Pattern Match on First and Last Items of List - haskell

Is it possible to pattern match on "starts with f", then any text, and "ends with b?
I tried:
f :: String -> Bool
f ('f':xs:'b') = True
f _ = False
But I got an error:
explore/PatternMatching.hs:2:11:
Couldn't match expected type ‘[Char]’ with actual type ‘Char’
In the pattern: 'b'
In the pattern: xs : 'b'
In the pattern: 'f' : xs : 'b'
Failed, modules loaded: none.

There is no easy way to do this without pattern matching language extensions. I would write it as:
f :: String -> Bool
f str = case (take 1 str, drop (length str - 1) str) of
("f", "b") -> True
otherwise -> False
(Using take and drop to avoid specially handling case of an empty string that might cause an error when using e.g. head or !!)
Prelude> f "flub"
True
Prelude> f "foo"
False
Prelude> f "fb"
True
Prelude> f "fbbbb"
True
Prelude> f "fbbbbf"
False
Prelude> f ""
False

As the previous answers state, there's no way to pattern-match directly for this. One might implement it as follows:
f 'f':xs#(_:_) = last xs == 'b' -- #(_:_) ensures nonempty tail
f _ = False

No, it is not possible directly.
: wants a list element on the left side, and a list on the right side.
'f':xs:'b' is invalid because there's something that is not a list on the right side of the second :.
'f':xs:"b" would be valid but won't do what you want, because xs is inferred to be a list element, not a list.
I would do this:
f s = f' (s, reverse s) where
f' ('f':_, 'b':_) = True
f' _ = False
Testing:
*Main> f ""
False
*Main> f "f"
False
*Main> f "b"
False
*Main> f "fb"
True
*Main> f "feeeeeeeb"
True
*Main> f (repeat 'b')
False
*Main> f (repeat 'f')
(hangs indefinitely)

For a list-like data-structure allowing you to access both its first and last element in constant time, you may want to have a look at Hinze and Paterson's fingertrees.
They are shipped by e.g. containers and here are the relevant views to deconstruct them. You may want to write your own view combining deconstruction on the left and the right if you are using this pattern a lot:
data ViewLR a = EmptyLR | SingleLR a | BothSides a (Seq a) a
viewlr :: Seq a -> ViewLR a
viewlr seq =
case viewl seq of
EmptyL -> EmptyLR
hd :< rest ->
case viewr rest of
EmptyR -> SingleLR hd
middle :> tl -> BothSides hd middle tl
You may also want to read up on View Patterns to be able to "pattern match" on the left rather than having to use case ... of.

Define a dedicated String data type and hence a form of pattern matching, for instance consider
data HString = Ends Char Char | Plain String
deriving (Show, Eq)
Thus
f :: HString -> Bool
f (Ends h l) = (h,l) == ('f','b')
f (Plain "") = False
f (Plain xs) = f $ Ends (head xs) (last xs)
and so
*Main> f (Plain "")
False
*Main> f (Plain "fabs")
False
*Main> f (Plain "fab")
True
Update
Similarly, consider the use of an infix operator :-: to denote a constructor, e.g
infixr 5 :-:
data HString = Char :-: Char | Plain String
deriving (Show, Eq)
and thus
f :: HString -> Bool
f (h :-: l) = (h,l) == ('f','b')
f (Plain "") = False
f (Plain xs) = f $ (head xs) :-: (last xs)

To understand the error simply check the signature of : operator
Prelude> :t (:)
(:) :: a -> [a] -> [a]
It can accept an element and a list to give the appended list. When you supply 'f':xs:'b', then it doesn't match the function call.

Related

Given a list, how can I perform some transformation only on sub-lists whose each two elements satisfy a binary predicate?

