[Haskell] Newbie : How come that cyclic recursive lists are efficient ?

[Graham Klyne]

Notice that 'hamming' *is* a list of integers, not a function to produce them:

   hamming :: [Integer]

Thus, the "magic" here is that you can define this list as a value, without 
having to actually evaluate any element until it's needed, either by direct 
reference from another function, or indirectly by the recursive definition 
to obtain a value directly required.  But once evaluated, the deferred 
evaluation is replaced by the resulting value.

This is the power of lazy evaluation.  Even  fixed values (as opposed to 
function calls) aren't evaluated until they're needed.

#g
--

At 10:38 24/01/05 +0100, Francis Girard wrote:
>Hi,
>
>The classical Hamming problem have the following solution in Haskell :
>
>*** BEGIN SNAP
>-- hamming.hs
>
>-- Merges two infinite lists
>merge :: (Ord a) => [a] -> [a] -> [a]
>merge (x:xs)(y:ys)
>   | x == y    = x : merge xs ys
>   | x <  y    = x : merge xs (y:ys)
>   | otherwise = y : merge (x:xs) ys
>
>-- Lazily produce the hamming sequence
>hamming :: [Integer]
>hamming
>   = 1 : merge (map (2*) hamming) (merge (map (3*) hamming) (map (5*) 
> hamming))
>*** END SNAP
>
>I just love these algorithms that run after their tail (they make my brain
>melt) but I don't know how is it that they are efficient.
>
>Here, the hamming recursively calls itself three times. For this algorithm to
>be efficient, the Haskell system, somehow, has to "remember" the already
>generated sequence THROUGH RECURSION (i.e. not only intermediate "local"
>results) otherwise it would end up regenerating the beginning of the sequence
>over and over again.
>
>Obviously, Haskell does remember what had already been generated THROUGH
>RECURSION since executing the program with GHCI runs quite smoothly and
>responsively.
>
>That Haskell manages to do that is for me "magnifique". But I need to know 
>(if
>only a little) about how it achieves this in order to know what I, as a
>lambda programmer, can do, and how to compute the Big-Oh complexity of the
>algorithm.
>
>Thank you,
>
>Francis Girard
>FRANCE
>
>_______________________________________________
>Haskell mailing list
>Haskell at haskell.org
>http://www.haskell.org/mailman/listinfo/haskell

------------
Graham Klyne
For email:
http://www.ninebynine.org/#Contact