interval (empty) → 1.20160821
raw patch · 8 files changed
+1918/−0 lines, 8 filesdep +basedep +deepseqdep +fingertreesetup-changed
Dependencies added: base, deepseq, fingertree, interval, tasty, tasty-hunit
Files
- COPYING +674/−0
- Data/Interval.hs +441/−0
- Data/Interval/Sieve.hs +254/−0
- Data/Interval/Sieve/Test.hs +298/−0
- Data/Interval/Test.hs +151/−0
- Setup.hs +2/−0
- interval.cabal +92/−0
- stack.yaml +6/−0
+ COPYING view
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+ Data/Interval.hs view
@@ -0,0 +1,441 @@+{-# LANGUAGE DeriveDataTypeable #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE TupleSections #-}+module Data.Interval where++import Control.DeepSeq (NFData(..))+import Data.Bool+import Data.Data (Data(..))+import Data.Eq (Eq(..))+import Data.Foldable (concat)+import Data.Function (($), flip)+import Data.Functor (Functor(..))+import qualified Data.Functor as Functor+import Data.Maybe (Maybe(..))+import Data.Ord (Ord(..), Ordering(..))+import Data.Tuple+import Data.Typeable (Typeable)+import Prelude (Bounded(..), seq)+import Text.Show (Show(..))++-- * Type 'Limit'++data Limit x+ = Limit+ { adherence :: Adherence+ , limit :: x }+ deriving (Eq, Data, Show, Typeable)++instance Functor Limit where+ fmap f (Limit a x) = Limit a (f x)+instance NFData x => NFData (Limit x) where+ rnf (Limit _a l) = rnf l++data Adherence = Out | In+ deriving (Eq, Data, Show, Typeable)++-- | Return given 'Limit' with its 'adherence' set to the opposite one.+flip_limit :: Limit x -> Limit x+flip_limit (Limit a x) = Limit (case a of { In -> Out; Out -> In }) x++-- ** Comparing 'Limit's++-- | Compare two 'low' 'Limit's.+newtype LL x = LL { unLL :: x }+ deriving (Eq)+instance Ord x => Ord (LL (Limit x)) where+ compare (LL x) (LL y) =+ case compare (limit x) (limit y) of+ EQ ->+ case (adherence x, adherence y) of+ (Out, In ) -> GT+ (In , Out) -> LT+ _ -> EQ+ o -> o++-- | Compare two 'high' 'Limit's.+newtype HH x = HH { unHH :: x }+ deriving (Eq)+instance Ord x => Ord (HH (Limit x)) where+ compare (HH x) (HH y) =+ case compare (limit x) (limit y) of+ EQ ->+ case (adherence x, adherence y) of+ (Out, In ) -> LT+ (In , Out) -> GT+ _ -> EQ+ o -> o++-- * Type 'Interval'++newtype Ord x+ => Interval x+ = Interval (Limit x, Limit x)+ deriving (Eq, Show, Data, Typeable)+instance (NFData x, Ord x) => NFData (Interval x) where+ rnf (Interval (x, y)) = rnf x `seq` rnf y++low :: Ord x => Interval x -> Limit x+low (Interval t) = fst t++high :: Ord x => Interval x -> Limit x+high (Interval t) = snd t++-- | Return 'Interval' with given 'low' then 'high' 'Limit's,+-- if they form a valid 'Interval'.+interval :: Ord x => Limit x -> Limit x -> Maybe (Interval x)+interval x y =+ case compare_without_adherence x y of+ LT -> Just $ Interval (x, y)+ EQ ->+ case (adherence x, adherence y) of+ (In, In) -> Just $ Interval (x, y)+ _ -> Nothing+ GT -> Nothing++-- | Like 'Functor.fmap', but may return 'Nothing', if mapped 'Interval' is not valid.+fmap :: (Ord x, Ord y) => (x -> y) -> Interval x -> Maybe (Interval y)+fmap f (Interval (il, ih)) = interval (Functor.fmap f il) (Functor.fmap f ih)++-- | Like 'Functor.fmap', but only safe if given map preserves 'Ordering'.+fmap_unsafe :: (Ord x, Ord y) => (x -> y) -> Interval x -> Interval y+fmap_unsafe f (Interval (il, ih)) = Interval (Functor.fmap f il, Functor.fmap f ih)++{-+-- | Like 'Functor.fmap', but on 'Limit's,+-- and may return 'Nothing', if mapped 'Interval' is not valid.+fmap_limits :: (Ord x, Ord y) => (Limit x -> Limit y) -> Interval x -> Maybe (Interval y)+fmap_limits f (Interval (il, ih)) = interval (f il) (f ih)++-- | Like 'Functor.fmap', but on 'Limit's+-- and only safe if given map preserves 'Ordering'.+fmap_limits_unsafe :: (Ord x, Ord y) => (Limit x -> Limit y) -> Interval x -> Interval y+fmap_limits_unsafe f (Interval (il, ih)) = Interval (f il, f ih)+-}++-- | Lexicographical order, handling 'Adherence' correctly.+instance Ord x => Ord (Interval x) where+ compare (Interval (il, ih)) (Interval (jl, jh)) =+ case compare (LL il) (LL jl) of+ EQ -> compare (HH ih) (HH jh)+ o -> o++-- | Return 'limit's of given 'Interval' as a tuple.+limits :: Ord x => Interval x -> (Limit x, Limit x)+limits (Interval t) = t++-- | Return an 'Interval' spanning over a single 'limit'.