(In my actual use case I have a list of type [SomeType], SomeType having a finite number of constructors, all nullary; in the following I'll use String instead of [SomeType] and use only 4 Chars, to simplify a bit.)
I have a list like this "aaassddddfaaaffddsssadddssdffsdf" where each element can be one of 'a', 's', 'd', 'f', and I want to do some further processing on each contiguous sequence of non-as, let's say turning them upper case and reversing the sequence, thus obtaining "aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD". (I've added the reversing requirement to make it clear that the processing involves all the contiguous non 'a'-s at the same time.)
To turn each sub-String upper case, I can use this:
func :: String -> String
func = reverse . map Data.Char.toUpper
But how do I run that func only on the sub-Strings of non-'a's?
My first thought is that Data.List.groupBy can be useful, and the overall solution could be:
concat $ map (\x -> if head x == 'a' then x else func x)
$ Data.List.groupBy ((==) `on` (== 'a')) "aaassddddfaaaffddsssadddssdffsdf"
This solution, however, does not convince me, as I'm using == 'a' both when grouping (which to me seems good and unavoidable) and when deciding whether I should turn a group upper case.
I'm looking for advices on how I can accomplish this small task in the best way.
You could classify the list elements by the predicate before grouping. Note that I’ve reversed the sense of the predicate to indicate which elements are subject to the transformation, rather than which elements are preserved.
{-# LANGUAGE ScopedTypeVariables #-}
import Control.Arrow ((&&&))
import Data.Function (on)
import Data.Monoid (First(..))
mapSegmentsWhere
:: forall a. (a -> Bool) -> ([a] -> [a]) -> [a] -> [a]
mapSegmentsWhere p f
= concatMap (applyMatching . sequenceA) -- [a]
. groupBy ((==) `on` fst) -- [[(First Bool, a)]]
. map (First . Just . p &&& id) -- [(First Bool, a)]
where
applyMatching :: (First Bool, [a]) -> [a]
applyMatching (First (Just matching), xs)
= applyIf matching f xs
applyIf :: forall a. Bool -> (a -> a) -> a -> a
applyIf condition f
| condition = f
| otherwise = id
Example use:
> mapSegmentsWhere (/= 'a') (reverse . map toUpper) "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
Here I use the First monoid with sequenceA to merge the lists of adjacent matching elements from [(Bool, a)] to (Bool, [a]), but you could just as well use something like map (fst . head &&& map snd). You can also skip the ScopedTypeVariables if you don’t want to write the type signatures; I just included them for clarity.
If we need to remember the difference between the 'a's and the rest, let's put them in different branches of an Either. In fact, let's define a newtype now that we are at it:
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE ViewPatterns #-}
import Data.Bifoldable
import Data.Char
import Data.List
newtype Bunched a b = Bunched [Either a b] deriving (Functor, Foldable)
instance Bifunctor Bunched where
bimap f g (Bunched b) = Bunched (fmap (bimap f g) b)
instance Bifoldable Bunched where
bifoldMap f g (Bunched b) = mconcat (fmap (bifoldMap f g) b)
fmap will let us work over the non-separators. fold will return the concatenation of the non-separators, bifold will return the concatenation of everything. Of course, we could have defined separate functions unrelated to Foldable and Bifoldable, but why avoid already existing abstractions?
To split the list, we can use an unfoldr that alternately searches for as and non-as with the span function:
splitty :: Char -> String -> Bunched String String
splitty c str = Bunched $ unfoldr step (True, str)
where
step (_, []) = Nothing
step (True, span (== c) -> (as, ys)) = Just (Left as, (False, ys))
step (False, span (/= c) -> (xs, ys)) = Just (Right xs, (True, ys))
Putting it to work:
ghci> bifold . fmap func . splitty 'a' $ "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
Note: Bunched is actually the same as Tannen [] Either from the bifunctors package, if you don't mind the extra dependency.
There are other answers here, but I think they get too excited about iteration abstractions. A manual recursion, alternately taking things that match the predicate and things that don't, makes this problem exquisitely simple:
onRuns :: Monoid m => (a -> Bool) -> ([a] -> m) -> ([a] -> m) -> [a] -> m
onRuns p = go p (not . p) where
go _ _ _ _ [] = mempty
go p p' f f' xs = case span p xs of
(ts, rest) -> f ts `mappend` go p' p f' f rest
Try it out in ghci:
Data.Char> onRuns ('a'==) id (reverse . map toUpper) "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
Here is a simple solution - function process below - that only requires that you define two functions isSpecial and func. Given a constructor from your type SomeType, isSpecial determines whether it is one of those constructors that form a special sublist or not. The function func is the one you included in your question; it defines what should happen with the special sublists.
The code below is for character lists. Just change isSpecial and func to make it work for your lists of constructors.
isSpecial c = c /= 'a'
func = reverse . map toUpper
turn = map (\x -> ([x], isSpecial x))
amalgamate [] = []
amalgamate [x] = [x]
amalgamate ((xs, xflag) : (ys, yflag) : rest)
| xflag /= yflag = (xs, xflag) : amalgamate ((ys, yflag) : rest)
| otherwise = amalgamate ((xs++ys, xflag) : rest)
work = map (\(xs, flag) -> if flag then func xs else xs)
process = concat . work . amalgamate . turn
Let's try it on your example:
*Main> process "aaassddddfaaaffddsssadddssdffsdf"
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
*Main>
Applying one function at a time, shows the intermediate steps taken:
*Main> turn "aaassddddfaaaffddsssadddssdffsdf"
[("a",False),("a",False),("a",False),("s",True),("s",True),("d",True),
("d",True),("d",True),("d",True),("f",True),("a",False),("a",False),
("a",False),("f",True),("f",True),("d",True),("d",True),("s",True),
("s",True),("s",True),("a",False),("d",True),("d",True),("d",True),
("s",True),("s",True),("d",True),("f",True),("f",True),("s",True),
("d",True),("f",True)]
*Main> amalgamate it
[("aaa",False),("ssddddf",True),("aaa",False),("ffddsss",True),
("a",False),("dddssdffsdf",True)]
*Main> work it
["aaa","FDDDDSS","aaa","SSSDDFF","a","FDSFFDSSDDD"]
*Main> concat it
"aaaFDDDDSSaaaSSSDDFFaFDSFFDSSDDD"
*Main>
We can just do what you describe, step by step, getting a clear simple minimal code which we can easily read and understand later on:
foo :: (a -> Bool) -> ([a] -> [a]) -> [a] -> [a]
foo p f xs = [ a
| g <- groupBy ((==) `on` fst)
[(p x, x) | x <- xs] -- [ (True, 'a'), ... ]
, let (t:_, as) = unzip g -- ( [True, ...], "aaa" )
, a <- if t then as else (f as) ] -- final concat
-- unzip :: [(b, a)] -> ([b], [a])
We break the list into same-p spans and unpack each group with the help of unzip. Trying it out:
> foo (=='a') reverse "aaabcdeaa"
"aaaedcbaa"
So no, using == 'a' is avoidable and hence not especially good, introducing an unnecessary constraint on your data type when all we need is equality on Booleans.

