I tried to make a very short code, because we have a reglementation that favors the shortest code.
We have to create a function that turns a list into a new list of ascending and descending lists in the same order: For example. [1,6,2,1,7,3,2,8,4], becomes [[1,6],[2,1],[7],[3,2],[8],[4]]
So i tried to do the following:
func :: Ord a => [a] -> [[a]]
func xs = f1 d [a]
f1 [] ys = [c]
f1 xs ys | a >= b = d `f1` a:ys
| otherwise = c: d `f2` [a]
f2 [] ys = [c]
f2 xs ys | a < b = d `f2` a:ys
| otherwise = c : d `f1` [a]
where a = head xs
b = head ys
c = reverse ys
d = tail xs
But i get
parse error on input '='
on the line "b = head ys".
I thought it is possible to define multiple functions in the where block?
Other indentations created errors like a lot of
not in scope 'a'
not in scope 'b'
not in scope 'c'
not in scope 'd'
or
parse error on input 'b'
I have to make it that way to save some tokens/ have shorter code.
That's how it looks to the compiler:
func :: Ord a => [a] -> [[a]]
func xs = f1 d [a]
f1 [] ys = [c]
f1 xs ys | a >= b = d `f1` a:ys
| otherwise = c: d `f2` [a]
f2 [] ys = [c]
f2 xs ys | a < b = d `f2` a:ys
| otherwise = c : d `f1` [a]
where a = head xs
b = head ys
c = reverse ys
d = tail xs
So for the compiler, the lines in the where clause after the first look like continuations of that line, and of course you can't have multiple = without an intervening semicolon on one line.
You should never mix tabs and spaces (you shouldn't ever use tabs, actually). And if you use tabs, configure your editor to interpret them as eight spaces.
And, the where clause only scopes over the last equation, so there are no a, b, c, d in scope in the first four equations for func.
You have a more fundamental problem than indentation: a where block is local to a single function case. You're trying to use your where block to provide bindings (e.g. a, b, c, d) to a whole bunch of functions. This won't work.
To clarify, this correctly indented code won't work:
foo :: Int -> Int
foo 0 = a
foo 1 = b
where a = 2
b = 3
You'll get an error like Not in scope: `a'. This is because the where only extends over the foo 1 case; it doesn't even go to the foo 0 case, much less any other function.
Your code, on the other hand, seems to expect the where block to work for all your functions. To have bindings that can be seen by different functions, you have to put them at the same level of scope as the functions themselves.
Also, Haskell indentation is a little finnicky. You really should avoid tabs; it also really helps to have an editor that understands Haskell properly. I've found Emacs is very good here--I never have to worry about Haskell indentation with Emacs.
Emacs might have a bit of a learning curve (you should do the tutorial), but I think it's well worth it. You'll also have to install the Haskell mode. If you get the newest version of Emacs, you should be able to do this using the package manager.
Your error messages are because you're mixing tabs and spaces. It's best to just use spaces.
Now, if you're writing
a = head xs
b = head ys
c = reverse ys
d = tail xs
then
xs = (a:ds)
ys = (b:es)
Let's rewrite your function with pattern matching:
func :: Ord a => [a] -> [[a]]
func [] = []
func (a:ds) = f1 ds [a]
f1 [] ys = [reverse ys]
f1 (a:ds) (b:es) | a >= b = ds `f1` (a:b:es)
| otherwise = reverse (b:es): ds `f2` [a]
f2 [] ys = [reverse ys]
f2 (a:ds) (b:es) | a < b = ds `f2` (a:b:es)
| otherwise = reverse (b:es) : ds `f1` [a]
I know this is longer, but bear with me. f1 is really the same as f2, but with the comparison changed. Let's get a function no to negate a comparison, so that (no (>=)) x y = not (x >= y):
no cmp x y = not (cmp x y)
In fact, we can write this as
no = ((not.).)
r = reverse
func' (a:ds) = f (>=) ds [a]
f :: Ord a => (a -> a -> Bool) -> [a] -> [a] -> [[a]]
f _ [] ys = [r ys]
f cp (a:ds) ys#(b:es) | cp a b = f cp ds (a:ys)
| True = r ys : f (no cp) ds [a]
Now that is shorter.
Related
I am trying to create a function split that can take either [Int] and Int or [Char] Char to split either a list of integers on an integer given or split a string on a character given. I.e.
Main> split [1,2,3,0,4,5,0,0,7,8,9] 0
[[1,2,3],[4,5],[7,8,9]]
Main> split "Mary had a little lamb" ' '
["Mary","had","a","little","lamb"]
I've tried using Either and (Eq a) but it still doesn't seem to work. Below is what I've tried doing using class instances but I know very little about this and get the error Haskell 98 does not support multiple parameter classes.
