Directed graphs in prolog - prolog

I have a graph that I am creating rules on. owes money graph
I have created rules that shows who owes money to who
owes(alice,5,charlie).
owes(alice,20,bob).
owes(bob,10,charlie).
I have created rules that display who owes someone under a certain amount or over
owesOver10(X,Y) :-owes(X,Y,Z),(Y>=10).
owesUnder10(X,Y) :-owes(X,Y,Z),(Y<10).
however know I need to write a rule that shows how much money a person owes in total so for instance it should display 25 for alice, and 10 for bob.

I propose the use of findall/3 to get a list of all owes and a simple sumList/2 to get the sum of the values.
By example
listSum([], 0).
listSum([H | T], S0) :-
listSum(T, S1),
S0 is S1 + H.
totOwes(X, S) :-
findall(Y, owes(X, Y, _), L),
listSum(L, S).
Calling totOwes(alice, S), I get that S is unified with 25; for bob with 10 and for charlie with 0.

Related

How to add limit in prolog?

Previously I wrote the predicate, reach(Arrivals,Departure) to find a list of names of departure points from which I can get to a given point arrivals. Now, how can I make sure that the total cost from the calculated route does not exceed a given limit, for example now it`s work like this:
?-reach(krum, Departure).
Answer: Departure = [uzhorod].
in this example, the total cost of the route = 6000, how can it be implemented if 7000 is entered, it is false and if 6000 is true.
This is my facts:
trip(01, kuiv, odessa, 1500).
trip(02, kuiv, lviv, 700).
trip(08, lviv, zaporizhya, 700).
trip(03, uzhorod, krum, 6000).
trip(04, vunohradiv, odessa, 2540).
trip(05, ternopil, kuiv, 3800).
trip(06, zaporizhya, donetsk, 900).
trip(07, lytsk, mariupol, 7500).
trip(Id, Departure, Arrivals, Price)
This is my code:
reachable(D, D, _).
reachable(Departure, Arrival, Visited) :-
trip(_, Departure, Point, _),
\+ member(Point, Visited),
reachable(Point, Arrival, [Point|Visited]).
reachable(Departure, Arrival) :-
reachable(Departure, Arrival, [Departure]).
reach(Arrival, Departures) :-
setof(
Departure,
reachable(Departure, Arrival),
Departures
).

