{-|
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 GHC.Show              ( Show )
import safe GHC.Int               ( Int )
import safe Control.Applicative   ( Applicative(pure)
                                  , (<*>) )
import qualified Control.Foldl as L
import safe Control.Monad         ( Functor(fmap) )
import safe Data.Bool             ( Bool, otherwise, not, (||), (&&) )
import safe Data.Eq               ( Eq((==)) )
import safe Data.Foldable         ( Foldable(null, foldl', toList)
                                  , all
                                  , any
                                  , or )
import safe Data.Function         ( ($), (.), flip )
import safe Data.Monoid           ( Monoid(mempty) )
import safe Data.Maybe            ( Maybe(..)
                                  , maybe
                                  , maybeToList )
import safe Data.Ord              ( Ord(min, max) )
import safe Data.Semigroup        ( Semigroup((<>)) )
import safe Data.Traversable      ( Traversable(sequenceA) )
import safe Data.Tuple            ( fst )
import safe Safe                  ( headMay, lastMay, initSafe, tailSafe)
import safe Witherable            ( Filterable(filter)
                                  , Witherable(..)
                                  , mapMaybe
                                  , catMaybes )
import safe IntervalAlgebra       ( (<|>),
                                  begin,
                                  end,
                                  after,
                                  before,
                                  beginerval,
                                  beginervalFromEnd,
                                  endervalFromBegin,
                                  concur,
                                  contains,
                                  disjoint,
                                  during,
                                  enclose,
                                  enclosedBy,
                                  enderval,
                                  equals,
                                  extenterval,
                                  finishedBy,
                                  finishes,
                                  meets,
                                  metBy,
                                  notDisjoint,
                                  overlappedBy,
                                  overlaps,
                                  relate,
                                  startedBy,
                                  starts,
                                  within,
                                  ComparativePredicateOf1,
                                  ComparativePredicateOf2,
                                  Interval,
                                  IntervalCombinable((<+>), (><)),
                                  IntervalRelation(..),
                                  IntervalSizeable(diff, duration),
                                  Intervallic(..) )
import safe IntervalAlgebra.PairedInterval
                                  ( PairedInterval
                                  , makePairedInterval
                                  , getPairData
                                  , equalPairData )



-------------------------------------------------
-- Unexported utilties used in functions below --
-------------------------------------------------

-- Just a synonym used to examples to save typing
iv :: Int -> Int -> Interval Int
iv :: Int -> Int -> Interval Int
iv = Int -> Int -> Interval Int
forall a b. IntervalSizeable a b => b -> a -> Interval a
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 :: (a -> a -> b) -> Fold a (m b)
makeFolder a -> a -> b
f = ((m b, Maybe a) -> a -> (m b, Maybe a))
-> (m b, Maybe a) -> ((m b, Maybe a) -> m b) -> Fold a (m b)
forall a b x. (x -> a -> x) -> x -> (x -> b) -> Fold a b
L.Fold (m b, Maybe a) -> a -> (m b, Maybe a)
forall (f :: * -> *).
(Semigroup (f b), Applicative f) =>
(f b, Maybe a) -> a -> (f b, Maybe a)
step (m b, Maybe a)
forall a. (m b, Maybe a)
begin (m b, Maybe a) -> m b
forall a b. (a, b) -> a
done
  where
    begin :: (m b, Maybe a)
begin = (m b
forall a. Monoid a => a
mempty, Maybe a
forall a. Maybe a
Nothing)
    step :: (f b, Maybe a) -> a -> (f b, Maybe a)
step (f b
fs, Maybe a
Nothing) a
y = (f b
fs, a -> Maybe a
forall a. a -> Maybe a
Just a
y)
    step (f b
fs, Just a
x) a
y  = (f b
fs f b -> f b -> f b
forall a. Semigroup a => a -> a -> a
<> b -> f b
forall (f :: * -> *) a. Applicative f => a -> f a
pure (a -> a -> b
f a
x a
y), a -> Maybe a
forall a. a -> Maybe a
Just a
y)
    done :: (a, b) -> a
done (a
fs, b
_) = a
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 :: (Maybe a -> Maybe a -> [a]) -> [a] -> [a] -> [a]
listCombiner Maybe a -> Maybe a -> [a]
f [a]
x [a]
y = [a] -> [a]
forall a. [a] -> [a]
initSafe [a]
x [a] -> [a] -> [a]
forall a. Semigroup a => a -> a -> a
<> Maybe a -> Maybe a -> [a]
f ([a] -> Maybe a
forall a. [a] -> Maybe a
lastMay [a]
x) ([a] -> Maybe a
forall a. [a] -> Maybe a
headMay [a]
y) [a] -> [a] -> [a]
forall a. Semigroup a => a -> a -> a
<> [a] -> [a]
forall a. [a] -> [a]
tailSafe [a]
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 :: f (i a) -> [IntervalRelation]
relationsL = f (i a) -> [IntervalRelation]
forall (f :: * -> *) (m :: * -> *) (i :: * -> *) a.
