[Haskell-beginners] Question about data structures

Patrick LeBoutillier patrick.leboutillier at gmail.com
Thu Nov 25 09:17:37 EST 2010


If I understand correctly KenKen is something like Sudoku except that
the (more complicated) "cages"
constraints replace the usual "square" constraints.

Have you seen these sudoku solvers: http://www.haskell.org/haskellwiki/Sudoku ?

Maybe you can get ideas there on how to attack the problem in a more
functional fashion.


On Wed, Nov 24, 2010 at 9:58 PM, Russ Abbott <russ.abbott at gmail.com> wrote:
> My previous two messages suggest a Haskell coding principle: distinguish
> between fixed and (quasi-)mutable data structures. (I know values don't
> change, but I hope you understand what I mean. The cage and the cell in my
> previous example are quasi-mutable. They are conceptually mutable in the
> context of the problem.)  The fixed data structures can be organized any way
> one wants. The quasi-/conceptually-mutable elements should be referred to
> symbolically and stored in a Map. The maps themselves should be stored at a
> global level of the system's data structure so that it is easy to replace
> them when values change.
> -- Russ
> On Wed, Nov 24, 2010 at 5:54 PM, Russ Abbott <russ.abbott at gmail.com> wrote:
>> Actually using a Map does solve the problem. The Map has to be kept at the
>> level of the Tree rather than have each leaf node point to it.  So instead
>> of just a Tree one has, say (Map, Tree). Then when one wants to change the
>> property of something associated with a leaf node, one can just change the
>> map. The Tree is unchanged.
>> -- Russ
>> On Wed, Nov 24, 2010 at 2:02 PM, Russ Abbott <russ.abbott at gmail.com>
>> wrote:
>>> OK. So putting a Map at Leaf nodes doesn't solve the problem.
>>> (Apparently I haven't been able to communicate what I see as the problem.)
>>> The problem that I'm trying to get to is the need to write excessive code
>>> for something that would require a lot less code in an OO world.  It's not a
>>> matter of execution time or space. It's a matter of the amount of code one
>>> is required to write.
>>> -- Russ
>>> On Wed, Nov 24, 2010 at 1:52 PM, Daniel Fischer
>>> <daniel.is.fischer at web.de> wrote:
>>>> On Wednesday 24 November 2010 22:12:37, Russ Abbott wrote:
>>>> > Cool. I wasn't aware of that notation.  It doesn't quite get to the
>>>> > issue though.
>>>> >
>>>> > The problem I'm concerned about is the need to define y in the first
>>>> > place. If one is chasing through a data structure and finds a need to
>>>> > change something buried within it, it seems necessary to rebuild
>>>> > everything that includes the changed thing.
>>>> In general, values are immutable, so you can't "change something buried
>>>> within it". You have to build a new value containing some of the old
>>>> stuff
>>>> and a new part. Building the new value usually consists mostly of
>>>> copying a
>>>> couple of pointers (plus building the new part of course), so isn't too
>>>> expensive normally.
>>>> You can have mutable values in the IO or (ST s) monads, if you need
>>>> them.
>>>> > That is, I can't change a
>>>> > component of somethingNew without creating y. The point is there's
>>>> > nothing about x that changed,
>>>> The thing with the changed component is not x anymore.
>>>> > and there may be nothing about (var1 x)
>>>> > that changed, and there may be nothing about var11 . var1 $ x that
>>>> > changed, etc. Yet one is apparently forced to keep track of and
>>>> > reconstruct all those elements.
>>>> The compiler takes care of that.
>>>> >
>>>> > Another example is to imagine a Tree in which the leaves contain
>>>> > "objects." If I want to change a property of one of those leaf
>>>> > objects,
>>>> You can't in general, the thing with a different property is a different
>>>> object.
>>>> > I am forced to rebuild all the ancestor nodes of that leaf down to
>>>> > rebuilding the root.
>>>> Yes (well, not you, the compiler does it), except if your tree contains
>>>> mutable objects (IORefs/STRefs for example).
>>>> >
>>>> > One way to avoid that is for the leaves to refer to their objects
>>>> > through a Map. Then changing a leaf object requires only that the
>>>> > value
>>>> > associated with key represented by the leaf be (re-)inserted into the
>>>> > Map.  The Tree itself need not change at all.
>>>> Oh, it will. If you change a Map, you get a new one, thus you get a new
>>>> tree containing the new Map.
>>>> >
>>>> > But that trick isn't always available.  In the example we are talking
>>>> > about we can't make a Map where they keys are the instance variable
>>>> > names and the values are their values.  That would seem to do the job,
>>>> > but since the values are of different types, we can't create such a
>>>> > Map.
>>>> >
>>>> > So now what?
>>>> Well, what's the problem with the compiler copying some nodes?
>>>> Normally, that doesn't cost very much performance, if it does in your
>>>> case,
>>>> we'd need to know more to suggest the best way to go.
>>>> > *
>>>> > -- Russ *
>>>> >
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Patrick LeBoutillier
Rosemère, Québec, Canada

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