The best way I think I'd understand it would be to use pattern matching or list comprehensions. Any help much appreciated.
class Split a where
split :: (Eq a) => [a] -> a -> [a]
instance Split [Char] Char where
split [] c = [""]
split (x:xs) c
| x == c = "" : (split xs c)
| otherwise = (x : head (split xs c)) : tail (split xs c)
instance Split [Int] Int where
split [] n = []
split (x:xs) n
| x == n = [] : (split xs n)
| otherwise = (x : head (split xs n)) : tail (split xs n)
I can get the split function to work with strings and characters but not lists of integers.
You need a polymorphic function split
split :: (Eq a) => [a]->a->[[a]]
Implementation is simple
split [] _ = [[]]
split (x:xs) c
| x == c = [] : (split xs c)
| otherwise = (x : head subSplit) : tail subSplit
where
subSplit = split xs c
EDIT
I suggest different implementation.
split :: Eq a => [a] -> a -> [[a]]
split x c = map reverse $ split' x c []
where
split' :: Eq a => [a] -> a -> [a] -> [[a]]
split' [] _ a = [a]
split' (x:xs) c a
| x == c = a : split' xs c []
| otherwise = split' xs c (x:a)
Just to contribute with an other approach. This solution uses foldr. I think it is quite neat but less undestable than #talex's
split :: (Eq a) => [a] -> a -> [[a]]
split l c = foldr f acc l
where acc = [[]]
f a t#(i#(x:_):xs) = if a == c then []:t else (a:i):xs -- Case when the current accumulator is not empty
-- | |- cons a to current accumulator
-- |- start a new accumulator
f a t#([]:xs) = if a == c then t else [a]:xs -- Case when the current accumulator is empty. Usefull when two separators are together
-- | |- cons a to current accumulator
-- |- Don't start a new accumulator, just continue with the current
Just correct solution.
split :: Eq a => [a] -> a -> [[a]]
split xs delim = go $ dropWhile (== delim) xs
where
go [] = []
go xs = let (tok, rest) = break (== delim) xs
in tok : go (dropWhile (== delim) rest)
Data.List.Split.splitOn (available from the split package) is close:
> splitOn [0] [1,2,3,0,4,5,0,0,7,8,9]
[[1,2,3],[4,5],[],[7,8,9]]
> splitOn " " "Mary had a little lamb"
["Mary","had","a","little","lamb"]
Your split :: Eq a => [a] -> a -> [[a]] would be
split lst d = filter (not.null) $ splitOn [d] lst
I would like to define a greaters function, which selects from a list items that are larger than the one before it.
For instance:
greaters [1,3,2,4,3,4,5] == [3,4,4,5]
greaters [5,10,6,11,7,12] == [10,11,12]
The definition I came up with is this :
greaters :: Ord a => [a] -> [a]
Things I tried so far:
greaters (x:xs) = group [ d | d <- xs, x < xs ]
Any tips?
We can derive a foldr-based solution by a series of re-writes starting from the hand-rolled recursive solution in the accepted answer:
greaters :: Ord a => [a] -> [a]
greaters [] = []
greaters (x:xs) = go x xs -- let's re-write this clause
where
go _ [] = []
go last (act:xs)
| last < act = act : go act xs
| otherwise = go act xs
greaters (x:xs) = go xs x -- swap the arguments
where
go [] _ = []
go (act:xs) last
| last < act = act : go xs act
| otherwise = go xs act
greaters (x:xs) = foldr g z xs x -- go ==> foldr g z
where
foldr g z [] _ = []
foldr g z (act:xs) last
| last < act = act : foldr g z xs act
| otherwise = foldr g z xs act
greaters (x:xs) = foldr g z xs x
where -- simplify according to
z _ = [] -- foldr's definition
g act (foldr g z xs) last
| last < act = act : foldr g z xs act
| otherwise = foldr g z xs act
Thus, with one last re-write of foldr g z xs ==> r,
greaters (x:xs) = foldr g z xs x
where
z = const []
g act r last
| last < act = act : r act
| otherwise = r act
The extra parameter serves as a state being passed forward as we go along the input list, the state being the previous element; thus avoiding the construction by zip of the shifted-pairs list serving the same purpose.