(Foldable f, Applicative m, Intervallic i a,
 Monoid (m IntervalRelation)) =>
f (i a) -> m IntervalRelation
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 :: f (i a) -> m IntervalRelation
relations = Fold (i a) (m IntervalRelation) -> f (i a) -> m IntervalRelation
forall (f :: * -> *) a b. Foldable f => Fold a b -> f a -> b
L.fold ((i a -> i a -> IntervalRelation) -> Fold (i a) (m IntervalRelation)
forall (m :: * -> *) b a.
(Monoid (m b), Applicative m) =>
(a -> a -> b) -> Fold a (m b)
makeFolder i a -> i a -> IntervalRelation
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
i0 a -> i1 a -> IntervalRelation
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 :: i a -> i a -> Maybe (Interval a)
intersect i a
x i a
y
    | ComparativePredicateOf2 (i a) (i a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
disjoint i a
x i a
y = Maybe (Interval a)
forall a. Maybe a
Nothing
    | Bool
otherwise    = Interval a -> Maybe (Interval a)
forall a. a -> Maybe a
Just (Interval a -> Maybe (Interval a))
-> Interval a -> Maybe (Interval a)
forall a b. (a -> b) -> a -> b
$ b -> a -> Interval a
forall a b. IntervalSizeable a b => b -> a -> Interval a
beginerval (a -> a -> b
forall a b. IntervalSizeable a b => a -> a -> b
diff a
e a
b) a
b
        where b :: a
b = a -> a -> a
forall a. Ord a => a -> a -> a
max (i a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin i a
x) (i a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin i a
y)
              e :: a
e = a -> a -> a
forall a. Ord a => a -> a -> a
min (i a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end i a
x) (i a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end i a
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 :: f (i a) -> f (Maybe (Interval a))
gapsM =  Fold (i a) (f (Maybe (Interval a)))
-> f (i a) -> f (Maybe (Interval a))
forall (f :: * -> *) a b. Foldable f => Fold a b -> f a -> b
L.fold ((i a -> i a -> Maybe (Interval a))
-> Fold (i a) (f (Maybe (Interval a)))
forall (m :: * -> *) b a.
(Monoid (m b), Applicative m) =>
(a -> a -> b) -> Fold a (m b)
makeFolder (\i a
i i a
j -> i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
i Interval a -> Interval a -> Maybe (Interval a)
forall (i :: * -> *) a.
IntervalCombinable i a =>
i a -> i a -> Maybe (i a)
>< i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
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 :: f (i a) -> Maybe (f (Interval a))
gaps = f (Maybe (Interval a)) -> Maybe (f (Interval a))
forall (t :: * -> *) (f :: * -> *) a.
(Traversable t, Applicative f) =>
t (f a) -> f (t a)
sequenceA(f (Maybe (Interval a)) -> Maybe (f (Interval a)))
-> (f (i a) -> f (Maybe (Interval a)))
-> f (i a)
-> Maybe (f (Interval a))
forall b c a. (b -> c) -> (a -> b) -> a -> c
.f (i a) -> f (Maybe (Interval a))
forall (i :: * -> *) a (f :: * -> *).
(IntervalCombinable i a, Traversable f,
 Monoid (f (Maybe (Interval a))), Applicative f) =>
f (i a) -> f (Maybe (Interval a))
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 :: f (i a) -> [Interval a]
gapsL f (i a)
x = [Interval a]
-> (f (Interval a) -> [Interval a])
-> Maybe (f (Interval a))
-> [Interval a]
forall b a. b -> (a -> b) -> Maybe a -> b
maybe [] f (Interval a) -> [Interval a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList (f (i a) -> Maybe (f (Interval a))
forall (i :: * -> *) a (f :: * -> *).
(IntervalCombinable i a, Traversable f,
 Monoid (f (Maybe (Interval a))), Applicative f) =>
f (i a) -> Maybe (f (Interval a))
gaps f (i a)
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 :: f (i a) -> f b
durations = (i a -> b) -> f (i a) -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap i a -> b
forall a b (i :: * -> *).