+point :: Ord x => x -> Interval x+point x = Interval (Limit In x, Limit In x)++-- | Return given 'Interval' with 'flip_limit' applied to its 'limit's.+flip_limits :: Ord x => Interval x -> Interval x+flip_limits (Interval (l, h)) = Interval (flip_limit l, flip_limit h)++-- | Return 'Ordering' comparing given 'Interval's according to their 'limit's.+compare_without_adherence :: Ord x => Limit x -> Limit x -> Ordering+compare_without_adherence (Limit _ x) (Limit _ y) = compare x y++-- | 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+locate x (Interval (l, h)) =+ case compare x (limit l) of+ LT -> LT+ EQ | adherence l == In -> EQ+ EQ -> LT+ GT ->+ case compare x (limit h) of+ LT -> EQ+ EQ | adherence h == In -> EQ+ EQ -> GT+ GT -> GT++-- | Return 'True' iif. given value is into the given 'Interval'.+within :: Ord x => x -> Interval x -> Bool+within x i = locate x i == EQ++-- | Return 'True' iif. every value of the first 'Interval' is into the second 'Interval'.+into :: Ord x => Interval x -> Interval x -> Bool+into i j =+ case position i j of+ (Prefix , LT) -> True+ (Suffixed, GT) -> True+ (Include , GT) -> True+ (Equal , _) -> True+ _ -> False++-- | Return 'True' iif. every value of the second 'Interval' is into the first 'Interval'.+onto :: Ord x => Interval x -> Interval x -> Bool+onto = flip into++infix 5 <=..<=+(<=..<=) :: Ord x => x -> x -> Maybe (Interval x)+(<=..<=) x y =+ case compare x y of+ LT -> Just $ Interval (Limit In x, Limit In y)+ EQ -> Just $ Interval (Limit In x, Limit In y)+ GT -> Nothing++infix 5 <..<=+(<..<=) :: Ord x => x -> x -> Maybe (Interval x)+(<..<=) x y =+ case compare x y of+ LT -> Just $ Interval (Limit Out x, Limit In y)+ EQ -> Nothing+ GT -> Nothing++infix 5 <=..<+(<=..<) :: Ord x => x -> x -> Maybe (Interval x)+(<=..<) x y =+ case compare x y of+ LT -> Just $ Interval (Limit In x, Limit Out y)+ EQ -> Nothing+ GT -> Nothing++infix 5 <..<+(<..<) :: Ord x => x -> x -> Maybe (Interval x)+(<..<) x y =+ case compare x y of+ LT -> Just $ Interval (Limit Out x, Limit Out y)+ EQ -> Nothing+ GT -> Nothing++-- * Type 'Position'++data Position+ = Away -- ^ @-_|@ ('LT') or @|_-@ ('GT')+ | Adjacent -- ^ @-|@ ('LT') or @|-@ ('GT')+ | Overlap -- ^ @-+|@ ('LT') or @|+-@ ('GT')+ | Prefix -- ^ @+|@ ('LT') or @+-@ ('GT')+ | Suffixed -- ^ @-+@ ('LT') or @|+@ ('GT')+ | Include -- ^ @-+-@ ('LT') or @|+|@ ('GT')+ | Equal -- ^ @+@ ('EQ')+ deriving (Eq, Show)++position :: Ord x => Interval x -> Interval x -> (Position, Ordering)+position (Interval (il, ih)) (Interval (jl, jh)) =+ case compare (LL il) (LL jl) of+ LT -> (, LT) $+ case compare_without_adherence ih jl of+ LT -> Away -- PATTERN: -_|+ EQ ->+ case (adherence ih, adherence jl) of+ (In , In) -> Overlap -- PATTERN: -+|+ (Out, Out) -> Away -- PATTERN: -_|+ _ -> Adjacent -- PATTERN: -|+ GT ->+ case compare (HH ih) (HH jh) of+ LT -> Overlap -- PATTERN: -+|+ EQ -> Suffixed -- PATTERN: -++ GT -> Include -- PATTERN: -+-+ EQ ->+ case compare (HH ih) (HH jh) of+ LT -> (Prefix, LT) -- PATTERN: +|+ EQ -> (Equal , EQ) -- PATTERN: ++ GT -> (Prefix, GT) -- PATTERN: +-+ GT -> (, GT) $+ case compare_without_adherence il jh of+ LT ->+ case compare (HH ih) (HH jh) of+ LT -> Include -- PATTERN: |+|+ EQ -> Suffixed -- PATTERN: |++ GT -> Overlap -- PATTERN: |+-+ EQ ->+ case (adherence il, adherence jh) of+ (In , In) -> Overlap -- PATTERN: |+-+ (Out, Out) -> Away -- PATTERN: |_-+ _ -> Adjacent -- PATTERN: |-+ GT -> Away -- PATTERN: |_-++infix 4 ..<<..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'LT').+(..<<..) :: Ord x => Interval x -> Interval x -> Bool+(..<<..) i j = case position i j of+ (Away, LT) -> True+ _ -> False++infix 4 ..>>..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'GT').+(..>>..) :: Ord x => Interval x -> Interval x -> Bool+(..>>..) i j = case position i j of+ (Away, GT) -> True+ _ -> False++infix 4 ..<..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'LT') or ('Adjacent', 'LT').+(..<..) :: Ord x => Interval x -> Interval x -> Bool+(..<..) i j = case position i j of+ (Away , LT) -> True+ (Adjacent, LT) -> True+ _ -> False+infix 4 ..>..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'GT') or ('Adjacent', 'GT').+(..>..) :: Ord x => Interval x -> Interval x -> Bool+(..>..) i j = case position i j of+ (Away , GT) -> True+ (Adjacent, GT) -> True+ _ -> False++infix 4 ..<=..