Parse error in pattern: xs - understanding - haskell

i have the following two functions in haskell:
plusList :: [[Int]] -> [Int]
plusList [xs ys] = add xs + plusList [ys]
plusList [[]] = 0
add::[Int] -> Int
add (x:xs) = x + add xs
add [] = 0
so, i think i have the error in plusList [xs ys] = add xs + plusList ys
My idea was to go through the set of the sets, namely [[Int]], by taking the first List xs, apply "add" on it and after that, call the second list ys recursively with "plusList ys"
I am new in haskell, can I do that? And if no, why?

You can certainly do what you want in Haskell, but your syntax is wrong. Your add function is correct, but plusList is not. In particular, the syntax [xs ys] makes no sense as a pattern to Haskell, you probably want
plusList (xs:ys) = add xs + plusList ys
Notice how this is exactly the same pattern as with add? Although, from your type signature it's hard to tell what exactly you want. The type says return a list of Int, but your function body says to just return an Int. If you want the former, you can achieve it with
plusList (xs:ys) = add xs : plusList ys
But this is exactly map add! If instead you want the latter, use the first snippet from above.
The second problem you have is
plusList [[]] = 0
This is a perfectly valid and legal line of Haskell code, but it won't do what you want. You see, there's a difference between [] :: [[Int]] and [[]] :: [[Int]]. The first is an empty list of lists of Ints, the second is a list containing an empty lists of Ints. If you run length ([] :: [[Int]]), you'll get 0, but for length ([[]] :: [[Int]]) you'll get 1!. Instead, just do
plusList [] = 0
Again, this is exactly like the pattern in add. If you want plusList to return [Int] instead, this line should just be
plusList [] = []
So the two versions we have are
plusList :: [[Int]] -> Int
plusList (xs:ys) = add xs + plusList ys
plusList [] = 0
And
plusList :: [[Int]] -> [Int]
plusList (xs:ys) = add xs : plusList ys
plusList [] = []
-- or just
-- plusList xs = map add xs
There is an easier way to do this, though. Firstly, add is merely the built-in sum function but specialized to Ints. However, the built-in sum is not very efficient due to the fact that it uses foldl. Instead, you can implement a faster variant with
add :: [Int] -> [Int]
add xs = foldr (+) 0 xs
The foldr and foldl functions generalize the kind of recursion you have used, since it is such a common pattern in functional programming. Instead of operating on the entire list, you provide a function for combining the next value and an accumulator together, an initial accumulator value, and the values to accumulate. In your case, the accumulator has the same type as your values, which is pretty common. The difference between foldl and foldr is subtle, their implementations look pretty similar, but Haskell's laziness means that foldl can have space leaks and efficiency problems (there's plenty of explanations out there as to why, look it up when you get there).
Additionally, if you want to sum a list of lists, you can do it using higher order functions with simply
plusList = add . map add
Nothing extra is needed, no patterns to match, much less syntax to get wrong.

Related

How to turn this recursive function into a list comprehension?

I've made a function that interchanges the elements of two lists in turn and it works recursively.
change :: [a] -> [a] -> [a]
change [] ys = ys
change xs [] = xs
change (x:xs) (y:ys) = x : y : change xs ys
Now this works fine but I am having difficulty with turning it into list comprehension. I want to do that to practice Haskell and it was just one of the questions I found.
You could do something like this:
change xs ys = [v | vs <- transpose [xs, ys], v <- vs]
But I wouldn't. That's a very confusing way to write this function -- and anyway, you haven't really converted manual recursion into a list comprehension this way, you've just shoved the manual recursion into transpose.

