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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...
Assuming I have some facts like the following
person(jessica,19,usa).
person(james,18,uk).
person(eric,34,italy).
person(jake,24,france).
how can I create a predicate that creates a large list of pairs of all the names and their corresponding country like so:
?-filter(L).
L=[(jessica,usa),(james,uk),(eric,italy),(jake,france)]
The best solution is this one:
?- bagof((P,C), Age^person(P,Age,C), People).
People = [(jessica, usa), (james, uk), (eric, italy), (jake, france)].
This gives you the same result as findall/3, because findall/3 implicitly assumes existential quantification on all variables not present in the template ((P,C) is the template). In your case you only have one, the age variable. Notice what happens if you don't include that:
?- bagof((P,C), person(P,_,C), People).
People = [(james, uk)] ;
People = [(jessica, usa)] ;
People = [(jake, france)] ;
People = [(eric, italy)].
What happened here? The value of the second parameter was the same across each solution because we didn't inform bagof/3 that we didn't care what it was bound to or even if it was bound to just one thing. This property of bagof/3 and setof/3 (but not findall/3) sometimes turns out to be surprisingly useful, so I tend to prefer using bagof/3 over findall/3 if I only need to mark a variable or two.
It's more obvious if we add another person the same age to the database:
person(janet,18,australia).
?- bagof((P,C), person(P,Age,C), People).
Age = 18,
People = [(james, uk), (janet, australia)] .
?- bagof((P,C), person(P,_,C), People).
People = [(james, uk), (janet, australia)] ;
Assuming person/3 is ground and terminates, you can implement it without setof as:
notin(_, []).
notin(X, [Y|Ys]) :-
dif(X,Y),
notin(X,Ys).
lt_list(_, []).
lt_list(X, [Y|Ys]) :-
X #< Y,
lt_list(X,Ys).
f( [ Name-Location | Rest], Acc) :-
person(Name, _, Location),
lt_list( Name-Location, Acc ),
f(Rest, [Name-Location | Acc]).
f( [], Acc) :-
\+ (person(Name,_,Location), notin(Name-Location,Acc)).
When we query f, we get our solutions:
?- f(Xs,[]).
Xs = [jessica-usa, james-uk, jake-france, eric-italy] ;
false.
I used X-Y instead of (X,Y) for better readability. The predicate notin describes an element that is not contained in a list and lt_list describes an element that is smaller than anything in the list by the standard term order.
The idea is that the first rule generates persons that I have not seen yet. Using the term order makes sure that we don't generate all permutations of the list (try replacing lt_list by notin to see what happens). The second rule makes sure we only terminate if there are no more solutions to generate. Be aware that the rule contains negation, which can have some unwanted side-effects. Most of them are filtered out by only looking at ground terms, but I have not thought well, how bad the impact is in this solution.
I am very new to prolog and although I’ve read some books I can definitely tell that my programming brain can’t think the Prolog way. The problem I would like to solve is pretty simple (I believe). I will describe it via an example.
Let’s say that I have a graph that contains 4 “types” of nodes and 3 edges that connect the nodes. The types can be A, B, C or D and as you can see from the image below (see Figure 1), A can be connected with B and C (A_To_B and A_To_C edges respectively), while C can be connected to D (C_To_D edge). There’s also an additional rule not shown on the picture: A can be connected to at most 1 C.
I would like to express these simple rules in Prolog to solve the problem shown in the second picture. There are 3 nodes which type is missing (labeled X?, Y? and Z?). By applying the above rules in my mind I can easily find that X? and Z? are of B type (as A can connect to no more than 1 Cs) and Y? is of type D as C can only connect to D.
Could please provide me any help on that? I am not writing just to pick the solution. I would like to learn Prolog as well so any suggestion on a book that explains Prolog to people who have never worked on such concepts before like me would be very welcome.
EDIT: Example that fails
I came up with the following two examples:
For example 1, the rules are
can_connect(a,b,_).
can_connect(a,c,1).
link(1,2).
type(1,a).
type(2,_).
The possible solutions returned are [b,c] which is correct as we request at most 1 link from A to C meaning that 0 links is also acceptable.
In example 2 the rules change to the following:
can_connect(a,b,_).
can_connect(a,c,**2**).
link(1,2).
link(1,3).
type(1,a).
type(2,_).
type(3,c).
Running the code here returns [c] which is wrong. b is also an acceptable solution as we require again at most 2 A to C links which means that having only 1 is OK.
I spent this weekend trying to figure out the solution. First of all, I believe that it works as intended in Example 1 simply because there's no link from A to C instantiated in the proposed solution (where checking if 2 can be b), so the can_connect(a,c,1) is not checked so the proposed solution is getting accepted. In Example 2, there's one A to C link already there so the can_connect(a,c,2) is checked and the solution where node 2 has type b is rejected as the rule checks if there are exactly 2 and not at most 2 links from A to C.
