CMSC 330, Fall 2015

Organization of Programming Languages

Project 5 - Prolog Programming

Due 11:59pm Mon, Nov 30th, 2015


For this project you will need to implement a number of functions in Prolog that together can be used to find solutions for mazes. This project will provide experience dealing with logic, recursion, lists, and other features in Prolog.

Extra credit opportunity: Implement a SAT solver

Note: The project is due the Monday after Thanksgiving. However, we have given you enough time to get it done before TG. Enjoy your holiday and finish it early! The course staff may not be monitoring piazza that much during the break. Work on the project while learning the language, not after you step away for a while.

Getting Started

Download the following archive file and extract its contents.

Along with files used to make direct submissions to the submit server (submit.jar, .submit, submit.rb), you will find the following project files:

The file you downloaded contains a number of utility functions, and comments describing the functions you are required to implement.

Note that you must implement your functions with the exact parameters specified, or else the submit server tests will fail.

Running Public Tests

The public tests are set up as a number of Prolog programs that will call functions from your code and test them with different inputs. To execute a public test, you need to load both and the public test file into the Prolog interpreter, then call the appropriate public test function for each function you were required to implement. The public test functions are:
  • public_ackermann
  • public_prod
  • public_fill
  • public_genN
  • public_genXY
  • public_flat
  • public_isprime
  • public_inlang
  • public_stats
  • public_validPath
  • public_findDistance
  • public_solve
Here's an example of how to run a public test manually:

swipl                                 % start prolog
?- working_directory(C,'path to p5'). % go to p5 directory
                        % start here if using swipl-win.exe
?- [''].                      % load your code
?- [''].                % load public test
?- maze1_public.                    % run public test
On Windows machines, opening the file with swipl-win.exe will bring up a window running the Prolog interpreter in the directory containing, so it is not necessary to start swipl or call the function working_directory manually.

Alternatively, you may run all of the public tests at once using the public test driver provided. It will load and all the public tests, then run all public tests at once.

swipl                                 % start prolog
?- working_directory(C,'path to p5'). % go to p5 directory
?- [''].                     % load test driver
                        % start here if using swipl-win.exe
?- run.                               % run all public tests

Prolog Library Functions Allowed

For this project you should write most code yourself, and only use Prolog's built-in and library functions where absolutely necessary. You are not allowed to use any library or built-in functions unless they are explicitly listed as permitted functions. The only built-in function that you are allowed to use for this project are:

Type Built-in Functions
Arithmetic +, -, *, div, mod, <, =<, >, >=, is, =:=, =\=, floor, float, sqrt
Logic ==, =, \==, \=, \+
Lists [H|T], [H1,H2|T], [H1,H2,H3|T], etc.
List Utilities member(X,L), append(X,Y,R), sort(X,R)
Cut !
findall(X,Y,R), setof(X,Y,R)

Since many functions you need to implement are similar to those from previous projects, you may find it useful to examine your previous solutions when writing your solution in Prolog.

Part 1: Recursion

Write the following recursive functions:

