157 lines
6.9 KiB
Text
157 lines
6.9 KiB
Text
|
(Print this page as a cover sheet for your printouts)
|
||
|
|
|
||
|
|
CSCE 420 HOMEWORK 3
|
||
|
|
Dr. Daugherity
|
||
|
|
Due: 11:59 P.M. Wednesday, November 15, 2017
|
||
|
|
|
||
|
|
"On my honor, as an Aggie, I have neither given nor received any unauthorized
|
||
|
|
aid on any portion of the academic work included in this assignment."
|
||
|
|
|
||
|
|
|
||
|
|
________________________________ ________________________________
|
||
|
|
Typed or printed name of student Signature of student
|
||
|
|
|
||
|
|
NOTE: Please follow your lab instructor's directions for submitting your
|
||
|
|
assignment through CSNET. ONLY ASSIGNMENTS SUBMITTED TO CSNET WILL BE GRADED!
|
||
|
|
Make a printout of each source file and staple it behind this cover sheet.
|
||
|
|
Sign it and turn it in in class Tuesday. IF YOU DO NOT TURN IN A SIGNED COVER
|
||
|
|
SHEET YOUR WORK WILL NOT BE GRADED!
|
||
|
|
|
||
|
|
NOTE: Homework will be graded on build.tamu.edu using gprolog 1.4.4.
|
||
|
|
|
||
|
|
You are free to develop your programs on any other platform, but it is your
|
||
|
|
responsibility to make sure your programs also compile and execute correctly on
|
||
|
|
build.tamu.edu as specified.
|
||
|
|
|
||
|
|
NOTE: Each file submitted (hw3pr1.pl, etc.--see below) must begin as follows:
|
||
|
|
//Your name and UIN
|
||
|
|
//CSCE 420
|
||
|
|
//Due: November 15, 2017
|
||
|
|
//hw3pr1.pl (or whatever this file name is)
|
||
|
|
|
||
|
|
NOTE: Also write a README.txt file with whatever information is needed to
|
||
|
|
compile and run your programs. Zip the README.txt and the homework files into
|
||
|
|
a single file named hw3.zip and submit to CSNET.
|
||
|
|
|
||
|
|
The grade for this lab will be based on style (formatting, variable names,
|
||
|
|
comments, etc.), syntax (no compilation or link errors), and correctness
|
||
|
|
(passes all test cases). Your grade for this lab is:
|
||
|
|
Problem # 1 2 3 4
|
||
|
|
Style /2 /4 /4 /2
|
||
|
|
Syntax /3 /6 /6 /3
|
||
|
|
Correctness /5 /10 /10 /5
|
||
|
|
-------------------------------------------------------------------
|
||
|
|
Total /10 /20 /20 /10
|
||
|
|
Grand total _____/50
|
||
|
|
|
||
|
|
1. (10 points) Use the my_max predicate developed in lecture to write a PROLOG
|
||
|
|
predicate my_sort(Unsorted, Sorted) using the following pseudocode outline:
|
||
|
|
|
||
|
|
Base cases go first.
|
||
|
|
my_sort(Unsorted, Sorted) :- Max is the largest element of Unsorted and
|
||
|
|
Unsorted2 is what is left after removing Max from Unsorted and
|
||
|
|
the sorted version of Unsorted2 is Sorted2 and
|
||
|
|
Sorted2 is Sorted without its last element Max.
|
||
|
|
|
||
|
|
Hint: Use the builtin append and select predicates.
|
||
|
|
|
||
|
|
Name your program hw3pr1.pl. Don't forget to try lots of test cases, like
|
||
|
|
sorting [2, 1, 1, 3, 2]. You can check your sort against the builtin predicate
|
||
|
|
msort (not sort).
|
||
|
|
|
||
|
|
Note: This is an inefficient way to do max and sort; the point of this problem
|
||
|
|
is to learn to think in PROLOG (i.e., recursively).
|
||
|
|
|
||
|
|
2. (20 points) Modify problem 1 to do a topological sort of a partial order,
|
||
|
|
which is a list of ordered pairs [left, right] which you can think of as
|
||
|
|
meaning left<=right. The predicate to define is
|
||
|
|
my_topo_sort(Partial_order, Total_order).
|
||
|
|
|
||
|
|
For example, we might have [[left_sock, left_shoe], [right_sock, right_shoe]]
|
||
|
|
to describe the constraints on the order in which to get dressed.
|
||
|
|
|
||
|
|
A topological sort of a partial order then produces a total order, which is a
|
||
|
|
linearization consistent with the partial order. For the example above,
|
||
|
|
[left_sock, left_shoe, right_sock, right_shoe] and
|
||
|
|
[left_sock, right_sock, left_shoe, right_shoe] would both be acceptable
|
||
|
|
linearizations. No linearization is possible in the case of a circular
|
||
|
|
majority, e.g., [[a,b], [b,c], [c,a]], since <= is transitive (unless of course
|
||
|
|
a, b, and c are all the same).
