Implement the functions using map and foldr, haskell

Question

I have two functions. The first one gives true if all elements of the list are zero

allZero :: [Int] -> Bool
allZero [] = False
allZero [0] = True
allZero (x:xs)
  | x == 0 && allZero xs = True
  |otherwise = False

The second function gives true if at least one element of the list is zero

oneZero :: [Int] -> Bool
oneZero [] = False
oneZero (x:xs)
   | x == 0 = True
   | otherwise = oneZero xs

Maybe there is another way to solve this problems. For example with map or foldr? Thank you

What did you try? Can you implement any and all in terms of foldr? — Willem Van Onsem
@WillemVanOnsem I don't quite understand how foldr works. I understand how map works, but I don't know how to apply it. — Theresa
allZero [] = False is surprising. Are you sure you don't want True in that case, as your informal specification implies? — chi
what the above comment by chi implies is that allZero can be seen as noNonZeros and there are certainly no zeroes in [], so it should return True then. and that's the usual thing to do. — Will Ness
allZero (x:xs) = x == 0 && allZero xs. oneZero (x:xs) = x == 0 || oneZero xs. allZero = all . map (== 0). oneZero = any . map (== 0). all == foldr (&&) True. any == foldr (||) False. <meta> (this is not a full answer as it has no words in it, hence it is left as a comment.) </meta> — Will Ness

chepner chepner · Accepted Answer · 2021-01-09T18:28:13

foldr basically takes your guard as its folding function:

allZero = foldr (\x acc -> x == 0 && acc) True

acc (for accumulator) is the already-computed value of the recursive call. Being right-associative, the first non-zero value in the list short-circuits the evaluation of the fold function on the rest of the list.

(Note that allZero [] == True by convention. The "hypothesis" is that allZero xs is true, with evidence in the form of a non-zero element to falsify the hypothesis. No elements in the list, no evidence to contradict the hypothesis.)

I leave it as an exercise to adapt this to compute oneZero.

Implement the functions using map and foldr, haskell

2 Answers