Question 1:

a- A range can be defined, using the three arguments start, stop, and step, as the list of integers that represents the arithmetic sequence that begins at the start element and terminates without including the stop element using a common difference of step. As a clarifying example, the range with start 3, stop 9, and step 2 would be represented with the list [3, 5, 7]. Write a recursive Haskell function (including a type declaration defined over Integers) that takes three arguments start, stop, and step (in that order) and computes the range using the definition provided. Your solution must be a single function (i.e., no helper functions) and may not call any other functions.

b- For this question you will implement (under specific constraints) a recursive function in Haskell that takes a list of characters as an argument and returns a list that contains only every third element from the argument list in the same order. As a clarifying example, this function, when passed the argument list ABCDEFGHIJKLMNO, should return the list CFILO. It should also be noted that your function must work (i.e., not terminate with an error) even if the number of elements in the argument list is less than three. You may NOT use the !! operator to complete this question, and you may NOT use any function that you havent written here (i.e., you may NOT use any built-in functions, but you may use other functions if you write them yourself). 1 Write this function (including a type declaration) by first writing a selector function (for retrieving the third element of a list) and then having your recursive function call your selector function as required. 2 Write this function (including a type declaration) without selector functions (even if you wrote them yourself), using only pattern matching.

c- For the purposes of this question, assume that the name orderedPairs refers to a list of all possible ordered pairs of integers, in RANDOM ORDER, where each component is between 0 and 5, inclusive. Using orderedPairs as a generator, write a list comprehension that produces a list of all possible ordered pairs of integers (in the order they appeared in the generator) for which the sum of the components is 6 and the first component is less than the second. You may use the fst and snd selector functions for this question if you wish, but your solution must be a list comprehension and cannot rely on any other functions.

d- Write a recursive function (including a type declaration) that takes a list of ordered pairs of integers as an argument and returns the same list you should receive from the list comprehension defined in 5 above. You may NOT use list comprehensions and you may NOT use any built-in functions, so your solution to this question may not call fst and snd unless you provide them yourself.

e- For the purposes of this question, assume that the name pixelData refers to a list of 3-tuples of integers, where each 3-tuple (R, G, B) is a reference to the colour of a particular pixel in a raster image (as defined by the specification for your second assignment). Under the assumption that you knew, for certain, that the image being represented was SQUARE (i.e., had the same width and height), write Haskell functions (including a type declarations) that allow you repack this one-dimensional list of pixels into a SQUARE two-dimensional list of pixels. You may use the built-in length, take, and drop functions to complete this question if you wish, but you may NOT use any other built-in functions.