-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | Intervals with adherences. -- -- Data types to represent, compare and combine intervals with -- adherences. -- -- See also: -- --

@package interval @version 1.20160821 module Data.Interval data Limit x Limit :: Adherence -> x -> Limit x [adherence] :: Limit x -> Adherence [limit] :: Limit x -> x data Adherence Out :: Adherence In :: Adherence -- | Return given Limit with its adherence set to the -- opposite one. flip_limit :: Limit x -> Limit x -- | Compare two low Limits. newtype LL x LL :: x -> LL x [unLL] :: LL x -> x -- | Compare two high Limits. newtype HH x HH :: x -> HH x [unHH] :: HH x -> x newtype Ord x => Interval x Interval :: (Limit x, Limit x) -> Interval x low :: Ord x => Interval x -> Limit x high :: Ord x => Interval x -> Limit x -- | Return Interval with given low then high -- Limits, if they form a valid Interval. interval :: Ord x => Limit x -> Limit x -> Maybe (Interval x) -- | Like fmap, but may return Nothing, if mapped -- Interval is not valid. fmap :: (Ord x, Ord y) => (x -> y) -> Interval x -> Maybe (Interval y) -- | Like fmap, but only safe if given map preserves -- Ordering. fmap_unsafe :: (Ord x, Ord y) => (x -> y) -> Interval x -> Interval y -- | Lexicographical order, handling Adherence correctly. -- | Return limits of given Interval as a tuple. limits :: Ord x => Interval x -> (Limit x, Limit x) -- | Return an Interval spanning over a single limit. point :: Ord x => x -> Interval x -- | Return given Interval with flip_limit applied to its -- limits. flip_limits :: Ord x => Interval x -> Interval x -- | Return Ordering comparing given Intervals according to -- their limits. compare_without_adherence :: Ord x => Limit x -> Limit x -> Ordering -- | Return: -- --

LT: if given value is lower than all values in given -- Interval.
EQ: if given value is into the given Interval.
GT: if given value is higher than all values in given -- Interval.

locate :: Ord x => x -> Interval x -> Ordering -- | Return True iif. given value is into the given Interval. within :: Ord x => x -> Interval x -> Bool -- | Return True iif. every value of the first Interval is -- into the second Interval. into :: Ord x => Interval x -> Interval x -> Bool -- | Return True iif. every value of the second Interval is -- into the first Interval. onto :: Ord x => Interval x -> Interval x -> Bool (<=..<=) :: Ord x => x -> x -> Maybe (Interval x) infix 5 <=..<= (<..<=) :: Ord x => x -> x -> Maybe (Interval x) infix 5 <..<= (<=..<) :: Ord x => x -> x -> Maybe (Interval x) infix 5 <=..< (<..<) :: Ord x => x -> x -> Maybe (Interval x) infix 5 <..< data Position -- | -_| (LT) or |_- (GT) Away :: Position -- | -| (LT) or |- (GT) Adjacent :: Position -- | -+| (LT) or |+- (GT) Overlap :: Position -- | +| (LT) or +- (GT) Prefix :: Position -- | -+ (LT) or |+ (GT) Suffixed :: Position -- | -+- (LT) or |+| (GT) Include :: Position -- | + (EQ) Equal :: Position position :: Ord x => Interval x -> Interval x -> (Position, Ordering) -- | Return True iif. Position of given Intervals is -- (Away, LT). (..<<..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..<<.. -- | Return True iif. Position of given Intervals is -- (Away, GT). (..>>..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..>>.. -- | Return True iif. Position of given Intervals is -- (Away, LT) or (Adjacent, LT). (..<..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..<.. -- | Return True iif. Position of given Intervals is -- (Away, GT) or (Adjacent, GT). (..>..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..>.. -- | Return True iif. Position of given Intervals is -- (Away, LT), (Adjacent, LT), -- (Overlap, LT), (Prefix, LT), -- (Suffixed, LT), (Include, GT), or -- (Equal, _). (..<=..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..<=.. -- | Return True iif. Position of given Intervals is -- (Away, GT), (Adjacent, GT), -- (Overlap, GT), (Prefix, GT), -- (Suffixed, GT), (Include, LT), or -- (Equal, _). (..>=..) :: Ord x => Interval x -> Interval x -> Bool infix 4 ..>=.. union :: Ord x => Interval x -> Interval x -> Maybe (Interval x) intersection :: Ord x => Interval x -> Interval x -> Maybe (Interval x) span :: Ord x => Interval x -> Interval x -> Interval x data Unlimitable x Unlimited_low :: Unlimitable x Limited :: x -> Unlimitable x [limited] :: Unlimitable x -> x Unlimited_high :: Unlimitable x unlimited :: Ord x => Interval (Unlimitable x) unlimit :: Ord x => Interval x -> Interval (Unlimitable x) (<..) :: Ord x => x -> Interval (Unlimitable x) (<=..) :: Ord x => x -> Interval (Unlimitable x) (..<) :: Ord x => x -> Interval (Unlimitable x) (..<=) :: Ord x => x -> Interval (Unlimitable x) newtype Pretty x Pretty :: x -> Pretty x instance GHC.Classes.Ord x => GHC.Classes.Ord (Data.Interval.Pretty x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.Pretty x) instance GHC.Show.Show x => GHC.Show.Show (Data.Interval.Unlimitable x) instance GHC.Classes.Ord x => GHC.Classes.Ord (Data.Interval.Unlimitable x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.Unlimitable x) instance GHC.Show.Show Data.Interval.Position instance GHC.Classes.Eq Data.Interval.Position instance (Data.Data.Data x, GHC.Classes.Ord x) => Data.Data.Data (Data.Interval.Interval x) instance (GHC.Classes.Ord x, GHC.Show.Show x) => GHC.Show.Show (Data.Interval.Interval x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.Interval x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.HH x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.LL x) instance GHC.Show.Show x => GHC.Show.Show (Data.Interval.Limit x) instance Data.Data.Data x => Data.Data.Data (Data.Interval.Limit x) instance GHC.Classes.Eq x => GHC.Classes.Eq (Data.Interval.Limit x) instance GHC.Show.Show Data.Interval.Adherence instance Data.Data.Data Data.Interval.Adherence instance GHC.Classes.Eq Data.Interval.Adherence instance GHC.Base.Functor Data.Interval.Limit instance Control.DeepSeq.NFData x => Control.DeepSeq.NFData (Data.Interval.Limit x) instance GHC.Classes.Ord x => GHC.Classes.Ord (Data.Interval.LL (Data.Interval.Limit x)) instance GHC.Classes.Ord x => GHC.Classes.Ord (Data.Interval.HH (Data.Interval.Limit x)) instance (Control.DeepSeq.NFData x, GHC.Classes.Ord x) => Control.DeepSeq.NFData (Data.Interval.Interval x) instance GHC.Classes.Ord x => GHC.Classes.Ord (Data.Interval.Interval x) instance GHC.Base.Functor Data.Interval.Unlimitable instance GHC.Enum.Bounded (Data.Interval.Unlimitable x) instance GHC.Enum.Bounded (Data.Interval.Limit (Data.Interval.Unlimitable x)) instance (GHC.Classes.Ord x, GHC.Show.Show x) => GHC.Show.Show (Data.Interval.Pretty (Data.Interval.Interval x)) instance (GHC.Classes.Ord x, GHC.Show.Show x) => GHC.Show.Show (Data.Interval.Pretty (Data.Interval.Unlimitable x)) module Data.Interval.Sieve -- | ..<<..-ordered union of Intervals. -- -- Ressources: -- --

