Hi guys :) I have encountered problem during programming in prolog. I have partial order defined as facts, and I have defined maximal and greatest element as predicates. We can think of partial order like greater or equal, so le(6,7) is something like 6 <= 7.
le(6,7).
le(4,4).
le(6,6).
le(5,6).
le(5,5).
le(4,5).
le(4,4).
maximal(X) :-
not((le(X,Z) , X\=Z)).
greatest(X) :-
not(le(X,_)).
minimal(X) :-
not((le(Z,X) , X\=Z)).
smallest(X) :-
not(le(_,X)).
When I have typed query like maximal(7) the prolog output is true, and when I ask prolog to find the solution like maximal(X) it gives mi fail. I am beginner prolog programmer, so sorry if the question is too trivial, but I couldn't find the solution on my own.
Prologs uses pre-defined steps to find the answer and negation is always tricky.
To make a long story short, to make the code easier to reason about most logic should be positive and negation applied to expressions where values of all variables are known.
Here is how you could make the code work.
le(6,7).
le(4,4).
le(6,6).
le(5,6).
le(5,5).
le(4,5).
le(4,4).
is_my_number(X) :- le(X, _).
is_my_number(X) :- le(_, X).
equal_or_not_le(X, Y) :- X = Y.
equal_or_not_le(X, Y) :- not(le(X, Y)).
maximal(X) :- is_my_number(X), forall(is_my_number(Y), equal_or_not_le(X, Y)).
Then query:
?- maximal(X).
X = 7 .
Good luck!
Related
As title stated above, how to make this possible?
For example:
**Facts:**
parent(child, parent).
parent(child, parent2).
parent(child2, parent).
parent(child2, parent2).
**Rules:**
childof(X,Y) :- parent(Y, X).
number_of_child(X,Y):- X has Y number of child
How should I implement the number_of_child rules?
My expected answer is Y will show 2 (since there are child and child2) or something like that.
Thank you.
You should learn about setof/3, bagof/3 and findall/3. They are general prolog predicates to find all solutions.
If you want something swi-prolog specific just to count the solutions then you can use aggregate_all.
num_children(X, N) :- aggregate_all(count, child_of(X, _Y), N).
https://www.swi-prolog.org/FAQ/SingletonVar.html
I am working through Seven Languages in Seven Weeks, but there is something I don't understand about prolog. I have the following program (based on their wallace and grommit program):
/* teams.pl */
onTeam(a, aTeam).
onTeam(b, aTeam).
onTeam(b, superTeam).
onTeam(c, superTeam).
teamMate(X, Y) :- \+(X = Y), onTeam(X, Z), onTeam(Y, Z).
and load it like this
?- ['teams.pl'].
true.
but it doesn't give me any solutions to the following
?- teamMate(a, X).
false.
it can solve simpler stuff (which is shown in the book):
?- onTeam(b, X).
X = aTeam ;
X = superTeam.
and there are solutions:
?- teamMate(a, b).
true ;
false.
What am I missing? I have tried with both gnu prolog and swipl.
...AND THERE IS MORE...
when you move the "can't be your own teammate" restriction to then end:
/* teams.pl */
onTeam(a, aTeam).
onTeam(b, aTeam).
onTeam(b, superTeam).
onTeam(c, superTeam).
teamMate(X, Y) :- onTeam(X, Z), onTeam(Y, Z), \+(X = Y).
it gives me the solutions I would expect:
?- ['teams.pl'].
true.
?- teamMate(a, X).
X = b.
?- teamMate(b, X).
X = a ;
X = c.
What gives?
You have made a very good observation! In fact, the situation is even worse, because even the most general query fails:
?- teamMate(X, Y).
false.
Declaratively, this means "there are no solutions whatsoever", which is obviously wrong and not how we expect relations to behave: If there are solutions, then more general queries must not fail.
The reason you get this strange and logically incorrect behaviour is that (\+)/1 is only sound if its arguments are sufficiently instantiated.
To express disequality of terms in a more general way, which works correctly no matter if the arguments are instantiated or not, use dif/2, or, if your Prolog system does not provide it, the safe approximation iso_dif/2 which you can find in the prolog-dif tag.
For example, in your case (note_that_I_am_using_underscores_for_readability instead of tuckingTheNamesTogetherWhichMakesThemHarderToRead):
team_mate(X, Y) :- dif(X, Y), on_team(X, Z), on_team(Y, Z).
Your query now works exactly as expected:
?- team_mate(a, X).
X = b.
The most general query of course also works correctly:
?- team_mate(X, Y).
