CSCI3180 – Principles of Programming Languages – Spring 2019
Assignment 4 — Declarative Programming Deadline: Apr 24, 2019 (Wednesday) 23:59
1 Introduction
Declarative programming is a programming paradigm that expresses the logic of a computation without describing its control flow. You will gain experience of declarative programming with an emphasis on Prolog and ML in this assignment.
2 Logic Programming
Implement the required predicates or queries of the following two problems in a Prolog program file named “asg4.pl”. You should clearly indicate using comments the corresponding question number of each sub-problem. Note that the answers which are queries should be written in comments as well.
1. Recall the successor notation for representing natural numbers, and the sum(X,Y,Z) relation defined in the lecture which is true if Z is the sum of X and Y.
(a) Define natNum(X) which is true if X is a natural number.
(b) Define lt(X,Y) which is true if X is less than Y.
(c) Give a query to find natural numbers less than 3.
(d) Define geq(X,Y) which is true if X is equal to or greater than Y.
(e) Define max(X,Y,Z) which is true if Z is the maximum of X and Y.
(f) Based on sum/3, define difference(X,Y,Z) which is true if X minus Y is equal to Z.
(g) Based on lt/2, geq/2 and difference/3, define mod(X,Y,Z) which is true if X mod Y is equal to Z.
2. A binary tree is either empty or composed of a root and two children, which are binary trees themselves. The root of a binary tree is a node containing a value. Diagramatically, a binary tree consists of a set of nodes and lines connecting parents and children. The nodes are depicted by circles with values written inside. Empty binary trees are not shown in the diagram.
Figure 1: An example of binary tree
In Prolog, we represent an empty tree by the atom “nil” and a non-empty tree by the term “bt(X,L,R)”, where X denotes the root node, L and R denote the left and right subtrees respectively.
1
(a) Represent the binary tree shown in Figure 1 as a Prolog term.
(b) Define the predicate isTree(Term), where “Term” can be any Prolog term. Predicate
isTree(Term) is true if “Term” represents a binary tree.
(c) Define the predicate isLeaf(X,Tree), where “X” is a tree node, “Tree” is a binary tree. A leaf is a node with no children. Predicate isLeaf(X,Tree) is true if “X” is a leaf node of the given “Tree”.
(d) Define the predicate numberOfLeaf(Tree,N), where “Tree” is a binary tree, “N” is the number of leaf nodes in the successor notation. Note that you could use the sum/3 defined previously.
(e) The height of a binary tree is the length of the path from the root to the deepest leaf node (which must be an empty tree) in the tree. Here we define the height of an empty tree to be zero. Thus a tree with a single element node (with both children as empty) will have a height of one (s(0)), and so on. Define the predicate height(Tree,H), where “Tree” is a term representing a binary tree and H is the height of this tree in the successor notation. You may want to use the max/3 defined above.
3 Functional Programming
Implement the required functions of the following problem in an ML program file named “asg4.ml”. You should clearly indicate using comments the corresponding question number of each sub- problem.
This problem involves a card game invented just for this question. You will write several helper functions first and then implement a main program to track the progress of this game. The card game is played with a card-list, and the player will have a list of held-cards, initially empty. During each round of play, the player makes a move by choosing to draw a card from the card-list, or discarding one of the held-cards. The game will end either when the player chooses to stop or when the player already has six cards.
The goal of this game is to end the game with a low score (0 is the best). The score is defined as the absolute value of the differences between sum of the red color card values and the sum of black color card values, and then plus six minuses the number of held cards. The details are shown in the following formula:
Score = abs(sum(red values) − sum(black values)) + (6 − #held cards).
The type definition of a card is shown below (The joker cards are not included in this game):
datatype suit = Clubs | Diamonds | Hearts | Spades;
datatype rank = Jack | Queen | King | Ace | Num of int;
type card = suit * rank;
Each card will have associated suit and rank. The suit of a card is related to the color and rank is related to the value of the card. The color type and move type are defined as
datatype color = Red | Black;
datatype move = Discard of card | Draw;
1. Write an ML function abs, which takes an integer and returns its absolute value.
2. Write an ML function cardColor, which takes a card as input and returns its color. Spades and clubs are black, while diamonds and hearts are red. Note that one case-expression is enough.
