UNIVERSITÄT BASEL
Thorsten Möller
Florian Spiess - [email protected]
Programming Paradigms – Prolog
Exercise 5
FS 2017
Due: 28.05.2017 23:59:59
Upload answers to the questions and source code before the deadline via
courses.cs.unibas.ch. Since this is the last exercise, running programs do not
have to be demonstrated during the exercise slots; only uploaded answers and
source will be graded. Also note, of all mandatory exercises given throughout the
course, you must score at least 2/3 of their total sum of points to get accepted
in the final exam.
Modalities of work: The exercise can be completed in groups of at the most
2 people. Do not forget to provide the full name of all group members together
with the submitted solution.
IMPORTANT: Because you will not have to present your answers to this exercise
during the exercise lesson, you will have no chance to explain your answers. Please make
sure that all your answers contain detailed explanations and are thoroughly documented.
If your answer is ambiguous, unclear or your code is insufficiently documented, you will
not be awarded the full score.
Additionally, don’t forget to include the names of all team members in your answer,
otherwise your answer might be corrected twice and, as a result, be falsely identified as
plagiarism.
Question 1: Bite-sized Prolog Tasks
(5 points)
For each of the following task descriptions write Prolog facts and/or rules that complete
the task.
Also include an example usage of the predicate that completes the task in a separate text
file or as a comment in the code.
a) Check if a list is sorted, assuming that it contains numerical values only.
Example:
?- sorted([2,3,1]).
false.
(1 points)
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b) Check if a three digit number is divisible without remainder, by another three digit
number. (Your predicate should also be able to suggest possible divisors.)
Example:
?- isDivisible(999,X).
X = 1 ;
X = 3 ;
X = 9 ;
X = 27 ;
X = 37 ;
X = 111 ;
X = 333 ;
X = 999.
(2 points)
c) Check if a number is a prime.
Example:
?- isPrime(13).
true.
(2 points)
Question 2: Knowledge Base
(5 points)
The following is a list of character occurrences in the first act of Shakespeare’s play
Macbeth:
2
Act 1, Scene 1:
- First Witch
- Second Witch
- Third Witch
Act 1, Scene 2:
- Duncan
- Malcolm
- Donalbain
- Lennox
- Ross
- Sergeant
- Attendants
Act 1, Scene 3:
- First Witch
- Second Witch
- Third Witch
- Macbeth
- Banquo
- Ross
- Angus
Act 1, Scene 4:
- Duncan
- Malcolm
- Donalbain
- Lennox
- Macbeth
- Banquo
- Ross
- Angus
- Attendants
Act 1, Scene 5:
- Lady Macbeth
- Messenger
- Macbeth
Act 1, Scene 6:
- Duncan
- Malcolm
- Donalbain
- Banquo
- Lennox
- Macduff
- Ross
- Angus
- Attendants
- Lady Macbeth
Act 1, Scene 7:
- Macbeth
- Lady Macbeth
a) Write a Prolog knowledge base containing the above information.
It should be possible to check if a character is in a given act and scene. The act should
be part of the predicate to allow extension of the knowledge base for further acts.
It should be possible to query the knowledge base to find out, for example, in what
scenes a given character is present.
(4 points)
b) Explain the concept of backtracking in Prolog, including how it is responsible for
being able to find a complete list of scenes in which a character is present in your
implementation.
(1 points)
Question 3: 4x4 Sudoku
(8 points)
4x4 Sudoku is a simplified version of sudoku (https://en.wikipedia.org/wiki/Sudoku),
using only four 2x2 blocks of numbers instead of nine 3x3 blocks.
In this task you will write a Prolog program that can solve such simple Sudokus.
a) Write a predicate piece/1 that checks whether a variable is a valid number for a 4x4
Sudoku (1-4).
(1 points)
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b) Write a predicate valid/1 that checks that a list contains no duplicate values.
(1 points)
c) Use your piece and valid predicates and write a predicate that can find a solution
to a partially solved 4x4 sudoku and determine if a given solution is valid.
Example:
?- simple([_,1,3,_,2,_,_,_,_,_,_,3,_,2,1,_],Row1,Row2,Row3,Row4).
Row1 = [4, 1, 3, 2],
Row2 = [2, 3, 4, 1],
Row3 = [1, 4, 2, 3],
Row4 = [3, 2, 1, 4] .
(6 points)
Question 4: More Steganography
(5 points)
The following (rather strange) paragraph about the French novelist Balzac contains a
hidden quote from the english translation of Dai Sijie’s novel ”Balzac et la Petit Tailleuse
chinoise”. In this task you will write a Prolog program to extract this quote with the
included array of indices.
”Balzac was a French novelist and playwright. His work inspired many fellow writers
and is referenced in Dai Sijie’s ’Balzac and the Little Chinese Seamstress’, in which an
uneducated mountain girl is transformed, and touched by the power of literature. He did
not include an invisible wizard. This work proves the little seamstress had at least one
finger, and a head with which she carried readers away to this dream.”
[47, 11, 0, 14, 2, 46, 40, 34, 21, 60, 38, 68, 29, 30, 61, 27, 45, 57, 5, 63, 1, 32, 64, 66, 16,
2, 69]
Write a predicate decipher/3 where the first argument is a string, the second a list of
indices and the third is the resultant string such that the indices are replaced with the
corresponding words from the string. Note that counting starts with zero, not one.
Example:
?- decipher("I think apples are very much like pears.", [0,6,2], Result).
Result = ’I like apples’ .
Check your implementation with the given paragraph and index array. The result should
be a meaningful string.
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