Michael Mossey mpm at alumni.caltech.edu
Fri Jul 9 00:59:03 EDT 2010

```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
>
> _______________________________________________