3. Write an ML function cardValue, which takes a card as input and returns its value. Num- bered cards have their numbers as the value. Aces are 11, and everything else is 10.
2
4
4. 5.
6. 7. 8.
Write an ML function numOfCard, which takes a card list cardList and returns the number of cards in the list.
Write an ML function removeCard(cardList, c), which takes a card list cardList repre- senting the held-cards, and a card c. It should return a list after removing card c from the list. If c is in the list more than once, remove only the first one. You could assume that c is always contained in the list. Note that “=” can be used to compare cards.
Write an ML function sumCards(cardList, col), which takes a list of cards cardList and a color col. It will return the sum of the given color card values.
Write an ML function score, which takes a card list cardList (the held-cards) and computes the score as defined earlier.
Write an ML function runGame(cardList, moveList), which takes a card list cardList representing the cards from which the player can draw, a move list moveList (the moves chosen by the player at each round of play), and returns the score at the end of the game after processing the moves in the move list in order. As described above:
• At the beginning of the game, the list representing held-cards should be empty.
• If there are no more moves (i.e. the move list is empty), the game will end.
• During each round of play, if the player choose to discard some card c, the game will continue with the held-cards having c removed and the card list remains unchanged.
• If a player chooses to draw a card and the card list is already empty, the game is over. If drawing causes the number of the held-cards to exceed five, the game is over (after drawing). Otherwise, the game continues with a larger held-cards and a smaller card-list.
Submission Guidelines
Please read the guidelines CAREFULLY. If you fail to meet the deadline because of submission problem on your side, marks will still be deducted. So please start your work early!
1. In
the following, SUPPOSE
your name is Chan Tai Man,
your student ID is 1155234567,
your username is tmchan, and
your email address is tmchan@cse.cuhk.edu.hk.
2. In
to the comment rule of Prolog and ML.
your source files, insert the following header. REMEMBER to insert the header according
/∗
∗ CSCI3180 Principles of Programming Languages ∗
∗ — Declaration — ∗
∗ I declare that the assignment here submitted is original except for source
∗ material explicitly acknowledged. I also acknowledge that I am aware of
∗ University policy and regulations on honesty in academic work, and of the
∗ disciplinary guidelines and procedures applicable to breaches of such policy
∗ and regulations, as contained in the website
∗ http://www.cuhk.edu.hk/policy/academichonesty/ ∗
∗ Assignment 4
∗ Name : Chan Tai Man
∗ Student ID : 1155234567
∗ Email Addr : tmchan@cse.cuhk.edu.hk ∗/
3
The sample file header is available at
http://course.cse.cuhk.edu.hk/~csci3180/resource/header.txt
3. Late submission policy: less 20% for 1 day late and less 50% for 2 days late. We shall not accept submissions more than 2 days after the deadline.
4. Your solutions for Section 2 will be graded using SICStus Prolog 3.12.7 in the CSE Unix platform. Solutions for Section 3 will be graded using Standard ML 110.0.7 in the CSE Unix platform.
5. Tar your source files to username.tar by
tar cvf tmchan.tar asg4.pl asg4.ml
6. Gzip the tarred file to username.tar.gz by gzip tmchan.tar
7. Uuencode the gzipped file and send it to the course account with the email title “HW4 studentID yourName” by
uuencode tmchan.tar.gz tmchan.tar.gz \
| mailx -s “HW4 1155234567 Chan Tai Man” csci3180@cse.cuhk.edu.hk
8. Please submit your assignment using your Unix accounts.
9. An acknowledgement email will be sent to you if your assignment is received. DO NOT delete or modify the acknowledgement email. You should contact your TAs for help if you do not receive the acknowledgement email within 5 minutes after your submission. DO NOT re-submit just because you do not receive the acknowledgement email.
10. You can check your submission status at http://course.cse.cuhk.edu.hk/~csci3180/submit/hw4.html.
11. You can re-submit your assignment, but we will only grade the latest submission.
12. Enjoy your work :>
4