(IntervalSizeable a b, Intervallic i a) =>
i a -> b
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 :: i0 a -> i1 a -> Maybe (Interval a)
clip i0 a
x i1 a
y
   | ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
overlaps i0 a
x i1 a
y     = Interval a -> Maybe (Interval a)
forall a. a -> Maybe a
Just (Interval a -> Maybe (Interval a))
-> Interval a -> Maybe (Interval a)
forall a b. (a -> b) -> a -> b
$ b -> a -> Interval a
forall a b. IntervalSizeable a b => b -> a -> Interval a
enderval   (a -> a -> b
forall a b. IntervalSizeable a b => a -> a -> b
diff (i0 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end i0 a
x) (i1 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin i1 a
y)) (i0 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end i0 a
x)
   | ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
overlappedBy i0 a
x i1 a
y = Interval a -> Maybe (Interval a)
forall a. a -> Maybe a
Just (Interval a -> Maybe (Interval a))
-> Interval a -> Maybe (Interval a)
forall a b. (a -> b) -> a -> b
$ b -> a -> Interval a
forall a b. IntervalSizeable a b => b -> a -> Interval a
beginerval (a -> a -> b
forall a b. IntervalSizeable a b => a -> a -> b
diff (i1 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end i1 a
y) (i0 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin i0 a
x)) (i0 a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin i0 a
x)
   | ComparativePredicateOf2 (i0 a) (i1 a)
jx i0 a
x i1 a
y           = Interval a -> Maybe (Interval a)
forall a. a -> Maybe a
Just (i0 a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i0 a
x)
   | ComparativePredicateOf2 (i0 a) (i1 a)
jy i0 a
x i1 a
y           = Interval a -> Maybe (Interval a)
forall a. a -> Maybe a
Just (i1 a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i1 a
y)
   | Bool
otherwise        = Maybe (Interval a)
forall a. Maybe a
Nothing {- disjoint x y case -}
   where jy :: ComparativePredicateOf2 (i0 a) (i1 a)
jy = ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
equals ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
startedBy ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
contains ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
finishedBy
         jx :: ComparativePredicateOf2 (i0 a) (i1 a)
jx = ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
starts ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
during ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
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 :: i0 a -> f (i1 a) -> Maybe (f (Interval a))
gapsWithin i0 a
i f (i1 a)
x 
  | f (Interval a) -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null f (Interval a)
ivs = Maybe (f (Interval a))
forall a. Maybe a
Nothing 
  | Bool
otherwise = f (Interval a) -> Maybe (f (Interval a))
forall a. a -> Maybe a
Just f (Interval a)
res
    where s :: f (Interval a)
s   = Interval a -> f (Interval a)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> i0 a -> Interval a
forall a b (i :: * -> *).
(IntervalSizeable a b, Intervallic i a) =>
b -> i a -> Interval a
endervalFromBegin b
0 i0 a
i)
          e :: f (Interval a)
e   = Interval a -> f (Interval a)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> i0 a -> Interval a
forall a b (i :: * -> *).
(IntervalSizeable a b, Intervallic i a) =>
b -> i a -> Interval a
beginervalFromEnd b
0 i0 a
i)
          ivs :: f (Interval a)
ivs = (i1 a -> Maybe (Interval a)) -> f (i1 a) -> f (Interval a)
forall (f :: * -> *) a b.
Filterable f =>
(a -> Maybe b) -> f a -> f b
mapMaybe (i0 a -> i1 a -> Maybe (Interval a)
forall (i0 :: * -> *) a (i1 :: * -> *) b.
(Intervallic i0 a, Intervallic i1 a, IntervalSizeable a b) =>
i0 a -> i1 a -> Maybe (Interval a)
clip i0 a
i) (i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
i0 a -> f (i1 a) -> f (i1 a)
filterNotDisjoint i0 a
i f (i1 a)
x)
          res :: f (Interval a)
res = f (Maybe (Interval a)) -> f (Interval a)
forall (f :: * -> *) a. Filterable f => f (Maybe a) -> f a
catMaybes (f (Maybe (Interval a)) -> f (Interval a))
-> f (Maybe (Interval a)) -> f (Interval a)
forall a b. (a -> b) -> a -> b
$ f (Interval a) -> f (Maybe (Interval a))
forall (i :: * -> *) a (f :: * -> *).
(IntervalCombinable i a, Traversable f,
 Monoid (f (Maybe (Interval a))), Applicative f) =>
f (i a) -> f (Maybe (Interval a))
gapsM ( f (Interval a)
s f (Interval a) -> f (Interval a) -> f (Interval a)
forall a. Semigroup a => a -> a -> a
<> f (Interval a)
ivs f (Interval a) -> f (Interval a) -> f (Interval a)
forall a. Semigroup a => a -> a -> a
<> f (Interval a)
e ) 
{-# INLINABLE gapsWithin #-}

-- The Box is an internal type used to hold accumulated, combined intervals in 
-- 'combineIntervalsL'.
newtype Box a = Box { Box a -> [a]
unBox :: [a] }

packIntervalBoxes :: (Intervallic i a)=> [i a] -> [Box (Interval a)]
packIntervalBoxes :: [i a] -> [Box (Interval a)]
packIntervalBoxes  = (i a -> Box (Interval a)) -> [i a] -> [Box (Interval a)]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\i a
z -> [Interval a] -> Box (Interval a)
forall a. [a] -> Box a
Box [i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
z])

instance (Ord a) => Semigroup (Box (Interval a)) where
    Box [Interval a]
x <> :: Box (Interval a) -> Box (Interval a) -> Box (Interval a)
<> Box [Interval a]
y = [Interval a] -> Box (Interval a)
forall a. [a] -> Box a
Box ([Interval a] -> Box (Interval a))
-> [Interval a] -> Box (Interval a)
forall a b. (a -> b) -> a -> b
$ (Maybe (Interval a) -> Maybe (Interval a) -> [Interval a])
-> [Interval a] -> [Interval a] -> [Interval a]
forall a. (Maybe a -> Maybe a -> [a]) -> [a] -> [a] -> [a]
listCombiner Maybe (Interval a) -> Maybe (Interval a) -> [Interval a]
forall (i :: * -> *) a.
