On Mon, 13 Aug 2012 07:37:48 +0200, Shakthi Kannan wrote:

Hi,

--- On Mon, Aug 13, 2012 at 10:51 AM, Christopher Howard wrote: | Say, for example, I have the list | [[1,2],[3,4]] and want to add 1 to each inner element, resulting in | [[2,3],[4,5]]. \--

Like this?

ghci> let xxs = [[1,2], [3,4]]

ghci> [ [ x+1 | x <- xs] | xs <- xxs ] [[2,3],[4,5]]

Or this?

map (map (+ 1)) [[1,2], [3,4]] [[2,3],[4,5]]

Regards, Henk-Jan van Tuyl -- http://Van.Tuyl.eu/ http://members.chello.nl/hjgtuyl/tourdemonad.html Haskell programming --

Equally, let map' = map . map map' (+1) . map (++[3]) $ [[1,2],[3,4]] -- [[2,3,4],[4,5,4]] And you can really keep stacking those up. I think this approach will be cleaner in the long run. For instance, let's start naming our parts. let list = [[1,2],[3,4]] let map' = map . map let addOne = map' (+1) let appendThree = map (++[3]) let reverseInner = map reverse So, from here we can do the following: list -- [[1,2],[3,4]] -- the first example addOne list -- [[2,3],[4,5]] -- now the second example addOne . appendThree $ list -- [[2,3,4],[4,5,4]] -- now add one to all members of the list, append three to the list, reverse the inner lists, -- then add one to all members of the new list addOne . reverseInner . appendThree . addOne $ list -- [[4,4,3],[4,6,5]] Now how would you construct that as a list comprehension? With the method I've proposed, you need only use map to operate on the nested lists themselves and map' to operate on the elements of those lists. ==== Jack Henahan jhenahan@uvm.edu On Aug 13, 2012, at 6:41 PM, Christopher Howard wrote:

On 08/12/2012 09:37 PM, Shakthi Kannan wrote:

...

Hi,

--- On Mon, Aug 13, 2012 at 10:51 AM, Christopher Howard wrote: | Say, for example, I have the list | [[1,2],[3,4]] and want to add 1 to each inner element, resulting in | [[2,3],[4,5]]. \--

Like this?

ghci> let xxs = [[1,2], [3,4]]

ghci> [ [ x+1 | x <- xs] | xs <- xxs ] [[2,3],[4,5]]

SK

Thanks everyone for the responses. I found the list comprehension approach satisfactory, as it allows me to cleanly modify each layer of the nested array as I unwrap it:

code: -------- b = [[ x+1 | x <- xs ++ [3] ] | xs <- [[1,2],[3,4]] ]

*Main> b [[2,3,4],[4,5,4]] --------

The only downside is that I have to write the layers out in reverse of the way I would normally think of them, but that isn't too big of a challenge.

I'm not sure how that would be done with map in a way that would be neat and readable and wouldn't require declaring extra identifiers. I can't give a fair evaluation of the Lens approach because I don't understand enough of the theory yet.

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There is a way. Please try to figure it out and if you fail post back with your code and we can help you from there. On Tue, Aug 14, 2012 at 11:05 AM, Carlos J. G. Duarte < carlos.j.g.duarte@gmail.com> wrote:

Ok, you all have been showing examples of running functions over elements. Add one, append value, and so on. This works well if there's one or more operations to apply indistinctly to a number of elements.

Now, what if we just want to make a single operation to a single element? For example, let's say I have this square matrix [[1,2,3], [4,5,6], [7,8,9]]

how can we increment the value 5 (position 2,2) *and* decrement the value 7 (position 3,1)?

This is a made up example of course, I just want to see / learn if there's a way to apply a function to a specific subset of elements.

On 08/14/12 00:06, Jack Henahan wrote:

...

Equally,

let map' = map . map map' (+1) . map (++[3]) $ [[1,2],[3,4]] -- [[2,3,4],[4,5,4]]

And you can really keep stacking those up. I think this approach will be cleaner in the long run.

