Completely new to Haskell and learning through Learn Haskell the greater good.
I am looking at the map function
map :: (a -> b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs
is it possible to add a predicate to this? for example, to only map to every other element in the list?
You can code your own version of map to apply f only to even (or odd) positions as follows. (Below indices start from 0)
mapEven :: (a->a) -> [a] -> [a]
mapEven f [] = []
mapEven f (x:xs) = f x : mapOdd f xs
mapOdd :: (a->a) -> [a] -> [a]
mapOdd f [] = []
mapOdd f (x:xs) = x : mapEven f xs
If instead you want to exploit the library functions, you can do something like
mapEven :: (a->a) -> [a] -> [a]
mapEven f = map (\(flag,x) -> if flag then f x else x) . zip (cycle [True,False])
or even
mapEven :: (a->a) -> [a] -> [a]
mapEven f = map (uncurry (\flag -> if flag then f else id)) . zip (cycle [True,False])
If you want to filter using an arbitrary predicate on the index, then:
mapPred :: (Int -> Bool) -> (a->a) -> [a] -> [a]
mapPred p f = map (\(i,x) -> if p i then f x else x) . zip [0..]
A more direct solution can be reached using zipWith (as #amalloy suggests).
mapEven :: (a->a) -> [a] -> [a]
mapEven f = zipWith (\flag x -> if flag then f x else x) (cycle [True,False])
This can be further refined as follows
mapEven :: (a->a) -> [a] -> [a]
mapEven f = zipWith ($) (cycle [f,id])
The "canonical" way to perform filtering based on positions is to zip the sequence with the naturals, so as to append an index to each element:
> zip [1, 1, 2, 3, 5, 8, 13] [0..]
[(1,0),(1,1),(2,2),(3,3),(5,4),(8,5),(13,6)]
This way you can filter the whole thing using the second part of the tuples, and then map a function which discards the indices:
indexedFilterMap p f xs = (map (\(x,_) -> f x)) . (filter (\(_,y) -> p y)) $ (zip xs [0..])
oddFibsPlusOne = indexedFilterMap odd (+1) [1, 1, 2, 3, 5, 8, 13]
To be specific to you question, one might simply put
mapEveryOther f = indexedFilterMap odd f
You can map with a function (a lambda is also possible):
plusIfOdd :: Int -> Int
plusIfOdd a
| odd a = a
| otherwise = a + 100
map plusIfOdd [1..5]
As a first step, write the function for what you want to do to the individual element of the list:
applytoOdd :: Integral a => (a -> a) -> a -> a
applytoOdd f x = if odd x
then (f x)
else x
So applytoOdd function will apply the function f to the element if the element is odd or else return the same element if it is even. Now you can apply map to that like this:
λ> let a = [1,2,3,4,5]
λ> map (applytoOdd (+ 100)) a
[101,2,103,4,105]
Or if you want to add 200 to it, then:
λ> map (applytoOdd (+ 200)) a
[201,2,203,4,205]
Looking on the comments, it seems you want to map based on the index position. You can modify your applytoOdd method appropriately for that:
applytoOdd :: Integral a => (b -> b) -> (a, b) -> b
applytoOdd f (x,y) = if odd x
then (f y)
else y
Here, the type variable a corresponds to the index element. If it's odd you are applying the function to the actual element of the list. And then in ghci:
λ> map (applytoOdd (+ 100)) (zip [1..5] [1..])
[101,2,103,4,105]
λ> map (applytoOdd (+ 200)) (zip [1..5] [1..])
[201,2,203,4,205]
Or use a list comprehension:
mapOdd f x = if odd x then f x else x
[ mapOdd (+100) x | x <- [1,2,3,4,5]]
I'm glad that you're taking the time to learn about Haskell. It's an amazing language. However it does require you to develop a certain mindset. So here's what I do when I face a problem in Haskell. Let's start with your problem statement:
Is it possible to add a predicate to the map function? For example, to only map to every other element in the list?
So you have two questions:
Is it possible to add a predicate to the map function?
How to map to every other element in the list?
So the way people think in Haskell is via type signatures. For example, when an engineer is designing a building she visualizes how the building should look for the top (top view), the front (front view) and the side (side view). Similarly when functional programmers write code they visualize their code in terms of type signatures.