Intermediate value in simple Haskell function

I need a function to double every other number in a list. This does the trick:
doubleEveryOther :: [Integer] -> [Integer]
doubleEveryOther [] = []
doubleEveryOther (x:[]) = [x]
doubleEveryOther (x:(y:zs)) = x : 2 * y : doubleEveryOther zs
However, the catch is that I need to double every other number starting from the right - so if the length of the list is even, the first one will be doubled, etc.
I understand that in Haskell it's tricky to operate on lists backwards, so my plan was to reverse the list, apply my function, then output the reverse again. I have a reverseList function:
reverseList :: [Integer] -> [Integer]
reverseList [] = []
reverseList xs = last xs : reverseList (init xs)
But I'm not quite sure how to implant it inside my original function. I got to something like this:
doubleEveryOther :: [Integer] -> [Integer]
doubleEveryOther [] = []
doubleEveryOther (x:[]) = [x]
doubleEveryOther (x:(y:zs)) =
| rev_list = reverseList (x:(y:zs))
| rev_list = [2 * x, y] ++ doubleEveryOther zs
I'm not exactly sure of the syntax of a function that includes intermediate values like this.
In case it's relevant, this is for Exercise 2 in CIS 194 HW 1.
This is a very simple combination of the two functions you've already created:
doubleEveryOtherFromRight = reverseList . doubleEveryOther . reverseList
Note that your reverseList is actually already defined in the standard Prelude as reverse. so you didn't need to define it yourself.
I'm aware that the above solution isn't very efficient, because both uses of reverse need to pass through the entire list. I'll leave it to others to suggest more efficient versions, but hopefully this illustrates the power of function composition to build more complex computations out of simpler ones.
As Lorenzo points out, you can make one pass to determine if the list has an odd or even length, then a second pass to actually construct the new list. It might be simpler, though, to separate the two tasks.
doubleFromRight ls = zipWith ($) (cycle fs) ls -- [f0 ls0, f1 ls1, f2 ls2, ...]
where fs = if odd (length ls)
then [(*2), id]
else [id, (*2)]
So how does this work? First, we observe that to create the final result, we need to apply one of two function (id or (*2)) to each element of ls. zipWith can do that if we have a list of appropriate functions. The interesting part of its definition is basically
zipWith f (x:xs) (y:ys) = f x y : zipWith f xs ys
When f is ($), we're just applying a function from one list to the corresponding element in the other list.
We want to zip ls with an infinite alternating list of id and (*2). The question is, which function should that list start with? It should always end with (*2), so the starting item is determined by the length of ls. An odd-length requires us to start with (*2); an even one, id.
Most of the other solutions show you how to either use the building blocks you already have or building blocks available in the standard library to build your function. I think it's also instructive to see how you might build it from scratch, so in this answer I discuss one idea for that.
Here's the plan: we're going to walk all the way to the end of the list, then walk back to the front. We'll build our new list during our walk back from the end. The way we'll build it as we walk back is by alternating between (multiplicative) factors of 1 and 2, multiplying our current element by our current factor and then swapping factors for the next step. At the end we'll return both the final factor and the new list. So:
doubleFromRight_ :: Num a => [a] -> (a, [a])
doubleFromRight_ [] = (1, [])
doubleFromRight_ (x:xs) =
-- not at the end yet, keep walking
let (factor, xs') = doubleFromRight_ xs
-- on our way back to the front now
in (3-factor, factor*x:xs')
If you like, you can write a small wrapper that throws away the factor at the end.
doubleFromRight :: Num a => [a] -> [a]
doubleFromRight = snd . doubleFromRight_
In ghci:
> doubleFromRight [1..5]
[1,4,3,8,5]
> doubleFromRight [1..6]
[2,2,6,4,10,6]
Modern practice would be to hide the helper function doubleFromRight_ inside a where block in doubleFromRight; and since the slightly modified name doesn't actually tell you anything new, we'll use the community standard name internally. Those two changes might land you here:
doubleFromRight :: Num a => [a] -> [a]
doubleFromRight = snd . go where
go [] = (1, [])
go (x:xs) = let (factor, xs') = go xs in (3-factor, factor*x:xs')
An advanced Haskeller might then notice that go fits into the shape of a fold and write this:
doubleFromRight :: Num a => [a] -> [a]
doubleFromRight = snd . foldr (\x (factor, xs) -> (3-factor, factor*x:xs)) (1,[])
But I think it's perfectly fine in this case to stop one step earlier with the explicit recursion; it may even be more readable in this case!
If we really want to avoid calculating the length, we can define
doubleFromRight :: Num a => [a] -> [a]
doubleFromRight xs = zipWith ($)
(foldl' (\a _ -> drop 1 a) (cycle [(2*), id]) xs)
xs
This pairs up the input list with the cycled infinite list of functions, [(*2), id, (*2), id, .... ]. then it skips along them both. when the first list is finished, the second is in the appropriate state to be - again - applied, pairwise, - on the second! This time, for real.
So in effect it does measure the length (of course), it just doesn't count in integers but in the list elements so to speak.
If the length of the list is even, the first element will be doubled, otherwise the second, as you've specified in the question:
> doubleFromRight [1..4]
[2,2,6,4]
> doubleFromRight [1..5]
[1,4,3,8,5]
The foldl' function processes the list left-to-right. Its type is
foldl' :: (b -> a -> b) -> b -> [a] -> b
-- reducer_func acc xs result
Whenever you have to work on consecutive terms in a list, zip with a list comprehension is an easy way to go. It takes two lists and returns a list of tuples, so you can either zip the list with its tail or make it indexed. What i mean is
doubleFromRight :: [Int] -> [Int]
doubleFromRight ls = [if (odd i == oddness) then 2*x else x | (i,x) <- zip [1..] ls]
where
oddness = odd . length $ ls
This way you count every element, starting from 1 and if the index has the same parity as the last element in the list (both odd or both even), then you double the element, else you leave it as is.
I am not 100% sure this is more efficient, though, if anyone could point it out in the comments that would be great