For instance, let's start naming our parts. let list = [[1,2],[3,4]] let map' = map . map let addOne = map' (+1) let appendThree = map (++[3]) let reverseInner = map reverse

So, from here we can do the following: list -- [[1,2],[3,4]]

-- the first example addOne list -- [[2,3],[4,5]] -- now the second example addOne . appendThree $ list -- [[2,3,4],[4,5,4]]

-- now add one to all members of the list, append three to the list, reverse the inner lists, -- then add one to all members of the new list

addOne . reverseInner . appendThree . addOne $ list -- [[4,4,3],[4,6,5]]

Now how would you construct that as a list comprehension? With the method I've proposed, you need only use map to operate on the nested lists themselves and map' to operate on the elements of those lists.

==== Jack Henahan jhenahan@uvm.edu

On Aug 13, 2012, at 6:41 PM, Christopher Howard > wrote:

On 08/12/2012 09:37 PM, Shakthi Kannan wrote:

...

...

Hi,

--- On Mon, Aug 13, 2012 at 10:51 AM, Christopher Howard > wrote: | Say, for example, I have the list | [[1,2],[3,4]] and want to add 1 to each inner element, resulting in | [[2,3],[4,5]]. \--

Like this?

ghci> let xxs = [[1,2], [3,4]]

ghci> [ [ x+1 | x <- xs] | xs <- xxs ] [[2,3],[4,5]]

SK

Thanks everyone for the responses. I found the list comprehension approach satisfactory, as it allows me to cleanly modify each layer of the nested array as I unwrap it:

code: -------- b = [[ x+1 | x <- xs ++ [3] ] | xs <- [[1,2],[3,4]] ]

*Main> b [[2,3,4],[4,5,4]] --------

The only downside is that I have to write the layers out in reverse of the way I would normally think of them, but that isn't too big of a challenge.

I'm not sure how that would be done with map in a way that would be neat and readable and wouldn't require declaring extra identifiers. I can't give a fair evaluation of the Lens approach because I don't understand enough of the theory yet.

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This is a bit more "functional". The coordinates are the opposite way around, and it can probably be expressed a bit more concisely, but I'll leave that to you. This is the basic idea. -- maps over a list supplying also the 'index' mapi f = map (uncurry f) . zip [0..] -- maps over a list supplying also the coordinate pair mapii f a = mapi f' a where f' i x = mapi (curry f $ i) x m0 = [[1,2,3], [4,5,6], [7,8,9]] f (1,1) a = a+1 f (0,2) a = a-1 f (_,_) a = a mapii f m0 -- [[1,2,3],[4,6,6],[6,8,9]] Peter On 14 August 2012 22:50, Carlos J. G. Duarte wrote:

I know it's doable. I was asking if there's a practical / elegant way to do it. I see a lot of Haskell elegance when the matter is defining math formulas, running functions over elements, and so on. But it seems most of that elegance goes away when the problem derails a bit.

Now for my problem I come up with this:

modify mat x y f = let (lrows, row, rrows) = getpart mat x (lcols, col, rcols) = getpart row y in lrows ++ [lcols ++ [f col] ++ rcols] ++ rrows where getpart xs x = let (ls, r:rs) = splitAt x xs in (ls, r, rs)

m0 = [[1,2,3], [4,5,6], [7,8,9]]

main = do print m0 let m1 = modify m0 1 1 succ let m2 = modify m1 2 0 pred print m2

Which is a bit "awkward" considering the ease it is done in other languages.

On 08/14/12 19:35, Tim Perry wrote:

There is a way. Please try to figure it out and if you fail post back with your code and we can help you from there.

On Tue, Aug 14, 2012 at 11:05 AM, Carlos J. G. Duarte wrote:

...

Ok, you all have been showing examples of running functions over elements. Add one, append value, and so on. This works well if there's one or more operations to apply indistinctly to a number of elements.

Now, what if we just want to make a single operation to a single element? For example, let's say I have this square matrix [[1,2,3], [4,5,6], [7,8,9]]

how can we increment the value 5 (position 2,2) *and* decrement the value 7 (position 3,1)?

This is a made up example of course, I just want to see / learn if there's a way to apply a function to a specific subset of elements.

On 08/14/12 00:06, Jack Henahan wrote:

...

Equally,

let map' = map . map map' (+1) . map (++[3]) $ [[1,2],[3,4]] -- [[2,3,4],[4,5,4]]

And you can really keep stacking those up. I think this approach will be cleaner in the long run.