IntervalCombinable i a =>
Maybe (i a) -> Maybe (i a) -> [Interval a]
(<->) [Interval a]
x [Interval a]
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 :: f (i a) -> f (Interval a)
combineIntervals f (i a)
x = 
  (f (Interval a) -> Interval a -> f (Interval a))
-> f (Interval a) -> [Interval a] -> f (Interval a)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' (\f (Interval a)
x Interval a
y -> f (Interval a)
x f (Interval a) -> f (Interval a) -> f (Interval a)
forall a. Semigroup a => a -> a -> a
<> Interval a -> f (Interval a)
forall (f :: * -> *) a. Applicative f => a -> f a
pure Interval a
y) f (Interval a)
forall a. Monoid a => a
mempty ([i a] -> [Interval a]
forall (i :: * -> *) a. Intervallic i a => [i a] -> [Interval a]
combineIntervalsL ([i a] -> [Interval a]) -> [i a] -> [Interval a]
forall a b. (a -> b) -> a -> b
$ f (i a) -> [i a]
forall (t :: * -> *) a. Foldable t => t a -> [a]
toList f (i a)
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 :: [i a] -> [Interval a]
combineIntervalsL [i a]
l = Box (Interval a) -> [Interval a]
forall a. Box a -> [a]
unBox (Box (Interval a) -> [Interval a])
-> Box (Interval a) -> [Interval a]
forall a b. (a -> b) -> a -> b
$ (Box (Interval a) -> Box (Interval a) -> Box (Interval a))
-> Box (Interval a) -> [Box (Interval a)] -> Box (Interval a)
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' Box (Interval a) -> Box (Interval a) -> Box (Interval a)
forall a. Semigroup a => a -> a -> a
(<>) ([Interval a] -> Box (Interval a)
forall a. [a] -> Box a
Box []) ([i a] -> [Box (Interval a)]
forall (i :: * -> *) a.
Intervallic i a =>
[i a] -> [Box (Interval a)]
packIntervalBoxes [i a]
l)
{-# INLINABLE combineIntervalsL #-}

-- Internal function for combining maybe intervals in the 'combineIntervalsL' 
-- function
(<->) :: (IntervalCombinable i a) =>
       Maybe (i a)
    -> Maybe (i a)
    -> [Interval a]
<-> :: Maybe (i a) -> Maybe (i a) -> [Interval a]
(<->) Maybe (i a)
Nothing Maybe (i a)
Nothing   = []
(<->) Maybe (i a)
Nothing (Just i a
y)  = [i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
y]
(<->) (Just i a
x) Maybe (i a)
Nothing  = [i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
x]
(<->) (Just i a
x) (Just i a
y) = Interval a -> Interval a -> [Interval a]
forall (i :: * -> *) a (f :: * -> *).
(IntervalCombinable i a, Semigroup (f (i a)), Applicative f) =>
i a -> i a -> f (i a)
(<+>) (i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
x) (i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval i a
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 :: ((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIf (i a -> Bool) -> f (i a) -> Bool
quantifier i a -> Bool
predicate f (i a)
x = if (i a -> Bool) -> f (i a) -> Bool
quantifier i a -> Bool
predicate f (i a)
x then Maybe (f (i a))
forall a. Maybe a
Nothing else f (i a) -> Maybe (f (i a))
forall a. a -> Maybe a
Just f (i a)
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 :: (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIfNone = ((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
forall (f :: * -> *) (i :: * -> *) a.
(Monoid (f (i a)), Filterable f) =>
((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIf (\i a -> Bool
f f (i a)
x -> (Bool -> Bool
not(Bool -> Bool) -> (f (i a) -> Bool) -> f (i a) -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(i a -> Bool) -> f (i a) -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
any i a -> Bool
f) f (i a)
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 :: (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIfAny = ((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
forall (f :: * -> *) (i :: * -> *) a.
(Monoid (f (i a)), Filterable f) =>
((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIf (i a -> Bool) -> f (i a) -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
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 :: (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIfAll = ((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
forall (f :: * -> *) (i :: * -> *) a.