Name Parameters Example
ackermann(M,N,R) M=int
• R=the ackermann function on M and N
• M and N will always be given
?- ackermann(0,1,R).
?- ackermann(2,3,R).
?- ackermann(3,4,R).
prod(L,R) L=list of ints
R=product of elements of L
• R=1 if L=[]
• L will always be given
?- prod([1,2,3],R).
?- prod([],R).
fill(N,X,R) N=int
R=list containing N copies of X
• R=[] if N=0
• N will always be given
• Either X or R will be given
?- fill(4,2,R).
?- fill(4,X,[2,2,2,2]).
genN(N,R) N=non-zero positive int
R=int values between 0 and N-1, inclusive, in ascending order
• N will always be given
?- genN(2,R).
genXY(N,R) N=non-zero positive int
R=pairs [X,Y], where X & Y are values between 0 and N-1, inclusive,
generated in ascending lexicographic order.
• N will always be given
?- genXY(2,R).
flat(L,R) L=list
R=elements of L concatenated together, preserving relative order,
first placing non-list elements in a list if necessary
• R=[] if L=[]
• L will always be given
• Only removes one level of list, unlike flatten/2
?- flat([[1],[2,3]],R).
?- flat([1,[2,3]],R).
?- flat([[1,[2]],3],R).
is_prime(N) N=int
Is true if the integer N is a prime number.
• A simple algorithm for primality checking is to start with the axioms that 2 and 3 are prime numbers (1 is not). Then, an arbitrary number N greater than 3 is prime iff N is not divisible by D, for all D from sqrt(N) up to N-1. You will need to implement a helper function to do this iteration. You will find =\=, float, and sqrt functions helpful. Note: your algorithm should aim to reject large non-primes quickly, or you might experience timeouts.
• N will always be given
?- is_prime(3).
?- is_prime(4).
?- is_prime(31).
in_lang(L) L=list of atoms a and b
Is true if the list L, viewed as a string, is contained in the language S defined by the following CFG:
   S -> T | V
   T -> UU
   U -> aUb | ab
   V -> aVb | aWb
   W -> bWa | ba
Put another way, the language S is specified as follows:
S = {a^n b^n a^m b^m | n,m >= 1} U {a^n b^m a^m b^n | n,m >= 1} .
• L will always be given
?- in_lang([a,a,b,b,a,b]).
?- in_lang([a,a,a,b,b,a,a,b,b,b]).
?- in_lang([a,a,a,b,b,a,b,b,b]).

Part 2: Maze solver

Maze descriptions

For this project, the mazes you will compute with will be given as Prolog databases. In particular, you will be given three kinds of facts
  • maze(N,SX,SY,EX,EY). This fact indicates that:
    • The height and width of the maze is N cells,
    • The default starting position is SX,SY, and
    • The ending position is EX,EY.

  • cell(X,Y,Dirs,Wts). A fact of this form describes a cell in the maze. In particular, it says that the cell at position X,Y, has open walls as described by Dirs, the list of directions. More precisely:
    • The list Dirs will contain at most one of each of the atoms u, d, l, and r, which designate openings going up, down, left, or right, respectively.
    • Recall from project one that the coordinate system places 0,0 in the upper left corner of the maze.
    • The Wts component of the fact indicates the weights granted to paths following the respective direction. That is, each element in Dirs has a corresponding weight in Wts.
    As an example, the fact cell(1,0,[r,d],[16.6, 0.89]) indicates that the cell at 1,0 has two open walls: one leading to the right (to cell 2,0) with weight 16.6, and one leading down (to cell 1,1) with weight 0.89.

  • path(N,SX,SY,Dirs). This fact describes a path named N (a string) through the maze starting at position SX,SY and following the directions given by Dirs. For example, the fact path('path1',0,3,[u,r,u,l,u]) indicates that there is a path 'path1' that starts at 0,3 and follows the given directions to end up at position 0,0.

Based on these maze facts, you need to implement the following functions for solving a maze.

Name Parameters Example
stats(U,D,L,R) U,D,L,R=number of cells with openings up, down, left, and right. ?- stats(U,D,L,R).
U = D, D = 8,
L = R, R = 7.
validPath(N,W) N=name of valid path (only goes through openings)
W=float value for weight of path (rounded to 4 decimal places)
• Return valid paths in same order as in database
• Use round4(X,Y) :- T1 is X*10000, T2 is round(T1), Y is T2/10000.
• Apply round4() to final float weight, not intermediate sums.
?- validPath(N,W).
N = path1,
W = 99.9958;
N = path2,
W = 103.779.
findDistance(L) L=list of coordinates of cells at distance D from maze start
• Elements of L are in form [D, [[X1,Y2],[X2,Y2],...]]
• Values of D range from 0 to D, in ascending order
• D=distance of cell furthest from start
• Cell coordinates [X,Y] are in lexicographic order
?- findDistance(L).
L = [[0, [[0, 3]]],
       [1, [[0, 2]]],
       [2, [[1, 2]]],
       [3, [[1, 1],[2,2]],
  ..., [6, [[3, 2]]].
solve • True if maze is solvable, fails otherwise. ?- solve.

The maze converter program convertMaze.rb may be used to convert simple maze files from Project 1 into Prolog for use as test cases. Run it as "ruby convertMaze.rb >".

