2. Function Syntax

Can you predict the result of the following code? Here sq is a function that squares its argument.

sq b = b * b
main = print $
-- show
    sq 3+1 
-- /show

Function Call

1. I defined a function pyth that takes two numbers and returns the sum of their squares. Add parentheses to the code below to make it compile (don't get scared by unintellegible error messages):

   pyth a b = a * a + b * b
   main = print $
   -- show
       pyth 3 * 2 pyth -1 8
   -- /show

   pyth a b = a * a + b * b
   main = print $
   -- show
       pyth (3 * 2) (pyth (-1) 8)
   -- /show

2. I also defined a function pyth' (yes, you can use apostrophes -- or 'primes', as they are called in mathematics -- in identifiers). pyth' takes a tuple of numbers, as in (a, b), and returns the sum of their squares. Add parentheses and commas to code below to make it compile. You may reduce the number of parentheses if you take into account that the comma inside a tuple has lower precedence than arithmetic operators.

   pyth' (a, b) = a * a + b * b
   main = print $
   -- show
       pyth' 3 * 2 pyth' -1 8
   -- /show

   pyth' (a, b) = a * a + b * b
   main = print $
   -- show
       pyth' (3 * 2, pyth' (-1, 8))
   -- /show

3. The print function prints its argument, as long as it is convertible to a string. Numbers are convertible to strings. The code below works but looks more like Lisp than Haskell. Try to remove as many parentheses as you can using $ signs (Hint: With some cleverness, you can get rid of them all).

   pyth a b = a * a + b * b
   main = do
   -- show
       print (sqrt (pyth 3 ((-1) - 3)))
   -- /show

   pyth a b = a * a + b * b
   main = 
   -- show
       print $ sqrt $ pyth 3 $ -1 -3
   -- /show

Function Definition

1. Define a function flop that reverses a pair.

   flop ? = ?
   main = print $ flop (1, "one")

   flop (a, b) = (b, a)
   main = print $ flop (1, "one")

2. Define a function that takes two points (pairs) and returns a segment (a pair of points).

   makeSegment ? = ?
   main = print $ makeSegment (1, 2) (3, 4)

   makeSegment p1 p2 = (p1, p2)
   main = print $ makeSegment (1, 2) (3, 4)

3. Define a function that takes a segment and returns it's center point.

   center ? = ?
   main = print $ center ((1,2), (3, 4))

   center ((x, y), (x', y')) = ((x + x')/2, (y + y')/2)
   main = print $ center ((1,2), (3, 4))

Recursion

Ex 1. Print squares of numbers from 1 to 10.

loop :: Int -> IO ()
loop n = undefined

main :: IO ()
main = loop 1

loop :: Int -> IO ()
loop n = do
    if n <= 10
    then do
        putStrLn (show (n * n))
        loop (n + 1)
    else
        return ()

main :: IO ()
main = loop 1

Ex 2. No exposition of recursion is complete without factorial. Use the following property: Factorial of n is n times the factorial of (n - 1), and the factorial of 0 is 1.

fact :: Int -> Int
fact n = undefined

main = print (fact 20)

fact :: Int -> Int
fact n = if n > 0 then n * fact (n - 1) else 1

main = print (fact 20)