I find a solution which works at these scenarios but fails at some others. Here it is:
% value #3 is the lower bound and #4 is the upper bound.
can_connect(a,b,0,500).
% A C node can be connected by 0, 1 or 2 A nodes
can_connect(a,c,0,2).
can_connect(d,c,1,1).
can_connect(c,e,0,1).
%The same as previous solution
link(1,2).
link(1,3).
% No change here
type(1,a).
type(2,_).
type(3,c).
% No change here
node_type(N, NT) :-
type(N, NT),
nonvar(NT),
!. % assume a node has only one type
% No change here
node_type(N, NT) :-
assoc_types(Typed),
maplist(check_connections(Typed), Typed),
memberchk(N:NT, Typed).
% No change here
assoc_types(Typed) :-
findall(N, type(N, _), L),
maplist(typed, L, Typed).
% No change here
typed(N, N:T) :-
type(N, T),
member(T, [a,b,c]).
% Changes here
check_connections(Graph, N:NT) :-
forall(link(N, M), (
memberchk(M:MT, Graph),
can_connect(NT, MT, L, U),
findall(X, (link(N, X), memberchk(X:MT, Graph)), Ts),
mybetween(L, U, Ts),
forall(can_connect(NT, Y, LM, UM), (
findall(P, (link(N,P),memberchk(P:Y, Graph)), Ss),
length(Ss, SsSize ),
SsSize>=LM,
SsSize=<UM
))
)).
% It is used to find if the length of a list is between two limits.
mybetween(Lower, Upper, MyList) :-
length(MyList, MySize),
MySize=<Upper,
MySize>=Lower.
This solution fails in this example
In this example, X? must be always b, Y? must always be C and Z? must always be D. It finds X? and Y? correctly but not Z?. I believe after some debugging that this is due the fact that in the current implementation I only check the can_connect rules that are related with links that start from a node and not that end to a node. However, I am not sure at all about that.
Any help is appreciated.
the representation of the problem needs to disambiguate nodes names, so we can express the links appropriately
now we can write
can_connect(a,b,_).
can_connect(a,c,1).
can_connect(c,d,_).
link(1,2).
link(1,3).
link(1,4).
link(4,5).
link(4,6).
link(7,4).
link(7,8).
type(1,a).
type(2,b).
type(3,_).
type(4,c).
type(5,d).
type(6,_).
type(7,a).
type(8,_).
The underscore (anonymous variable) in Prolog plays a role similar to NULL in SQL, it can assume any value.
So, a first snippet
node_type(N, NT) :- type(N, NT), nonvar(NT), !. % assume a node has only one type
can be used to express what we know about the problem.
Facts can_connect/3 then can be read like
a can connect to any number of b
a can connect to just 1 c
etc
Where we don't know the node type, a complex rule is needed, that infers the type of source node from the type of target node, and accounts for the counting constraint, something like
node_type(N, NT) :-
link(M, N),
type(M, MT),
can_connect(MT, NT, C),
aggregate(count, Y^(link(M, Y), type(Y, NT)), C).
?- forall(between(1,8,N), (node_type(N,T),writeln(N:T))).
1:a
2:b
3:b
4:c
5:d
6:d
7:a
8:b
true.
edit if your Prolog doesn't have library(aggregate), from where aggregate/3 has been loaded, you can try
node_type(N, NT) :-
link(M, N),
type(M, MT),
can_connect(MT, NT, C),
findall(t, (link(M, Y), type(Y, NT)), Ts), length(Ts, C).
edit first of all, the updated graph, marked with types where known:
my previous code worked only under very restricted assumptions. Here is something more general, that checks the constraints over the full graph (as was suggested by #false comment), with a 'generate and test' approach.
node_type(N, NT) :-
assoc_types(Typed),
maplist(check_connections(Typed), Typed),
memberchk(N:NT, Typed).
assoc_types(Typed) :-
findall(N, type(N, _), L),
maplist(typed, L, Typed).
typed(N, N:T) :- type(N, T), member(T, [a,b,c,d]).
check_connections(Graph, N:NT) :-
forall(link(N, M), (
memberchk(M:MT, Graph),
can_connect(NT, MT, C),
aggregate(count, X^(link(N, X), memberchk(X:MT, Graph)), C)
)).
now ?- node_type(4,X). fails...
I'm having trouble wrapping my head around how I would return a list of everyone related to a certain person. So, if I say relatives(A,B), A would be a person and B is a list of all of the people related to that person. I can write any additional rules needed to assist in doing this. Here is what I have so far.
man(joe).
man(tim).
man(milan).
man(matt).
man(eugene).
woman(mary).
woman(emily).
woman(lily).
woman(rosie).
woman(chris).
parent(milan, mary).
parent(tim, milan).
parent(mary, lily).
parent(mary, joe).
parent(mary, matt).
parent(chris, rosie).
parent(eugene, mary).
parent(eugene, chris).
cousins(A, B) :- parent(C, A), parent(D, B), parent(E, C), parent(E, D), not(parent(C, B)), not(parent(D, A)), A \=B.
paternalgrandfather(A, C) :- man(A), man(B), parent(B, C), parent(A, B).
sibling(A, B) :- parent(C, A), parent(C, B), A \= B.