I would start from here:
greaters :: Ord a => [a] -> [a]
greaters [] = []
greaters (x:xs) = greatersImpl x xs
where
greatersImpl last [] = <fill this out>
greatersImpl last (x:xs) = <fill this out>
The following functions are everything you’d need for one possible solution :)
zip :: [a] -> [b] -> [(a, b)]
drop 1 :: [a] -> [a]
filter :: (a -> Bool) -> [a] -> [a]
(<) :: Ord a => a -> a -> Bool
uncurry :: (a -> b -> c) -> (a, b) -> c
map :: (a -> b) -> [a] -> [b]
snd :: (a, b) -> b
Note: drop 1 can be used when you’d prefer a “safe” version of tail.
If you like over-generalization like me, you can use the witherable package.
{-# language ScopedTypeVariables #-}
import Control.Monad.State.Lazy
import Data.Witherable
{-
class (Traversable t, Filterable t) => Witherable t where
-- `wither` is an effectful version of mapMaybe.
wither :: Applicative f => (a -> f (Maybe b)) -> t a -> f (t b)
-}
greaters
:: forall t a. (Ord a, Witherable t)
=> t a -> t a
greaters xs = evalState (wither go xs) Nothing
where
go :: a -> State (Maybe a) (Maybe a)
go curr = do
st <- get
put (Just curr)
pure $ case st of
Nothing -> Nothing
Just prev ->
if curr > prev
then Just curr
else Nothing
The state is the previous element, if there is one. Everything is about as lazy as it can be. In particular:
If the container is a Haskell list, then it can be an infinite one and everything will still work. The beginning of the list can be produced without withering the rest.
If the container extends infinitely to the left (e.g., an infinite snoc list), then everything will still work. How can that be? We only need to know what was in the previous element to work out the state for the current element.
"Roll your own recursive function" is certainly an option here, but it can also be accomplished with a fold. filter can't do it because we need some sort of state being passed, but fold can nicely accumulate the result while keeping that state at the same time.
Of course the key idea is that we keep track of last element add the next one to the result set if it's greater than the last one.
greaters :: [Int] -> [Int]
greaters [] = []
greaters (h:t) = reverse . snd $ foldl (\(a, r) x -> (x, if x > a then x:r else r)) (h, []) t
I'd really love to eta-reduce it but since we're dropping the first element and seeding the accumulator with it it kinda becomes awkward with the empty list; still, this is effectively an one-liner.
So i have come up with a foldr solution. It should be similar to what #Will Ness has demonstrated but not quite i suppose as we don't need a separate empty list check in this one.
The thing is, while folding we need to encapsulate the previous element and also the state (the result) in a function type. So in the go helper function f is the state (the result) c is the current element of interest and p is the previous one (next since we are folding right). While folding from right to left we are nesting up these functions only to run it by applyying the head of the input list to it.
go :: Ord a => a -> (a -> [a]) -> (a -> [a])
go c f = \p -> let r = f c
in if c > p then c:r else r
greaters :: Ord a => [a] -> [a]
greaters = foldr go (const []) <*> head
*Main> greaters [1,3,2,4,3,4,5]
[3,4,4,5]
*Main> greaters [5,10,6,11,7,12]
[10,11,12]
*Main> greaters [651,151,1651,21,651,1231,4,1,16,135,87]
[1651,651,1231,16,135]
*Main> greaters [1]
[]
*Main> greaters []
[]
As per rightful comments of #Will Ness here is a modified slightly more general code which hopefully doesn't break suddenly when the comparison changes. Note that const [] :: b -> [a] is the initial function and [] is the terminator applied to the result of foldr. We don't need Maybe since [] can easily do the job of Nothing here.
gs :: Ord a => [a] -> [a]
gs xs = foldr go (const []) xs $ []
where
go :: Ord a => a -> ([a] -> [a]) -> ([a] -> [a])
go c f = \ps -> let r = f [c]
in case ps of
[] -> r
[p] -> if c > p then c:r else r
How can I propagate information backwards in a recursive call-chain?
For example:
f :: [Int] -> [Int]
f (x:xs)
| x `mod` 17 = ...
| otherwise = (x + 1) : f xs
f [] = []
I want to stop the evaluation at the ..., and I also want to propagate that information back to the caller (the fact that it stopped). I tried to use return types like Maybe, but then I had to pattern-match the recursive call, and thus lost tail-call optimization, since I had to evaluate it after the call returned (note: one could easily transform the above code to TR form, but I left it like this for easier understanding).
Can you come up with a better solution that still benefits from TCO?
You can always use extra parameters, and return a tuple with the accumulated results. This way you still benefit from TCO, and get the information you needed.