Extra credit: Boolean Formulae & SAT

As extra credit (up to 2 percent), you are invited to implement a function that determines whether a collection of boolean formulae can be solved (satisfied). Boolean formula will be represented using lists of Prolog terms as follows:
  • t and f represent true & false, respectively.
  • [and, X, Y], [or, X, Y], [no, X] represent the and, or, not operations applied to formulas X, Y.
  • [every, V, F], [exists, V, F] represent the forall & exists quantifiers applied to variable V in formula F.
  • Any other term x (identifier beginning with lower case letter) represents a variable x.
  • Instead of associative lists, we will use a list of true variables. Any variables not in the list are considered false.
Note that we use no and every in place of not and forall, since those names are already taken in Prolog.

Based on these definitions for boolean formulae, you need to implement the following functions for determining whether a formula is satisfiable.

Name Parameters Example
eval(F,A,R) F=formula to be evaluated
A=list of true variables (may be empty)
R=result (either t or f)
• F and A will always be given
• Not all variables in A must be free variables in F
?- eval(x,[x],R).
R = t.
?- eval([and,t,x],[x],R).
R = t.
varsOf(F,R) F=formula to be examined
R=list of free variables in F (sorted, no duplicates, may be empty)
• F will always be given
?- varsOf(x,R).
R = [x].
?- varsOf([every,x,x],R).
R = [].
sat(F,R) F=formula to be examined
R=list of true variables that satisfies (solves) F
• R must be sorted, no duplicates, and contain only free variables of F
• If multiple values are possible for R, may return them in any order
• May not return the same value for R multiple times
• Return R=[] if F is true with no true free variables
• Fail if F is not satisfiable
• F will always be given
?- sat(t,R).
R = [].
?- sat([or,x,y],R).
R = [x];
R = [x,y];
R = [y].
?- sat(f,R).

This is obviously a terse description; if you have further questions (once you have completed the rest of the assignment), as the course staff.


We have provided some sample tests for you, to help with the extra credit portion. To receive any extra credit you must get all of these tests to pass. The tests will not be public on the submit server, but will be kept secret, so that you are not prevented from release testing the regular part of the project. There will also be some secret tests (e.g., handling forall and exists). As described above, to execute a public test, you need to load both and the public test file into the Prolog interpreter, then call the appropriate public test function for each function you were required to implement. The public test functions are:
  • public_eval
  • public_varsOf
  • public_sat
If you want to run these public tests using the public test driver, you will need to edit it to uncomment-out the three functions listed above.


  • Unlike previous projects, you may be able to rely on Prolog's backtracking to find multiple possible solutions through multiple queries.
  • The Prolog functions findall will collect all results from a function using backtracking. The function setof will, in addition, sort the result and remove duplicates. These functions are used in the public tests.


You can submit your project in two ways:
  • Submit your file directly to the submit server by clicking on the submit link in the column "web submission".

    Next, use the submit dialog to submit your file.

    Select your file using the "Browse" button, then press the "Submit project!" button.

  • You may also submit directly by executing a Java program on a computer with Java and network access. Use the submit.jar file from the archive, To submit, go to the directory containing your project, then either execute submit.rb (preferred method) by typing:

    ruby submit.rb

    or use the java jar directly using the following command:

    java -jar submit.jar

    You will be asked to enter your class account and password, then all files in the directory (and its subdirectories) will be put in a jar file and submitted to the submit server. If your submission is successful you will see the message:

    Successful submission # received for project 5

Academic Integrity

The Campus Senate has adopted a policy asking students to include the following statement on each assignment in every course: "I pledge on my honor that I have not given or received any unauthorized assistance on this assignment." Consequently your program is requested to contain this pledge in a comment near the top.

Please carefully read the academic honesty section of the course syllabus. Any evidence of impermissible cooperation on projects, use of disallowed materials or resources, or unauthorized use of computer accounts, will be submitted to the Student Honor Council, which could result in an XF for the course, or suspension or expulsion from the University. Be sure you understand what you are and what you are not permitted to do in regards to academic integrity when it comes to project assignments. These policies apply to all students, and the Student Honor Council does not consider lack of knowledge of the policies to be a defense for violating them. Full information is found in the course syllabus---please review it at this time.

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