Can someone guide me as to how I would go about doing this? Thanks.
I think that you should concentrate on the 'true' relation, i.e. parent(Old,Jung), other predicates are irrelevant here. The obvious assumption it's that atoms occurring in parent/2 are identifiers (i.e. names are unique). From this picture seems that all persons here are relatives:
Then your problem should be equivalent to find all connected vertices in parent relation. You can implement a depth first visit, passing down the list of visited nodes to avoid loops (note that you need to go back to parents and down to children!), something like
relatives(Person, Relatives) :-
relatives([], Person, [Person|Relatives]).
relatives(Visited, Person, [Person|Relatives]) :-
findall(Relative, immediate(Person, Visited, R), Immediates),
... find relatives of immediates and append all in relatives.
immediate(Person, Visited, R) :-
(parent(Person, R) ; parent(R, Person)),
\+ member(R, Visited).
See if you can complete this snippet. Note the order of arguments in relatives/3 is choosen to easy maplist/3.
If you are willing to study more advanced code, SWI-Prolog library(ugraph) offers a reachable(+Vertex, +Graph, -Vertices) predicate that does it on a list based graph representation.
Here the SWI-Prolog snippet to get the image (a file to be feed to dot):
graph(Fact2) :-
format('digraph ~s {~n', [Fact2]),
forall(call(Fact2, From, To), format(' ~s -> ~s;~n', [From, To])),
format('}\n').
you can call in this way:
?- tell('/tmp/parent.gv'),graph(parent),told.
and then issue on command line dot -Tjpg /tmp/parent.gv | display
I think you should use builtin predicate findall/3 and maybe sort/2 to avoid duplicates
It would go along these lines:
relatives(Person, Relatives):-
findall(Relative, is_relative(Person, Relative), LRelatives),
sort(LRelatives, Relatives).
is_relative(Person, Relative):-
(cousins(Person, Relative) ; paternalgrandfather(Person, Relative) ; sibling(Person, Relative)).
You might want to add more clauses to is_relative to get more relationships.
I starting to study for my upcoming exam and I'm stuck on a trivial prolog practice question which is not a good sign lol.
It should be really easy, but for some reason I cant figure it out right now.
The task is to simply count the number of odd numbers in a list of Int in prolog.
I did it easily in haskell, but my prolog is terrible. Could someone show me an easy way to do this, and briefly explain what you did?
So far I have:
odd(X):- 1 is X mod 2.
countOdds([],0).
countOdds(X|Xs],Y):-
?????
Your definition of odd/1 is fine.
The fact for the empty list is also fine.
IN the recursive clause you need to distinguish between odd numbers and even numbers. If the number is odd, the counter should be increased:
countOdds([X|Xs],Y1) :- odd(X), countOdds(Xs,Y), Y1 is Y+1.
If the number is not odd (=even) the counter should not be increased.
countOdds([X|Xs],Y) :- \+ odd(X), countOdds(Xs,Y).
where \+ denotes negation as failure.
Alternatively, you can use ! in the first recursive clause and drop the condition in the second one:
countOdds([X|Xs],Y1) :- odd(X), !, countOdds(Xs,Y), Y1 is Y+1.
countOdds([X|Xs],Y) :- countOdds(Xs,Y).
In Prolog you use recursion to inspect elements of recursive data structs, as lists are.
Pattern matching allows selecting the right rule to apply.
The trivial way to do your task:
You have a list = [X|Xs], for each each element X, if is odd(X) return countOdds(Xs)+1 else return countOdds(Xs).
countOdds([], 0).
countOdds([X|Xs], C) :-
odd(X),
!, % this cut is required, as rightly evidenced by Alexander Serebrenik
countOdds(Xs, Cs),
C is Cs + 1.
countOdds([_|Xs], Cs) :-
countOdds(Xs, Cs).
Note the if, is handled with a different rule with same pattern: when Prolog find a non odd element, it backtracks to the last rule.
ISO Prolog has syntax sugar for If Then Else, with that you can write
countOdds([], 0).
countOdds([X|Xs], C) :-
countOdds(Xs, Cs),
( odd(X)
-> C is Cs + 1
; C is Cs
).
In the first version, the recursive call follows the test odd(X), to avoid an useless visit of list'tail that should be repeated on backtracking.
edit Without the cut, we get multiple execution path, and so possibly incorrect results under 'all solution' predicates (findall, setof, etc...)
This last version put in evidence that the procedure isn't tail recursive. To get a tail recursive procedure add an accumulator:
countOdds(L, C) :- countOdds(L, 0, C).
countOdds([], A, A).
countOdds([X|Xs], A, Cs) :-
( odd(X)
-> A1 is A + 1
; A1 is A
),
countOdds(Xs, A1, Cs).