Haskell map until first condition met

I want to map a conditional function only on the first item that passes.
map (>5) [1,2,3,4,5,6,7,8,9]
would result in
[False,False,False,False,False,True,True,True,True]
I'm looking for something that would result in
[False,False,False,False,False,True,False,False,False]
So only the first occurrence of being greater than 5 results in True.
I tried scanl, various folds and tried to roll my own mapUntil kind of thing.
Seems like a simple problem but I'm drawing a blank.
break specifically separates the list in 2 parts where the first part is all False, the opposite of span.
break (>5) [1,2,3,8,2,5,1,7,9]
>>> ([1,2,3],[8,2,5,1,7,9])
Then it's just what chi did:
oneTrue f lst = map (const False) a ++ rest b
where (a,b) = break f lst
rest [] = []
rest (x:xs) = True : map (const False) xs
A basic solution:
mapUntil p = onlyOne . map p
where
onlyOne [] = []
onlyOne (x:xs)
| x = True : map (const False) xs
| otherwise = False : onlyOne xs
With library helpers:
mapUntil p = snd . mapAccumL (\x y -> (x||y, not x && y)) False . map p
Above x is a boolean standing for "have seen a true before?", as a kind-of state. y is the list element. x||y is the new state, while not x && y is the new list element.
Alternatively (using Control.Arrow.second):
mapUntil p = uncurry (++) . second go . break id . map p
where
go [] = []
go (x:xs) = x : map (const False) xs
I would use the mapAccumL tool like;
λ> Data.List.mapAccumL (\b n -> if b then (b, (not b)) else (n > 5, n > 5)) False [1,2,3,4,5,6,7,8,9]
(True,[False,False,False,False,False,True,False,False,False])
Here we carry the b as the state of our interim calculations and in every step decide according to it's previous state. Obviously you need the snd part of the final result.
Edit : After reading the new comment of #Gord under his question I decided to extend my answer to cover his true problem.
Rephrasing the case event of branch that starts with pointerPress (x,y) into...
To start with, you never use x or y from the pattern match (x,y) so lets call it c. Then...
PointerPress c -> State circleCoords circleColors circleDraggeds c
where
bools = fmap checkMouseOverlaps $ (,) <$> circleCoords <*> [c]
circleDraggeds = snd $ mapAccumL (\a b -> if a then (a, not a)
else (b,b)) False bools
What's happening part;
(,) <$> circleCoords <*> [c]
circleCoords is a list of coordinates like [c0,c1,c2] and we fmap (the infix version (<$>) here) (,) function to it and it becomes an applicative of coordinates like [(c0,),(c1,),(c2,)]. Then we apply it to [c] aka [(x,y)] to turn it into [(c0,c),(c1,c),(c2,c)].
fmap checkMouseOverlaps $ toAbove
obviously yields to
[checkMouseOverlaps (c0,c), checkMouseOverlaps (c1,c), checkMouseOverlaps (c2,c)]
which is bools :: [Bool].
The the rest follows the logic explained at the top of my answer.
circleDraggeds = snd $ mapAccumL (\a b -> if a then (a, not a)
else (b,b)) False bools
This can be solve directly with recursion. Similar to chi's solution but without function composition
mapUntil :: (a -> Bool) -> [a] -> [Bool]
mapUntil _ [] = []
mapUntil f (x:xs) =
let b = f x -- calculate f x
in if b -- if true
then b : map (const False) xs -- prepend to the solution and map False to the rest of the list (b is True)
else b : mapUntil f xs -- keep applying mapUntil (b is False)
>>> mapUntil (>5) [1,2,3,4,5,6,7,8,9]
[False,False,False,False,False,True,False,False,False]
Map the condition over the list, then zip the result with the False prefix of the result concatenated with a True followed by an infinite list of Falses:
{-# LANGUAGE BlockArguments, ApplicativeDo, ViewPatterns #-}
import Control.Applicative (ZipList(..))
f :: (a -> Bool) -> [a] -> [Bool]
f cond (map cond -> bs) = getZipList do
r <- ZipList $ takeWhile not bs ++ [True] ++ repeat False
_ <- ZipList $ bs
pure r
or, equivalently:
f' :: (a -> Bool) -> [a] -> [Bool]
f' cond (map cond -> bs) = zipWith const (takeWhile not bs ++ [True] ++ repeat False) bs

