HOMEWORK 2.

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1. Exercise 2.1 (from the book).

Say whether the following goals would succeed, and which variables, if
any, would be instantiated to what values:

pilots(A,london) = pilots(london,paris)

point(X,Y,Z) = point(X1,Y1,Z1)

letter(C) = word(letter)

noun(alpha) = alpha

'vicar' = vicar

f(X,X) = f(a,b)

f(X,a(b,c)) = f(Z,a(Z,c)).

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2. Write a predicate that accepts a list and succeeds if that list has
exactly three elements.

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3. Write a predicate that accepts a list and generates from it a similar
list with the first two elements swapped.

It should work like this:

?-swap_first_two([a,b,c,d], [b,a,c,d]).

Yes

?-swap_first_two([a,b,c,d], X).

X= [b,a,c,d];

No

?-swap_first_two(X, [b,a,c,d]).

X=[a,b,c,d];

No

?-swap_first_two([a,b,c,d], [b,a,d,c]).

No

?-swap_first_two([a,b,c,d], [X,Y,c,d]).

X=b
Y=a;

No

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4. Exercise 3.1 from the book:

You have the program:

aless(X,Y):-name(X,L), name(Y,M),alessx(L,M).
alessx([],[_|_]).
alessx([X|_],[Y|_]):-X<Y.
alessx([H|Q],[H|S]):-alessx(Q,S).

Work out what clause you need to add to this definition so that it succeeds
when the two words are equal. This would create a predicate that checks if
the first argument is alphabetically less then or equal the seconds
argument. Hint: look at condition (4) in the book, and insert a clause to
handle it.

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5. Exercise 3.2 from the book:

Why does the first rule of alessx in the program above have [_|_]? Why is
[_] insufficient for the purpose?


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6. Define the relation reverse_list(List, Reversed_List) that
reverses lists, e.g.:

?- reverse_list([a,b,c,d],[d,c,b,a]).

yes

?- reverse_list([a,b,c,d],X).

X=[d,c,b,a];

No

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7. Define the predicate palindrome(List) that recognizes palindromes.

A list is a palindrome if it reads the same in the forward and in
the backward direction. For example:

?- palindrome([m,a,d,a,m]).

yes

?- palindrome([s,i,r]).

No

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8. Define the relation shift(List1, List2) so that List2 is List1
"shifted rotationally" by one element to the left. For example,

?- shift([1,2,3,4,5], L1), shift(L1,L2).

L1=[2,3,4,5,1]
L2=[3,4,5,1,2];

No

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9. Define the relation maximum(List,Integer) that succeeds if Integer
is the maximal element of the list of integers List. Example,

?- maximum([1,2,3,4,2,-1,4],Max).

Max=4;

No

?- maximum([],Max).

No