List processing calculation in Prolog to find a destination friends will visit

I'm trying to write a predicate that calculates which destination a group of friends will visit.
The friends list their countries of preferences like this
choice(marie, [peru,greece,vietnam]).
choice(jean, [greece,peru,vietnam]).
choice(sasha, [vietnam,peru,greece]).
choice(helena,[peru,vietnam,greece]).
choice(emma, [greece,peru,vietnam]).
I want to write a predicate called where that takes 2 arguments to perform the calculation.
The formula I have in mind is that the first country is worth 3 points, the second one is worth 2 points, and the last one is worth 1 point.
Here's an example of what I'm trying to achieve.
?- where([marie,jean,sasha,helena,emma],Country).
peru .
So far I have this
where([], X).
where([H|T], N) :- choice(H, [A|B]), where(T,N).
It lets me iterate through all the different friends and shows their choices but I can't iterate through the list of choices and assign points to the destinations.
How should I go about iterating through the list of choices for each friend and assigning points to calculate the best destination?
While this will solve your problem, I know it uses many predicates that you have not seen. So think of this an opportunity to excel and learn a lot.
Even if you don't understand it all, there is enough detail and intermediate results in the test that you should be able to navigate your way to a proper solution you create.
Also this is by no means efficient, it was just a quick proof of concept I did to see how this could be done.
choice(marie, [peru,greece,vietnam]).
choice(jean, [greece,peru,vietnam]).
choice(sasha, [vietnam,peru,greece]).
choice(helena,[peru,vietnam,greece]).
choice(emma, [greece,peru,vietnam]).
destinations(Destinations) :-
findall(D1,choice(_,D1),D2),
flatten(D2,D3),
list_to_set(D3,Destinations).
init_weights(Destinations,Weights) :-
empty_assoc(Assoc),
init_weights(Destinations,Assoc,Weights).
init_weights([],Weights,Weights).
init_weights([H|T],Assoc0,Weights) :-
put_assoc(H,Assoc0,0,Assoc1),
init_weights(T,Assoc1,Weights).
update_weights([C1,C2,C3],Weights0,Weights) :-
del_assoc(C1,Weights0,Value0,Weights1),
Value1 is Value0 + 3,
put_assoc(C1,Weights1,Value1,Weights2),
del_assoc(C2,Weights2,Value2,Weights3),
Value3 is Value2 + 2,
put_assoc(C2,Weights3,Value3,Weights4),
del_assoc(C3,Weights4,Value4,Weights5),
Value5 is Value4 + 1,
put_assoc(C3,Weights5,Value5,Weights).
person_weight(Person,Weights0,Weights) :-
choice(Person,[C1,C2,C3]),
update_weights([C1,C2,C3],Weights0,Weights).
people(People) :-
findall(Person,choice(Person,_),People).
choice(Destination) :-
destinations(Destinations),
init_weights(Destinations,Weights0),
people(People),
update_choices(People,Weights0,Weights1),
cross_ref_assoc(Weights1,Weights),
max_assoc(Weights, _, Destination),
true.
cross_ref_assoc(Assoc0,Assoc) :-
assoc_to_list(Assoc0,List0),
maplist(key_reverse,List0,List),
list_to_assoc(List,Assoc).
key_reverse(Key-Value,Value-Key).
update_choices([],Weights,Weights).
update_choices([Person|People],Weights0,Weights) :-
person_weight(Person,Weights0,Weights1),
update_choices(People,Weights1,Weights).
Tests
:- begin_tests(destination).
test(destinations) :-
destinations([peru, greece, vietnam]).
test(init_weights) :-
destinations(Destinations),
init_weights(Destinations,Weights),
assoc_to_list(Weights,[greece-0, peru-0, vietnam-0]).
test(update_weights) :-
destinations(Destinations),
init_weights(Destinations,Weights0),
update_weights([peru,greece,vietnam],Weights0,Weights),
assoc_to_list(Weights,[greece-2,peru-3,vietnam-1]).
test(person_weight) :-
destinations(Destinations),
init_weights(Destinations,Weights0),
person_weight(jean,Weights0,Weights),
assoc_to_list(Weights,[greece-3,peru-2,vietnam-1]).
test(people) :-
people([marie,jean,sasha,helena,emma]).
test(update_choices) :-
destinations(Destinations),
init_weights(Destinations,Weights0),
people(People),
update_choices(People,Weights0,Weights),
assoc_to_list(Weights,[greece-10,peru-12,vietnam-8]).
test(cross_ref_assoc) :-
List0 = [1-a,2-b,3-c],
list_to_assoc(List0,Assoc0),
cross_ref_assoc(Assoc0,Assoc),
assoc_to_list(Assoc,[a-1,b-2,c-3]).
test(choice) :-
choice(peru).
:- end_tests(destination).
As suggested by GuyCoder, you need an accumulator to sum each person preferences, and foldl/N allows to does exactly this.
choice(marie, [peru,greece,vietnam]).
choice(jean, [greece,peru,vietnam]).
choice(sasha, [vietnam,peru,greece]).
choice(helena,[peru,vietnam,greece]).
choice(emma, [greece,peru,vietnam]).
where(People,Where) :-
foldl([Person,State,Updated]>>(choice(Person,C),update(State,C,Updated)),
People,
[0=greece,0=peru,0=vietnam],
Pref),
aggregate(max(S,S=W),member(S=W,Pref),max(_,_=Where)).
% sort(Pref,Sorted),
% last(Sorted,_=Where).
update(S0,[A,B,C],S3) :-
update(S0,3,A,S1),
update(S1,2,B,S2),
update(S2,1,C,S3).
update(L,V,C,U) :-
append(X,[Y=C|Z],L),
P is Y+V,
append(X,[P=C|Z],U).
I have left commented the last two goals replaced by the single goal aggregate/3, so you can try to understand the syntax...