higher order function haskell

I'm new to Haskell, I've to do a function that counts the number of vowels in a string using the higher order function foldr
I've tried to create this function
vowels [] = 0
vowels (x:xs)= if elem x "aeiou" then 1 + vowels xs else vowels xs
But it doesn't work and I'm not able to do it using foldr, any suggestion?
Well a foldr :: (a -> b -> b) -> b -> [a] -> b is a function where the first parameter is a function f :: a -> b -> b. You can here see the a parameter as the "head" of the list, the second parameter b as the result of the recursion with foldr, and you thus want to produce a result in terms of these two for the entire function. This logic is basically encapsulated in the second clause of your function.
Indeed:
vowels (x:xs) = if elem x "aeiou" then 1 + vowels xs else vowels xs
can be rewritten as:
vowels (x:xs) = if elem x "aeiou" then 1 + rec else rec
where rec = vowels xs
and rec is thus the outcome of the recursive call, the second parameter of the "fold"-function. x on the other hand is the first parameter of the "fold"-function. We thus need to write this function, only in terms of x and rec, and this is simply:
\x rec -> if elem x "aeiou" then 1 + rec else rec
Furthermore we need to handle the case of an empty list, this is the first clause of your function. In that case the result is 0, this is the second paramter of the foldr, so we got:
vowels = foldr (\x rec -> if elem x "aeiou" then 1 + rec else rec) 0
Or a more clean syntax:
vowels = foldr f 0
where f x rec | elem x "aeiou" = 1 + rec
| otherwise = rec
We can further clean it up, by abstracting away rec:
vowels = foldr f 0
where f x | elem x "aeiou" = (1+)
| otherwise = id
You need to take a look at foldr's signature.
foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b
Never mind the Foldable part and focus on the first function it takes.
(a -> b -> b) b is the same type that you are supposed to return, so directly translating the signature into a lambda gives you \x acc -> acc, but you want to do more than just ignore every element.
Take a look at your function if elem x "aeiou" then 1 + vowels xs else vowels xs. You need to return b, not recurse adding one to it.
if elem x "aeiou" this part is fine. then 1 + acc <- see what I'm doing here? I'm adding one to the accumulator, not recursing manually, that is done by foldr, as for the else case: acc. That's it. You don't need to even touch x.
Putting it all together: vowels = foldr (\x acc -> if elem x "aeiou" then 1 + acc else acc) 0
The 0 is what the acc will start as.
If you want to know more about folds, I suggest you reimplement them yourself.
The easiest way to write something like that is to let the compiler guide you.
First, look only at the obvious parts of the foldr signature. This is the traditional signature, specialised to lists. Nowedays, foldr can actually work on any other suitable container as well, but this isn't important here.
foldr :: (a -> b -> b) -- ^ Not obvious
-> b -- ^ Not obvious
-> [a] -- ^ A list... that'll be the input string
-> b -- ^ Final result, so nothing to be done here.
So, your implementation will be of the form
vowels :: String -> Int
vowels s = foldr _ _ s
where we yet need to find out what to put in the _ gaps. The compiler will give you useful hints as to this:
$ ghc wtmpf-file6869.hs
[1 of 1] Compiling Main ( wtmpf-file6869.hs, wtmpf-file6869.o )
/tmp/wtmpf-file6869.hs:2:18: error:
• Found hole: _ :: Char -> Int -> Int
• In the first argument of ‘foldr’, namely ‘_’
In the expression: foldr _ _ s
In an equation for ‘Main.vowels’: Main.vowels s = foldr _ _ s
• Relevant bindings include
s :: String (bound at /tmp/wtmpf-file6869.hs:2:8)
vowels :: String -> Int (bound at /tmp/wtmpf-file6869.hs:2:1)
|
2 | vowels s = foldr _ _ s
| ^
So, a function that merely takes a single character, and then modifies an integer. That was actually already part of your original implementation:
vowels (x:xs) = if elem x "aeiou" then 1 + vowels xs else vowels xs
The bold part is essentially a function of a single character, that yields a number-modifier. So we can put that in the foldr implementation, using lambda syntax:
vowels s = foldr (\x -> if x`elem`"aeiou" then (1+) else _) _ s
I had to put the 1+ in parenthesis so it works without an explicit argument, as an operator section.
Ok, more gaps:
• Found hole: _ :: Int -> Int
• In the expression: _
In the expression: if x `elem` "aeiou" then (1 +) else _
In the first argument of ‘foldr’, namely
‘(\ x -> if x `elem` "aeiou" then (1 +) else _)’
• Relevant bindings include
x :: Char (bound at wtmpf-file6869.hs:2:20)
s :: String (bound at wtmpf-file6869.hs:2:8)
vowels :: String -> Int (bound at wtmpf-file6869.hs:2:1)
|
2 | vowels s = foldr (\x -> if x`elem`"aeiou" then (1+) else _) _ s
| ^
So that's the modifier that should take action when you've found a non-vowel. What do you want to modify in this case? Well, nothing actually: the count should stay as-is. That's accomplished by the id function.
vowels s = foldr (\x -> if x`elem`"aeiou" then (1+) else id) _ s
• Found hole: _ :: Int
• In the second argument of ‘foldr’, namely ‘_’
In the expression:
foldr (\ x -> if x `elem` "aeiou" then (1 +) else id) _ s
In an equation for ‘vowels’:
vowels s
= foldr (\ x -> if x `elem` "aeiou" then (1 +) else id) _ s
• Relevant bindings include
s :: String (bound at wtmpf-file6869.hs:2:8)
vowels :: String -> Int (bound at wtmpf-file6869.hs:2:1)
|
2 | vowels s = foldr (\x -> if x`elem`"aeiou" then (1+) else id) _ s
| ^
So that's an integer that's completely outside of the foldr. I.e. it can't depend on the string. In particular, it will also be used if the string is empty. Can only be 0!
vowels s = foldr (\x -> if x`elem`"aeiou" then (1+) else id) 0 s
No more gaps, so the compiler will just accept this. Test it:
$ ghci wtmpf-file6869
GHCi, version 8.2.1: http://www.haskell.org/ghc/ :? for help
Loaded GHCi configuration from /home/sagemuej/.ghc/ghci.conf
Loaded GHCi configuration from /home/sagemuej/.ghci
[1 of 1] Compiling Main ( wtmpf-file6869.hs, interpreted )
Ok, 1 module loaded.
*Main> vowels "uwkaefdohinurheoi"
9
Your definition can be tweaked into
vowels [] = 0
vowels (x:xs) = g x (vowels xs)
where
g x rec = if elem x "aeiou" then 1 + rec else rec
which matches the pattern
foldr r z [] = z
foldr r z (x:xs) = r x (foldr r z xs)
if we have foldr r z = vowels and r = g, and also z = 0.
That "pattern" is in fact a valid definition of the foldr function.
Thus we indeed have
vowels xs = foldr g 0 xs
where
g x rec = if elem x "aeiou" then 1 + rec else rec

