[Haskell-cafe] Newbie question about automatic memoization

[Jules Bean]

Bryan Burgers wrote:
> On 7/30/07, peterv <bf3 at telenet.be> wrote:
>> Does Haskell support any form of automatic memorization?
>>
>> For example, does the function
>>
>>         iterate f x
>>
>> which expands to
>>
>>         [x, f(x), f(f(x)), f(f(f(x))), …
>>
>> gets slower and slower each iteration, or can it take advantage of the fact
>> that f is referentially transparent and hence can be "memoized / cached"?
>>
>> Thanks,
>> Peter
> 
> For 'iterate' the answer does not really need to be memoized.

Or, another way of phrasing that answer is 'yes'. The definition of 
iteration does memoize - although normally one would say 'share' - the 
intermediate results.

> 
> I imagine the definition of 'iterate' looks something like this:
> 
> iterate f x = x : iterate f (f x)
> 

Haskell doesn't automatically memoize. But you are entitled to assume 
that named values are 'shared' rather than calculated twice. For 
example, in the above expression "x", being a named value, is shared 
between (a) the head of the list and (b) the parameter of the function 
"f" inside the recursive call to iterate.

Of course sharing "x" may not seem very interesting, on the outermost 
call, but notice that on the next call the new "x" is the old "f x", and 
on the call after that the new "x" is "f (f x)" w.r.t the original "x".

Jules