Prolog find flights

I'm having some issues with the findall/3 in Prolog.
Facts:
%
country(dublin,ireland).
country(cork,ireland).
country(london,uk).
country(rome,italy).
country(moscow,russia).
country(hongkong,china).
country(amsterdam,holland).
country(berlin,germany).
country(paris,france).
country(newyork,usa).
country(chicago,usa).
country(sao_paulo,brazil).
country(rio,brazil).
I need to write predicate to show the connections from city X to city Y (one by one). X and Y are the two inputs (city) and T is the output. Each solution T is a list of all the cities connecting X to Y (X and Y included).
Example:
| ?- trip(rome,dublin,T).
T=[rome,london,dublin] ;
//first solution T=[rome,paris,dublin];
//second solution
my try is
path(X,Y,[X|Y]):- edge(X,Y).
path(X,Y,[]):- edge(X,Z),not(member(Z,V)),path(Z,Y,[Z|V]).
Any ideas would be greatly appreciated.
Cheers,
I think your question is: "how can I display all possible trip between two country ?". If so I advice you to do something like that:
trip(X,Y,T) :- X \= Y,
path(X, Y, [X], T).
path(Departure, Arrival, Visited, go(Departure, Arrival)) :- direct(Departure, Arrival) , !.
path(Departure, Arrival, Visited, go(Departure, Intermediate, GO)) :-
direct(Departure, Intermediate),
Intermediate \= Departure,
\+ member(Intermediate,Visited),
path(Intermediate, Arrival, [Intermediate|Visited], GO).
So I also advice you to modify the facts in your knowledge base like:
direct(rome, moskow).
direct(moskow, paris).
direct(paris, chicago).
direct(sau_paolo, rio).
direct(rio, honkong).
and so on.
What you did is logically uncorrect. How can you know if you can travel from a city to another only knowing where they are? There should be some facts that state that is possible travel from a city to another, e.g. direct(rome, milan) (or travel(rome, milan), you choose the functor).
I hope to have help you.
If you have some dubt, just ask ;)
by use prolog
Timetable of air routes
Each air route can be described by a structure:
country of departure, country of landing, date of departure, time of departure, duration, tariffs.
Tariff can described by a structure:
price for business class, price for economy class.
Implement the following rules:
• Find all routes from the given country
• Find all routes to the given country with duration less then than the given number
• Find all routes with the cheapest price for economy class
• Find all prices for flying from one given country to another given country

Strange warning and computation result in constraint logic program

First, sorry for posting the whole program, but as I don't know were the problem is I don't know which parts are irrelevant. These are two slightly different implementations of the same logic puzzle in SWI-Prolog, the first one succeeds the second one fails and I can't find the reason for the failure.
The puzzle:
4 persons are having a diner:
Donna, Doreen, David, Danny
the woman (Donna,Doreen) are sitting vis-a-vis.
the men (David,Danny) are sitting vis-a-vis.
Each of them picked a unique meal and beverage.
1) Doreen sits next to the person that ordered risotto.
2) the salad came with a coke.
3) the person with the lasagna sits vis-a-vis the person with the milk.
4) david never drinks coffee.
5) donna only drinks water.
6) danny had no appetite for risotto.
who ordered the pizza?
I choose the following approach
table with positions:
1
4 O 2
3
domain: positions{1,2,3,4}
variables: persons, meals, beverages
First the inefficient succeeding implementation:
solution(Pizza, Doreen, Donna, David, Danny) :-
% assignment of unique positions to the variables
unique(Doreen,Donna,David,Danny),
unique(Lasagna,Pizza,Risotto,Salad),
unique(Water,Coke,Coffee,Milk),
% general setting
vis_a_vis(Donna,Doreen),
vis_a_vis(David,Danny),
% the six constraints
next_to(Doreen,Risotto),
Salad = Coke,
vis_a_vis(Lasagna,Milk),
\+ David = Coffee,
Donna = Water,
\+ Danny = Risotto.
unique(X1,X2,X3,X4) :-
pos(X1),
pos(X2),
\+ X1 = X2,
pos(X3),
\+ X1 = X3, \+ X2 = X3,
pos(X4),
\+ X1 = X4, \+ X2 = X4, \+ X3 = X4.
right(1,2).
right(2,3).
right(3,4).
right(4,1).
vis_a_vis(1,3).
vis_a_vis(3,1).
vis_a_vis(2,4).
vis_a_vis(4,2).
next_to(X,Y) :- right(X,Y).
next_to(X,Y) :- right(Y,X).
pos(1).
pos(2).
pos(3).
pos(4).
This works and gives the right result. But when I try to reorder the clauses of the solution procedure to be more efficient (this is the second implementation)
solution(Pizza, Doreen, Donna, David, Danny) :-
% general setting
vis_a_vis(Donna,Doreen),
vis_a_vis(David,Danny),
% the six constraints
Salad = Coke,
vis_a_vis(Lasagna,Milk),
\+ David = Coffee,
Donna = Water,
\+ Danny = Risotto,
% assignment of unique positions to the variables
unique(Doreen,Donna,David,Danny),
unique(Lasagna,Pizza,Risotto,Salad),
unique(Water,Coke,Coffee,Milk).
%% all other predicates are like the ones in the first implementation
I get a unassigned variable warning when trying to load the file:
Warning: /home/pizza.pl:28:
Singleton variable in \+: Coffee
and the computation returns false. But shouldn't it return the same result?
I see no reason for the difference...
the warning is due to the fact that Coffe and Risotto are unbound when the negation is executed. If you replace \+ David = Coffee, by David \= Coffee, you will avoid the warning, but the solution cannot will not be computed. Should be clear indeed that since Coffee is unbound, David \= Coffee will always fail. You can use dif/2, the solution will work and will be more efficient. I've named solution1/2 your first snippet, and solution2/5 this one (using dif/2):
solution2(Pizza, Doreen, Donna, David, Danny) :-
% general setting
vis_a_vis(Donna,Doreen),
vis_a_vis(David,Danny),
% the six constraints
next_to(Doreen,Risotto), % note: you forgot this one
Salad = Coke,
vis_a_vis(Lasagna,Milk),
dif(David, Coffee),
Donna = Water,
dif(Danny, Risotto),
% assignment of unique positions to the variables
unique(Doreen,Donna,David,Danny),
unique(Lasagna,Pizza,Risotto,Salad),
unique(Water,Coke,Coffee,Milk).
a small test:
?- time(aggregate_all(count,solution1(P,A,B,C,D),N)).
% 380,475 inferences, 0.058 CPU in 0.058 seconds (100% CPU, 6564298 Lips)
N = 8.
?- time(aggregate_all(count,solution2(P,A,B,C,D),N)).
% 10,626 inferences, 0.002 CPU in 0.002 seconds (100% CPU, 4738996 Lips)
N = 8.

