Question

I want to know whether shift is a higher order function or not.

chartoInt  :: Char -> Int
chartoInt c  =  ord c 

Inttochar  :: Int -> Char
Inttochar  n   =  chr n

shift :: Int -> Char -> Char
shift n c  =  Inttochar  (chartoInt c + n)

Answer 1

None of these functions are higher order functions, because none of these functions take a function as a parameter.

shift‘s parameters are n (an Int) and c (a Char): neither are functions.

(Also: Inttochar should be inttochar: function names in Haskell cannot start with an upper case letter.)

---

Here’s a higher order function that looks like your shift:

higherShift :: (Int -> Char) -> Int -> Char -> Char
higherShift f n c = f (chartoInt c + n)

shift = higherShift inttochar   -- same as your original shift

Or, perhaps more usefully:

anotherHigherShift :: (Int -> Int) -> Char -> Char
anotherHigherShift f c = inttochar (f (chartoInt c))

shift n = anotherHigherShift (+n)   -- same as your original shift

You can read the type signature for anotherHigherShift as saying that

• it’s a function
• whose first parameter is a function (this function takes an Int and returns an Int)
• whose second parameter is a Char
• and which returns a Char

(+n) is shorthand for \m -> m + n.