[Haskell-cafe] What's the deal with Clean?

Roman Leshchinskiy rl at cse.unsw.edu.au
Tue Nov 3 23:20:14 EST 2009

On 04/11/2009, at 13:35, wren ng thornton wrote:

> Roman Leshchinskiy wrote:
>> On 04/11/2009, at 13:23, Daniel Peebles wrote:
>>> In the presence of fusion (as is the case in uvector), it's hard to
>>> give meaningful time complexities for operations as they depend on
>>> what operations they are paired with. We need to think of a better  
>>> way
>>> to express this behavior in the documentation though.
>> I have to disagree here. Fusion never makes the complexity of  
>> operations worse. If it does, it's a bug.
> I think the point was more that the relevant complexity bound can  
> change in the presence of fusion. For a poor example: the first map  
> over a list is O(n) but all subsequent ones in a chain of maps are  
> O(1) with fusion. I'm sure there are better examples than that, but  
> you get the idea. Some people may care to know about that latter  
> complexity rather than just the "independent" complexity.

I think asymptotic complexity is the wrong tool for what you're trying  
to do. You implement your algorithm using operations with known  
complexities. This allows you to compute the complexity of the entire  
algorithm. That's all you can use operation complexities for. The  
compiler is then free to optimise the algorithm as it sees fit but is  
supposed to preserve (or improve) its complexity. It is not guaranteed  
or even supposed to preserve the original operations. To stay with  
your example, each of the two maps is linear regardless of whether  
fusion happens. Executing the two maps, be it one after another or  
interlocked, is linear simply because O(n) + O(n) = O(n), not because  
of fusion.

Essentially, you're trying to use complexity to describe an  
optimisation which doesn't actually affect the complexity.


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