Recursion with Maybe

I'm having difficulty try to write a function to find the sum of two lists using recursion, that possibly could be Nothing if any list is empty.
The math of the following functions are:
Σw[i]x[i]
where w and x are equal length int arrays
Here is my working code:
example :: [Int] -> [Int] -> Int
example [] [] = 0
example (x:xs) (l:ls) = ((x*l) + (example xs ls))
Here is the idea of what I want to work:
example :: [Int] -> [Int] -> Maybe Int
example [] [] = Nothing
example (x:xs) (l:ls) = Just((x*l) + (example xs ls))
Thanks
I'm guessing at what your intent is here, not sure whether I read it correctly: You want the function to produce Nothing when the two input lists have difference lengths?
The "happy" base case is 0 just like in the first attempt, but lifted into Maybe.
example [] [] = Just 0
To handle situations where the lists have different lengths, include the cases where only one of the lists is empty. You should have gotten a compiler warning about a non-exhaustive pattern match for not including these cases.
example [] _ = Nothing
example _ [] = Nothing
The final case, then, is where you have two nonempty lists. It looks a lot like that line from your first attempt, except rather than applying the addition directly to example xs ys, we fmap the addition over example xs ys, taking advantage of the fact that Maybe is a Functor.
example (x : xs) (y : ys) = fmap (x * y +) (example xs ys)
Example usage:
λ> example [1,2] [3,4]
Just 11
λ> example [1,2] [3,4,5]
Nothing
By the way, if you wanted to use a library this, safe would be a nice choice to turn this into a one-liner.
import Safe.Exact
example xs ys = fmap sum (zipWithExactMay (*) xs ys)
You're close, but your recursive call to example xs ls returns a Maybe Int, and you can't add an Int and a Maybe Int (in x*l + example xs ls), hence your error on the last line.
You can use fromMaybe to deal with this case, using 0 as the default sum:
example :: [Int] -> [Int] -> Maybe Int
example [] [] = Nothing
example (x:xs) (l:ls) = Just $ x * l + fromMaybe 0 (example xs ls)
Alternatively (and more neatly), you can avoid the explicit recursion using something like this:
example [] [] = Nothing
example xl yl = Just $ sum $ zipWith (*) xl yl
Note that you have non-exhaustive patterns in your pattern match. Two lists of different lengths will cause a pattern-match exception.

