[Haskell-cafe] Set of reals...?

[Keean Schupke]

Well, its functional of course:

    union :: Interval -> Interval -> Interval
    union i j = Interval {
       isin x = isin i x || isin j x
    }

    intersection :: Interval -> Interval -> Interval
    intersection i j = Interval {
       isin x = isin i x && isin j x
    }

    Keean.


Stijn De Saeger wrote:

>That seems like a very clean way to define the sets indeed, but how
>would you go about implementing operations like intersection,
>complement etc... on those structures? define some sort of algebra
>over the functions? or extend such sets by adding elements? hm...
>sounds interesting,.
>
>thanks,
>stijn.
>
>
>On Wed, 27 Oct 2004 11:52:54 +0100, Keean Schupke
><k.schupke at imperial.ac.uk> wrote:
>  
>
>>I think someone else mentioned using functions earlier,
>>rather than a datatype why not define:
>>
>>    data Interval = Interval { isin :: Float -> Bool }
>>
>>Then each range becomes a function definition, for example:
>>
>>    myInterval = Interval {
>>       isin r
>>          | r == 0.6 = True
>>          | r > 0.7 && r < 1.0 = True
>>          | otherwise = False
>>       }
>>
>>Then you can test with:
>>
>>    (isin myInterval 0.6)
>>
>>Keean
>>
>>
>>    
>>