For instance, let's start naming our parts. let list = [[1,2],[3,4]] let map' = map . map let addOne = map' (+1) let appendThree = map (++[3]) let reverseInner = map reverse

So, from here we can do the following: list -- [[1,2],[3,4]]

-- the first example addOne list -- [[2,3],[4,5]] -- now the second example addOne . appendThree $ list -- [[2,3,4],[4,5,4]]

-- now add one to all members of the list, append three to the list, reverse the inner lists, -- then add one to all members of the new list

addOne . reverseInner . appendThree . addOne $ list -- [[4,4,3],[4,6,5]]

Now how would you construct that as a list comprehension? With the method I've proposed, you need only use map to operate on the nested lists themselves and map' to operate on the elements of those lists.

==== Jack Henahan jhenahan@uvm.edu

On Aug 13, 2012, at 6:41 PM, Christopher Howard wrote:

...

On 08/12/2012 09:37 PM, Shakthi Kannan wrote:

...

Hi,

--- On Mon, Aug 13, 2012 at 10:51 AM, Christopher Howard wrote: | Say, for example, I have the list | [[1,2],[3,4]] and want to add 1 to each inner element, resulting in | [[2,3],[4,5]]. \--

Like this?

ghci> let xxs = [[1,2], [3,4]]

ghci> [ [ x+1 | x <- xs] | xs <- xxs ] [[2,3],[4,5]]

SK

Thanks everyone for the responses. I found the list comprehension approach satisfactory, as it allows me to cleanly modify each layer of the nested array as I unwrap it:

code: -------- b = [[ x+1 | x <- xs ++ [3] ] | xs <- [[1,2],[3,4]] ]

*Main> b [[2,3,4],[4,5,4]] --------

The only downside is that I have to write the layers out in reverse of the way I would normally think of them, but that isn't too big of a challenge.

I'm not sure how that would be done with map in a way that would be neat and readable and wouldn't require declaring extra identifiers. I can't give a fair evaluation of the Lens approach because I don't understand enough of the theory yet.

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On Mon, 13 Aug 2012, Jay Sulzberger wrote:

On Sun, 12 Aug 2012, Christopher Howard wrote:

...

Hi. Is the some generic, clean syntax to unwrap a nested list, modify the value, and put it back together? Say, for example, I have the list [[1,2],[3,4]] and want to add 1 to each inner element, resulting in [[2,3],[4,5]].

I think there is a forgetful functor from a part of Haskell to Scheme, and this code lies in the image of this functor:

...

(define map-1+ (lambda (l) (map (lambda (n) (+ 1 n)) l))) #<unspecified> (map-1+ (list 0 1 2 3 4)) (1 2 3 4 5) (define map-map-1+ (lambda (l-of-l-of-numbers) (map map-1+ l-of-l-of-numbers))) #<unspecified> (map-map-1+ (list (list 1 2) (list 3 4))) ((2 3) (4 5)) (quit)

Process scheme finished

Further we have for this forgetful functor, that the original Haskell code and the transformed-to-Scheme code have the "same" running behavior, and the "same" input output behavior. And under this functor the image of the object called "map" in Haskell is the object called "map" in Scheme.

Haskell has map in the prelude:

map :: (a -> b) -> [a] -> [b]

map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]

Above quote taken from

http://www.haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html

So, likely, I do not know Haskell, something like:

m1 = map 1+ l m2 = map m1 l

Ah, above likely wrong. OK, what about m1 l = map 1+ l m2 l = map m1 l or perhaps m1 = map 1+ m2 = map m1 oo--JS.

should work. Likely a bit more source code might be required for various Haskell systems. And the procedure 1+ might have to be defined, up to getting the right type of number specified, as

1+ n = (n + 1)

oo--JS.

...

After reading about the list monad, I was rather excited, because I (mistakenly) thought something like this would work:

code: -------- a = do b <- [[1,2],[3,4]] c <- b return (c + 1) --------

That would be awesome, because I would be able to modify the list at each level of unwrapping, while leaving the code very neat and readable. However, what the above example actually does is produce a /single/ list from the values:

code: -------- *Main> a [2,3,4,5] --------

Obviously wishing won't change how the list monad works, but I thought it might be worth asking if there is some other monad or syntactic trick that does something along the lines of what I am looking for.

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