úÎ0É,Ë-      !"#$%&'()*+,(c) Masahiro Sakai 2011-2013 BSD-stylemasahiro.sakai@gmail.com provisional6non-portable (ScopedTypeVariables, DeriveDataTypeable) Safe-Inferred+M)Endpoints of intervalsIntervalLower bound of the intervalUpper bound of the interval|Lower bound of the interval and whether it is included in the interval. The result is convenient to use as an argument for  . |Upper bound of the interval and whether it is included in the interval. The result is convenient to use as an argument for  . smart constructor for  closed interval [l,u] !left-open right-closed interval (l,u] !left-closed right-open interval [l, u)open interval (l, u)whole real number line (-", ")empty (contradicting) intervalsingleton set [x,x]intersection of two intervals$intersection of a list of intervals.convex hull of two intervals#convex hull of a list of intervals.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 i2.6Is 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 0)For all x in X, y in Y. x 1 yFor all x in X, y in Y. x 2 y For all x in X, y in Y. x 3 y!For all x in X, y in Y. x 4 y"For all x in X, y in Y. x 5 y#Does there exist an x in X, y in Y such that x 1 y?$Does there exist an x in X, y in Y such that x 1 y?%Does there exist an x in X, y in Y such that x 2 y?&Does there exist an x in X, y in Y such that x 2 y?'Does there exist an x in X, y in Y such that x 3 y?(Does there exist an x in X, y in Y such that x 3 y?)Does there exist an x in X, y in Y such that x 4 y?*Does there exist an x in X, y in Y such that x 5 y?+Does there exist an x in X, y in Y such that x 4 y?,Does there exist an x in X, y in Y such that x 5 y?A6 'lower bound and whether it is included &upper bound and whether it is included  lower bound l upper bound u  lower bound l upper bound u  lower bound l upper bound u lower bound l upper bound u !"#$%&'()*+,789:;<=>?@ABCDEFGHIJKLM-  !"#$%&'()*+,-   !"#%')*$&(+,@6  !"#$%&'()*+,789:;<=>?@ABCDEFGHIJKLMN      !"#$%&'()*+,-./01231451461789:;9:<9:=9:>9:? @ABCDEFGHIJKLMNOPQRSTUVWdata-interval-1.0.0 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<<===>=>appPrecappPrec1 scaleIntervalcmpUBcmpLB scaleInf' scaleEndPointmulInf'recipLBrecipUB$fFractionalInterval $fNumInterval$fDataInterval$fReadInterval$fShowInterval$fBoundedLatticeInterval $fBoundedMeetSemiLatticeInterval $fBoundedJoinSemiLatticeInterval$fLatticeInterval$fMeetSemiLatticeInterval$fJoinSemiLatticeInterval$fHashableInterval$fNFDataInterval