a => [i a] -> Maybe (Meeting [i a])
parseMeeting x | all (== Meets) (relationsL x) = Just $ Meeting x
| otherwise = Nothing
-- A specific case of 'joinMeeting' for @PairedIntervals@.
joinMeetingPairedInterval
:: (Eq b, Ord a, Show a)
=> Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a]
joinMeetingPairedInterval = joinMeeting equalPairData
-- A general function for combining any two @Meeting [i a]@ by 'listCombiner'.
joinMeeting
:: Intervallic i a
=> ComparativePredicateOf1 (i a)
-> Meeting [i a]
-> Meeting [i a]
-> Meeting [i a]
joinMeeting f (Meeting x) (Meeting y) =
Meeting $ listCombiner (join2MeetingWhen f) x y
-- The intervals @x@ and @y@ should meet! The predicate function @p@ determines
-- when the two intervals that meet should be combined.
join2MeetingWhen
:: Intervallic i a
=> ComparativePredicateOf1 (i a)
-> Maybe (i a)
-> Maybe (i a)
-> [i a]
join2MeetingWhen p Nothing Nothing = []
join2MeetingWhen p Nothing (Just y) = [y]
join2MeetingWhen p (Just x) Nothing = [x]
join2MeetingWhen p (Just x) (Just y) | p x y = [setInterval y (extenterval x y)]
| otherwise = pure x <> pure y
{- |
Takes two *ordered* events, x <= y, and "disjoins" them in the case that the
two events have different states, creating a sequence (list) of new events that
sequentially meet one another. Since x <= y, there are 7 possible interval
relations between x and y. If the states of x and y are equal and x is not
before y, then x and y are combined into a single event.
-}
disjoinPaired
:: (Eq b, Monoid b, Show a, IntervalSizeable a c)
=> (PairedInterval b) a
-> (PairedInterval b) a
-> Meeting [(PairedInterval b) a]
disjoinPaired o e = case relate x y of
Before -> Meeting [x, evp e1 b2 mempty, y]
Meets -> foldMeeting $ Meeting [x, y]
Overlaps -> foldMeeting $ Meeting [evp b1 b2 s1, evp b2 e1 sc, evp e1 e2 s2]
FinishedBy -> foldMeeting $ Meeting [evp b1 b2 s1, ev i2 sc]
Contains -> foldMeeting $ Meeting [evp b1 b2 s1, evp b2 e2 sc, evp e2 e1 s1]
Starts -> foldMeeting $ Meeting [ev i1 sc, evp e1 e2 s2]
_ -> Meeting [ev i1 sc] {- Equals case -}
where
x = min o e
y = max o e
i1 = getInterval x
i2 = getInterval y
s1 = getPairData x
s2 = getPairData y
sc = s1 <> s2
b1 = begin x
b2 = begin y
e1 = end x
e2 = end y
ev = flip makePairedInterval
evp b e = ev (beginerval (diff e b) b)
{-# INLINABLE disjoinPaired #-}
{- |
The internal function for converting a non-disjoint, ordered sequence of
events into a disjoint, ordered sequence of events. The function operates
by recursion on a pair of events and the input events. The first of the
is the accumulator set -- the disjoint events that need no longer be
compared to input events. The second of the pair are disjoint events that
still need to be compared to be input events.
-}
recurseDisjoin
:: (Monoid b, Eq b, IntervalSizeable a c, Show a)
=> ([(PairedInterval b) a], [(PairedInterval b) a])
-> [(PairedInterval b) a]
-> [(PairedInterval b) a]
recurseDisjoin (acc, o : os) [] = acc <> (o : os) -- the "final" pattern
recurseDisjoin (acc, [] ) [] = acc -- another "final" pattern
recurseDisjoin (acc, [] ) (e : es) = recurseDisjoin (acc, [e]) es -- the "initialize" pattern
recurseDisjoin (acc, o : os) (e : es)
| -- the "operating" patterns
-- If input event is equal to the first comparator, skip the comparison.
e == o = recurseDisjoin (acc, o : os) es
|
{- If o is either before or meets e, then
the first of the combined events can be put into the accumulator.
That is, since the inputs events are ordered, once the beginning of o
is before or meets e, then we are assured that all periods up to the
beginning of o are fully disjoint and subsequent input events will
not overlap these in any way. -}
(before <|> meets) o e = recurseDisjoin
(acc <> nh, recurseDisjoin ([], nt) os)
es
|
--The standard recursive operation.
otherwise = recurseDisjoin (acc, recurseDisjoin ([], n) os) es
where
n = getMeeting $ disjoinPaired o e
nh = maybeToList (headMay n)
nt = tailSafe n
{-# INLINABLE recurseDisjoin #-}
{- |
Convert an ordered sequence of @PairedInterval b a@. that may have any interval relation
('before', 'starts', etc) into a sequence of sequentially meeting @PairedInterval b a@.
That is, a sequence where one the end of one interval meets the beginning of
the subsequent event. The 'getPairData' of the input @PairedIntervals@ are
combined using the Monoid '<>' function, hence the pair data must be a
'Monoid' instance.
-}
formMeetingSequence
:: (Eq b, Show a, Monoid b, IntervalSizeable a c)
=> [PairedInterval b a]
-> [PairedInterval b a]
formMeetingSequence x
| null x = []
| allMeet x && not (hasEqData x) = x
| otherwise = formMeetingSequence (recurseDisjoin ([], []) x)
-- recurseDisjoin ([], []) (recurseDisjoin ([], []) (recurseDisjoin ([], []) x))
-- the multiple passes of recurseDisjoin is to handle the situation where the
-- initial passes almost disjoins all the events correctly into a meeting sequence
-- but due to nesting of intervals in the input -- some of the sequential pairs have
-- the same data after the first pass. The recursive passes merges any sequential
-- intervals that have the same data.
--
-- There is probably a more efficient way to do this
{-# INLINABLE formMeetingSequence #-}
allMeet :: (Ord a) => [PairedInterval b a] -> Bool
allMeet x = all (== Meets) (relationsL x)
hasEqData :: (Eq b) => [PairedInterval b a] -> Bool
hasEqData x = or (L.fold (makeFolder (==)) (fmap getPairData x) :: [Bool])