IntervalAlgebra.IntervalUtilities

In the examples below, iv is a synonym for beginerval used to save space.

Documentation

relations :: (IntervalAlgebraic i a, Foldable f) => f (i a) -> [IntervalRelation (i a)]

Returns a list of the IntervalRelation between each consecutive pair of intervals. This the specialized form of relations' which can return any Applicative, Monoid structure.

>>> relations [iv 1 0, iv 1 1]
[Meets]

relations' :: (IntervalAlgebraic i a, Foldable f, Applicative m, Monoid (m (IntervalRelation (i a)))) => f (i a) -> m (IntervalRelation (i a))

A generic form of relations which can output any Applicative and Monoid structure. >>> (relations' [iv 1 0, iv 1 1]) :: [IntervalRelation (Interval Int)] [Meets]

intersect :: (IntervalSizeable a b, IntervalAlgebraic i a) => i a -> i a -> Maybe (Interval a)

Forms a Just new interval from the intersection of two intervals, provided the intervals are not disjoint.

combineIntervals :: (IntervalAlgebraic Interval a, Applicative f, Monoid (f (Interval a)), Foldable f) => f (Interval a) -> f (Interval a)

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 combineIntervals' 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' :: IntervalAlgebraic Interval a => [Interval a] -> [Interval a]

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*.

>>> combineIntervals' [iv 10 0, iv 5 2, iv 2 10, iv 2 13]
[(0, 12),(13, 15)]

gaps :: (IntervalCombinable Interval a, Applicative f, Monoid (f (Interval a)), Foldable f) => f (Interval a) -> f (Interval a)

Returns a (possibly empty) container of intervals consisting of the gaps between intervals in the input. *To work properly, the input should be sorted*. See gaps' for a version that returns a list.

>>> gaps [iv 4 1, iv 4 8, iv 3 11]
[(5, 8)]

gaps' :: (IntervalCombinable Interval a, Applicative f, Monoid (f (Interval a)), Foldable f) => f (Interval a) -> [Interval a]

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.

durations :: (Functor f, Intervallic i a, IntervalSizeable a b) => f (i a) -> f b

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]

clip :: (IntervalAlgebraic Interval a, IntervalSizeable a b) => Interval a -> Interval a -> Maybe (Interval a)

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

gapsWithin

Arguments

:: (Applicative f, Foldable f, Monoid (f (Interval a)), IntervalSizeable a b, IntervalCombinable Interval a, Filterable f, IntervalAlgebraic Interval a)

=> Interval a

i

-> f (Interval a)

x

-> Maybe (f (Interval a))

Applies gaps to all the non-disjoint intervals in x that are *not* disjoint from i. Intervals that overlaps or are overlappedBy i are clipped to i, so that all the intervals are within i. If there are no gaps, then Nothing is returned.

>>> gapsWithin (iv 9 1) [iv 5 0, iv 2 7, iv 3 12]
Just [(5, 7),(9, 10)]

nothingIf

Arguments

:: (Monoid (f (i a)), Filterable f, IntervalAlgebraic i a)

=> ((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))

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.

nothingIfNone

Arguments

:: (Monoid (f (i a)), Foldable f, Filterable f, IntervalAlgebraic i a)

=> (i a -> Bool)

predicate to apply to each element of input list

-> f (i a)

-> Maybe (f (i a))

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)]

nothingIfAny

Arguments

:: (Monoid (f (i a)), Foldable f, Filterable f, IntervalAlgebraic i a)

=> (i a -> Bool)

predicate to apply to each element of input list

-> f (i a)

-> Maybe (f (i a))

Returns Nothing if *any* of the element of input satisfy the predicate condition.

nothingIfAll

Arguments

:: (Monoid (f (i a)), Foldable f, Filterable f, IntervalAlgebraic i a)

=> (i a -> Bool)

predicate to apply to each element of input list

-> f (i a)

-> Maybe (f (i a))

Returns Nothing if *all* of the element of input satisfy the predicate condition

Operations on Meeting sequences of intervals

foldMeetingSafe

Arguments

:: (IntervalAlgebraic (PairedInterval b) a, Eq b)

=> [PairedInterval b a]

Be sure this only contains intervals that sequentially meets.

-> [PairedInterval b a]

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.

formMeetingSequence :: (Eq b, Monoid b, IntervalSizeable a c) => [PairedInterval b a] -> [PairedInterval b a]

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.

Filtering functions

compareIntervals :: (IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => ComparativePredicateOf (Interval a) -> i0 a -> i1 a -> Bool

Filter functions provides means for filtering Filterable containers of 'Intervallic i a's based on IntervalAlgebraic relations.

Lifts a predicate to be able to compare two different IntervalAlgebraic structure by comparing the intervals contain within each.

filterBefore :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by before.

filterMeets :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by meets.

filterOverlaps :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by overlaps.

filterFinishedBy :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter byfinishedBy.

filterContains :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by contains.

filterStarts :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by starts.

filterEquals :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by equals.

filterStartedBy :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by startedBy.

filterDuring :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by during.

filterFinishes :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by finishes.

filterOverlappedBy :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by overlappedBy.

filterMetBy :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by metBy.

filterAfter :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by after.

filterDisjoint :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by disjoint.

filterNotDisjoint :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by notDisjoint.

filterConcur :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by concur.

filterWithin :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by within.

filterEnclose :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by enclose.

filterEnclosedBy :: (Filterable f, IntervalAlgebraic Interval a, IntervalAlgebraic i0 a, IntervalAlgebraic i1 a) => i0 a -> f (i1 a) -> f (i1 a)

Filter by enclosedBy.