úÎ)%y$      !"#`non-portable (ScopedTypeVariables, FlexibleInstances, MultiParamTypeClasses, DeriveDataTypeable) provisionalmasahiro.sakai@gmail.com Safe-Inferred&Endpoints of intervals positive infinity (+")  finite value negative infinity (-")  Interval Lower bound of the interval Upper bound of the interval GLower bound of the interval and whether it is included in the interval GUpper bound of the interval and whether it is included in the interval 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] 6intersection (greatest lower bounds) of two intervals convex hull of two 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. 7Is this a proper subset? (ie. 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. For all x in X, y in Y. x $ y For all x in X, y in Y. x % y For all x in X, y in Y. x & y For all x in X, y in Y. x ' y For 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 A+ (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  !"#,-./0123456789)*:;<=>?@ABCDE$  !"#$  !"#=+  !"#,-./0123456789)*:;<=>?@ABCDEF      !"#$%&'(&')&'*&'+&',-./0123456789:;<=>?@ABCDEFGHIdata-interval-0.1.0 Data.IntervalEndPointPosInfFiniteNegInfInterval lowerBound upperBound lowerBound' upperBound'interval<=..<=<..<=<=..<<..<wholeempty singleton intersectionhullnullmember notMember isSubsetOfisProperSubsetOfwidthpickup=!>!=?>?ghc-prim GHC.Classes<<===>=> combineMaybe isIntegerappPrecappPrec1 scaleIntervalcmpUBcmpLBisFinitenegateEndPoint scaleInf' scaleEndPointmulInf' mulEndPointrecipLBrecipUB recipEndPoint$fFunctorEndPoint$fBoundedEndPoint$fFractionalInterval $fNumInterval$fReadInterval$fShowInterval$fBoundedLatticeInterval $fBoundedMeetSemiLatticeInterval $fBoundedJoinSemiLatticeInterval$fLatticeInterval$fMeetSemiLatticeInterval$fJoinSemiLatticeInterval