(Monoid (f (i a)), Filterable f) =>
((i a -> Bool) -> f (i a) -> Bool)
-> (i a -> Bool) -> f (i a) -> Maybe (f (i a))
nothingIf (i a -> Bool) -> f (i a) -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
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 :: ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
f i0 a
p = (i1 a -> Bool) -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) a. Filterable f => (a -> Bool) -> f a -> f a
Witherable.filter (ComparativePredicateOf2 (i0 a) (i1 a)
f i0 a
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 :: i0 a -> f (i1 a) -> f (i1 a)
filterOverlaps          = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
overlaps
filterOverlappedBy :: i0 a -> f (i1 a) -> f (i1 a)
filterOverlappedBy      = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
overlappedBy
filterBefore :: i0 a -> f (i1 a) -> f (i1 a)
filterBefore            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
before
filterAfter :: i0 a -> f (i1 a) -> f (i1 a)
filterAfter             = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
after
filterStarts :: i0 a -> f (i1 a) -> f (i1 a)
filterStarts            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
starts
filterStartedBy :: i0 a -> f (i1 a) -> f (i1 a)
filterStartedBy         = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
startedBy
filterFinishes :: i0 a -> f (i1 a) -> f (i1 a)
filterFinishes          = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
finishes
filterFinishedBy :: i0 a -> f (i1 a) -> f (i1 a)
filterFinishedBy        = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
finishedBy
filterMeets :: i0 a -> f (i1 a) -> f (i1 a)
filterMeets             = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
meets
filterMetBy :: i0 a -> f (i1 a) -> f (i1 a)
filterMetBy             = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
metBy
filterDuring :: i0 a -> f (i1 a) -> f (i1 a)
filterDuring            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
during
filterContains :: i0 a -> f (i1 a) -> f (i1 a)
filterContains          = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
contains
filterEquals :: i0 a -> f (i1 a) -> f (i1 a)
filterEquals            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
equals
filterDisjoint :: i0 a -> f (i1 a) -> f (i1 a)
filterDisjoint          = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
disjoint
filterNotDisjoint :: i0 a -> f (i1 a) -> f (i1 a)
filterNotDisjoint       = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
notDisjoint
filterConcur :: i0 a -> f (i1 a) -> f (i1 a)
filterConcur            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
concur
filterWithin :: i0 a -> f (i1 a) -> f (i1 a)
filterWithin            = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
within
filterEnclose :: i0 a -> f (i1 a) -> f (i1 a)
filterEnclose           = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
enclose
filterEnclosedBy :: i0 a -> f (i1 a) -> f (i1 a)
filterEnclosedBy        = ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
forall (f :: * -> *) (i0 :: * -> *) a (i1 :: * -> *).
(Filterable f, Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> i0 a -> f (i1 a) -> f (i1 a)
makeFilter ComparativePredicateOf2 (i0 a) (i1 a)
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
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 :: [PairedInterval b a] -> [PairedInterval b a]
foldMeetingSafe [PairedInterval b a]
l = [PairedInterval b a]
-> (Meeting [PairedInterval b a] -> [PairedInterval b a])
-> Maybe (Meeting [PairedInterval b a])
-> [PairedInterval b a]
forall b a. b -> (a -> b) -> Maybe a -> b
maybe [] (Meeting [PairedInterval b a] -> [PairedInterval b a]
forall a. Meeting a -> a
getMeeting (Meeting [PairedInterval b a] -> [PairedInterval b a])
-> (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a]
-> [PairedInterval b a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting) ([PairedInterval b a] -> Maybe (Meeting [PairedInterval b a])
forall (i :: * -> *) a.
Intervallic i a =>
[i a] -> Maybe (Meeting [i a])
parseMeeting [PairedInterval b a]
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 [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a]
l) = (Meeting [PairedInterval b a]
 -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a]
-> [Meeting [PairedInterval b a]]
-> Meeting [PairedInterval b a]
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
joinMeetingPairedInterval ([PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting []) ([PairedInterval b a] -> [Meeting [PairedInterval b a]]
forall a. [a] -> [Meeting [a]]
packMeeting [PairedInterval b a]
l)

-- This type identifies that @a@ contains intervals that sequentially meet one 
-- another.
newtype Meeting a = Meeting { Meeting a -> a
getMeeting :: a } deriving (Meeting a -> Meeting a -> Bool
(Meeting a -> Meeting a -> Bool)
-> (Meeting a -> Meeting a -> Bool) -> Eq (Meeting a)
forall a. Eq a => Meeting a -> Meeting a -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Meeting a -> Meeting a -> Bool
$c/= :: forall a. Eq a => Meeting a -> Meeting a -> Bool
== :: Meeting a -> Meeting a -> Bool
$c== :: forall a. Eq a => Meeting a -> Meeting a -> Bool
Eq, Int -> Meeting a -> ShowS
[Meeting a] -> ShowS
Meeting a -> String
(Int -> Meeting a -> ShowS)
-> (Meeting a -> String)
-> ([Meeting a] -> ShowS)
-> Show (Meeting a)
forall a. Show a => Int -> Meeting a -> ShowS
forall a. Show a => [Meeting a] -> ShowS
forall a. Show a => Meeting a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Meeting a] -> ShowS
$cshowList :: forall a. Show a => [Meeting a] -> ShowS
show :: Meeting a -> String
$cshow :: forall a. Show a => Meeting a -> String
showsPrec :: Int -> Meeting a -> ShowS
$cshowsPrec :: forall a. Show a => Int -> Meeting a -> ShowS
Show)

-- Box up Meeting.
packMeeting :: [a] -> [Meeting [a]]
packMeeting :: [a] -> [Meeting [a]]
packMeeting = (a -> Meeting [a]) -> [a] -> [Meeting [a]]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\a
z -> [a] -> Meeting [a]
forall a. a -> Meeting a
Meeting [a
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 :: [i a] -> Maybe (Meeting [i a])
parseMeeting [i a]
x
    | (IntervalRelation -> Bool) -> [IntervalRelation] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ( IntervalRelation -> IntervalRelation -> Bool
forall a. Eq a => a -> a -> Bool
== IntervalRelation
Meets ) ([i a] -> [IntervalRelation]
forall (f :: * -> *) (i :: * -> *) a.
