Gregory Crosswhite gcross at phys.washington.edu
Fri Jul 9 01:54:50 EDT 2010

```  You're correct in pointing out that f uses memoization inside of
itself to cache the intermediate values that it commutes, but those
values don't get shared between invocations of f;  thus, if you call f
with the same value of n several times then the memo table might get
reconstructed redundantly.  (However, there are other strategies for
memoization that are persistent across calls.)

Cheers,
Greg

On 7/8/10 9:59 PM, Michael Mossey wrote:
> Thanks, okay the next question is: how does the memoization work? Each
> call to memo seems to construct a new array, if the same f(n) is
> encountered several times in the recursive branching, it would be
> computed several times. Am I wrong?
> Thanks,
> Mike
>
> Gregory Crosswhite wrote:
>>  On 7/8/10 9:17 PM, Michael Mossey wrote:
>>>
>>>
>>> Daniel Fischer wrote:
>>>>
>>>> If f has the appropriate type and the base case is f 0 = 0,
>>>>
>>>> module Memo where
>>>>
>>>> import Data.Array
>>>>
>>>> f :: (Integral a, Ord a, Ix a) => a -> a
>>>> f n = memo ! n
>>>>   where
>>>>     memo = array (0,n) \$ (0,0) :            [(i, max i (memo!(i
>>>> `quot` 2) + memo!(i `quot` 3)                      + memo!(i `quot`
>>>> 4))) | i <- [1 .. n]]
>>>>
>>>> is wasteful regarding space, but it calculates only the needed
>>>> values and very simple.
>>>
>>> Can someone explain to a beginner like me why this calculates only
>>> the needed values? The list comprehension draws from 1..n so I don't
>>> understand why all those values wouldn't be computed.
>>>
>>
>> The second pair of each element of the list will remain unevaluated
>> until demanded --- it's the beauty of being a lazy language.  :-)
>> Put another way, although it might look like the list contains values
>> (and technically it does due to referential transparency), at a lower
>> level what it actually contains are pairs such that the second
>> element is represented not by number but rather by a function that
>> can be called to obtain its value.
>>
>> Cheers,
>> Greg
>>
>> _______________________________________________