-- exhl6.hs  example  create and use functions

factorial :: (Integral a) => a -> a  -- special type, multiple precision
factorial n = if n < 2
              then 1
              else n * factorial (n - 1)

-- factorial Using recursion (with pattern matching)
factr :: (Integral a) => a -> a
factr 0 = 1
factr n = n * factr (n - 1)

-- Using recursion (with guards)
factrg :: (Integral a) => a -> a
factrg n
  | n < 2     = 1
  | otherwise = n * factrg (n - 1)

-- Using a list and the "product" function
factp :: (Integral a) => a -> a
factp n = product [1..n]

calc :: String -> [Float] -- define function  calc
calc = foldl f [] . words
  where 
    f (x:y:zs) "+" = y+x:zs
    f (x:y:zs) "-" = y-x:zs
    f (x:y:zs) "*" = y*x:zs
    f (x:y:zs) "/" = y/x:zs
    f xs y = read y : xs

a = "2.0 3.0 *"
b = "2.0 3.0 * 1.5 +"
c = "2.0 3.0 * 3.0 0.5 * +"

main :: IO ()
main = do
  print "haskell  exhl6.hs  running";
  print "4 versions of factorial function"
  putStr "factorial(3) = "
  print (factorial(3))
  putStr "factorial(20) = "
  print (factorial(20))
  putStr "factorial(52) = "
  print (factorial(52))

  putStr "factr(3) = "
  print (factr(3))

  putStr "factrg(3) = "
  print (factrg(3))

  putStr "factp(3) = "
  print (factp(3))

  putStrLn "fact4.hs finished"

  print "function calc takes reverse polish expressions"
  putStr(a++" = ")
  print(calc a)
  putStr(b++" = ")
  print(calc b)
  putStr(c++" = ")
  print(calc c)

  print "exhl6.hs finished";