Ticket 996: Add ranged sets

[Paul Johnson]

The ticket is at http://hackage.haskell.org/trac/ghc/ticket/996

Ranged sets represent sets of ordered values as lists of ranges. Each 
range has a lower and upper boundary, and for any value and boundary the 
value is either above or below the boundary: no value can ever sit on a 
boundary. There are also boundaries for +/- infinity (BoundaryBelowAll? 
<http://hackage.haskell.org/trac/ghc/wiki/BoundaryBelowAll> and 
BoundaryAboveAll? 
<http://hackage.haskell.org/trac/ghc/wiki/BoundaryAboveAll>).

The upshot is that you can represent a set of reals such as

        [ 2.0 < x <= 3.4, 6.7 < x]

or a couple of encyclopedia volumes as:

        ["a" <= x < "blob", "goo" <= x < "hun"]

The usual set operators are provided. The library also does the Right 
Thing with adjacent values:

        [2 < x <= 3] Union [4 <= x < 5] == [2 < x < 5]

        [2.0 < x <= 3.0] Union [4.0 <= x < 5.0] == [2.0 < x <= 3.0, 4.0
        <= x < 5.0]

I've needed something like this more than once over the years, in 
various languages. Haskell is the first one that can actually do the 
Right Thing efficiently for a polymorphic type.

The source contains Haddock comments and a comprehensive set of 
QuickCheck? <http://hackage.haskell.org/trac/ghc/wiki/QuickCheck> 
properties. I've integrated these into the documentation. So far I've 
tested this on GHC 6.4.1, although this patch is against the HEAD of the 
current libraries.

If this patch is accepted I'll also add patches for ranged sets of times 
(e.g. the set of all times within the first Tuesday of each month), and 
to filter finite maps against ranged sets.