This may give a false positive (but should try not to).
This may give a false positive (but should try not to). Note the case of (0,1) for the integers. If they were doubles, this would intersect, but since there are no members of the set Int that are bigger than 0 and less than 1, they don't really intersect. So, ordering is not enough here. You need a stronger notion, which we don't have a typeclass for.
The smallest value that is contained here This is an Option, because of cases like ExclusiveLower(Int.MaxValue) which are pathological and equivalent to Empty
The smallest value that is contained here This is an Option, because of cases like ExclusiveLower(Int.MaxValue) which are pathological and equivalent to Empty
Map the Interval with a non-decreasing function.
Map the Interval with a non-decreasing function. If you use a non-monotonic function (like x^2) then the result is meaningless. TODO: It might be good to have types for these properties in algebird.
Iterates all the items in this Lower[T] from lowest to highest
Iterates all the items in this Lower[T] from lowest to highest