h$aU\       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ Safe3 data-intervalThe intervals (i.e.. connected and convex subsets) over integers (Z). data-intervalLower endpoint (i.e.( greatest lower bound) of the interval. of the empty interval is .! of a left unbounded interval is .; of an interval may or may not be a member of the interval. data-intervalUpper endpoint (i.e.$ least upper bound) of the interval. of the empty interval is ." of a right unbounded interval is ., of an interval is a member of the interval. data-intervalclosed interval [l,u] data-intervalempty (contradicting) interval data-interval lower bound l data-interval upper bound u5Safe38 R data-intervalThe intervals (i.e.1 connected and convex subsets) over real numbers R. data-intervalBoundary of an interval may be open (excluding an endpoint) or closed (including an endpoint).  data-intervalLower endpoint (i.e.7 greatest lower bound) of the interval, together with  information. The result is convenient to use as an argument for  .  data-intervalUpper endpoint (i.e.4 least upper bound) of the interval, together with  information. The result is convenient to use as an argument for  .  data-intervalempty (contradicting) interval  data-intervalsmart constructor for   data-interval&lower bound and whether it is included data-interval&upper bound and whether it is included (c) Masahiro Sakai 2016 BSD-stylemasahiro.sakai@gmail.com provisional5non-portable (CPP, DeriveDataTypeable, DeriveGeneric)Safe38   data-intervaldescribes how two intervals x and y can be related. See 8https://en.wikipedia.org/wiki/Allen%27s_interval_algebraAllen's interval algebra data-intervalinverts a relation, such that  (  x y) =   y x  4(c) Masahiro Sakai 2011-2013, Andrew Lelechenko 2020 BSD-stylemasahiro.sakai@gmail.com provisional;non-portable (CPP, ScopedTypeVariables, DeriveDataTypeable)Safe .$ data-intervalLower endpoint (i.e.( greatest lower bound) of the interval.$ of the empty interval is .$! of a left unbounded interval is .$; of an interval may or may not be a member of the interval.% data-intervalUpper endpoint (i.e.$ least upper bound) of the interval.% of the empty interval is .%" of a right unbounded interval is .%; of an interval may or may not be a member of the interval.& data-intervalclosed interval [l,u]' data-interval!left-open right-closed interval (l,u]( data-interval!left-closed right-open interval [l, u)) data-intervalopen interval (l, u)* data-intervalwhole real number line (-D, D)+ data-intervalsingleton set [x,x], data-intervalintersection of two intervals- data-interval$intersection of a list of intervals. Since 0.6.0. data-intervalconvex hull of two intervals/ data-interval#convex hull of a list of intervals. Since 0.6.00 data-intervalIs the interval empty?1 data-intervalIs the interval single point?2 data-interval5If the interval is a single point, return this point.3 data-intervalIs the element in the interval?4 data-interval#Is the element not in the interval?5 data-intervalIs this a subset? (i1 `5` i2) tells whether i1 is a subset of i2.6 data-intervalIs this a proper subset? (i.e. a subset but not equal).7 data-interval1Does the union of two range form a connected set? Since 1.3.08 data-interval7Width of a interval. Width of an unbounded interval is  undefined.9 data-intervalpick up an element from the interval if the interval is not empty.: data-interval:: returns the simplest rational number within the interval.A rational number y is said to be simpler than another y' if ( y) <=  ( y'), and y <=  y'. (see also ) Since 0.4.0; data-intervalmapMonotonic f i is the image of i under f, where f must be a strict monotone function, preserving negative and positive infinities.< data-intervalFor all x in X, y in Y. x  y?= data-intervalFor all x in X, y in Y. x  y?> data-intervalFor all x in X, y in Y. x  y?? data-intervalFor all x in X, y in Y. x  y? Since 1.0.1@ data-intervalFor all x in X, y in Y. x  y?A data-intervalFor all x in X, y in Y. x  y?B data-intervalDoes there exist an x in X, y in Y such that x  y?C data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0D data-intervalDoes there exist an x in X, y in Y such that x  y?E data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0F data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0G data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0H data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.1I data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.1J data-intervalDoes there exist an x in X, y in Y such that x  y?K data-intervalDoes there exist an x in X, y in Y such that x  y?L data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0M data-intervalDoes there exist an x in X, y in Y such that x  y? Since 1.0.0N data-interval8Computes how two intervals are related according to the   classificationO data-intervalWhen results of  or  do not form a connected interval, a convex hull is returned instead.P data-interval returns *) when 0 is an interior point. Otherwise recip (recip xs) equals to xs without 0.Q data-intervalWhen results of  or  do not form a connected interval, a convex hull is returned instead.