Let's start with what we know (i.e. the type signature of the map function):
map :: (a -> b) -> [a] -> [b]
Now you want to add a predicate to the map function. A predicate is a function of the type a -> Bool. Hence a map function with a predicate will be of the type:
mapP :: (a -> Bool) -> (a -> b) -> [a] -> [b]
However, in your case, you also want to keep the unmapped values. For example mapP odd (+100) [1,2,3,4,5] should result in [101,2,103,4,105] and not [101,103,105]. Hence it follows that the type of the input list should match the type of the output list (i.e. a and b must be of the same type). Hence mapP should be of the type:
mapP :: (a -> Bool) -> (a -> a) -> [a] -> [a]
It's easy to implement a function like this:
map :: (a -> Bool) -> (a -> a) -> [a] -> [a]
mapP p f = map (\x -> if p x then f x else x)
Now to answer your second question (i.e. how to map to every other element in the list). You could use zip and unzip as follows:
snd . unzip . mapP (odd . fst) (fmap (+100)) $ zip [1..] [1,2,3,4,5]
Here's what's happening:
We first zip the index of each element with the element itself. Hence zip [1..] [1,2,3,4,5] results in [(1,1),(2,2),(3,3),(4,4),(5,5)] where the fst value of each pair is the index.
For every odd index element we apply the (+100) function to the element. Hence the resulting list is [(1,101),(2,2),(3,103),(4,4),(5,105)].
We unzip the list resulting in two separate lists ([1,2,3,4,5],[101,2,103,4,105]).
We discard the list of indices and keep the list of mapped results using snd.
We can make this function more general. The type signature of the resulting function would be:
mapI :: ((Int, a) -> Bool) -> (a -> a) -> [a] -> [a]
The definition of the mapI function is simple enough:
mapI :: ((Int, a) -> Bool) -> (a -> a) -> [a] -> [a]
mapI p f = snd . unzip . mapP p (fmap f) . zip [1..]
You can use it as follows:
mapI (odd . fst) (+100) [1,2,3,4,5]
Hope that helps.
Is it possible to add a predicate to this? for example, to only map to every other element in the list?
Yes, but functions should ideally do one relatively simple thing only. If you need to do something more complicated, ideally you should try doing it by composing two or more functions.
I'm not 100% sure I understand your question, so I'll show a few examples. First: if what you mean is that you only want to map in cases where a supplied predicate returns true of the input element, but otherwise just leave it alone, then you can do that by reusing the map function:
mapIfTrue :: (a -> Bool) -> (a -> a) -> [a] -> [a]
mapIfTrue pred f xs = map step xs
where step x | pred x = f x
| otherwise = x
If what you mean is that you want to discard list elements that don't satisfy the predicate, and apply the function to the remaining ones, then you can do that by combining map and filter:
filterMap :: (a -> Bool) -> (a -> b) -> [a] -> [b]
filterMap pred f xs = map f (filter pred xs)
Mapping the function over every other element of the list is different from these two, because it's not a predicate over the elements of the list; it's either a structural transformation of the list of a stateful traversal of it.
Also, I'm not clear whether you mean to discard or keep the elements you're not applying the function to, which would imply different answers. If you're discarding them, then you can do it by just discarding alternate list elements and then mapping the function over the remaining ones:
keepEven :: [a] -> [a]
keepEven xs = step True xs
where step _ [] = []
step True (x:xs) = x : step False xs
step False (_:xs) = step True xs
mapEven :: (a -> b) -> [a] -> [b]
mapEven f xs = map f (keepEven xs)
If you're keeping them, one way you could do it is by tagging each list element with its position, filtering the list to keep only the ones in even positions, discard the tags and then map the function:
-- Note: I'm calling the first element of a list index 0, and thus even.
mapEven :: (a -> a) -> [a] -> [a]
mapEven f xs = map aux (filter evenIndex (zip [0..] xs))
where evenIndex (i, _) = even i
aux (_, x) = f x
As another answer mentioned, zip :: [a] -> [b] -> [(a, b)] combines two lists pairwise by position.
But this is the general philosophy: to do a complex thing, use a combination of general-purpose generic functions. If you're familiar with Unix, it's similar to that.
Another simple way to write the last one. It's longer, but keep in mind that evens, odds and interleave all are generic and reusable:
evens, odds :: [a] -> [a]
evens = alternate True
odds = alternate False
alternate :: Bool -> [a] -> [a]
alternate _ [] = []
alternate True (x:xs) = x : alternate False xs
alternate False (_:xs) = alternate True xs
interleave :: [a] -> [a] -> [a]
interleave [] ys = ys
interleave (x:xs) ys = x : interleave ys xs
mapEven :: (a -> a) -> [a] -> [a]
mapEven f xs = interleave (map f (evens xs)) (odds xs)
You can't use a predicate because predicates operate on list values, not their indices.
