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Today's Topics:
1. Infinite recursion in list comprehension (Dushyant Juneja)
2. Re: Infinite recursion in list comprehension (akash g)
3. Re: Infinite recursion in list comprehension (Dushyant Juneja)
4. Re: Double vs. Num (Ben Rogalski)
----------------------------------------------------------------------
Message: 1
Date: Thu, 05 May 2016 12:43:02 +0000
From: Dushyant Juneja <[email protected]>
To: [email protected]
Subject: [Haskell-beginners] Infinite recursion in list comprehension
Message-ID:
<cajkb0uolfxhmbbzvzhku7ee-lzb91+ps0kfb3wwh2vjmrc+...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
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?
Thanks in advance!
DJ
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Message: 2
Date: Thu, 5 May 2016 18:31:15 +0530
From: akash g <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Infinite recursion in list
comprehension
Message-ID:
<caliga_fchzpwlvfcohfdau7nt8xfj_myhidyipzip_knwsw...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
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 <[email protected]>
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?
>
> Thanks in advance!
>
> DJ
>
> _______________________________________________
> Beginners mailing list
> [email protected]
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
>
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Message: 3
Date: Thu, 05 May 2016 13:44:26 +0000
From: Dushyant Juneja <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Infinite recursion in list
comprehension
Message-ID:
<CAJkb0UM7bY7=ohohyj2hw+gu+ce1xylojjkg4sp4o1xpqk9...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
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 <[email protected]> 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 <[email protected]
> > 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?
>>
>> Thanks in advance!
>>
>> DJ
>>
>> _______________________________________________
>> Beginners mailing list
>> [email protected]
>> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>>
>>
> _______________________________________________
> Beginners mailing list
> [email protected]
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
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------------------------------
Message: 4
Date: Thu, 5 May 2016 10:10:45 -0400
From: Ben Rogalski <[email protected]>
To: [email protected]
Subject: Re: [Haskell-beginners] Double vs. Num
Message-ID:
<cal-j+nkyicvf6omsa+hc6epyqna-0ea+wxi8tduqtkjyy+e...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Tim and Christopher, here is my code. There is a lot of it, but I've tried
to cut out the irrelevent parts.
If I change the type of Transform3D.append from
append :: (Floating a) => Transformer a -> Transform a -> Transformer a
to
append :: Transformer Double -> Transform Double -> Transformer Double
The framerate goes from ~1400 fps to ~2200 fps.
module Render where
...
renderTree :: GLInfo -> Tree (Attribute Double) -> IO ()
renderTree (GLInfo names attribs uniforms) t = fst $ cFold2 f (return
(),identity) t
where f acc Hidden = Skip acc
f (a,tr) (Transformation t) = Continue (a, append tr t)
f (a,tr) (Clip b) =
let (x1:.y1:._, x2:.y2:._) = extremes $ applyAABB tr b
a' = do
glUniform2f (uniforms M.! "maskMin") (realToFrac x1)
(realToFrac y1)
glUniform2f (uniforms M.! "maskMax") (realToFrac x2)
(realToFrac y2)
in Continue (a >> a', tr)
f (a,tr) (Texture _ (x1:.y1:.x2:.y2:._)) =
let a' = do
glUniform1i (uniforms M.! "texSampler") 0
glUniform4f (uniforms M.! "uvCoords") (realToFrac x1)
(realToFrac y1) (realToFrac x2) (realToFrac y2)
glUniformMatrix4fv' (uniforms M.! "mvp") 1 (fromBool False)
(map realToFrac $ transformerToList tr)
glDrawElements gl_TRIANGLES (fromIntegral $ attribs M.!
"iboLenSquare") gl_UNSIGNED_INT nullPtr
in Continue (a >> a', tr)
f acc _ = Continue acc
...
module Transform3D where
...
data Transform a =
RotationZ a
| Scale (Vec3 a)
| Translation (Vec3 a) deriving (Eq, Read, Show)
newtype Transformer a = Transformer (Vec4 (Vec4 a))
append :: (Floating a) => Transformer a -> Transform a -> Transformer a
append (Transformer m) t = Transformer $ m #*# toMatrix t
identity :: (Num a) => Transformer a
identity = Transformer identityMatrix
toMatrix :: (Floating a) => Transform a -> Vec4 (Vec4 a)
toMatrix (RotationZ z) = rotationZMatrix z
toMatrix (Scale (x:.y:.z:._)) = scaleMatrix x y z
toMatrix (Translation (x:.y:.z:._)) = translationMatrix x y z
identityMatrix :: (Num a) => Vec4 (Vec4 a)
identityMatrix =
(1:.0:.0:.0:.Nil):.
(0:.1:.0:.0:.Nil):.
(0:.0:.1:.0:.Nil):.
(0:.0:.0:.1:.Nil):.Nil
rotationZMatrix :: (Floating a) => a -> Vec4 (Vec4 a)
rotationZMatrix a =
let c = cos a
s = sin a
in (c:.(-s):.0:.0:.Nil):.
(s:.c:.0:.0:.Nil):.
(0:.0:.1:.0:.Nil):.
(0:.0:.0:.1:.Nil):.Nil
scaleMatrix :: (Num a) => a -> a -> a -> Vec4 (Vec4 a)
scaleMatrix x y z =
(x:.0:.0:.0:.Nil):.
(0:.y:.0:.0:.Nil):.
(0:.0:.z:.0:.Nil):.
(0:.0:.0:.1:.Nil):.Nil
translationMatrix :: (Num a) => a -> a -> a -> Vec4 (Vec4 a)
translationMatrix x y z =
(1:.0:.0:.x:.Nil):.
(0:.1:.0:.y:.Nil):.
(0:.0:.1:.z:.Nil):.
(0:.0:.0:.1:.Nil):.Nil
...
module Vector where
...
infixr 5 :.
--data Cons u t = (:.) t (u t) deriving (Eq, Read, Show)
data Cons u t = (:.) ! t ! (u t) deriving (Eq, Read, Show)
data Nil t = Nil deriving (Eq, Read, Show)
...
(|*#) :: (Num t, Vector w, Vector u) => w t -> w (u t) -> u t
(|*#) v m = (transpose m) #*| v
(#*#) :: (Num t, Vector u, Vector v, Vector w) => u (v t) -> v (w t) -> u
(w t)
(#*#) x y = transpose $ fmap (x #*|) (transpose y)
dot :: (Num t, Vector v) => v t -> v t -> t
dot xs ys = sum ((*) <$> xs <*> ys)
...
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