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'LT'), ('Adjacent', 'LT'), ('Overlap', 'LT'), ('Prefix', 'LT'), ('Suffixed', 'LT'), ('Include', 'GT'), or ('Equal', _).+(..<=..) :: Ord x => Interval x -> Interval x -> Bool+(..<=..) i j = case position i j of+ (Away , LT) -> True+ (Adjacent, LT) -> True+ (Overlap , LT) -> True+ (Prefix , LT) -> True+ (Suffixed, LT) -> True+ (Include , GT) -> True+ (Equal , _ ) -> True+ _ -> False++infix 4 ..>=..+-- | Return 'True' iif. 'Position' of given 'Interval's is ('Away', 'GT'), ('Adjacent', 'GT'), ('Overlap', 'GT'), ('Prefix', 'GT'), ('Suffixed', 'GT'), ('Include', 'LT'), or ('Equal', _).+(..>=..) :: Ord x => Interval x -> Interval x -> Bool+(..>=..) i j = case position i j of+ (Away , GT) -> True+ (Adjacent, GT) -> True+ (Overlap , GT) -> True+ (Prefix , GT) -> True+ (Suffixed, GT) -> True+ (Include , LT) -> True+ (Equal , _ ) -> True+ _ -> False++-- * Merge++union :: Ord x => Interval x -> Interval x -> Maybe (Interval x)+union i j =+ case position i j of+ (Away, _) -> -- PATTERN: -_| or |_-+ Nothing+ (Adjacent, o) ->+ case o of+ LT -> Just $ Interval (low i, high j) -- PATTERN: -|+ EQ -> Nothing+ GT -> Just $ Interval (low j, high i) -- PATTERN: |-+ (Overlap, o) ->+ case o of+ LT -> Just $ Interval (low i, high j) -- PATTERN: -+|+ EQ -> Nothing+ GT -> Just $ Interval (low j, high i) -- PATTERN: |+-+ (Prefix, o) ->+ case o of+ LT -> Just j -- PATTERN: +|+ EQ -> Nothing+ GT -> Just i -- PATTERN: +-+ (Suffixed, o) ->+ case o of+ LT -> Just i -- PATTERN: -++ EQ -> Nothing+ GT -> Just j -- PATTERN: |++ (Include, o) ->+ case o of+ LT -> Just i -- PATTERN: -+-+ EQ -> Nothing+ GT -> Just j -- PATTERN: |+|+ (Equal, _) -> -- PATTERN: ++ Just i++intersection :: Ord x => Interval x -> Interval x -> Maybe (Interval x)+intersection i j =+ case position i j of+ (Away, _) -> -- PATTERN: -_| or |_-+ Nothing+ (Adjacent, _) -> -- PATTERN: -| or |-+ Nothing+ (Overlap, o) ->+ case o of+ LT -> Just $ Interval (low j, high i) -- PATTERN: -+|+ EQ -> Nothing+ GT -> Just $ Interval (low i, high j) -- PATTERN: |+-+ (Prefix, o) ->+ case o of+ LT -> Just i -- PATTERN: +|+ EQ -> Nothing+ GT -> Just j -- PATTERN: +-+ (Suffixed, o) ->+ case o of+ LT -> Just j -- PATTERN: -++ EQ -> Nothing+ GT -> Just i -- PATTERN: |++ (Include, o) ->+ case o of+ LT -> Just j -- PATTERN: -+-+ EQ -> Nothing+ GT -> Just i -- PATTERN: |+|+ (Equal, _) -> -- PATTERN: ++ Just i++span :: Ord x => Interval x -> Interval x -> Interval x+span i j =+ Interval+ ( unLL (min (LL $ low i) (LL $ low j))+ , unHH (max (HH $ high i) (HH $ high j))+ )++-- * Type 'Unlimitable'++data Unlimitable x+ = Unlimited_low+ | Limited { limited :: x }+ | Unlimited_high+ deriving (Eq, Ord, Show)+instance Functor Unlimitable where+ fmap _f Unlimited_low = Unlimited_low+ fmap _f Unlimited_high = Unlimited_high+ fmap f (Limited x) = Limited (f x)+instance Bounded (Unlimitable x) where+ minBound = Unlimited_low+ maxBound = Unlimited_high+instance Bounded (Limit (Unlimitable x)) where+ minBound = Limit In Unlimited_low+ maxBound = Limit In Unlimited_high++unlimited :: Ord x => Interval (Unlimitable x)+unlimited = Interval ( Limit In Unlimited_low+ , Limit In Unlimited_high )++unlimit :: Ord x => Interval x -> Interval (Unlimitable x)+unlimit = fmap_unsafe Limited++(<..) :: Ord x => x -> Interval (Unlimitable x)+(<..) x = Interval (Limit Out (Limited x), Limit In Unlimited_high)++(<=..) :: Ord x => x -> Interval (Unlimitable x)+(<=..) x = Interval (Limit In (Limited x), Limit In Unlimited_high)++(..<) :: Ord x => x -> Interval (Unlimitable x)+(..<) x = Interval (Limit In Unlimited_low, Limit Out (Limited x))++(..<=) :: Ord x => x -> Interval (Unlimitable x)+(..<=) x = Interval (Limit In Unlimited_low, Limit In (Limited x))++-- * Type 'Pretty'++newtype Pretty x = Pretty x+ deriving (Eq, Ord)+instance (Ord x, Show x) => Show (Pretty (Interval x)) where+ show (Pretty i) =+ concat+ [ case adherence (low i) of+ In -> "["+ Out -> "]"+ , show (limit $ low i)+ , ".."+ , show (limit $ high i)+ , case adherence (high i) of+ In -> "]"+ Out -> "["+ ]+instance (Ord x, Show x) => Show (Pretty (Unlimitable x)) where+ show (Pretty x) =+ case x of+ Unlimited_low -> "-oo"+ Limited l -> show l+ Unlimited_high -> "+oo"
+ Data/Interval/Sieve.hs view