I quite like this format for what you're trying to do, since it makes the case handling quite clear for the function:
newMap :: (t -> t) -> [t] -> [t]
newMap f [] = [] -- no items in list
newMap f [x] = [f x] -- one item in list
newMap f (x:y:xs) = (f x) : y : newMap f xs -- 2 or more items in list
For example, running:
newMap (\x -> x + 1) [1,2,3,4]
Yields:
[2,2,4,4]
Related
According to following rules, I tried to solve the following problem:
No definition of recursion
No List of Comprehension
Only Prelude-Module is allowed.
Now I have to implement higher-order for concat and filter.
Im at this point:
concat' :: [[a]] -> [a]
concat' a = (concat a)
filter' :: (a -> Bool) -> [a] -> [a]
filter' p [] = []
filter' p (x:xs)
| p x = x : filter p xs
| otherwise = filter p xs
The concat function is working (nothing special so far) -> Is that a defined recursion? I mean I use the predefined concat from standard-prelude but myself I don't define it - or am I wrong?
For the filter, the function I've looked up the definition of standard prelude but that's either not working and it contains a definition of recursion.
I'm supposing the concat and filter functions should be avoided. Why would we need to implement concat and filter if they're already available? So try implementing them from scratch.
We can use folding instead of recursion and list comprehensions. The below solutions use the function foldr.
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
concat' :: [[a]] -> [a]
concat' = foldr (++) []
filter' :: (a -> Bool) -> [a] -> [a]
filter' p = foldr (\x acc -> if p x then x:acc else acc) []
Examples:
main = do
print $ concat' ["A", "B", "CAB"] -- "ABCAB"
print $ filter' (\x -> x `mod` 2 == 0) [1..9] -- [2, 4, 6, 8]
You may do as follows;
concat' :: Monad m => m (m b) -> m b
concat' = (id =<<)
filter' p = ((\x-> if p x then [x] else []) =<<)
=<< is just flipped version of the monadic bind operator >>=.
filter' (< 10) [1,2,3,10,11,12]
[1,2,3]
Given a condition, I want to search through a list of elements and return the first element that reaches the condition, and the previous one.
In C/C++ this is easy :
int i = 0;
for(;;i++) if (arr[i] == 0) break;
After we get the index where the condition is met, getting the previous element is easy, through "arr[i-1]"
In Haskell:
dropWhile (/=0) list gives us the last element I want
takeWhile (/=0) list gives us the first element I want
But I don't see a way of getting both in a simple manner. I could enumerate the list and use indexing, but that seems messy. Is there a proper way of doing this, or a way of working around this?
I would zip the list with its tail so that you have pairs of elements
available. Then you can just use find on the list of pairs:
f :: [Int] -> Maybe (Int, Int)
f xs = find ((>3) . snd) (zip xs (tail xs))
> f [1..10]
Just (3,4)
If the first element matches the predicate this will return
Nothing (or the second match if there is one) so you might need to special-case that if you want something
different.
As Robin Zigmond says break can also work:
g :: [Int] -> (Int, Int)
g xs = case break (>3) xs of (_, []) -> error "not found"
([], _) -> error "first element"
(ys, z:_) -> (last ys, z)
(Or have this return a Maybe as well, depending on what you need.)
But this will, I think, keep the whole prefix ys in memory until it
finds the match, whereas f can start garbage-collecting the elements
it has moved past. For small lists it doesn't matter.
I would use a zipper-like search:
type ZipperList a = ([a], [a])
toZipperList :: [a] -> ZipperList a
toZipperList = (,) []
moveUntil' :: (a -> Bool) -> ZipperList a -> ZipperList a
moveUntil' _ (xs, []) = (xs, [])
moveUntil' f (xs, (y:ys))
| f y = (xs, (y:ys))
| otherwise = moveUntil' f (y:xs, ys)
moveUntil :: (a -> Bool) -> [a] -> ZipperList a
moveUntil f = moveUntil' f . toZipperList
example :: [Int]
example = [2,3,5,7,11,13,17,19]
result :: ZipperList Int
result = moveUntil (>10) example -- ([7,5,3,2], [11,13,17,19])
The good thing about zippers is that they are efficient, you can access as many elements near the index you want, and you can move the focus of the zipper forwards and backwards. Learn more about zippers here:
http://learnyouahaskell.com/zippers
Note that my moveUntil function is like break from the Prelude but the initial part of the list is reversed. Hence you can simply get the head of both lists.