(Foldable f, Intervallic i a) =>
f (i a) -> [IntervalRelation]
relationsL [i a]
x) = Meeting [i a] -> Maybe (Meeting [i a])
forall a. a -> Maybe a
Just (Meeting [i a] -> Maybe (Meeting [i a]))
-> Meeting [i a] -> Maybe (Meeting [i a])
forall a b. (a -> b) -> a -> b
$ [i a] -> Meeting [i a]
forall a. a -> Meeting a
Meeting [i a]
x
    | Bool
otherwise = Maybe (Meeting [i a])
forall a. Maybe a
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 :: Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
joinMeetingPairedInterval = ComparativePredicateOf1 (PairedInterval b a)
-> Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a]
-> Meeting [PairedInterval b a]
forall (i :: * -> *) a.
Intervallic i a =>
ComparativePredicateOf1 (i a)
-> Meeting [i a] -> Meeting [i a] -> Meeting [i a]
joinMeeting ComparativePredicateOf1 (PairedInterval b a)
forall b a. Eq b => ComparativePredicateOf1 (PairedInterval b a)
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 :: ComparativePredicateOf1 (i a)
-> Meeting [i a] -> Meeting [i a] -> Meeting [i a]
joinMeeting ComparativePredicateOf1 (i a)
f (Meeting [i a]
x) (Meeting [i a]
y) = [i a] -> Meeting [i a]
forall a. a -> Meeting a
Meeting ([i a] -> Meeting [i a]) -> [i a] -> Meeting [i a]
forall a b. (a -> b) -> a -> b
$ (Maybe (i a) -> Maybe (i a) -> [i a]) -> [i a] -> [i a] -> [i a]
forall a. (Maybe a -> Maybe a -> [a]) -> [a] -> [a] -> [a]
listCombiner (ComparativePredicateOf1 (i a)
-> Maybe (i a) -> Maybe (i a) -> [i a]
forall (i :: * -> *) a.
Intervallic i a =>
ComparativePredicateOf1 (i a)
-> Maybe (i a) -> Maybe (i a) -> [i a]
join2MeetingWhen ComparativePredicateOf1 (i a)
f) [i a]
x [i a]
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 :: ComparativePredicateOf1 (i a)
-> Maybe (i a) -> Maybe (i a) -> [i a]
join2MeetingWhen ComparativePredicateOf1 (i a)
p Maybe (i a)
Nothing Maybe (i a)
Nothing   = []
join2MeetingWhen ComparativePredicateOf1 (i a)
p Maybe (i a)
Nothing (Just i a
y)  = [i a
y]
join2MeetingWhen ComparativePredicateOf1 (i a)
p (Just i a
x) Maybe (i a)
Nothing  = [i a
x]
join2MeetingWhen ComparativePredicateOf1 (i a)
p (Just i a
x) (Just i a
y)
    | ComparativePredicateOf1 (i a)
p i a
x i a
y      = [ i a -> Interval a -> i a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a -> i a
setInterval i a
y (i a -> i a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> i a -> Interval a
extenterval i a
x i a
y) ]
    | Bool
otherwise  =  i a -> [i a]
forall (f :: * -> *) a. Applicative f => a -> f a
pure i a
x [i a] -> [i a] -> [i a]
forall a. Semigroup a => a -> a -> a
<> i a -> [i a]
forall (f :: * -> *) a. Applicative f => a -> f a
pure i a
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 :: PairedInterval b a
-> PairedInterval b a -> Meeting [PairedInterval b a]
disjoinPaired PairedInterval b a
o PairedInterval b a
e = case PairedInterval b a -> PairedInterval b a -> IntervalRelation
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
i0 a -> i1 a -> IntervalRelation
relate PairedInterval b a
x PairedInterval b a
y of
     IntervalRelation
Before     -> [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ PairedInterval b a
x, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
e1 a
b2 b
forall a. Monoid a => a
mempty, PairedInterval b a
y ]
     IntervalRelation
Meets      -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ PairedInterval b a
x, PairedInterval b a
y ]
     IntervalRelation
Overlaps   -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
b1 a
b2 b
s1, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
b2 a
e1 b
sc, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
e1 a
e2 b
s2 ]
     IntervalRelation
FinishedBy -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
b1 a
b2 b
s1, Interval a -> b -> PairedInterval b a
forall a b. Interval a -> b -> PairedInterval b a
ev Interval a
i2 b
sc ]
     IntervalRelation
Contains   -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
b1 a
b2 b
s1, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
b2 a
e2 b
sc, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
e2 a
e1 b
s1 ]
     IntervalRelation
Starts     -> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall b a.
