% Pt 6
% Ex 2

positive(X) :- X>0.

filter(_,[],[]).

filter(F,[H1|L1], [H1|L2]):-
    call(F,H1),!,
    filter(F,L1,L2).

filter(F,[_|L1],L2):-
    filter(F,L1,L2).

% ex 7


vertex(a).
vertex(b).
vertex(c).
vertex(d).
vertex(e).
vertex(f).

edge(a,b).
edge(a,c).
edge(a,d).
edge(a,e).
edge(a,f).
edge(b,c).
edge(b,e).
edge(b,f).
edge(c,d).
edge(d,e).
edge(e,f).

color(rouge). 
color(vert). 
color(jaune). 
color(bleu).

all_vertices(Vertices):- 
    findall(V, vertex(V), Vertices).

create_coloring([],[]).
create_coloring([Vertex|Vertices], [c(Vertex, Color)| Colors]):-
    color(Color),
    create_coloring(Vertices, Colors).

valid_coloring([c(V,C)|Colors])
    .

goal(Colors):-
    all_vertices(Vertices),
    create_coloring(Vertices,Colors),
    valid_coloring(Colors).

colored_vertex(X,C):-
    vertex(X),
    color(C).

ok_vertices(X,Y):-
    X \= Y,
    edge(X,Y),
    colored_vertex(X,C1),
    colored_vertex(Y,C2),
    C2 \= C1.

goal2(Colors):-
    vertex(Y),findall(vertex(X),ok_vertices(X,Y),Colors).