úÎ=k9,0      !"#$%&'()*+,-./6non-portable (ScopedTypeVariables, DeriveDataTypeable) provisionalmasahiro.sakai@gmail.com Safe-Inferred,Endpoints of intervals The intervals (i.e.8 connected and convex subsets) over real numbers __R__. Lower 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. Upper 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. = of the interval and whether it is included in the interval. 4 The result is convenient to use as an argument for  . = of the interval and whether it is included in the interval. 4 The result is convenient to use as an argument for  . smart constructor for  closed interval [l,u] !left-open right-closed interval (l,u] !left-closed right-open interval [l, u) open interval (l, u) whole real number line (-", ") empty (contradicting) interval singleton set [x,x] intersection of two intervals %intersection of a list of intervals.  Since 0.6.0 convex hull of two intervals $convex hull of a list of intervals.  Since 0.6.0 Is the interval empty?  Is the element in the interval? $Is the element not in the interval? Is this a subset?  (i1 `` i2) tells whether i1 is a subset of i2. Is this a proper subset? (i.e. a subset but not equal). 7Width of a interval. Width of an unbounded interval is  undefined. Cpick up an element from the interval if the interval is not empty. ; returns the simplest rational number within the interval. A rational number y is said to be simpler than another y' if  0 (1 y) <= 0 (1 y'), and  2 y <= 2 y'.  (see also 3)  Since 0.4.0 For all x in X, y in Y. x 4 y? For all x in X, y in Y. x 5 y? For all x in X, y in Y. x 6 y? !For all x in X, y in Y. x 7 y?  Since 1.0.1 "For all x in X, y in Y. x 8 y? #For all x in X, y in Y. x 9 y? $Does there exist an x in X, y in Y such that x 4 y? %Does there exist an x in X, y in Y such that x 4 y?  Since 1.0.0 &Does there exist an x in X, y in Y such that x 5 y? 'Does there exist an x in X, y in Y such that x 5 y?  Since 1.0.0 (Does there exist an x in X, y in Y such that x 6 y?  Since 1.0.0 )Does there exist an x in X, y in Y such that x 6 y?  Since 1.0.0 *Does there exist an x in X, y in Y such that x 7 y?  Since 1.0.1 +Does there exist an x in X, y in Y such that x 7 y?  Since 1.0.1 ,Does there exist an x in X, y in Y such that x 8 y? -Does there exist an x in X, y in Y such that x 9 y? .Does there exist an x in X, y in Y such that x 8 y?  Since 1.0.0 /Does there exist an x in X, y in Y such that x 9 y?  Since 1.0.0 E: (lower bound and whether it is included 'upper bound and whether it is included  lower bound l  upper bound u  lower bound l  upper bound u  lower bound l  upper bound u  lower bound l  upper bound u ; !"#$%&'()*+,-./<=>?@ABCDEFGHIJKLMNOPQR0  !"#$%&'()*+,-./0   "#!$&(,-*%')./+D: ; !"#$%&'()*+,-./<=>?@ABCDEFGHIJKLMNOPQRS      !"#$%&'()*+,-./01234564784794:;<=><=?<=@<=A<=B<=C DEFGHIJKLMNOPQRSTUVWXYZ[\data-interval-1.0.1 Data.Intervalextended-reals-0.1.0.0Data.ExtendedRealNegInfFinitePosInfExtendedEndPointInterval lowerBound upperBound lowerBound' upperBound'interval<=..<=<..<=<=..<<..<wholeempty singleton intersection intersectionshullhullsnullmember notMember isSubsetOfisProperSubsetOfwidthpickupsimplestRationalWithin=!>!=?>?>=??>??baseGHC.NumabsGHC.Real numerator denominator Data.RatioapproxRationalghc-prim GHC.Classes<<===/=>=> isSingletonappPrecappPrec1 scaleIntervalcmpUBcmpLB scaleInf' scaleEndPointmulInf'recipLBrecipUB$fFractionalInterval $fNumInterval$fDataInterval$fReadInterval$fShowInterval$fBoundedLatticeInterval $fBoundedMeetSemiLatticeInterval $fBoundedJoinSemiLatticeInterval$fLatticeInterval$fMeetSemiLatticeInterval$fJoinSemiLatticeInterval$fHashableInterval$fNFDataInterval