X = a,
Y = b ;
X = b,
Y = a ;
X = b,
Y = c ;
etc.
Thus, using dif/2 to express disequality preserves logical-purity of your relations: The system now no longer simply says false even though there are solutions. Instead, you get the answer you expect! Note that, in contrast to before, this also works no matter where you place the call!
The answer by mat gives you some high-level considerations and a solution. My answer is a more about the underlying reasons, which might or might not be interesting to you.
(By the way, while learning Prolog, I asked pretty much the same question and got a very similar answer by the same user. Great.)
The proof tree
You have a question:
Are two players team mates?
To get an answer from Prolog, you formulate a query:
?- team_mate(X, Y).
where both X and Y can be free variables or bound.
Based on your database of predicates (facts and rules), Prolog tries to find a proof and gives you solutions. Prolog searches for a proof by doing a depth-first traversal of a proof tree.
In your first implementation, \+ (X = Y) comes before anything else, so it at the root node of the tree, and will be evaluated before the following goals. And if either X or Y is a free variable, X = Y must succeed, which means that \+ (X = Y) must fail. So the query must fail.
On the other hand, if either X or Y is a free variable, dif(X, Y) will succeed, but a later attempt to unify them with each other must fail. At that point, Prolog will have to look for a proof down another branch of the proof tree, if there are any left.
(With the proof tree in mind, try to figure out a way of implementing dif/2: do you think it is possible without either a) adding some kind of state to the arguments of dif/2 or b) changing the resolution strategy?)
And finally, if you put \+ (X = Y) at the very end, and take care that both X and Y are ground by the time it is evaluated, then the unification becomes more like a simple comparison, and it can fail, so that the negation can succeed.
What is the best way to express a total order relation in Prolog ?
For example, say I have a set of facts
person(tim)
person(ana)
person(jack)
...
and I want to express the following truth about a person's fortune: for each two persons X and Y, if not(X==Y), either X is richer than Y or Y is richer than X.
So my problem is that the richer clause should be capable of instantiating its variables and also to ensure that it is never the case that richer(X, Y) and richer(Y, X) at the same time.
Here is a better example to see what I mean:
person(tim).
person(john).
happier(tim, john).
hates(X, Y) :- person(X), person(Y), richer(Y, X).
hates(X, Y) :- person(X), person(Y), richer(X, Y), happier(Y, X).
Now the answer to the query hates(john, tim) should return true, because if richer satisfies the mentioned property, one of those two hates clauses must be true. In a resolution based inference engine I could assert the fact (richer(X, Y) V richer(Y, X)) and the predicate hates(john, tim) could be proved to be true.
I don't expect to be able to express this the same way in Prolog with the same effect. However, how can I implement this condition so the given example will work ?
Note also that I don't know who is richer: tim or john. I just now that one is richer than the other.
Thank you.
you cannot write in pure Prolog that a predicate should be a total order: that would require higher order logic since you want to declare a property about a predicate.
this is a predicate that checks if a relationship is total order on a finite set:
is_total_order(Foo,Set):-
forall(
(member(X,Set),
member(Y,Set)),
(
XY =.. [Foo,X,Y],
YX =.. [Foo,Y,X],
(call(XY);call(YX)), %checking if the relationship is total
\+ (call(XY),call(YX), X\=Y) %checking if it's an order
)
).
the operator =../2 (univ operator) creates a predicate from a list (ie: X =.. [foo,4,2]. -> X = foo(4,2)) and the predicate call/1 calls another predicate.
As you can see we use meta-predicates that operate on other predicates.
For an total order on infinite sets things get more complicated since we cannot check every single pair as we did before. I dont even think that it can be written since proving that a relationship is a total order isn't something trivial.
Still, this doesnt declare that a predicate is a total order; it just checks if it is.
So I believe your question is the best way to represent the relation between these 3 people. If you don't actually care about their wealth #'s, just their relative order, you could add predicates like this -
is_richer(tim, anna).
is_richer(anna, jack).
and then a predicate to find all people who X is richer than -
richer(X, Z) :-
is_richer(X, Z).
richer(X, Z) :-
is_richer(X, Y),
richer(Y, Z).
If your is_richer predicate contains cycles though (in this example, if you added is_richer(jack, tim)), this could explode. You need to track where you have visited in this tree.
An example run of richer would be:
?- richer(X, Y).
X=tim
Y=anna ;
X=anna
Y=jack ;
X=tim
y=jack ;
no
(This is NOT a coursework question. Just my own personal learning.)