& data-interval lower bound l data-interval upper bound u' data-interval lower bound l data-interval upper bound u( data-interval lower bound l data-interval upper bound u) data-interval lower bound l data-interval upper bound u: $%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMN3 &'()* +01234567$% 8<=>@A?BDFJKHCEGLMI,-./;9:N&5'5(5)5<4=4>4?4@4A4B4C4D4E4F4G4H4I4J4K4L4M4(c) Masahiro Sakai 2011-2014 BSD-stylemasahiro.sakai@gmail.com provisional6non-portable (ScopedTypeVariables, DeriveDataTypeable)Safe34|.T data-interval of the interval and whether it is included in the interval. The result is convenient to use as an argument for V.U data-interval of the interval and whether it is included in the interval. The result is convenient to use as an argument for V.V data-intervalsmart constructor for W data-interval!left-open right-closed interval (l,u]X data-interval!left-closed right-open interval [l, u)Y data-intervalopen interval (l, u)Z data-intervalwhole real number line (-D, D)[ data-intervalsingleton set [x,x]\ data-intervalintersection of two intervals] data-interval$intersection of a list of intervals.^ data-intervalconvex hull of two intervals_ data-interval#convex hull of a list of intervals.` data-intervalmapMonotonic f i is the image of i under f, where f$ must be a strict monotone function.a data-intervalIs the interval empty?b data-intervalIs the interval single point?c data-intervalIs the element in the interval?d data-interval#Is the element not in the interval?e data-intervalIs this a subset? (i1 `e` i2) tells whether i1 is a subset of i2.f data-intervalIs this a proper subset? (i.e. a subset but not equal).g data-intervalDoes the union of two range form a set which is the intersection between the integers and a connected real interval?h data-interval7Width of a interval. Width of an unbounded interval is  undefined.i data-intervalpick up an element from the interval if the interval is not empty.j data-intervalj: returns the simplest rational number within the interval. An integer y is said to be simpler than another y' if  y <=  y' (see also   and  )k data-intervalFor all x in X, y in Y. x  y?l data-intervalFor all x in X, y in Y. x  y?m data-intervalFor all x in X, y in Y. x  y?n data-intervalFor all x in X, y in Y. x  y?o data-intervalFor all x in X, y in Y. x  y?p data-intervalFor all x in X, y in Y. x  y?q data-intervalDoes there exist an x in X, y in Y such that x  y?r data-intervalDoes there exist an x in X, y in Y such that x  y?s data-intervalDoes there exist an x in X, y in Y such that x  y?t data-intervalDoes there exist an x in X, y in Y such that x  y?u data-intervalDoes there exist an x in X, y in Y such that x  y?v data-intervalDoes there exist an x in X, y in Y such that x  y?w data-intervalDoes there exist an x in X, y in Y such that x  y?x data-intervalDoes there exist an x in X, y in Y such that x  y?y data-intervalDoes there exist an x in X, y in Y such that x  y?z data-intervalDoes there exist an x in X, y in Y such that x  y?{ data-intervalDoes there exist an x in X, y in Y such that x  y?| data-intervalDoes there exist an x in X, y in Y such that x  y?} data-intervalConvert the interval to  data type.~ data-intervalConversion from  data type. data-intervalGiven a  I over R, compute the smallest  J such that I E J. data-intervalGiven a  I over R, compute the largest  J such that J E I. data-interval8Computes how two intervals are related according to the   classificationV data-interval&lower bound and whether it is included data-interval&upper bound and whether it is includedW data-interval lower bound l data-interval upper bound uX data-interval lower bound l data-interval upper bound uY data-interval lower bound l data-interval upper bound u=TUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~6VWXYZ[abcdefgTUhklmopnqsuyzwrtv{|x\]^_`ij}~W5X5Y5k4l4m4n4o4p4q4r4s4t4u4v4w4x4y4z4{4|4(c) Masahiro Sakai 2016 BSD-stylemasahiro.sakai@gmail.com provisionalnon-portable (CPP, ScopedTypeVariables, TypeFamilies, DeriveDataTypeable, MultiWayIf) Trustworthy 3< data-interval)A set comprising zero or more non-empty,  disconnected intervals.Any connected intervals are merged together, and empty intervals are ignored. data-intervalwhole real number line (-D, D) data-intervalempty interval set data-intervalsingle interval data-intervalIs the interval set empty? data-interval#Is the element in the interval set? data-interval'Is the element not in the interval set? data-intervalIs this a subset? (is1 `` is2) tells whether is1 is a subset of is2. data-intervalIs this a proper subset? (i.e. a subset but not equal). data-interval"convex hull of a set of intervals. data-intervalComplement the interval set. data-interval,Insert a new interval into the interval set. data-interval)Delete an interval from the interval set. data-intervalunion of two interval sets data-interval union of a list of interval sets data-interval!intersection of two interval sets data-interval'intersection of a list of interval sets data-intervaldifference of two interval sets data-interval.Build a interval set from a list of intervals. data-interval2Build a map from an ascending list of intervals.  