An example:
f :: [Int] -> Bool -> [Int] -> (Bool, [Int])
f (x:xs) l accum
| x `mod` 17 == 0 = (False, accum)
| otherwise = f xs l ((x+1) : accum)
f [] l accum = (True, accum)
Or in a more elegant way:
data CheckedValue a = Valid a | Invalid a
deriving Show
f :: [Int] -> [Int] -> CheckedValue [Int]
f (x:xs) accum
| x `mod` 17 == 0 = Invalid accum
| otherwise = f xs ((x+1) : accum)
f [] accum = Valid accum
Note: These functions also reverse the list, but pay no attention to that.
my title might be a bit off and i'll try to explain a bit better what i'm trying to achieve.
Basically let's say i have a list:
["1234x4","253x4",2839",2845"]
Now i'd like to add all the positions of the strings which contain element 5 to a new list. On a current example the result list would be:
[1,3]
For that i've done similar function for elem:
myElem [] _ = False
myElem [x] number =
if (firstCheck x) then if digitToInt(x) == number then True else False else False
myElem (x:xs) number =
if (firstCheck x) then (if digitToInt(x) == number then True else myElem xs number) else myElem xs number
where firstCheck x checks that the checked element isn't 'x' or '#'
Now in my current function i get the first element position which contains the element, however my head is stuck around on how to get the full list:
findBlock (x:xs) number arv =
if myElem x number then arv else findBlock xs number arv+1
Where arv is 0 and number is the number i'm looking for.
For example on input:
findBlock ["1234x4","253x4",2839",2845"] 5 0
The result would be 1
Any help would be appreciated.
The function you want already exists in the Data.List module, by the name of findIndices. You can simply use (elem '5') as the predicate.
http://hackage.haskell.org/package/base-4.8.1.0/docs/Data-List.html#v:findIndices
If, for some reason, you're not allowed to use the built-in one, it comes with a very pretty definition (although the one actually used has a more complicated, more efficient one):
findIndices p xs = [ i | (x,i) <- zip xs [0..], p x]
By the way, I found this function by searching Hoogle for the type [a] -> (a -> Bool) -> [Int], which (modulo parameter ordering) is obviously the type such a function must have. The best way to find out of Haskell has something is to think about the type it would need to have and search Hoogle or Hayoo for the type. Hoogle is better IMO because it does slightly fuzzy matching on the type; e.g. Hayoo wouldn't find the function here by the type I've given, because it take the arguments in the reverse order.
An implementation of findIndices, for instructional purposes:
findIndices ok list = f list 0 where
f [] _ = []
f (x:xs) ix
| ok x = ix : f xs (ix+1)
| otherwise = f xs (ix+1)
Use it like findIndices (elem '5') my_list_o_strings
You're trying to work your way through a list, keeping track of where you are in the list. The simplest function for doing this is
mapWithIndex :: (Int -> a -> b) -> [a] -> [b]
mapWithIndex = mwi 0 where
mwi i _f [] = i `seq` []
mwi i f (x:xs) = i `seq` f i x : mwi (i+1) f xs
This takes a function and a list, and applies the function to each index and element. So
mapWithIndex (\i x -> (i, x)) ['a', 'b', 'c'] =
[(0,'a'), (1,'b'),(2,'c')]
Once you've done that, you can filter the list to get just the pairs you want:
filter (elem '5' . snd)
and then map fst over it to get the list of indices.
A more integrated approach is to use foldrWithIndex.
foldrWithIndex :: (Int -> a -> b -> b) -> b -> [a] -> b
foldrWithIndex = fis 0 where
fis i _c n [] = i `seq` n
fis i c n (x:xs) = i `seq` c i x (fis (i+1) c n xs)
This lets you do everything in one step.
It turns out that you can implement foldrWithIndex using foldr pretty neatly, which makes it available for any Foldable container:
foldrWithIndex :: (Foldable f, Integral i) =>
(i -> a -> b -> b) -> b -> f a -> b
foldrWithIndex c n xs = foldr go (`seq` n) xs 0 where
go x r i = i `seq` c i x (r (i + 1))
Anyway,
findIndices p = foldrWithIndex go [] where
go i x r | p x = i : r
| otherwise = r
I have recently been teaching myself Haskell, and one of my exercises was to re-implement the filter function. However, of all the exercises I have performed, my answer for this one seems to me the most ugly and long. How could I improve it? Are there any Haskell tricks I don't yet know?
