HOMEWORK 3.

Deadlines:
  For the exercises 1-5: Monday, November 1.
  For the exercise 6-7: Friday, November 5.


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1. 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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2. 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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3. 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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4. Define the relation flatten_list(InputList, FlatList) where
InputList can be a list with nested occurrences of lists, and
FlatList is InputList "flattened" so that the elements of
InputList's sublists (or sub-lists, sub-sub-lists, etc) are
reorganized as one plain list. For example,

?- flatten_list([a,b,[c,[d]],e],L).

L=[a,b,c,d,e];

no

?- flatten_list([a,b,[c,[]],e],L).

L=[a,b,c,e];

no

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5. Write a predicate that accepts a list and succeeds if that list
has exactly four elements, where the first and the third elements
are the same.

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6. 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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7. Assume you have to fly from Linz to Stockholm, and want to
examine possible connections between these two cities. There
are no direct flights. Therefore, you have to transfer. Write a
Prolog program that meets the requirements below:

- Choose at least one city where you will transfer.

- Represent the information on the flight timetable in a Prolog
database.

- Create the set of rules to find the possible flights given a started
time and a maximum waiting time in the transfer city (giving the
times of departure and arrival at each city).

- Make use of structures, if possible.

In addition, give a set of examples (just the question formulated)
asking questions about the info in the timetable.