Programming Paradigms-Lab 11 Solved

Understanding member
Exercise 11.1(a)
Draw the search tree for the query member(3, [X, 3, Y]).

member member
(X, [X|_]).

(X, [_|T]) :- member(X, T).

Understanding member
Exercise 11.1(b)
Verify your solution to Exercise 11.1(a):

Run the following query in SWISH and hit “Step into” button repeatedly.

?- trace, member(X, [X|_]).

 

List prefix
Exercise 11.2
Implement a predicate prefix/2 that checks if a given list is a prefix of another list.

?- prefix([1, 2], [1, 2, 3, 4]) true

?- prefix(X, [1, 2, 3])

X = []

X = [1]

X = [1, 2]

X = [1, 2, 3]

Interleaving lists
Exercise 11.3
Implement a predicate interleave/3 that checks if first two lists give the third when interleaved.

?- interleave([1, 2], [a, b], X) X = [1, a, 2, b]

?- interleave([1, 2], [a, b, c], X) X = [1, a, 2, b, c]

?- interleave(X, Y, [1, 2, 3, 4])

X = [1, 3], Y = [2, 4]

Squares
Exercise 11.4
Implement a predicate squares/2 that checks if the second list is a list of squares of numbers from the first list (in the same order).

?- squares([1, 2, 3, 4], X)

X = [1, 4, 9, 16]

Selecting elements from lists
Exercise 11.5
Implement a predicate select/3 that splits a list into its element a list of remaining elements.

?- select([6, 3, 8, 5], X, R)

H = 6, R = [3, 8, 5]

H = 3, R = [6, 8, 5]

H = 8, R = [6, 3, 5]

H = 5, R = [6, 3, 8]

Permutations
Exercise 11.6
Implement a predicate anagram/2 that checks whether a list is a permutation of another list.

?- anagram([d,o,r,m,i,t,o,r,y], [d,i,r,t,y, r,o,o,m]) true

?- anagram([1, 2], X)

X = [1, 2]

X = [2, 1]

A logic puzzle
Exercise 11.7
There is a street with three neighbouring houses that all have a different colour, namely red, blue, and green. People of different nationalities live in the different houses and they all have a different pet. Here are some more facts about them:

●        The Englishman lives in the red house.

●        The jaguar is the pet of the Spanish family.

●        The Japanese lives to the right of the snail keeper.

●        The snail keeper lives to the left of the blue house.

Who keeps the zebra? Don’t work it out for yourself: define a predicate zebra/1 that tells you the nationality of the owner of the zebra!

Hint: Think of a representation for the houses and the street.

Code the four constraints in Prolog. You may find member/2 and sublist/2 useful.

Sorted lists
Exercise 11.8
Implement a predicate sorted/1 that checks if a list is sorted.

?- sorted([6, 3, 8, 5]) false

?- sorted([3, 5, 6, 8]) true

Sorted lists
Exercise 11.9
Implement a predicate sort/2 that checks if the second list is a sorted version of the first one.

?- sort([6, 3, 8, 5], X)

X = [3, 5, 6, 8]

Shuffling both ways
Exercise 11.10 (***)
Examine current implementation of shuffled/2. Explain why it’s not working in one direction. Update the implementation of shuffled/2 to work in both directions:

?- shuffled([1, 2], X)

X = [1, 2]

X = [2, 1]

?- shuffled(X, [1, 2])

X = [1, 2]

X = [2, 1]