|
||
|
|
|
||
|
|
To code a topological sort in PROLOG we can use "negation as failure" so that
|
||
|
|
if we cannot prove two elements in the list to be topologically sorted are
|
||
|
|
out of order, we can assume they are not out of order (the closed-world
|
||
|
|
assumption). That allows us to say an element of a list is the max if we can't
|
||
|
|
prove it's not the max.
|
||
|
|
|
||
|
|
For the example above, first make a list of all the elements in all the
|
||
|
|
constraints: [left_sock, left_shoe, right_sock, right_shoe]. Then eliminate
|
||
|
|
duplicates (if any). Next sort as in problem 1 but with my_max finding an
|
||
|
|
element M which you can't prove is not the maximum (i.e., you can't prove there
|
||
|
|
is a constraint [M, M2] in the list of constraints, which would mean M2 >= M
|
||
|
|
and M would not be guaranteed to be the maximum).
|
||
|
|
|
||
|
|
Name your program hw3pr2.pl. Don't forget to try lots of test cases in addition
|
||
|
|
to
|
||
|
|
?-my_topo_sort([[left_sock, left_shoe], [right_sock, right_shoe]], TotalOrder).
|
||
|
|
|
||
|
|
3. (20 points) Add the next generation to Figure 8.7 (i.e., William's wife and
|
||
|
|
children, etc.) and then do Exercise 8.14 on page 318 in PROLOG. However, you
|
||
|
|
do not need to write mth cousin n times removed. You may add additional
|
||
|
|
predicates if needed. Follow the PROLOG convention of only capitalizing
|
||
|
|
variable names; e.g,
|
||
|
|
|
||
|
|
?- mother(X, charles).
|
||
|
|
|
||
|
|
returns X = elizabeth. You should write enough predicates to deduce
|
||
|
|
|
||
|
|
?- grandchild(X, elizabeth).
|
||
|
|
?- brother_in_law(X, diana).
|
||
|
|
?- ancestor(X, eugenie).
|
||
|
|
|
||
|
|
as specified, plus
|
||
|
|
|
||
|
|
?- cousin(X, charlotte).
|
||
|
|
|
||
|
|
Name your program hw3pr3.pl.
|
||
|
|
|
||
|
|
Hints: Remember gprolog requires that you place all statements for each
|
||
|
|
predicate together. Also, be careful writing too many statements or you may
|
||
|
|
cause an infinite loop, e.g.,
|
||
|
|
|
||
|
|
child(A, B) :- parent(B, A).
|
||
|
|
parent(A, B) :- child(B, A).
|
||
|
|
|
||
|
|
is true logically but may cause PROLOG to loop till stack space is exhausted.
|
||
|
|
|
||
|
|
OPTIONAL EXTRA CREDIT
|
||
|
|
=====================
|
||
|
|
4. (10 points) Problem 3 returns true for ancestor(george, george), unless
|
||
|
|
you used database semantics, but according to the less-than-memorable Ray
|
||
|
|
Stevens song (https://www.youtube.com/watch?v=eYlJH81dSiw and
|
||
|
|
and www.metrolyrics.com/im-my-own-grandpa-lyrics-ray-stevens.html), problem 3
|
||
|
|
can be extended to prove that you are your own grandpa!
|
||
|
|
|
||
|
|
The story (from Niklaus Wirth's "Algorithms + Data Structures = Programs")
|
||
|
|
is as follows:
|
||
|
|
I married a widow W who has a grown daughter D. My
|
||
|
|
father F, who visited us quite often, fell in love with
|
||
|
|
my step-daughter and married her. Hence my father
|
||
|
|
became my son-in-law and my step-daughter became my
|
||
|
|
mother. Some months later, my wife gave birth to a son
|
||
|
|
S1, who became the brother-in-law of my father, as well
|
||
|
|
as my uncle. The wife of my father, that is, my
|
||
|
|
step-daughter, also had a son S2.
|
||
|
|
|
||
|
|
First write the facts and relationships in the song as predicate calculus
|
||
|
|
clauses, e.g., "If X is the child of Y and Y is the child of Z and Z is male
|
||
|
|
then Z is the grandpa of X" becomes
|
||
|
|
Child(X,Y) AND Child(Y,Z) AND Male(Z) --> Grandpa(Z,X)
|
||
|
|
and so on, and then write as PROLOG statements. Note: You will need to be
|
||
|
|
pretty loose in your definitions of family relationships; e.g., stepchild must
|
||
|
|
also count as child. Also, you will have to write explicitly some necessary
|
||
|
|
clauses which are only implied by the song, e.g., Male(me). The gprolog query
|
||
|
|
is then
|
||
|
|
?-grandpa(me,me).
|
||
|
|
Name your program hw3pr4.pl.
|