# [Haskell-beginners] Infinite recursion in list comprehension

Silent Leaf silent.leaf0 at gmail.com
Thu May 5 18:10:29 UTC 2016

```Implicitly, primesBelow shouldn't ever in fact call itself, not as it is
articulated here **at the very least**, not without wasting a lot of
calculus.

As it is, and maybe no matter what (i'm not sure, don't have the knowledge
to certify that), when primesBelow checks if a value "v" is prime or not,
well no matter what it'll already have calculated and stored all primes
below this value n (this, according to how primesBelow is articulated, aka
filtering of Naturals bottom-top).

Thus, if for each potential element "v" of the result (in my version,
"list") of primesBelow, you call once again primesBelow, asking it to
generate again all primes below sqrt(v), you'll do nothing more than doing
again what you already did, because all those previous primes have already
been generated, stored away, and especially very accessible, in the
list-result in-construction of the **current** call to primesBelow, so if
you don't use it but call again primesBelow to get a copy of what you
already have, you'll multiply immensely the work without any gain.
That's why I named the very result of primesBelow, to get a way to use
"list" (the previously generated items of the future result-list) in
"checker".

2016-05-05 15:44 GMT+02:00 Dushyant Juneja <juneja.dushyant at gmail.com>:

> Hi Akash,
>
> Thanks for the response. A very simple and lucid explanation. Looks
> interesting.
>
> So, here's the big picture now, for which I need this. I intend to
> implement a lookalike Sieve of Eratosthenes algorithm in haskell. For this,
> I intend to use the earlier function recursively, as follows:
>
> primesBelowN :: Integer -> [Integer]
> primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1, 1]]
>                      where f x = foldr g True xs
>                                  where g t ac = (x `rem` t /= 0) && ac
>                                        xs = [ m | m <- primesBelowN n, m
> <= (truncate (sqrt (fromInteger x)))]
>
> Of course, I could do something like this:
>
> primesBelowN :: Integer -> [Integer]
> primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1, 1]]
>                      where f x = foldr g True xs
>                                  where g t ac = (x `rem` t /= 0) && ac
>                                        xs = [ m | m <- primesBelowN (truncate
> (sqrt (fromInteger x)))]
>
> However, this calls primesBelowN function with a new argument everytime. I
> suppose that is not optimal (correct me if I am wrong).
>
> Point number 2: both fail. Grrh.
>
> Any ideas how I could go recursive with this function?
>
> Dushyant
>
>
> On Thu, May 5, 2016 at 6:31 PM akash g <akaberto at gmail.com> wrote:
>
>> Hi Dushyant,
>>
>> The problem most likely is
>> [m | m <- [5,7..], m <= (truncate (sqrt (fromInteger x)))]
>>
>>  This is because, the filter condition (the last part) does a very simple
>> thing:  It filters out any element that does not fulfil the criteria.  You
>> are operating on a list that is monotonically increasing.  However, the
>> filter isn't aware of this property.  Hence, this list comprehension never
>> ends because it doesn't know that once the condition fails, it will always
>> fail.
>>
>> Thus, the solution would be to generate a finite set (or take a part of
>> the infinite set using takeWhile or something like that), instead of using
>> an infinite one.
>>
>> Regards,
>> G Akash.
>>
>> On Thu, May 5, 2016 at 6:13 PM, Dushyant Juneja <
>> juneja.dushyant at gmail.com> wrote:
>>
>>> Hi,
>>>
>>> I seem to be landing into infinite recursion when using higher order
>>> functions with list comprehension. Take this for an example. The following
>>> works well, and gives answers for numbers like 2000000 as well:
>>>
>>> primesBelowN :: Integer -> [Integer]
>>> primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1,
>>> 1]]
>>>                      where f x = foldr g True xs
>>>                                  where g t ac = (x `rem` t /= 0) && ac
>>>                                        xs = [5, 7..(truncate (sqrt
>>> (fromInteger x)))]
>>>
>>>
>>> However, the following never returns anything for the same number,
>>> probably due to some kind of loop malfunction:
>>>
>>> primesBelowN :: Integer -> [Integer]
>>> primesBelowN n = 2:3:filter f [6*k+i | k <- [1..(n-1)`div`6], i <- [-1,
>>> 1]]
>>>                      where f x = foldr g True xs
>>>                                  where g t ac = (x `rem` t /= 0) && ac
>>>                                        xs = [ m | m <- [5, 7, ..], m <= (truncate
>>> (sqrt (fromInteger x)))]
>>>
>>> Any ideas what might be going wrong?
>>>
>>>
>>> DJ
>>>
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