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|| Part 1
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|| Definitions

cube x = x*x*x

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

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

my_map2 f [] []         = []
my_map2 f (a:as) (b:bs) = f a b : my_map2 f as bs

rev f x y = f y x

alligator x y = 3+y


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|| Results

|| cube 3 => 27
|| cube :: => num->num
|| my_map :: => (*->**)->[*]->[**]
|| my_map cube :: => [num]->[num]
|| my_map cube [1..] => [3 8 ...]
|| my_append :: => [*]->[*]->[*]
|| my_map2 :: => (*->**->***)->[*]->[**]->[***]
|| my_map2 alligator :: => [*]->[num]->[num]
|| my_map2 (rev alligator) :: => [num]->[*]->[num]
|| alligator (1/0) (6/2) => 6.0
|| alligator (6/2) (1/0) => program error
|| alligator :: => *->num->num
|| (rev alligator) 10 20 => 13
|| rev :: => (*->**->***)->**->*->***
|| rev my_map2:: => [*]->(*->**->***)->[**]->[***]


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|| Part II
|||||||||||||||||||||||||||||||||||||||||||||||||||

|||||||||||||||||
|| Problem 2.1


|| calculates midpoint of two points
midpoint (a,b) (c,d) = ((a+c)/2, (b+d)/2)

    
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|| Problem 2.2


|| helper for no_duplicates
remove_element [] x = []
remove_element (x:xs) x = remove_element xs x
remove_element (y:xs) x = y : remove_element xs x

|| removes duplicate elements from a list
no_duplicates [] = []
no_duplicates (x:xs) = x : no_duplicates (remove_element xs x)


    
|||||||||||||||||
|| Problem 2.3

next_pascal :: [num]->[num]

|| next_pascal works like this:
|| next_pascal [a, b, c, ..., n] <==>
||
||       [0, a, b, c, ..., n]
||     + [a, b, c, ..., n, 0]
||     ----------------------
||       [a+0, a+b, b+c, ..., n+0]

next_pascal xs = my_map2 (+) (xs ++ [0]) (0 : xs)

pascal = [1] : map next_pascal pascal