2025-10-20 Daily Worksheet

Review

1. Inside a function f x, use let to create variables x2 holding x squared, and x3 holding x cubed. Then create the function below.

   $$ f(x) = x^3 (x^2-1) $$

Semi-New

An official data type is Maybe a. The data definition is:

    data Maybe a = Nothing | Just a
        deriving (Show, Eq, ...)

Do not recopy that code; it is built into the Haskell interpreter that we use.

2. Write a function g2 that takes in a Maybe Int and returns 0 if it is given Nothing and otherwise 10 more than the absolute value of the int.

     checks_2 = [   0 == g2 Nothing
                 , 12 == g2 (Just 2)
                 , 25 == g2 (Just 15) ]
   

3. Write a function h2 that takes in a Maybe String and puts out a Maybe String, doubling the string if it exists.

     check_h2 = [ Just "mommom" == h2 (Just "mom")
                 , Nothing == h2 Nothing ]
   

Higher Order Functions

4. (myor) The or function returns True when any item in a list is True; otherwise it returns False. Use foldl to create your own version of this function.

    myor :: [Bool] -> Bool
   

5. Use recursion to write a function myall that applies a function to every item in a list, and returns True if every function application returns True.

    myall :: (a -> Bool) -> [a] -> Bool
    check_myall = [ myall even [2,4,10,20] == True
                   ,myall (<5) [1,3,6,2,4] == False
                   ]