-- Solutions to CSE 341 Haskell Discussion Questions #1

-- Write a Haskell function to find the cube of a  number.  
cube :: Double -> Double
cube n = n^3

-- Write a Haskell function to find the sum of three Doubles
sum3 :: Double -> Double -> Double -> Double
sum3 x y z = x+y+z


-- Write a Haskell function to find the value of the quadratic
-- expression ax^2 + bx + c for parameters a, b, c, and x.   
quad_expr :: Double -> Double -> Double -> Double -> Double
quad_expr a b c x = a*x^2 + b*x + c


-- Write a Haskell function to reverse a list.  
my_rev :: [a] -> [a]
my_rev [] = []
my_rev (x:xs) = my_rev xs ++ [x]

-- here's a more efficient version that uses a helper function revappend
my_rev2 :: [a] -> [a]
my_rev2 s = revappend s []

-- reverse the first list, appending the second to the result
revappend :: [a] -> [a] -> [a]
revappend [] rest = rest
revappend (x:xs) rest = revappend xs (x:rest)

-- Write a function my_map2 that is analogous to map but works
-- for functions of two arguments rather than one.  
my_map2 :: (a->b->c) -> [a] -> [b] -> [c]
my_map2 f [] [] = []
my_map2 f (x:xs) (y:ys) = f x y : my_map2 f xs ys

-- Suppose that the following Haskell script has been filed in ...

my_const c x = c

append [] ys = ys
append (x:xs) ys = x : append xs ys

my_map f [] = []
my_map f (x:xs) = f x : my_map f xs

-- What is the result of evaluating the following Haskell expressions?  
-- Try them and see ...