Summary of Chapter 6

Many programming languages provide 'for loops' which enable a set of instructions to be executed a fixed number of times. No such facility is available in Prolog (directly), but a similar effect can be obtained using recursion, as shown in the example programs below.

Example 1

The following program outputs integers from a specified value down to 1.

loop(0).
loop(N):-N>0,write('The value is: '),write(N),nl,
M is N-1,loop(M).

The loop predicate is defined in terms of itself. The second clause can be thought of as: 'to loop from N, first write the value of N, then subtract one to give M, then loop from M'. This process clearly needs to be terminated and this is achieved by the first clause: 'when the argument is zero, do nothing (and hence stop)'. The first clause can be regarded as a terminating condition for the recursion.

?- loop(6).
The value is: 6
The value is: 5
The value is: 4
The value is: 3
The value is: 2
The value is: 1
yes

Example 2

The next program outputs integers from First to Last inclusive.
/* output integers from First to Last inclusive */
output_values(Last,Last):- write(Last),nl,
write('end of example'),nl.
output_values(First,Last):-First=\=Last,write(First),
nl,N is First+1,output_values(N,Last).

Here output_values has two arguments, which can be read as 'output the integers from First to Last inclusive'. The loop terminates when both arguments are the same.

?- output_values(5,12).
5
6
7
8
9
10
11
12
end of example
yes

Looping Until a Condition Is Satisfied

Many languages have an 'until loop' which enables a set of instructions to be
executed repeatedly until a given condition is met. Again, no such facility is
available directly in Prolog, but a similar effect can be obtained in several ways.

Recursion

The first example below shows the use of recursion to read terms entered by the
user from the keyboard and output them to the screen, until end is encountered.

go:-loop(start). /* start is a dummy value used to get the looping process started.*/
loop(end).
loop(X):-X\=end,write('Type end to end'),read(Word),
write('Input was '),write(Word),nl,loop(Word).

?- go.
Type end to end: university.
Input was university
Type end to end: of.
Input was of
Type end to end: portsmouth.
Input was portsmouth
Type end to end: end.
Input was end
yes

Using the 'repeat' Predicate

Although it can often be used to great effect, recursion is not always the easiest way to provide the types of looping required in Prolog programs. Another method that is often used is based on the built-in predicate repeat. The name of this predicate is really a misnomer. The goal repeat does not repeat anything; it merely succeeds whenever it is called. The great value of repeat is that it also succeeds (as many times as necessary) on backtracking. The effect of this, as for any other goal succeeding, is to change the order of evaluating goals from 'right to left' (i.e. backtracking) back to 'left-to-right'. This can be used to create a looping effect, as shown in the examples below. This program repeatedly prompts the user to enter a term until either yes or no is entered. It is an alternative to the recursive program shown at the end of the previous section. In this case it is debatable whether using repeat is an improvement on using recursion, but the example is included for purposes of illustration.

get_answer(Ans):-
write('Enter answer to question'),nl,
repeat,write('answer yes or no'),read(Ans),
valid(Ans),write('Answer is '),write(Ans),nl.
valid(yes). valid(no).

The first five goals in the body of get_answer will always succeed. Evaluating the fifth goal: read(Ans) will prompt the user to enter a term. If the term input is anything but yes or no, say unsure, the following goal valid(Ans) will fail. Prolog will then backtrack over read(Ans) and write('answer yes or no'), both of which are unresatisfiable, i.e. will always fail on backtracking. Backtracking will then reach the predicate repeat and succeed, causing evaluation to proceed forward (left-to-right) again, with write('answer yes or no') and read(Ans) both succeeding, followed by a further evaluation of valid(Ans). Depending on the value of Ans, i.e. the user's input, the valid(Ans) goal will either fail, in which case Prolog will backtrack as far as repeat, as before, or it will succeed in which case the final three goals write('Answer is'), write(Ans) and nl will all succeed. The overall effect is that the two goals write('answer yes or no') and read(Ans) are called repeatedly until the terminating condition valid(Ans) is satisfied, effectively creating a loop between repeat and valid(Ans).

?- get_answer(X).
Enter answer to question
answer yes or no: unsure.
answer yes or no: possibly.
answer yes or no: no.
answer is no
X = no

Goals to the left of repeat in the body of a clause will never be reached on backtracking.

Backtracking with Failure

As the name implies, the predicate fail always fails, whether on 'standard' evaluation left-to-right or on backtracking. Advantage can be taken of this, combined with Prolog's automatic backtracking, to search through the database to find all the clauses with a specified property.

Searching the Prolog Database

Supposing the database contains clauses such as
dog(fido).
dog(fred).
dog(jonathan).

Each dog clause can be processed in turn using the alldogs predicate defined below.

alldogs:-dog(X),write(X),write(' is a dog'),nl,fail.
alldogs.

Calling alldogs will cause dog(X) to be matched with the dog clauses in the database. Initially X will be bound to fido and 'fido is a dog' will be output. The final goal in the first clause of the alldogs predicate will then cause evaluation to fail. Prolog will then backtrack over nl and the two write goals (all of which are unresatisfiable) until it reaches dog(X). This goal will succeed for a second time causing X to be bound to fred.

This process will continue until fido, fred and jonathan have all been output, when evaluation will again fail. This time the call to dog(X) will also fail as there are no further dog clauses in the database. This will cause the first clause for alldogs to fail and Prolog to examine the second clause of alldogs. This will succeed and evaluation will stop.

The effect is to loop through the database finding all possible values of X that satisfy the goal dog(X).

?- alldogs.
fido is a dog
fred is a dog
jonathan is a dog
yes

Note the importance of the second clause of the alldogs predicate. It is there to ensure that, after the database has been searched, the goal succeeds. With only the first line, any call to alldogs will eventually fail.

alldogs:-dog(X),write(X),write(' is a dog'),nl,fail.

?- alldogs.
fido is a dog
fred is a dog
jonathan is a dog
no

Finding Multiple Solutions

Backtracking with failure can also be used to find all the ways of satisfying a goal. Suppose that a predicate findroute(Town1,Town2,Route) finds a route Route between two towns Town1 and Town2. The details of this predicate are irrelevant here. It may be assumed that Town1 and Town2 are atoms and that Route is a list. Backtracking with failure can then be used to find all possible routes between Town1 and Town2 and write out each one on a separate line, as follows:

find_all_routes(Town1,Town2):-
findroute(Town1,Town2,Route),
write('Possible route: '),write(Route),nl,fail.
find_all_routes(_,_).