A non-awkward way of implementing this as a fold is making it a paramorphism. For general explanatory notes, see this answer by dfeuer (I took foldrWithTails from it):
-- The extra [a] argument f takes with respect to foldr
-- is the tail of the list at each step of the fold.
foldrWithTails :: (a -> [a] -> b -> b) -> b -> [a] -> b
foldrWithTails f n = go
where
go (a : as) = f a as (go as)
go [] = n
boundary :: (a -> Bool) -> [a] -> Maybe (a, a)
boundary p = foldrWithTails findBoundary Nothing
where
findBoundary x (y : _) bnd
| p y = Just (x, y)
| otherwise = bnd
findBoundary _ [] _ = Nothing
Notes:
If p y is true we don't have to look at bnd to get the result. That makes the solution adequately lazy. You can check that by trying out boundary (> 1000000) [0..] in GHCi.
This solution gives no special treatment to the edge case of the first element of the list matching the condition. For instance:
GHCi> boundary (<1) [0..9]
Nothing
GHCi> boundary even [0..9]
Just (1,2)
There's several alternatives; either way, you'll have to implement this yourself. You could use explicit recursion:
getLastAndFirst :: (a -> Bool) -> [a] -> Maybe (a, a)
getLastAndFirst p (x : xs#(y:ys))
| p y = Just (x, y)
| otherwise = getLastAndFirst p xs
getLastAndFirst _ [] = Nothing
Alternately, you could use a fold, but that would look fairly similar to the above, except less readable.
A third option is to use break, as suggested in the comments:
getLastAndFirst' :: (a -> Bool) -> [a] -> Maybe (a,a)
getLastAndFirst' p l =
case break p l of
(xs#(_:_), (y:_)) -> Just (last xs, y)
_ -> Nothing
(\(xs, ys) -> [last xs, head ys]) $ break (==0) list
Using break as Robin Zigmond suggested ended up short and simple, not using Maybe to catch edge-cases, but I could replace the lambda with a simple function that used Maybe.
I toyed a bit more with the solution and came up with
breakAround :: Int -> Int -> (a -> Bool) -> [a] -> [a]
breakAround m n cond list = (\(xs, ys) -> (reverse (reverse take m (reverse xs))) ++ take n ys) $ break (cond) list
which takes two integers, a predicate, and a list of a, and returns a single list of m elements before the predicate and n elements after.
Example: breakAround 3 2 (==0) [3,2,1,0,10,20,30] would return [3,2,1,0,10]
I want to filter a list by predicates curried from another list.
For instance:
multifilter :: (a -> a -> Bool) -> [a] -> [a] -> [a]
multifilter _ _ [] = []
multifilter _ [] _ = []
multifilter f (x:xs) ys = (filter (f x) ys) ++ (multifilter f xs ys)
With usage such as:
prelude> multifilter (==) [1,2,3] [5,3,2]
[2,3]
Is there a standard way to do this?
You can use intersectBy:
λ> :t intersectBy
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
λ> intersectBy (==) [1,2,3] [5,3,2]
[2,3]
You can use hoogle to search functions using type signature and finding them.
Note: This answer implements the specification expressed by the words and example in the question, rather than the different one given by the implementation of multifilter there. For the latter possibility, see gallais' answer.
Sibi's answer shows how you should actually do it. In any case, it is instructive to consider how you might write your function using filter. To begin with, we can establish two facts about it:
multifilter can be expressed directly as filter pred for some appropriate choice of pred. Given a fixed "predicate list", whether an element of the list you are multifiltering will be in the result only depends on the value of that element.
In multifilter f xs ys, the list you are filtering is xs, and the "predicate list" is ys. Were it not so, you would get [3,2] rather than [2,3] in your (quite well-chosen) example.