@@ -0,0 +1,254 @@+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE TupleSections #-}+{-# LANGUAGE TypeFamilies #-}+{-# OPTIONS_GHC -fno-warn-orphans #-}+module Data.Interval.Sieve where++import Control.Applicative (Applicative(..))+import Control.Exception (assert)+import Data.Bool+import Data.Eq (Eq(..))+import Data.FingerTree (FingerTree, ViewL(..), ViewR(..), (><), (<|), (|>))+import qualified Data.FingerTree as FT+import Data.Foldable (Foldable)+import qualified Data.Foldable as Foldable+import Data.Function (($), (.))+import Data.Functor ((<$>))+import qualified Data.List+import Data.Maybe (Maybe(..), fromMaybe)+import Data.Monoid (Monoid(..))+import Data.Ord (Ord(..), Ordering(..))+import Prelude (Bounded(..), undefined)+import Text.Show (Show(..))++import qualified Data.Interval as Interval+import Data.Interval ( Interval(..)+ , low, high+ , (..<..), (..<<..)+ , Position(..), position+ , flip_limit+ , Pretty(..) )++-- * Type 'Sieve'++-- | '..<<..'-ordered union of 'Interval's.+--+-- __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 { unSieve :: FingerTree (Measure x) (Interval x) }++instance (Ord x, Show x) => Show (Pretty (Sieve x)) where+ show (Pretty s) | Data.Interval.Sieve.null s = "empty"+ show (Pretty s) = Data.List.intercalate " u " $ Data.List.map (show . Pretty) $ intervals s++-- | Like 'Data.Functor.fmap' but working on 'Interval's.+fmap_interval+ :: (Ord x, Ord y)+ => (Interval x -> Interval y) -> Sieve x -> Sieve y+fmap_interval f (Sieve ft) = Sieve (FT.fmap' f ft)++-- | Like 'Data.Functor.fmap' but working on 'Interval's,+-- and safe only if 'Measure' is preserved.+fmap_interval_unsafe+ :: Ord x+ => (Interval x -> Interval x)+ -> Sieve x -> Sieve x+fmap_interval_unsafe f (Sieve ft) = Sieve (FT.unsafeFmap f ft)++-- | Like 'Data.Traversable.traverse' but working on 'Interval's.+traverse_interval+ :: (Ord x, Ord y, Applicative f)+ => (Interval x -> f (Interval y))+ -> Sieve x -> f (Sieve y)+traverse_interval f (Sieve ft) = Sieve <$> FT.traverse' f ft++-- | Like 'Data.Traversable.traverse' but working on 'Interval's,+-- and safe only if 'Measure' is preserved.+traverse_interval_unsafe+ :: (Ord x, Applicative f)+ => (Interval x -> f (Interval x))+ -> Sieve x -> f (Sieve x)+traverse_interval_unsafe f (Sieve ft) = Sieve <$> FT.unsafeTraverse f ft++-- | 'FT.Measure' of each leaf or node of the 'Sieve' 'FingerTree'.+data Measure x+ = Measure_Empty -- ^ Measure of 'FT.empty' 'Fingertree'.+ | Measure+ { max_high_of_max_low :: Interval x+ -- ^ An __'Interval' with the max 'high' 'Limit'__+ -- __amongst those having the max 'low' 'Limit'__+ -- (which is the 'max' 'Interval'+ -- because of lexicographical ordering).+ {- NOTE: not useful in the particular case of '..<..'-ordered 'Interval's+ , max_high :: Interval x+ -- ^ An __'Interval' with the max 'high' 'Limit'__+ -- (which may be a different 'Interval'+ -- as it can have a lower 'low' 'Limit',+ -- and thus not be the 'max' 'Interval').+ -}+ }+instance Ord x => Monoid (Measure x) where+ mempty = Measure_Empty+ + Measure_Empty `mappend` i = i+ i `mappend` Measure_Empty = i+ _i `mappend` j = Measure (max_high_of_max_low j)+ {- NOTE: not useful in the particular case of '..<..'-ordered 'Interval's+ i `mappend` j =+ Measure (max_high_of_max_low j) $+ case compare_without_adherence (high (max_high i)) (high (max_high j)) of+ LT -> max_high j+ EQ ->+ case (adherence (high (max_high i)), adherence (high (max_high j))) of+ (In , In) -> max_high i+ (In , Out) -> max_high i+ (Out, In) -> max_high j+ (Out, Out) -> max_high i+ GT -> max_high i+ -}+instance Ord x => FT.Measured (Measure x) (Interval x) where+ measure = Measure++empty :: Ord x => Sieve x+empty = Sieve FT.empty++-- | Return the 'True' iif. the given 'Sieve' is 'empty'.+null :: Ord x => Sieve x -> Bool+null (Sieve ft) = FT.null ft++singleton :: Ord x => Interval x -> Sieve x+singleton = Sieve . FT.singleton++-- | Return an 'Interval' with:+--+-- * the 'Interval.low' 'Interval.Limit' of the 'min' 'Interval',+-- * the 'Interval.high' 'Interval.Limit' of the 'max' 'Interval'.+interval :: Ord x => Sieve x -> Maybe (Interval x)+interval (Sieve ft) =+ case FT.viewl ft of+ FT.EmptyL -> Nothing+ -- l :< ls | FT.null ls -> Just l+ l :< _ ->+ case FT.viewr ft of+ FT.EmptyR -> Nothing+ _ :> r -> Just $ Interval (low l, high r)++-- | All the 'Interval's of the 'Sieve' in '..<<..' order.