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105SpecificationforAssignment4.pdf
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Haskell/Prolog
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countZerofree [997, 998, 999, 1000, 1001] 3 PROLOG ?- countZerofree ([997, 998, 999, 1000, 1001], X). X=3; false. n.b., The specification for this question continues on the following page. COMP3007A (Winter 2019) − "Programming Paradigms" Specification for Assignment 4 of 4 For this question, you will write this function twice - once using Haskell and once using Prolog. Both solutions must be recursive, and the countZerofree function itself in the Haskell solution must be tail-call optimized. Neither solution may use higher order functions. Obviously, you will need to start by writing a function to test whether an integer is "Zerofree" or not, and this must be a recursive function. Furthermore, as has been the case for most of our assignments, you may not use any built-in functions to complete your submission. This means that you will need to write your own implementations of basic functions like length, mod, rem, take, drop, and reverse, should you wish to use them. You are, however, free to use operators, like the list constructor operator (:), the list concatenation operator (++), and the arithmetic operators, etc. to complete this assignment. Question 2: "Best Behaviour" Use structural induction to prove (length x) - (length (filterPQ x)) = (countIf x). Use the following implementations for myLength, filterPQ, beforeP, afterQ, and countIf and refer to the individual lines in these implementations using the labels L1, L2, F1, F2A, F2B, F2C, B1, A1, C1, C2A, C2B, and C2C. You must follow the process of structural induction as it was demonstrated in class and you must show all your work (including the line applied during each step of your equational reasoning). myLength :: [Char] -> Int L1 myLength [] = 0 L2 myLength (h:t) = 1 + (myLength t) filterPQ :: [Char] -> [Char] F1 filterPQ [] = [] filterPQ (h:t) F2A | beforeP h = h : (filterPQ t) F2B | afterQ h = h : filterPQ t F2C | otherwise = filterPQ t beforeP :: [Char] -> Bool B1 beforeP x = ord x < 80 afterQ :: [Char] -> Bool A1 afterQ x = ord x > 81 countIf :: [Char] -> Char C1 countIf [] = 0 countIf (h:t) C2A | h == "P" = 1 + (countIf t) C2B | h == "Q" = 1 + (countIf t) C2C | otherwise = countIf t COMP3007A (Winter 2019) − "Programming Paradigms" Specification for Assignment 4 of 4 Question 3: "Ancient History" For this question, you must write a Prolog program that will solve the following logic puzzle by modeling it as a finite state machine. Your solution to this question MUST follow the approach we demonstrated in class for solving this type of logic puzzle with a finite state machine. Additionally, your solution must answer True or False for the first question (i.e., Is it possible...?) and it must provide an unambiguous description of the action plan for the second question (i.e., How?). If more than one solution is possible, your program must provide all solutions. A group of three humans, one neanderthal, and his two pet saber-toothed tigers have found themselves on the west bank of a river, and they need to cross to the east side using a small rowboat. The rowboat only has enough room for two entities at any given time, and only the neanderthal or one of the humans is capable of actually rowing the boat from one bank of the river to the other. It is also necessary, at all times, for the number of humans on either side of the river to be greater than or equal to the number of saber-toothed tigers (to ensure the tigers do not eat the humans). Is it possible for all of them to cross the river in 15 moves or less? How? ">
