diff --git a/COPYING b/COPYING new file mode 100644 --- /dev/null +++ b/COPYING @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Data/Interval.hs b/Data/Interval.hs new file mode 100644 --- /dev/null +++ b/Data/Interval.hs @@ -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" diff --git a/Data/Interval/Sieve.hs b/Data/Interval/Sieve.hs new file mode 100644 --- /dev/null +++ b/Data/Interval/Sieve.hs @@ -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. +-- +-- * +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 diff --git a/Data/Interval/Sieve/Test.hs b/Data/Interval/Sieve/Test.hs new file mode 100644 --- /dev/null +++ b/Data/Interval/Sieve/Test.hs @@ -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 + ] + , [ + ] + ) + ] + ] diff --git a/Data/Interval/Test.hs b/Data/Interval/Test.hs new file mode 100644 --- /dev/null +++ b/Data/Interval/Test.hs @@ -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 + ] diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/interval.cabal b/interval.cabal new file mode 100644 --- /dev/null +++ b/interval.cabal @@ -0,0 +1,92 @@ +author: Julien Moutinho +-- 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 +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 diff --git a/stack.yaml b/stack.yaml new file mode 100644 --- /dev/null +++ b/stack.yaml @@ -0,0 +1,6 @@ +resolver: lts-6.12 +flags: {} +packages: +- '.' +extra-deps: +extra-package-dbs: []