Haskell - converting High Order Function to recursive function

requirement:write function single - Tests whether exactly one element of a list satisfies a given condition.
single :: (a -> Bool) -> [a] -> Bool
I wrote this function:
single p xs = count p xs == 1
where count pred = length . filter pred
Question: What is the easy (correct) way to convert the above functions into one recursive function without using " High Order Functions"?
You can do like that:
single p = lookupFirst
where
lookupFirst [] = False
lookupFirst (x:xs) | p x = lookupSecond xs
| otherwise = lookupFirst xs
lookupSecond [] = True
lookupSecond (x:xs) | p x = False
| otherwise = lookupSecond xs
We can use a none predicate that checks if the remainder of the list does not satisfy the condition:
single :: (a -> Bool) -> [a] -> Bool
single p [] = False
single p (x:xs) | p x = none p xs
| otherwise = single p xs
none :: (a -> Bool) -> [a] -> Bool
none _ [] = True
none p (x:xs) = not (p x) && none p xs
We thus also defined a none function that checks that no element in the given list satisfies a given predicate.
Or without passing the predicate through the recursion:
single :: (a -> Bool) -> [a] -> Bool
single p = helper
where helper [] = False
helper (x:xs) | p x = none xs
| otherwise = helper xs
none [] = True
none (x:xs) = not (p x) && none xs
The above written functions will also immediately stop from the moment a second item is found that satisfies the predicate. This can be useful if we work for instance with an infinite list. If there is a second item that satisfies the constraint, then the function will stop, if no such element or only one such element will ever be generated, we will however get stuck in an infinite loop (there is no much we can do about this). For example:
*Main> single even [1..] -- two or more elements satisfy the constraint
False
*Main> single even [1,3..] -- no element satisfies the constraint
^CInterrupted.
*Main> single even ([1,2]++[3,5..]) -- one element satisfies the constraint
^CInterrupted.
xor and foldl
The most intuitive thing I can thing of is to just fold xor (exclusive or) and your function f thru the list. In case you're not familiar with the binary function xor, it returns True only when (at most) 1 of its arguments are True; otherwise False
xor :: Bool -> Bool -> Bool
xor True b = not b
xor False b = b
single :: (a -> Bool) -> [a] -> Bool
single f [] = False
single f xs = foldl (\acc -> xor acc . f) False xs
main = do
putStrLn $ show (single even []) -- False
putStrLn $ show (single even [1]) -- False
putStrLn $ show (single even [2]) -- True
putStrLn $ show (single even [1,2]) -- True
putStrLn $ show (single even [1,2,3]) -- True
putStrLn $ show (single even [1,2,3,4]) -- False
Xor monoid
xor can be nicely encoded as a Monoid tho, which lends single to a more algebraic implementation using foldMap.
data Xor = Xor Bool
instance Monoid Xor where
mempty = Xor False
mappend (Xor True) (Xor b) = Xor (not b)
mappend (Xor False) (Xor b) = Xor b
single f xs = aux $ foldMap (Xor . f) xs
where
aux (Xor b) = b
main = do
putStrLn $ show (single even []) -- False
putStrLn $ show (single even [1]) -- False
putStrLn $ show (single even [2]) -- True
putStrLn $ show (single even [1,2]) -- True
putStrLn $ show (single even [1,2,3]) -- True
putStrLn $ show (single even [1,2,3,4]) -- False
auxiliary helper
This is another way you can do it with an auxiliary helper. This one has an added benefit in that it exits immediately (stops iteration thru the list) after an answer is determined
single :: (a -> Bool) -> [a] -> Bool
single f xs = aux False f xs
where
aux b f [] = b
aux True f (x:xs) = if (f x) then False else aux True f (xs)
aux False f (x:xs) = aux (f x) f xs
main = do
putStrLn $ show (single even []) -- False
putStrLn $ show (single even [1]) -- False
putStrLn $ show (single even [2]) -- True
putStrLn $ show (single even [1,2]) -- True
putStrLn $ show (single even [1,2,3]) -- True
putStrLn $ show (single even [1,2,3,4]) -- False
feedback welcome!
I'm a Haskell newbie but maybe these ideas are interesting to you. Or maybe they're bad! Leave me a comment if there's anything I can do to improve the answer ^_^