myfilter :: (a -> Bool) -> [a] -> [a]
myfilter f (x:xs) = if f x
then x : myfilter f xs
else myfilter f xs
myfilter _ [] = []
Thank You
The simplest way to neaten your implementation is to use guards. Instead of pattern = value, you can write write pattern | boolean = value; this will only match when boolean is true. Thus, we can get
filter1 :: (a -> Bool) -> [a] -> [a]
filter1 p (x:xs) | p x = x : filter1 p xs
| otherwise = filter1 p xs
filter1 _ [] = []
(Note that otherwise is just a synonym for True.) Now, we have filter p xs in two places, so we can move it out into a where clause; these are shared by everything which shares a common pattern, even if it has a different guard:
filter2 :: (a -> Bool) -> [a] -> [a]
filter2 p (x:xs) | p x = x : xs'
| otherwise = xs'
where xs' = filter2 p xs
filter2 _ [] = []
(This implementation is the one used by GHCs Prelude.)
Now, neither of these are tail-recursive. This can be disadvantageous, but it does make the function lazy. If we want a tail-recursive version, we could write
filter3 :: (a -> Bool) -> [a] -> [a]
filter3 p xs = let filter3' p (x:xs) ys | p x = next $! x:ys
| otherwise = next $! ys
where next = filter3' p xs
filter3' _ [] ys = reverse ys
in filter3' p xs []
Note, however, that this would fail on infinite lists (though all the other implementations will work), thanks to the reverse, so we make it strict with $!. (I think I did this right—I could have forced the wrong variable. I think I got this one right, though.)
Those implementations all look like yours. There are, of course, others. One is based on foldr:
filter4 :: (a -> Bool) -> [a] -> [a]
filter4 p = let check x | p x = (x :)
| otherwise = id
in foldr check []
We take advantage of point-free style here; since xs would be the last argument to both filter4 and foldr check [], we can elide it, and similarly with the last argument of check.
You could also take advantage of the list monad:
import Control.Monad
filter5 :: MonadPlus m => (a -> Bool) -> m a -> m a
filter5 p xs = do x <- xs
guard $ p x
return x
The list monad represents nondeterminism. You pick an element x from xs, make sure that it satisfies p, and then return it if it does. All of these results are then collected together. But note that this is now more general; this works for any MonadPlus (a monad which is also a monoid; that is, which has an associative binary operation mplus—++ for lists—and an identity element mzero—[] for lists), such as [] or Maybe. For instance, filter5 even $ Just 1 == Nothing, and filter5 even $ Just 2 == Just 2.
We can also adapt the foldr-based version to get a different generic type signature:
import Control.Monad
import qualified Data.Foldable as F
import qualified Data.Monoid as M
filter6 :: (F.Foldable f, MonadPlus m, M.Monoid (m a))
=> (a -> Bool) -> f a -> m a
filter6 p = let check x | p x = return x
| otherwise = mzero
in F.foldMap check
The Data.Foldable module provides the Foldable type class, which represents any structure which can be folded like a list (placing the result in a generic Monoid instead.) Our filter requires a MonadPlus constraint on the result as well so that we can write return x. The foldMap function requires a function which converts everything to elements of a Monoid, and then concatenates all of them together. The mismatch between the f a on the left and the m a on the right means you could, for instance, filter6 a Maybe and get back a list.
I'm sure that there are (many!) other implementations of filter, but these are the 6 that I could think of relatively quickly. Now, which of these do I actually like best? It's a tossup between the straightforward filter2 and the foldr-based filter4. And filter5 is nice for its generic type signature. (I don't think I've ever needed a type signature like filter6's.) The fact that filter2 is used by GHC is a plus, but GHC also uses some funky rewrite rules, so it's not obvious to me that it's superior without those. Personally, I would probably go with filter4 (or filter5 if I needed the genericity), but filter2 is definitely fine.
How about a list comprehension?
myfilter f xs = [x | x <- xs, f x]
You could at least DRY it up a bit by pulling out that common myfilter f xs code:
myfilter :: (a -> Bool) -> [a] -> [a]
myfilter f (x:xs) = if f x
then x : rest
else rest
where rest = myfilter f xs
myfilter _ [] = []
For comparison, here's Wikipedia's implementation:
myfilter :: (a -> Bool) -> [a] -> [a]
myfilter _ [] = []
myfilter f (x:xs) | f x = x : myfilter f xs
| otherwise = myfilter f xs
In Haskell, most of the time you can (and should) use guards instead of if-then-else:
myfilter :: (a -> Bool) -> [a] -> [a]
myfilter f (x:xs)
| f x = x : myfilter f xs
| otherwise = myfilter f xs
myfilter _ [] = []
This ends up being basically the same definition as used in the standard library.