+intervals :: Ord x => Sieve x -> [Interval x]+intervals (Sieve t) = Foldable.toList t++-- * Union++-- | Return a 'Sieve' merging the given 'Sieve's with 'Interval.union'.+union :: Ord x => Sieve x -> Sieve x -> Sieve x+union (Sieve s0) (Sieve s1) =+ Sieve (merge s0 s1)+ where+ merge is js =+ case FT.viewl is of+ FT.EmptyL -> js+ i :< gt_i ->+ let (js_not_away_lt_i, js_away_gt_i ) = FT.split ( (i ..<<..) . max_high_of_max_low) js in+ let (js_away_lt_i , js_not_away_i) = FT.split (not . (..<<.. i) . max_high_of_max_low) js_not_away_lt_i in+ js_away_lt_i ><+ -- NOTE: flip merge when possible+ -- (i.e. when high i is majoring high-s of intersecting Interval-s)+ -- to preserve complexity over commutativity.+ case FT.viewl js_not_away_i of+ FT.EmptyL -> i <| merge js_away_gt_i gt_i+ lu :< us ->+ case FT.viewr us of+ FT.EmptyR ->+ let u = lu in+ case position i u of+ (Adjacent, LT) -> merge gt_i (Interval (low i, high u) <| js_away_gt_i) -- flip: NO+ (Overlap , LT) -> merge gt_i (Interval (low i, high u) <| js_away_gt_i) -- flip: NO+ (Prefix , LT) -> merge gt_i (Interval (low i, high u) <| js_away_gt_i) -- flip: NO+ (Include , GT) -> merge gt_i (u <| js_away_gt_i) -- flip: NO+ (Suffixed, LT) -> i <| merge js_away_gt_i gt_i -- flip: YES+ (Include , LT) -> i <| merge js_away_gt_i gt_i -- flip: YES+ (Equal , _ ) -> i <| merge js_away_gt_i gt_i -- flip: YES+ (Adjacent, GT) -> Interval (low u, high i) <| merge js_away_gt_i gt_i -- flip: YES+ (Overlap , GT) -> Interval (low u, high i) <| merge js_away_gt_i gt_i -- flip: YES+ (Prefix , GT) -> Interval (low u, high i) <| merge js_away_gt_i gt_i -- flip: YES+ (Suffixed, GT) -> Interval (low u, high i) <| merge js_away_gt_i gt_i -- flip: YES+ _ -> assert False undefined+ _ :> hu ->+ let l = low $+ case position i lu of+ (Adjacent, GT) -> lu+ (Overlap , GT) -> lu+ (Prefix , GT) -> lu+ (Suffixed, GT) -> lu+ _ -> i in+ case position i hu of+ (Adjacent, LT) -> merge gt_i (Interval (l, high hu) <| js_away_gt_i) -- flip: NO+ (Overlap , LT) -> merge gt_i (Interval (l, high hu) <| js_away_gt_i) -- flip: NO+ (Prefix , LT) -> merge gt_i (Interval (l, high hu) <| js_away_gt_i) -- flip: NO+ _ -> Interval (l, high i) <| merge js_away_gt_i gt_i -- flip: YES++-- | Return a 'Sieve' merging the 'Interval's in the given 'Foldable' with 'Interval.union'.+from_Foldable :: (Foldable f, Ord x) => f (Interval x) -> Sieve x+from_Foldable = Foldable.foldr (union . singleton) empty++-- * Intersection++-- | Return a 'Sieve' merging the given 'Sieve's with 'Interval.intersection'.+intersection :: Ord x => Sieve x -> Sieve x -> Sieve x+intersection (Sieve s0) (Sieve s1) =+ Sieve (merge s0 s1)+ where+ intersect i j = fromMaybe (assert False undefined) $ Interval.intersection i j+ merge is js =+ case FT.viewl is of+ FT.EmptyL -> FT.empty+ i :< gt_i ->+ let (_, js_not_lt_i) = FT.split (not . (..<.. i) . max_high_of_max_low) js in+ let (js_intersecting_i, _) = FT.split ( (i ..<..) . max_high_of_max_low) js_not_lt_i in+ case FT.viewl js_intersecting_i of+ li :< li' ->+ intersect li i <|+ case FT.viewr li' of+ hi' :> hi -> hi' |> intersect i hi+ _ -> li'+ >< merge js_not_lt_i gt_i+ _ -> merge js_not_lt_i gt_i+ -- NOTE: swap merging to preserve complexity over commutativity++-- | All 'Interval's having a non-'Nothing' 'Interval.intersection' with the given 'Interval',+-- in '..<<..' order.+intersecting :: Ord x => Interval x -> Sieve x -> [Interval x]+intersecting i = Foldable.toList . unSieve . intersection (singleton i)++-- * Complement++-- | Return the 'Sieve' spanning over all the values not within the given 'Sieve'.+complement :: (Ord x, Bounded (Interval.Limit x)) => Sieve x -> Sieve x+complement = complement_with (Interval (minBound, maxBound))++-- | Return the 'Sieve' spanning over all the values not within the given 'Sieve',+-- but within the given 'Interval' which MUST be 'Interval.onto' every 'Interval' inside the 'Sieve'.+complement_with :: Ord x => Interval x -> Sieve x -> Sieve x+complement_with b (Sieve s) =+ let (last_low, c) =+ Foldable.foldr+ (\i (previous_low, ft) ->+ ( low i+ , if (Interval.HH $ high i) < (Interval.HH $ high b)+ then Interval (flip_limit $ high i, flip_limit previous_low) <| ft+ else ft+ ))+ (flip_limit $ high b, FT.empty) s in+ Sieve $+ case compare (Interval.LL $ low b) (Interval.LL last_low) of+ LT -> Interval (low b, flip_limit last_low) <| c+ EQ | low b == high b && FT.null s -> FT.singleton b+ _ -> c
