úÎ-E)-%      !"#$(c) Masahiro Sakai 2011-2013 BSD-stylemasahiro.sakai@gmail.com provisional6non-portable (ScopedTypeVariables, DeriveDataTypeable) Safe-Inferred+M'Endpoints of intervalspositive infinity (+") finite valuenegative infinity (-")IntervalLower bound of the intervalUpper bound of the interval|Lower bound of the interval and whether it is included in the interval. The result is convenient to use as an argument for  .|Upper bound of the interval and whether it is included in the interval. The result is convenient to use as an argument for  . smart constructor for  closed interval [l,u] !left-open right-closed interval (l,u] !left-closed right-open interval [l, u) open interval (l, u)whole real number line (-", ")empty (contradicting) intervalsingleton set [x,x]intersection of two intervalsconvex hull of two intervalsIs the interval empty?Is the element in the interval?#Is the element not in the interval?Is this a subset? (i1  i2) tells whether i1 is a subset of i2.6Is this a proper subset? (ie. a subset but not equal).7Width of a interval. Width of an unbounded interval is  undefined.Bpick up an element from the interval if the interval is not empty.N returns the simplest rational number within the interval. A rational number y is said to be simpler than another y' if% (& y) <= % (& y'), and' y <= ' y'. (see also ()For all x in X, y in Y. x ) yFor all x in X, y in Y. x * yFor all x in X, y in Y. x + yFor all x in X, y in Y. x , yFor all x in X, y in Y. x - y Does there exist an x in X, y in Y such that x ) y?!Does there exist an x in X, y in Y such that x * y?"Does there exist an x in X, y in Y such that x + y?#Does there exist an x in X, y in Y such that x , y?$Does there exist an x in X, y in Y such that x - y?.Combining two Maybe values using given function./is the number integral? , isInteger x = fromInteger (round x) == x G0 '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 !"#$123456789:;<=>./?@ABCDEFGHIJKLMNO%  !"#$%  !"#$C0  !"#$123456789:;<=>./?@ABCDEFGHIJKLMNOP      !"#$%&'()'*+'*,'-./01/02/03/04/056789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWdata-interval-0.5.0 Data.IntervalEndPointPosInfFiniteNegInfInterval lowerBound upperBound lowerBound' upperBound'interval<=..<=<..<=<=..<<..<wholeempty singleton intersectionhullnullmember notMember isSubsetOfisProperSubsetOfwidthpickupsimplestRationalWithin=!>!=?>?baseGHC.NumabsGHC.Real numerator denominator Data.RatioapproxRationalghc-prim GHC.Classes<<===>=> combineMaybe isIntegerappPrecappPrec1 scaleIntervalcmpUBcmpLBisFinitenegateEndPoint scaleInf' scaleEndPointmulInf' mulEndPointrecipLBrecipUB recipEndPoint$fHashableEndPoint$fNFDataEndPoint$fFunctorEndPoint$fBoundedEndPoint$fFractionalInterval $fNumInterval$fDataInterval$fReadInterval$fShowInterval$fBoundedLatticeInterval $fBoundedMeetSemiLatticeInterval $fBoundedJoinSemiLatticeInterval$fLatticeInterval$fMeetSemiLatticeInterval$fJoinSemiLatticeInterval$fHashableInterval$fNFDataInterval