So we have:
multifilter :: (a -> a -> Bool) -> [a] -> [a] -> [a]
multifilter f xs ys = filter pred xs
where
pred = undefined -- TODO
All we need to do is implementing pred. Given an element x, pred should produce True if, for some element y of ys, f x y is true. We can conveniently express that using any:
pred x = any (\y -> f x y) ys
-- Or, with less line noise:
pred x = any (f x) ys
Therefore, multifilter becomes...
multifilter :: (a -> a -> Bool) -> [a] -> [a] -> [a]
multifilter f xs ys = filter pred xs
where
pred x = any (f x) ys
-- Or, more compactly:
multifilter :: (a -> a -> Bool) -> [a] -> [a] -> [a]
multifilter f xs ys = filter (\x -> any (f x) ys) xs
... which is essentially equivalent to intersectBy, as you can see by looking at intersectBy's implementation.
A third option is to use a list comprehension:
multifilter rel xs ys = [ x | x <- xs, y <- ys, x `rel` y ]
or, if you want partial application:
multifilter p xs ys = [ x | x <- xs, let f = p x, y <- ys, f y ]
If you want to use filter,
relate rel xs ys = filter (uncurry rel) $ liftM2 (,) xs ys
(and throw in map fst)
The answer you have accepted provides a function distinct from the one defined in your post: it retains elements from xs when yours retains elements from ys. You can spot this mistake by using a more general type for multifilter:
multifilter :: (a -> b -> Bool) -> [a] -> [b] -> [b]
Now, this can be implemented following the specification described in your post like so:
multifilter p xs ys = fmap snd
$ filter (uncurry p)
$ concatMap (\ x -> fmap (x,) ys) xs
If you don't mind retaining the values in the order they are in in ys then you can have an even simpler definition:
multifilter' :: (a -> b -> Bool) -> [a] -> [b] -> [b]
multifilter' p xs = filter (flip any xs . flip p)
Simply use Hoogle to find it out via the signature (a -> a -> Bool) -> [a] -> [a] -> [a]
https://www.haskell.org/hoogle/?hoogle=%28a+-%3E+a+-%3E+Bool%29+-%3E+%5Ba%5D+-%3E+%5Ba%5D+-%3E+%5Ba%5D
yields intersectBy:
intersectBy :: (a -> a -> Bool) -> [a] -> [a] -> [a]
I just wanted to multiply two lists element by element, so I'd pass (*) as the first argument to that function:
apply :: Num a => (a -> a -> a) -> [a] -> [a] -> [a]
apply f xs ys = [f (xs !! i) (ys !! i) | i <- [0..(length xs - 1)]]
I may be asking a silly question, but I actually googled a lot for it and just couldn't find. Thank you, guys!
> :t zipWith
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
> zipWith (*) [1,2,3] [4,5,6]
[4,10,18]
It's the eighth result provided by Hoogle when queried with your type
(a -> a -> a) -> [a] -> [a] -> [a]
Moreover, when you need to implement your own function, use list !! index only as a last resort, since it usually leads to a bad performance, having a cost of O(index). Similarly, length should be used only when necessary, since it needs to scan the whole list.
In the zipWith case, you can avoid both and proceed recursively in a natural way: it is roughly implemented as
zipWith _ [] _ = []
zipWith _ _ [] = []
zipWith f (x:xs) (y:ys) = f x y : zipWith f xs ys
Note that this will only recurse as much as needed to reach the end of the shortest list. The remaining part of the longer list will be discarded.
I am trying to create a function that accepts a function as parameter, and applies that function on every pair of elements in a list. For example, if I call my function foldPairs, then I would use it as so:
foldPairs (+) [1..10]
[3,7,11,15,19]
I tried using foldl in my attempt...
foldPairs :: (a->a->a) -> [a] -> [a]
foldPairs func lis = foldl func lis
However this clearly does not work. I think I might have to use curried and uncurried but I am not quite sure how. Could someone help me out?
Assuming, that for an odd-numbered input list we just discard the last element, the following will do the required:
foldPairs :: (a->a->a) -> [a] -> [a]
foldPairs _ [] = []
foldPairs _ [_] = []
foldPairs f (x:y:xs) = f x y : foldPairs f xs
The solution I would go with is to turn [1..10] into [[1,2],[3,4],[5,6],[7,8],[9,10]], then filter out any lists of length 1, convert to tuples, then map your function:
chunks :: Int -> [a] -> [[a]]
chunks n = reverse . go []
where
go acc [] = acc
go acc xs =
let (h, t) = splitAt n xs
in go (h:acc) t
Then simply
foldpairs :: (a -> a -> b) -> [a] -> [b]
foldpairs f
= map (uncurry f)
. map (\[x, y] -> (x, y))
. filter ((== 2) . length)
. chunks 2