+ Data/Interval/Sieve/Test.hs view
@@ -0,0 +1,298 @@+{-# LANGUAGE NamedFieldPuns #-}+{-# LANGUAGE OverloadedStrings #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TupleSections #-}+module Sieve.Test where++import Data.Function (($), (.), flip, on)+import Data.Functor ((<$>))+import Data.List (concatMap, foldl, foldr, unwords, reverse)+import Data.Maybe (Maybe(..), fromJust)+import Data.Monoid ((<>))+import Prelude (Integer)+import Test.Tasty+import Test.Tasty.HUnit+import Text.Show (Show(..))++import qualified Data.Interval as Interval+import qualified Data.Interval.Sieve as Interval.Sieve++tests :: TestTree+tests = testGroup "Sieve"+ [ testGroup "union" $+ concatMap+ (\(mis, me) ->+ let is = fromJust <$> mis in+ let e = fromJust <$> me in+ let sil = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty is in+ let sir = foldr+ (Interval.Sieve.union . Interval.Sieve.singleton)+ Interval.Sieve.empty is in+ [ testCase (unwords $ (show . Interval.Pretty) <$> is) $+ Interval.Sieve.intervals sil @?= e+ , testCase (unwords $ (show . Interval.Pretty) <$> reverse is) $+ Interval.Sieve.intervals sir @?= e+ ]+ )+ [ ( [ (Interval.<=..<) 0 (5::Integer)+ , (Interval.<=..<=) 5 9+ ]+ , [ (Interval.<=..<=) 0 9 ]+ )+ , ( [ (Interval.<=..<=) 0 5+ , (Interval.<=..<=) 0 9+ ]+ , [ (Interval.<=..<=) 0 9 ]+ )+ , ( [ (Interval.<=..<=) 0 4+ , (Interval.<=..<=) 5 9+ , (Interval.<=..<=) 3 6+ ]+ , [ (Interval.<=..<=) 0 9 ]+ )+ , ( [ (Interval.<=..<=) 1 4+ , (Interval.<=..<=) 5 8+ ]+ , [ (Interval.<=..<=) 1 4+ , (Interval.<=..<=) 5 8+ ]+ )+ , ( [ (Interval.<=..<=) 1 8+ , (Interval.<=..<=) 0 9+ ]+ , [ (Interval.<=..<=) 0 9 ]+ )+ , ( [ (Interval.<=..<=) 1 4+ , (Interval.<=..<=) 5 8+ , (Interval.<=..<=) 0 9+ ]+ , [ (Interval.<=..<=) 0 9 ]+ )+ ] <>+ concatMap+ (\(mis, mjs, me) ->+ let is = fromJust <$> mis in+ let js = fromJust <$> mjs in+ let e = fromJust <$> me in+ let iu = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty is in+ let ju = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty js in+ [ testCase (unwords ((show . Interval.Pretty) <$> is) <> " u " <>+ unwords ((show . Interval.Pretty) <$> js)) $+ Interval.Sieve.intervals (Interval.Sieve.union iu ju) @?= e+ , testCase (unwords ((show . Interval.Pretty) <$> js) <> " u " <>+ unwords ((show . Interval.Pretty) <$> is)) $+ Interval.Sieve.intervals (Interval.Sieve.union ju iu) @?= e+ ]+ )+ [ ( [ (Interval.<=..<=) 0 (1::Integer)+ , (Interval.<=..<=) 2 4+ ]+ , [ (Interval.<=..<=) 0 3+ ]+ , [ (Interval.<=..<=) 0 4+ ]+ )+ , ( [ (Interval.<=..<=) 0 1+ , (Interval.<=..<=) 2 3+ , (Interval.<=..<=) 4 5+ , (Interval.<=..<=) 6 7+ ]+ , [ (Interval.<=..<=) 1 2+ , (Interval.<=..<=) 3 4+ , (Interval.<=..<=) 5 6+ ]+ , [ (Interval.<=..<=) 0 7+ ]+ )+ , ( [ (Interval.<=..<=) 0 1+ , (Interval.<=..<=) 2 3+ ]+ , [ (Interval.<=..<=) 4 5+ ]+ , [ (Interval.<=..<=) 0 1+ , (Interval.<=..<=) 2 3+ , (Interval.<=..<=) 4 5+ ]+ )+ , ( [ (Interval.<=..<=) 0 1+ , (Interval.<=..<=) 4 5+ ]+ , [ (Interval.<=..<=) 2 3+ ]+ , [ (Interval.<=..<=) 0 1+ , (Interval.<=..<=) 2 3+ , (Interval.<=..<=) 4 5+ ]+ )+ ]+ , testGroup "intersection" $+ concatMap+ (\(mis, mjs, me) ->+ let is = fromJust <$> mis in+ let js = fromJust <$> mjs in+ let e = fromJust <$> me in+ let iu = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty is in+ let ju = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty js in+ [ testCase (unwords ((show . Interval.Pretty) <$> is) <> " n " <>+ unwords ((show . Interval.Pretty) <$> js)) $+ Interval.Sieve.intervals (Interval.Sieve.intersection iu ju) @?= e+ , testCase (unwords ((show . Interval.Pretty) <$> js) <> " n " <>+ unwords ((show . Interval.Pretty) <$> is)) $+ Interval.Sieve.intervals (Interval.Sieve.intersection ju iu) @?= e+ ]+ )+ [ ( [ (Interval.<=..<) 0 (5::Integer) ]+ , [ (Interval.<=..<=) 5 9 ]+ , [ ]+ )+ , ( [ (Interval.<=..<=) 0 5 ]+ , [ (Interval.<=..<=) 5 9 ]+ , [ (Interval.<=..<=) 5 5 ]+ )+ , ( [ (Interval.<=..<=) 0 5 ]+ , [ (Interval.<=..<=) 0 9 ]+ , [ (Interval.<=..<=) 0 5 ]+ )+ , ( [ (Interval.<=..<=) 0 4+ , (Interval.<=..<=) 5 9+ ]+ , [ (Interval.<=..<=) 3 6 ]+ , [ (Interval.<=..<=) 3 4+ , (Interval.<=..<=) 5 6+ ]+ )+ , ( [ (Interval.<=..<=) 1 4+ , (Interval.<=..<=) 6 8+ ]+ , [ (Interval.<=..<=) 2 3+ , (Interval.<=..