The precondition is not checked. data-interval0Convert a interval set into a list of intervals. data-intervalConvert a interval set into a list of intervals in ascending order. data-intervalConvert a interval set into a list of intervals in descending order. data-interval recip (recip xs) == delete 0 xs(c) Masahiro Sakai 2016 BSD-stylemasahiro.sakai@gmail.com provisionalnon-portable (CPP, ScopedTypeVariables, TypeFamilies, DeriveDataTypeable, MultiWayIf, GeneralizedNewtypeDeriving) Trustworthy 3RT* data-intervalReturn all keys of the map in ascending order. Subject to list data-interval An alias for . Return all key/value pairs in the map in ascending key order. data-intervalThe set of all keys of the map. data-interval-Convert the map to a list of key/value pairs. data-intervalConvert the map to a list of key/value pairs where the keys are in ascending order. data-intervalConvert the map to a list of key/value pairs where the keys are in descending order. data-intervalBuild a map from a list of key/value pairs. If the list contains more than one value for the same key, the last value for the key is retained. data-intervalBuild a map from a list of key/value pairs with a combining function. data-interval.Filter all values that satisfy some predicate. data-intervalThe expression ( i map) is a triple (map1,map2,map3) where the keys in map1 are smaller than i, the keys in map2 are included in i, and the keys in map3 are larger than i. data-intervalThis function is defined as ( =  (==)). data-intervalThe expression ( f t1 t2 ) returns  if all keys in t1 are in tree t2 , and when f returns * when applied to their respective values. data-intervalIs this a proper submap? (ie. a submap but not equal). Defined as ( =  (==)). data-intervalIs this a proper submap? (ie. a submap but not equal). The expression ( f m1 m2 ) returns  when m1 and m2 are not equal, all keys in m1 are in m2 , and when f returns * when applied to their respective values.29 9 (c) Masahiro Sakai 2016 BSD-stylemasahiro.sakai@gmail.com provisional*non-portable (BangPatterns, TupleSections)SafeZ/  data-interval(The map that maps whole range of k to a. data-intervalA map with a single interval. data-intervalinsert a new key and value in the map. If the key is already present in the map, the associated value is replaced with the supplied value. data-interval?@ABC DEFGHIJKLMNOPQRSTUV WXYZ[123456789D:;=>?@ABC\EFGHIJKLMNOPQRSTUV]^_` abcd45:=>?@efghij67klmnopqrstuvwxyz{|}~:=>e45ghijk6nopl45gl |*data-interval-2.1.0-78eKnHCuQyp2rhaaEQhqk7Data.IntegerInterval Data.IntervalData.IntervalRelationData.IntervalSetData.IntervalMap.StrictData.IntervalMap.LazyData.IntegerInterval.InternalData.Interval.Internalrelate Data.RatioapproxRationalIntervalsimplestRationalWithinData.IntervalMap.BaseIntegerInterval lowerBound upperBound<=..<=emptyBoundaryOpenClosed lowerBound' upperBound'intervalRelationBefore JustBeforeOverlapsStartsDuringFinishesEqual FinishedByContains StartedBy OverlappedBy JustAfterAfterinvert $fEqRelation $fOrdRelation$fEnumRelation$fBoundedRelation$fShowRelation$fReadRelation$fGenericRelation$fDataRelation<..<=<=..<<..<whole singleton intersection intersectionshullhullsnull isSingletonextractSingletonmember notMember isSubsetOfisProperSubsetOf isConnectedwidthpickup mapMonotonic=!>!=?>?>=??>??$fFloatingInterval$fFractionalInterval $fNumInterval$fReadInterval$fShowIntervalsimplestIntegerWithin toInterval fromIntervalfromIntervalOverfromIntervalUnder$fNumIntegerInterval$fReadIntegerInterval$fShowIntegerInterval IntervalSetspan complementinsertdeleteunionunions differencefromList fromAscListtoList toAscList toDescList$fIsListIntervalSet$fFractionalIntervalSet$fNumIntervalSet$fSemigroupIntervalSet$fMonoidIntervalSet$fHashableIntervalSet$fNFDataIntervalSet$fDataIntervalSet$fReadIntervalSet$fShowIntervalSet$fEqIntervalSet IntervalMap!\\lookupfindWithDefault insertWithadjustupdatealter unionWith unionsWithintersectionWithmapmapKeysMonotonicelemskeysassocskeysSet fromListWithfiltersplit isSubmapOf isSubmapOfByisProperSubmapOfisProperSubmapOfBy-extended-reals-0.2.4.0-H00uNdF8f8cG6AqnImgKRIData.ExtendedRealPosInfNegInfbaseGHC.NumabsGHC.Real numerator denominatorghc-prim GHC.Classes<<===/=>=> GHC.Floattan**recipsignum isInfiniteisFiniteinfExtendedFiniteGHC.Errerror GHC.MaybeJustNothing Data.Foldablefoldl GHC.TypesTrue