Question

I need a program that checks if the difference between all pairs of elements is in the interval from -2 up to 2 ( >= -2 && < 2). If it is, then return True, else return False. Foe example, [1,2,3] is True, but [1,3,4] is False.
I am using the all function. What is wrong with my if clause?

allfunc (x : xs)
   = if all (...) xs
      then allfunc xs
      else [x] ++ allfunc xs
allfunc _
   = []

Or I am doing something completely wrong?

Answer 1

For this, it’s probably easier to use list comprehensions or do-notation.

pairsOf lst = do 
  x <- lst
  y <- lst
  return (x, y)

pairsOf returns the list of pairs of numbers in the input lst. For example, pairsOf [1,2,3] results in [(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)].

Now, you can define the difference between a pair in a one-liner \(x, y) -> x - y and map that over the list:

differences lst = map (\(x, y) -> x - y) (pairsOf lst)

Now you just have to make sure that each element in differences lst is between -2 and 2.

Of course, this is just one possible way to do it. There are many other ways as well.