<=) 5 7+ ]+ , [ (Interval.<=..<=) 2 3+ , (Interval.<=..<=) 6 7+ ]+ )+ ]+ , testGroup "complement" $+ concatMap+ (\(mis, me) ->+ let is = fromJust <$> mis in+ let e = fromJust <$> me in+ let iu = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty is in+ [ testCase (show (Interval.Pretty $+ Interval.Sieve.fmap_interval+ (Interval.fmap_unsafe Interval.Pretty) iu)) $+ Interval.Sieve.intervals (Interval.Sieve.complement iu) @?= e+ ]+ )+ [ ( [ ((Interval.<=..<) `on` Interval.Limited) 0 (5::Integer)+ , ((Interval.<=..<=) `on` Interval.Limited) 5 9+ ]+ , [ Just $ (Interval...<) 0+ , Just $ (Interval.<..) 9+ ]+ )+ , ( [ Just Interval.unlimited ]+ , [ ]+ )+ , ( [ ]+ , [ Just Interval.unlimited ]+ )+ , ( [ Just $ (Interval...<) 0+ , Just $ (Interval.<..) 0+ ]+ , [ Just $ Interval.point $ Interval.Limited 0+ ]+ )+ , ( [ ((Interval.<=..<) `on` Interval.Limited) 0 1+ , ((Interval.<=..<) `on` Interval.Limited) 2 3+ , ((Interval.<..<=) `on` Interval.Limited) 3 4+ ]+ , [ Just $ (Interval...<) 0+ , ((Interval.<=..<) `on` Interval.Limited) 1 2+ , Just $ Interval.point $ Interval.Limited 3+ , Just $ (Interval.<..) 4+ ]+ )+ ]+ , testGroup "complement_with" $+ concatMap+ (\(mib, mis, me) ->+ let ib = fromJust mib in+ let is = fromJust <$> mis in+ let e = fromJust <$> me in+ let iu = foldl+ (flip (Interval.Sieve.union . Interval.Sieve.singleton))+ Interval.Sieve.empty is in+ [ testCase (show (Interval.Pretty iu)) $+ Interval.Sieve.intervals+ (Interval.Sieve.complement_with ib iu) @?= e+ ]+ )+ [ ( (Interval.<=..<=) (-10) (10::Integer)+ , [ (Interval.<=..<) 0 5+ , (Interval.<=..<=) 5 9+ ]+ , [ (Interval.<=..<) (-10) 0+ , (Interval.<..<=) 9 10+ ]+ )+ , ( (Interval.<=..<=) (-10) 10+ , [ (Interval.<=..<=) (-10) 10 ]+ , [ ]+ )+ , ( (Interval.<=..<=) (-10) 10+ , [ ]+ , [ (Interval.<=..<=) (-10) 10 ]+ )+ , ( (Interval.<=..<=) (-10) 10+ , [ (Interval.<=..<) (-10) 0+ , (Interval.<..<=) 0 10+ ]+ , [ Just $ Interval.point 0+ ]+ )+ , ( (Interval.<=..<=) (-10) 10+ , [ Just $ Interval.point 0+ ]+ , [ (Interval.<=..<) (-10) 0+ , (Interval.<..<=) 0 10+ ]+ )+ , ( (Interval.<=..<=) 0 10+ , [ (Interval.<..<=) 0 10+ ]+ , [ Just $ Interval.point 0+ ]+ )+ , ( (Interval.<=..<=) 0 10+ , [ (Interval.<=..<) 0 10+ ]+ , [ Just $ Interval.point 10+ ]+ )+ , ( Just $ Interval.point 0+ , [+ ]+ , [ Just $ Interval.point 0+ ]+ )+ , ( Just $ Interval.point 0+ , [ Just $ Interval.point 0+ ]+ , [+ ]+ )+ ]+ ]
+ Data/Interval/Test.hs view
@@ -0,0 +1,151 @@+{-# LANGUAGE OverloadedStrings #-}+{-# LANGUAGE ScopedTypeVariables #-}+module Test where++import Data.Function (($), (.))+import qualified Data.List as List+import Data.Maybe (Maybe(..), fromJust)+import Data.Monoid ((<>))+import Data.Ord (Ordering(..))+import Prelude (Integer)+import System.IO (IO)+import Test.Tasty+import Test.Tasty.HUnit+import Text.Show (Show(..))++import qualified Data.Interval as Interval+import qualified Sieve.Test as Sieve++main :: IO ()+main =+ defaultMain $+ testGroup "Interval"+ [ testGroup "position" $+ List.concatMap+ (\(mi, mj, p) ->+ let i = fromJust mi in+ let j = fromJust mj in+ let (le, ge) =+ case p of+ Interval.Equal -> (EQ, EQ)+ _ -> (LT, GT) in+ [ testCase ((show . Interval.Pretty) i <> " " <> (show . Interval.Pretty) j) $+ Interval.position i j @?= (p, le)+ , testCase ((show . Interval.Pretty) j <> " " <> (show . Interval.Pretty) i) $+ Interval.position j i @?= (p, ge)+ ]+ )+ [ ( (Interval.<..<) 0 (4::Integer)+ , (Interval.<..<) 5 9+ , Interval.Away )+ , ( (Interval.<..<) 0 4+ , (Interval.<=..<) 4 9+ , Interval.Adjacent )+ , ( (Interval.<..<) 0 5+ , (Interval.<..<) 4 9+ , Interval.Overlap )+ , ( (Interval.<..<) 0 5+ , (Interval.<..<) 0 9+ , Interval.Prefix )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<) 1 8+ , Interval.Include )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<) 5 9+ , Interval.Suffixed )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<) 0 9+ , Interval.Equal )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<=) 0 9+ , Interval.Prefix )+ , ( (Interval.<=..<) 0 9+ , (Interval.<..<) 0 9+ , Interval.Suffixed )+ , ( (Interval.<=..<=) 0 9+ , (Interval.<..<) 0 9+ , Interval.Include )+ ]+ , testGroup "intersection" $+ List.concatMap+ (\(mi, mj, e) ->+ let i = fromJust mi in+ let j = fromJust mj in+ [ testCase ((show . Interval.Pretty) i <> " " <> (show . Interval.Pretty) j) $+ Interval.intersection i j @?