(Eq b, Ord a, Show a) =>
Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
foldMeeting (Meeting [PairedInterval b a] -> Meeting [PairedInterval b a])
-> Meeting [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ Interval a -> b -> PairedInterval b a
forall a b. Interval a -> b -> PairedInterval b a
ev Interval a
i1 b
sc, a -> a -> b -> PairedInterval b a
forall b. a -> a -> b -> PairedInterval b a
evp a
e1 a
e2 b
s2 ]
     IntervalRelation
_          -> [PairedInterval b a] -> Meeting [PairedInterval b a]
forall a. a -> Meeting a
Meeting [ Interval a -> b -> PairedInterval b a
forall a b. Interval a -> b -> PairedInterval b a
ev Interval a
i1 b
sc ] {- Equals case -}
   where x :: PairedInterval b a
x  = PairedInterval b a -> PairedInterval b a -> PairedInterval b a
forall a. Ord a => a -> a -> a
min PairedInterval b a
o PairedInterval b a
e
         y :: PairedInterval b a
y  = PairedInterval b a -> PairedInterval b a -> PairedInterval b a
forall a. Ord a => a -> a -> a
max PairedInterval b a
o PairedInterval b a
e
         i1 :: Interval a
i1 = PairedInterval b a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval PairedInterval b a
x
         i2 :: Interval a
i2 = PairedInterval b a -> Interval a
forall (i :: * -> *) a. Intervallic i a => i a -> Interval a
getInterval PairedInterval b a
y
         s1 :: b
s1 = PairedInterval b a -> b
forall b a. PairedInterval b a -> b
getPairData PairedInterval b a
x
         s2 :: b
s2 = PairedInterval b a -> b
forall b a. PairedInterval b a -> b
getPairData PairedInterval b a
y
         sc :: b
sc = b
s1 b -> b -> b
forall a. Semigroup a => a -> a -> a
<> b
s2
         b1 :: a
b1 = PairedInterval b a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin PairedInterval b a
x
         b2 :: a
b2 = PairedInterval b a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
begin PairedInterval b a
y
         e1 :: a
e1 = PairedInterval b a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end PairedInterval b a
x
         e2 :: a
e2 = PairedInterval b a -> a
forall (i :: * -> *) a. Intervallic i a => i a -> a
end PairedInterval b a
y
         ev :: Interval a -> b -> PairedInterval b a
ev = (b -> Interval a -> PairedInterval b a)
-> Interval a -> b -> PairedInterval b a
forall a b c. (a -> b -> c) -> b -> a -> c
flip b -> Interval a -> PairedInterval b a
forall b a. b -> Interval a -> PairedInterval b a
makePairedInterval
         evp :: a -> a -> b -> PairedInterval b a
evp = \a
b a
e b
s -> Interval a -> b -> PairedInterval b a
forall a b. Interval a -> b -> PairedInterval b a
ev (c -> a -> Interval a
forall a b. IntervalSizeable a b => b -> a -> Interval a
beginerval (a -> a -> c
forall a b. IntervalSizeable a b => a -> a -> b
diff a
e a
b) a
b) b
s
{-# 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 :: ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([PairedInterval b a]
acc, PairedInterval b a
o:[PairedInterval b a]
os) []     = [PairedInterval b a]
acc [PairedInterval b a]
-> [PairedInterval b a] -> [PairedInterval b a]
forall a. Semigroup a => a -> a -> a
<> (PairedInterval b a
oPairedInterval b a -> [PairedInterval b a] -> [PairedInterval b a]
forall a. a -> [a] -> [a]
:[PairedInterval b a]
os)           -- the "final" pattern
recurseDisjoin ([PairedInterval b a]
acc, [])   []     = [PairedInterval b a]
acc                 -- another "final" pattern 
recurseDisjoin ([PairedInterval b a]
acc, [])   (PairedInterval b a
e:[PairedInterval b a]
es) = ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([PairedInterval b a]
acc, [PairedInterval b a
e]) [PairedInterval b a]
es -- the "initialize" pattern
recurseDisjoin ([PairedInterval b a]
acc, PairedInterval b a
o:[PairedInterval b a]
os) (PairedInterval b a
e:[PairedInterval b a]
es)                       -- the "operating" patterns 
     -- If input event is equal to the first comparator, skip the comparison.
    | PairedInterval b a
e PairedInterval b a -> PairedInterval b a -> Bool
forall a. Eq a => a -> a -> Bool
== PairedInterval b a
o    = ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([PairedInterval b a]
acc, PairedInterval b a
oPairedInterval b a -> [PairedInterval b a] -> [PairedInterval b a]
forall a. a -> [a] -> [a]
:[PairedInterval b a]
os) [PairedInterval b a]
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. -}
    | (PairedInterval b a -> PairedInterval b a -> Bool
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
before (PairedInterval b a -> PairedInterval b a -> Bool)
-> (PairedInterval b a -> PairedInterval b a -> Bool)
-> PairedInterval b a
-> PairedInterval b a
-> Bool
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
-> ComparativePredicateOf2 (i0 a) (i1 a)
<|> PairedInterval b a -> PairedInterval b a -> Bool
forall (i0 :: * -> *) a (i1 :: * -> *).