Checking to see if a list is ordered consecutively

Is there any library function in Haskell that'll allow me to check if a list is ordered consecutively? eg. [1,2,3,4] is valid, [1,2,3,10] is invalid.
Basically I can have a list that ranges anywhere between 3 to 5 elements and I'm trying to check if that list is ordered consecutively.
My Attempt (I'm not sure if this is the right way to approach it, seems to be way too much repetition)
isSucc:: [Integer] -> Bool
isSucc[] = True
isSucc(x:y:zs) =
if (x+1) == y
then True && isSucc(y:zs)
else isSucc(y:zs)
After I have this function working, I'm planning on using it to filter a lists of lists (Keep the list inside the list only and only if it is ordered consecutively)
You can use the trick zipWith f xs (drop 1 xs) to apply f to consecutive pairs of list elements. (Notice drop 1 rather than tail, because the latter fails if the list is empty!)
If you replace f with <= you'll get a list of Bool values. Now see whether they're all True.
isSucc xs = and $ zipWith (<=) xs (drop 1 xs)
There's no standard function for that.
Here's a fixed version of your function, making it generic, removing the redundant conditions and adding the missing ones:
isSucc :: (Enum a, Eq a) => [a] -> Bool
isSucc [] = True
isSucc (x:[]) = True
isSucc (x:y:zs) | y == succ x = isSucc $ y:zs
isSucc _ = False
I prefer to use a little more readable solution than one that has been offered by MathematicalOrchid.
First of all we will define the utilitarian function pairwise that might be useful in many different circumstances:
pairwise xs = zip xs $ tail xs
or in more modern way:
import Control.Applicative ((<*>))
pairwise = zip <*> tail
and then use it with the other combinators:
isSucc xs = all (\(x,y) -> succ x == y) $ pairwise xs
There is another way,
isOrdered :: (Enum a, Eq a) => (a -> a -> Bool) -> [a] -> Bool
isOrdered op (a:b:ls) = op a b && isOrdered op (b:ls)
isOrdered op _ = True
Thus,
isSucc = isOrdered ((==) . succ)
If you want to check that all consecutive differences are equal to one, you can use
isIncreasingByOne :: (Eq a, Num a) => [a] -> Bool
isIncreasingByOne = all (==1) (zipWith (-) (tail xs) xs)
This works for numeric types (hence the Num a constraint), including Float and Double. It's also easy to adapt if you want to check that a sequence is increasing by more than 5 at a time, say.
-- This checks if ordered
isordd:: [Int] -> Bool
isordd [] = True
isordd (x:y:xs)
| x > y = False
| lengh xs == 0 = True
| otherwise = isordd (y:xs)
-- This calculates the length of the list
lengh::[Int]->Int
lengh [] = 0
lengh (x:xs) = 1+lengh xs

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