Haskell Programming: Simply answer the question (Code)

Problems [50 points total] Haskell Programming 1. (5 points] Using head and reverse, define a function (i.e., write the definition for a function) last' that mimics last: It takes a list and return the last element. E.g. last' [1,2,3]- 3. You should cause a runtime error if you're passed the empty list, but it doesn't have to be the same error message as last. 2. 8 points] Define a function head_repeats n x that returns True if the first n elements of x equals the second n elements of X. Eg., head-repeats 2 [ 3 , 5 , 3 , 5, 71 should return True. If n s 0, return True. 3 [10 points] What's wrong with the following definition? Suggest a change to the definition that changes the arguments of f but preserves the spirit of the definition below. Also give the type of your new function f. f 01 4.[15 points] Define a function swap_ends that takes a list and returns the same list but with the first and last elements swapped. E.g., swap_ends "hello" - 'oellh" (remember, strings are lists of characters). Use function definition by cases to ensure that swap-ends [ ] = [ ] and swap-ends [x] = [xj. (Le., return empty and singleton lists as is). 5. 8 points] Here's a buggy definition for the general case of swap_ends. Briefly explain the nature of the bug and why we can't eliminate the bug if we rewrite the left hand side of the definition but use the same right-hand side of the definition. Two or three sentences is enough swap_ends ([x]+ y ++ [z])-[z] y tt [x] 6 4 points] What is wrong with the definition below? Give a corrected definition of f. Explain briefly f :: (Num a) => a-> [a] fx=[x / 2]