= e+ , testCase ((show . Interval.Pretty) j <> " " <> (show . Interval.Pretty) i) $+ Interval.intersection j i @?= e+ ]+ )+ [ ( (Interval.<..<) 0 (4::Integer)+ , (Interval.<..<) 5 9+ , Nothing )+ , ( (Interval.<..<=) 0 5+ , (Interval.<=..<) 5 9+ , (Interval.<=..<=) 5 5 )+ , ( (Interval.<..<) 0 6+ , (Interval.<..<) 4 9+ , (Interval.<..<) 4 6 )+ , ( (Interval.<..<=) 0 6+ , (Interval.<=..<) 4 9+ , (Interval.<=..<=) 4 6 )+ , ( (Interval.<..<) 0 6+ , (Interval.<=..<) 4 9+ , (Interval.<=..<) 4 6 )+ , ( (Interval.<..<=) 0 6+ , (Interval.<..<) 4 9+ , (Interval.<..<=) 4 6 )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<) 0 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<=..<) 0 9+ , (Interval.<..<=) 0 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<..<=) 0 9+ , (Interval.<=..<) 0 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<=..<=) 0 9+ , (Interval.<=..<=) 0 9+ , (Interval.<=..<=) 0 9 )+ ]+ , testGroup "union" $+ List.concatMap+ (\(mi, mj, e) ->+ let i = fromJust mi in+ let j = fromJust mj in+ [ testCase ((show . Interval.Pretty) i <> " " <> (show . Interval.Pretty) j) $+ Interval.union i j @?= e+ , testCase ((show . Interval.Pretty) j <> " " <> (show . Interval.Pretty) i) $+ Interval.union j i @?= e+ ]+ )+ [ ( (Interval.<..<) 0 (4::Integer)+ , (Interval.<..<) 5 9+ , Nothing )+ , ( (Interval.<..<=) 0 5+ , (Interval.<..<) 5 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<..<) 0 5+ , (Interval.<=..<) 5 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<..<=) 0 5+ , (Interval.<=..<) 5 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<..<) 0 6+ , (Interval.<..<) 4 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<..<) 0 9+ , (Interval.<..<) 0 9+ , (Interval.<..<) 0 9 )+ , ( (Interval.<=..<) 0 9+ , (Interval.<..<=) 0 9+ , (Interval.<=..<=) 0 9 )+ , ( (Interval.<..<=) 0 9+ , (Interval.<=..<) 0 9+ , (Interval.<=..<=) 0 9 )+ , ( (Interval.<=..<=) 0 9+ , (Interval.<=..<=) 0 9+ , (Interval.<=..<=) 0 9 )+ ]+ , Sieve.tests+ ]
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ interval.cabal view
@@ -0,0 +1,92 @@+author: Julien Moutinho <julm+haskell+interval@autogeree.net>+-- bug-reports: http://bug.autogeree.net/haskell/interval/+build-type: Simple+cabal-version: >= 1.8+category: Data Structures+-- data-dir: data+-- data-files: +description: Data types to represent, compare and combine intervals with adherences.+ .+ See also:+ .+ - https://hackage.haskell.org/package/data-interval+ - https://hackage.haskell.org/package/intervals+extra-source-files:+ stack.yaml+extra-tmp-files:+-- homepage: http://pad.autogeree.net/informatique/haskell/interval/+license: GPL-3+license-file: COPYING+maintainer: Julien Moutinho <julm+haskell+interval@autogeree.net>+name: interval+stability: experimental+synopsis: Intervals with adherences.+tested-with: GHC==7.10.3+version: 1.20160821++source-repository head+ location: git://git.autogeree.net/haskell/interval+ type: git++Flag dev+ Default: False+ Description: Turn on development settings.+ Manual: True++Flag dump+ Default: False+ Description: Dump some intermediate files.+ Manual: True++Flag prof+ Default: False+ Description: Turn on profiling settings.+ Manual: True++Flag threaded+ Default: False+ Description: Enable threads.+ Manual: True++Library+ extensions: NoImplicitPrelude+ ghc-options: -Wall -fno-warn-tabs+ if flag(dev)+ cpp-options: -DDEVELOPMENT+ ghc-options:+ if flag(dump)+ ghc-options: -ddump-simpl -ddump-stg -ddump-to-file+ if flag(prof)+ cpp-options: -DPROFILING+ ghc-options: -fprof-auto+ -- default-language: Haskell2010+ exposed-modules:+ Data.Interval+ Data.Interval.Sieve+ build-depends:+ base >= 4.6 && < 5+ , deepseq+ , fingertree++Test-Suite interval-test+ type: exitcode-stdio-1.0+ -- default-language: Haskell2010+ extensions: NoImplicitPrelude+ ghc-options: -Wall -fno-warn-tabs+ -main-is Test+ hs-source-dirs: Data/Interval+ main-is: Test.hs+ other-modules:+ Sieve.Test+ if flag(threaded)+ ghc-options: -threaded -rtsopts -with-rtsopts=-N+ if flag(dev)+ cpp-options: -DDEVELOPMENT+ if flag(prof)+ cpp-options: -DPROFILING+ ghc-options: -fprof-auto+ build-depends:+ base >= 4.6 && < 5+ , interval+ , tasty >= 0.11+ , tasty-hunit
+ stack.yaml view
@@ -0,0 +1,6 @@+resolver: lts-6.12+flags: {}+packages:+- '.'+extra-deps:+extra-package-dbs: []