I'm trying to do an exercise in Prolog to delete elements from a list. Here's my code :
deleteall([],X,[]).
deleteall([H|T],X,Result) :-
H==X,
deleteall(T,X,Result).
deleteall([H|T],X,[H|Result]) :- deleteall(T,X,Result).
When I test it, I first get a good answer (ie. with all the Xs removed.) But then the backtracking offers me all the other variants of the list with some or none of the instances of X removed.
Why should this be? Why do cases where H==X ever fall through to the last clause?
When you are using (==)/2 for comparison you would need the opposite in the third rule, i.e. (\==)/2. On the other hand, such a definition is no longer a pure relation. To see this, consider deleteall([X],Y,Zs), X = Y.
For a pure relation we need (=)/2 and dif/2. Many Prologs like SWI, YAP, B, SICStus offer dif/2.
deleteall([],X,[]).
deleteall([H|T],X,Result) :-
H=X,
deleteall(T,X,Result).
deleteall([H|T],X,[H|Result]) :-
dif(H,X),
deleteall(T,X,Result).
Look at the answers for deleteall([X,Y],Z,Xs)!
Edit (after four years):
More efficiently, but in the same pure vein, this can be written using if_/3 and (=)/3:
deleteall([], _X, []).
deleteall([E|Es], X, Ys0) :-
if_( E = X, Ys0 = Ys, Ys0 = [E|Ys] ),
deleteall(Es, X, Ys).
The last clause says that when removing X from a list, the head element may stay (independently of its value). Prolog may use this clause at any time it sees fit, independently of whether the condition in the preceding clause is true or not backtrack into this clause if another clause fails, or if you direct it to do so (e.g. by issuing ; in the top-level to get the next solution). If you add a condition that the head element may not equal X, it should work.
Edit: Removed the incorrect assertion I originally opened with.
I know how to iterate over lists in Prolog to find the maximum, but what if each thing is a separate clause? For example if I had a bunch of felines and their ages, how would I find the oldest kitty?
cat(sassy, 5).
cat(misty, 3).
cat(princess, 2).
My first thought was "hmm, the oldest cat is the one for which no older exists". But I couldn't really translate that well to prolog.
oldest(X) :- cat(X, AgeX), cat(Y, AgeY), X \= Y, \+ AgeX < AgeY, print(Y).
This still errorenously matches "misty". What's the proper way to do this? Is there some way to more directly just iterate over the ages to choose max?
One way is
oldest(X) :- cat(X, AgeX), \+ Y^(cat(Y, AgeY), Y \= X, AgeX < AgeY).
You can also use setof/3 to get a list of all cats and get the maximum from that.
A cat is the oldest if it's a cat and there is not a cat older than it. Let's write that in Prolog:
oldest(X):- cat(X, _), not( thereAreOlders(X)), !.
thereAreOlders(X):- cat(X, N), cat(C, M), C\=X, M > N.
If you consult:
?- oldest(X).
X = sassy.
Here is a solution that loops through all the solutions, always recording the solution that is better than the previous best. In the end, the best solution is returned.
The recording is done using assert/1, you could also use a non-backtrackable global variable if your Prolog provides that (SWI-Prolog does).
The benefit of this approach is that is considers each solution only once, i.e. complexity O(n). So, even though it looks uglier than starblue's solution, it should run better.
% Data
cat(sassy, 5).
cat(misty, 3).
cat(miisu, 10).
cat(princess, 2).
% Interface
oldest_cat(Name) :-
loop_through_cats,
fetch_oldest_cat(Name).
loop_through_cats :-
cat(Name, Age),
record_cat_age(Name, Age),
fail ; true.
:- dynamic current_oldest_cat/2.
record_cat_age(Name, Age) :-
current_oldest_cat(_, CAge),
!,
Age > CAge,
retract(current_oldest_cat(_, _)),
assert(current_oldest_cat(Name, Age)).
record_cat_age(Name, Age) :-
assert(current_oldest_cat(Name, Age)).
fetch_oldest_cat(Name) :-
retract(current_oldest_cat(Name, _Age)).
Usage example:
?- oldest_cat(Name).
Name = miisu
Miisu is a typical Estonian cat name. ;)
On a stylistic point- there are a few different approaches here (some are very elegant, others more 'readable'). If you're a beginner- chose your own, preferred, way of doing things- however inefficient.
You can learn techniques for efficiency later. Enjoy Prolog- its a beautiful language.
I don't remember much Prolog, but I do know that you shouldn't think about solving problems as you would with an imperative programming language.