Ralf Hinze and Ross Paterson, "Finger trees: a simple -- general-purpose data structure", Journal of Functional -- Programming 16:2 (2006) pp 197-217. -- http://staff.city.ac.uk/~ross/papers/FingerTree.html
https://hackage.haskell.org/package/fingertree/docs/Data-IntervalMap-FingerTree.html

newtype Sieve x Sieve :: FingerTree (Measure x) (Interval x) -> Sieve x [unSieve] :: Sieve x -> FingerTree (Measure x) (Interval x) -- | Like fmap but working on Intervals. fmap_interval :: (Ord x, Ord y) => (Interval x -> Interval y) -> Sieve x -> Sieve y -- | Like fmap but working on Intervals, and safe only if -- Measure is preserved. fmap_interval_unsafe :: Ord x => (Interval x -> Interval x) -> Sieve x -> Sieve x -- | Like traverse but working on Intervals. traverse_interval :: (Ord x, Ord y, Applicative f) => (Interval x -> f (Interval y)) -> Sieve x -> f (Sieve y) -- | Like traverse but working on Intervals, and safe only if -- Measure is preserved. traverse_interval_unsafe :: (Ord x, Applicative f) => (Interval x -> f (Interval x)) -> Sieve x -> f (Sieve x) -- | Measure of each leaf or node of the Sieve -- FingerTree. data Measure x -- | Measure of empty Fingertree. Measure_Empty :: Measure x Measure :: Interval x -> Measure x -- | An Interval with the max high Limit -- amongst those having the max low Limit (which -- is the max Interval because of lexicographical -- ordering). [max_high_of_max_low] :: Measure x -> Interval x empty :: Ord x => Sieve x -- | Return the True iif. the given Sieve is empty. null :: Ord x => Sieve x -> Bool singleton :: Ord x => Interval x -> Sieve x -- | Return an Interval with: -- --

the low Limit of the min -- Interval,
the high Limit of the max -- Interval.

interval :: Ord x => Sieve x -> Maybe (Interval x) -- | All the Intervals of the Sieve in ..<<.. -- order. intervals :: Ord x => Sieve x -> [Interval x] -- | Return a Sieve merging the given Sieves with -- union. union :: Ord x => Sieve x -> Sieve x -> Sieve x -- | Return a Sieve merging the Intervals in the given -- Foldable with union. from_Foldable :: (Foldable f, Ord x) => f (Interval x) -> Sieve x -- | Return a Sieve merging the given Sieves with -- intersection. intersection :: Ord x => Sieve x -> Sieve x -> Sieve x -- | All Intervals having a non-Nothing intersection -- with the given Interval, in ..<<.. order. intersecting :: Ord x => Interval x -> Sieve x -> [Interval x] -- | Return the Sieve spanning over all the values not within the -- given Sieve. complement :: (Ord x, Bounded (Limit x)) => Sieve x -> Sieve x -- | Return the Sieve spanning over all the values not within the -- given Sieve, but within the given Interval which MUST be -- onto every Interval inside the Sieve. complement_with :: Ord x => Interval x -> Sieve x -> Sieve x instance (GHC.Classes.Ord x, GHC.Show.Show x) => GHC.Show.Show (Data.Interval.Pretty (Data.Interval.Sieve.Sieve x)) instance GHC.Classes.Ord x => GHC.Base.Monoid (Data.Interval.Sieve.Measure x) instance GHC.Classes.Ord x => Data.FingerTree.Measured (Data.Interval.Sieve.Measure x) (Data.Interval.Interval x)