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### a) Writing polymorphic functions Write a polymorphic function that accepts two lists, if the second list is a substring of the first then it should return the index of the substring and its length. If it is not a substring then it should return (-1,-1). Some expected output from this function is shown below: Main> substring [1,4,6,2,4,6,7,2,3] [4,6,7] (4, 3) Main> substring “abbacdaacdcfa” “acdc” (7, 4) Main> substring [(1,5),(2,4),(6,6),(9,7)] [(2,4),(9,7)] (-1, -1) b) Writing a higher-order function Write a higher-order function that accepts a function and two lists. The higher-order function should return true if the given function returns true for every pair of elements in the second list and some substring of the first list. For example: Main> hsubstring (<) [4,1,2,5,2,4,4] [2,3,6] (1, 3) Main> hsubstring (<) [4,1,2,5,2,4,4] [2,3,1] (-1, -1) c) Using higher-order functions Write a higher-order function that accepts a function and three lists. The higher-order should determine if the second list is a substring of the first. If it is then it should remove it and replace it with the third list, if it is not then it should return the original list unchanged. Note that the third list may not be the same length. Main> replace (==) [4,1,2,5,2,4,4] [2,5,2] [4,2,1] [4,1,4,2,1,4,4] Main> replace (==) “Hello World!” “World” “159.202 Class” “Hello 159.202 Class!” d) Using lambda functions & functional-level definitions Define a function that can replace substrings in a sentence regardless of whether they are uppercase or lower case. You should use only a lambda function, a functional-level definition and your previous functions. Main> replaceString “To be, or not to be, that is the question” “QUESTION” “end” “To be, or not to be, that is the end” You must put the following comments at the top of your program code and provide the appropriate information. — Assignment number, 159.202, 2016 S5 — Family Name, Given Name, Student ID, — Explain what the program is doing . . . Hand-in: Submit your script electronically through stream

–Required for ‘toUpper’
import Data.Char

–a)
substring :: (Eq a) => [a] -> [a] -> (Int, Int)
substring x y = substring’ x y 0

— susbstring’: auxiliar function that does the substring but has an extra parameter to count the index of the found substring
— checkEqual a b: checks if all elements from list a are equal to all elements from list b
substring’ [] _ _ = (-1,-1)
substring’ (x:xs) (y:ys) c | x==y && checkEqual xs ys = (c, 1 + length ys)
| otherwise = substring’ xs (y:ys) (c+1)
where
checkEqual _ [] = True
checkEqual (x:xs) (y:ys) | x==y = checkEqual xs ys
| otherwise = False

——————————————————————–
–b)

hsubstring :: (a->a->Bool) -> [a] -> [a] -> (Int, Int)
hsubstring f x y = hsubstring’ f x y 0

— hsubstring’: auxiliar function that does the hsubstring, but has an extra parametrer to count the index of the found substring
— checkFunction f a b: checks if f x y is true for elements x from a and y from b
hsubstring’ _ [] _ _ = (-1, -1)
hsubstring’ f (x:xs) (y:ys) c | f x y && checkFunction f xs ys = (c, 1 + length ys)
| otherwise = hsubstring’ f xs (y:ys) (c + 1)
where
checkFunction _ _ [] = True
checkFunction f (x:xs) (y:ys) | f x y = checkFunction f xs ys
| otherwise = False
——————————————————————–
–c)
replace :: (a->a->Bool) -> [a] -> [a] -> [a] -> [a]
replace f a b c | index > -1 = (take index a) ++ c ++ (drop (index+l) a)
| otherwise = a
where
(index, l) = hsubstring f a b

——————————————————————–
–d)
replaceString :: [Char] -> [Char] -> [Char] -> [Char]
replaceString a b c = replace (\x y->toUpper x == toUpper y) a b c

### Project Details

• Date November 3, 2016