Haskell's span function

I'm relatively new to Haskell and I'm struggling to figure out a way to implement Haskell's span function. However, my problem is more general than that in that I don't know how to make a function return a list of lists or list of tuples containing the elements I want. My problem with a list of lists such as:
[[1],[2]]
is that I can't make the function add an element to the first list in the list of lists. I only know how to append another list to the list of lists.
In short, if you explain to me how to implement the span function, this all should hopefully come clear to me.
So I think what you're saying is that you know how to recursively append to a list by doing something like
foobar :: [x] -> [y]
foobar ( []) = []
foobar (x:xs) = {- ...stuff... -} : foobar xs
but you have no idea how to do that with two lists:
foobar :: [x] -> ([y], [z])
foobar (x:xs) = ???
In general, when the result isn't a list, but something that contains a list, you end up doing something like this:
foobar :: [x] -> ([y], [z])
foobar (x:xs) =
let
y = {- whatever -}
z = {- whatever -}
(ys, zs) = foobar xs -- The recursive call
in (y:ys, z:zs)
The same applies if, say, the result is a monadic action
foobar :: [x] -> IO [y]
foobar (x:xs) = do
y <- {- whatever -}
ys <- foobar xs
return (y:ys)
Note that this forces the function to not be lazy.
The general pattern I think you'll want to use here is the following:
span :: (a -> Bool) -> [a] -> ([a], [a])
span pred [] = ([], [])
span pred (x:xs) = if pred x then _ else _ -- fill in the blanks
where (prefix', suffix') = span pred xs
There are two non-obvious things there. First, note the pattern match in the where condition. This means that we're:
Calling span pred xs, which produces a pair of lists;
Pattern matching on this pair;
Naming the first and second element of the pair prefix' and suffix' respectively.
I suspect that step #2, the pattern match on the result of the recursive call, is something you might not have understood.
The second non-obvious thing is recursion. It's a tricky thing because, counterintutively, to solve a problem with recursion you need to assume that you've already solved it, but for the "wrong" argument--a tough step to picture yourself taking if you haven't solved it yet! But the trick is this:
Imagine you've actually already solved the problem, but for the tail of the list. That's what the prefix' and suffix' variables contain: a correct solution but for the wrong list--the tail of the one you're actually trying to solve for.
Given that (non)solution, how could you reuse it to arrive at a correct solution for your problem?

Learning Haskell: confusion with reverse function and recursion

I've just started to learn Haskell and I am trying to write a simple function that takes a list of strings and reverses each string in the list:
revComp :: [String] -> [String]
revComp [] = []
revComp [x] = [] ++ [reverse x]
revComp (x:xs) = revComp [xs]
When I try to load my code in GHCI, I get an error:
Couldn't match expected type `Char' with actual type `[Char]'
Expected type: String
Actual type: [String]
Could anyone explain what and where my problem is? Thanks very much.
The first three lines are fine. Your type signature is correct, the second line is correct, and so is the third. (However, [] ++ [reverse x] is the same as [reverse x].)
The fourth line, however, is wrong. Not only do you not use x at all on the right-hand side, but you have a type error: revComp [xs] calls revComp with a single-element list that has xs as its only element. Here, x is the first element of the list, and xs is the rest of the list. So, since xs has the type [String], [xs] has the type [[String]], but revComp takes a [String]! You want to reverse x, and prepend that to the result of reversing the rest of the list.
You can use revComp xs to reverse each string in the rest of the list, and (:) to prepend a value to a list (with the same syntax seen in the x:xs pattern you used on the left-hand side). That should be enough information for you to fix the last line. This makes the third line redundant, by the way, since [x] is just x:[].
ehird's answer is really complete, but I wanted to point out -- as a reference -- the "good/shorter" way to implement that function in real code, since you're new.
It can be defined as the partial application of map to reverse:
Prelude> let revComp = map reverse
Prelude> revComp ["olleh", "dlrow"]
["hello","world"]
It results in a function revComp :: [[a]] -> [[a]] (and not [String] -> [String] since both map and reverse work on any type of lists) that maps reverse to every element of the input list, returning the list of results.
The third line might not be required even with your example. The edge case (terminating condition) can be only the empty list. You can skip the condition for the single element.
revComp :: [String] -> [String]
revComp [] = []
revComp (x:xs) = reverse x : revComp xs
Don't know if there is a CS term for this. Someone in the community can add that information.
A few more ways to do the same thing:
revstr [] = []
revstr (x:xs) = reverse x : revstr xs
revstr2 [] = []
revstr2 (x:xs) = [reverse x] ++ revstr2 xs
revstr3 xs = map reverse xs
revstr4 = map reverse -- map takes 2 arguments ;)
revstr5 xs = foldl step [] xs
where step acc x = acc ++ [reverse x]
revstr6 xs = foldr step [] xs
where step x acc = reverse x : acc

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