(Intervallic i0 a, Intervallic i1 a) =>
ComparativePredicateOf2 (i0 a) (i1 a)
meets) PairedInterval b a
o PairedInterval b a
e = ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([PairedInterval b a]
acc [PairedInterval b a]
-> [PairedInterval b a] -> [PairedInterval b a]
forall a. Semigroup a => a -> a -> a
<> [PairedInterval b a]
nh, ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([], [PairedInterval b a]
nt) [PairedInterval b a]
os ) [PairedInterval b a]
es

    --The standard recursive operation.
    | Bool
otherwise = ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([PairedInterval b a]
acc,  ([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([], [PairedInterval b a]
n) [PairedInterval b a]
os ) [PairedInterval b a]
es
  where n :: [PairedInterval b a]
n  = Meeting [PairedInterval b a] -> [PairedInterval b a]
forall a. Meeting a -> a
getMeeting (Meeting [PairedInterval b a] -> [PairedInterval b a])
-> Meeting [PairedInterval b a] -> [PairedInterval b a]
forall a b. (a -> b) -> a -> b
$ PairedInterval b a
-> PairedInterval b a -> Meeting [PairedInterval b a]
forall b a c.
(Eq b, Monoid b, Show a, IntervalSizeable a c) =>
PairedInterval b a
-> PairedInterval b a -> Meeting [PairedInterval b a]
disjoinPaired PairedInterval b a
o PairedInterval b a
e
        nh :: [PairedInterval b a]
nh = Maybe (PairedInterval b a) -> [PairedInterval b a]
forall a. Maybe a -> [a]
maybeToList ([PairedInterval b a] -> Maybe (PairedInterval b a)
forall a. [a] -> Maybe a
headMay [PairedInterval b a]
n)
        nt :: [PairedInterval b a]
nt = [PairedInterval b a] -> [PairedInterval b a]
forall a. [a] -> [a]
tailSafe [PairedInterval b a]
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 :: [PairedInterval b a] -> [PairedInterval b a]
formMeetingSequence [PairedInterval b a]
x
  | [PairedInterval b a] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [PairedInterval b a]
x  = []
  | [PairedInterval b a] -> Bool
forall a b. Ord a => [PairedInterval b a] -> Bool
allMeet [PairedInterval b a]
x Bool -> Bool -> Bool
&& Bool -> Bool
not ([PairedInterval b a] -> Bool
forall b a. Eq b => [PairedInterval b a] -> Bool
hasEqData [PairedInterval b a]
x) = [PairedInterval b a]
x
  | Bool
otherwise  = [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Eq b, Show a, Monoid b, IntervalSizeable a c) =>
[PairedInterval b a] -> [PairedInterval b a]
formMeetingSequence (([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
forall b a c.
(Monoid b, Eq b, IntervalSizeable a c, Show a) =>
([PairedInterval b a], [PairedInterval b a])
-> [PairedInterval b a] -> [PairedInterval b a]
recurseDisjoin ([], []) [PairedInterval b a]
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 :: [PairedInterval b a] -> Bool
allMeet [PairedInterval b a]
x = (IntervalRelation -> Bool) -> [IntervalRelation] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all ( IntervalRelation -> IntervalRelation -> Bool
forall a. Eq a => a -> a -> Bool
== IntervalRelation
Meets) ( [PairedInterval b a] -> [IntervalRelation]
forall (f :: * -> *) (i :: * -> *) a.
(Foldable f, Intervallic i a) =>
f (i a) -> [IntervalRelation]
relationsL [PairedInterval b a]
x )

hasEqData :: (Eq b) => [PairedInterval b a] -> Bool
hasEqData :: [PairedInterval b a] -> Bool
hasEqData [PairedInterval b a]
x = [Bool] -> Bool
forall (t :: * -> *). Foldable t => t Bool -> Bool
or (Fold b [Bool] -> [b] -> [Bool]
forall (f :: * -> *) a b. Foldable f => Fold a b -> f a -> b
L.fold ((b -> b -> Bool) -> Fold b [Bool]
forall (m :: * -> *) b a.
(Monoid (m b), Applicative m) =>
(a -> a -> b) -> Fold a (m b)
makeFolder b -> b -> Bool
forall a. Eq a => a -> a -> Bool
(==)) ((PairedInterval b a -> b) -> [PairedInterval b a] -> [b]
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap PairedInterval b a -> b
forall b a. PairedInterval b a -> b
getPairData [PairedInterval b a]
x) :: [Bool])