How to write prolog rule?

I am trying to create a prolog rule which will generate all the people in a social network using S number degrees of separation.
This is the rule that i have made but it is only printing empty lists. Can somebody please help me into helping me understand why this is happening and me where i am going wrong?:
socialN(_,N):- N<1,!.
socialN(_,N,_,_):- N<1,!.
socialN(P1,Separation,S1,S):-
(message(P1,P2,_); message(P2,P1,_)),
D is Separation-1,
\+(member(P2,S1)),
append(P2,S1,S2),socialN(P1,D,S2,S),!.
socialN(P2,Separation,S,S).
These are the facts:
message(allan, steve, 2013-09-03).
message(nayna, jane, 2013-09-03).
message(steve, jane, 2013-09-04).
message(steve, allan, 2013-09-04).
message(mark, martin, 2013-09-04).
message(martin, steve, 2013-09-04).
message(allan, martin, 2013-09-05).
E.g. Mark’s network includes just Martin for 1 degree of separation; it includes Martin, Steve and Allan for 2 degrees of separation; and Martin, Steve, Allan and Jane for 3.
I see you are using append and member, so I suppose you are trying to build up a list of people. I was a bit surprised that you were not using findall. Like this:
allDirectLinks(P1, L) :- findall(P2, directlyLinked(P1, P2), L).
directlyLinked(P1, P1).
directlyLinked(P1, P2) :- message(P1, P2, _).
directlyLinked(P1, P2) :- message(P2, P1, _).
From there, you can write a recursive function to find the indirect links:
socialN(0, P, [P]) :- !.
socialN(N, P1, L3) :-
N>0, !,
N1 is N-1,
socialN(N1, P1, L1)
maplist(allDirectLinks, L1, L2),
append(L2, L3).
For example, this yields in Y a list of people separated 2 steps or less from Mark:
socialN(2, mark, X), list_to_set(X, Y).
Please note, Mark himself is included in the resulting list (being a 'level 0' link); I suppose it cannot be too hard to filter that out afterwards.
I hope this makes sense; I am a bit rusty, haven't done any Prolog in 25 years.
EDIT: explanation of the rules I defined:
directlyLinked: true if there is a message between two persons (regardless of the direction of the message)
allDirectLinks: accumulates into list L all persons directly linked to a given person P1; just read the manual about findall
socialN: builds up a list of people connected to a given person (P) at a distance less than or equal to a given distance (N)
socialN(0, ...): at distance 0, every person is linked to himself
socialN(N, ...): makes a recursive call to get a list of connections at distance N-1, then uses maplist to apply allDirectLinks to every connection found, and finally uses append to concatenate the results together.

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