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980a80d6af
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2e8a1dec2f
24
TODO.md
24
TODO.md
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- Demo doing graph colouring program
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- Explain graph colouring
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- Goal is to learn how to learn
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- Manual too
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- Small examples
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- Hypothesize and test
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- No one "right" way to model a problem
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- Less complicated is generally better
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- First: direct example (color_prim.lp)
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- Show basic grounding
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- Uncomment vertex: we're missing some
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- Uncomment arc to make the graph symmetric (undirected)
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- Show basic solving and disjunctive rule
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- Ground it first.
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- We have dupes
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- Ferry problem
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- Explain time
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CLPFD
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% Graph colouring
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%#show color/2.
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%{ color(X,1..n) } = 1 :- vertex(X).
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%:- arc(X,Y), color(X,C), color(Y,C).
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27
asp/clp.pl
27
asp/clp.pl
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:- use_module(library(clpfd)).
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vertex(1).
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vertex(2).
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vertex(3).
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link(1, 2).
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link(1, 3).
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link(2, 3).
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arc(X, Y) :- link(X, Y).
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arc(X, Y) :- link(Y, X).
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coloring(Colors) :-
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findall(V, vertex(V), Vertices),
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length(Vertices, N),
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same_length(Colors, Vertices),
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Colors ins 0..N, % At most N different colors
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maplist(constrain1(Vertices, Colors), Vertices, Colors),
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sum(Colors, #=, Sum),
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labeling([min(Sum)], [Sum | Colors]).
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constrain1(Vertices, Colors, Vertex, Color) :-
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maplist(constrain2(Vertex, Color), Vertices, Colors).
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constrain2(V1, C1, V2, C2) :-
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arc(V1, V2), !,
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C1 #\= C2.
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constrain2(_, _, _, _).
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33
asp/color.lp
33
asp/color.lp
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arc(1, (2; 3)).
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arc(2, 3).
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% Collect the vertices
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vertex(X) :- arc(X, _).
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% Symmetry (undirected graph)
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arc(X, Y) :- arc(Y, X).
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% Representation 1:
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% #show red/1. #show green/1. #show blue/1.
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% red(Vertex), green(Vertex), blue(Vertex) :- vertex(Vertex).
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% % Remove the dupes
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% :- red(V1), red(V2), V1 != V2.
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% :- green(V1), green(V2), V1 != V2.
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% :- blue(V1), blue(V2), V1 != V2.
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% Remove the adjacent edges with same color
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% :- arc(X, Y), red(X), red(Y).
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% :- arc(X, Y), green(X), green(Y).
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% :- arc(X, Y), blue(X), blue(Y).
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% Representation 2:
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% #const n = 6.
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% #show color/2.
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% { color(X,1..n) } = 1 :- vertex(X).
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% :- arc(X,Y), color(X,C), color(Y,C).
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144
asp/ferry.lp
144
asp/ferry.lp
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% Initially, there are cars at various locations, and there is a
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% ferry at some location. The ferry can only transport one car at
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% a time and the goal is to transport all cars to their
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% destinations. No paralell actions are allowed.
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#show board/3.
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#show move/4.
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#show unboard/3.
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%#show at/3.
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%#show in/3.
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%#show moving/3.
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time(0..steps).
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% Clingo processes "safe programs": any variable occuring in a
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% negative literal of rule r must appear in a positive atom in the body of r.
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%
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% There is nothing wrong to use domains predicates. One may first write
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% these predicates and then comment the unnessary ones out (as shown).
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% Nothing wrong to leave them there.
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% Not all of them can be removed, specially when there is a possibility
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% a variable can be instantiated (during grounding) to something unintended.
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% You may discover this during debugging using the "#show" diretive.
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% actions
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{board(Car,Loc,T)} :-
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car(Car),
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% location(Loc), time(T),
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empty(ferry,T),
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at(Car,Loc,T),
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at(ferry,Loc,T),
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not moving(ferry,Loc,T),
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not goal(T).
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{unboard(Car,Loc,T)} :-
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car(Car),
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% location(Loc), time(T),
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in(ferry,Car,T),
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at(ferry,Loc,T),
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not moving(ferry,Loc,T),
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not goal(T).
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{move(ferry,From,To,T)} :-
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% car(Car),location(From), time(T),
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location(To),
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at(ferry,From,T),
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From != To,
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not goal(T).
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moving(ferry,From,T):- % irrelevant of where ferry moves to
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% location(From),location(Loc), time(T),
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at(ferry,From,T),
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move(ferry,From,Loc,T).
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% Below is the wrong code to define empty: it says if there exists
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% a Car not in ferry, then ferry is empty.
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%
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% empty(ferry,T):-
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% car(Car), time(T),
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% not in(ferry,Car,T).
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empty(ferry,T):- time(T), not occupied(ferry,T).
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occupied(ferry,T) :- in(_,_,T).
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%fluents
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in(ferry,Car,T+1):- %an action causes a property to hold
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% car(Car), location(Loc), time(T),
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at(ferry,Loc,T),
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board(Car,Loc,T).
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in(ferry,Car,T+1):-
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% car(Car),
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time(T),
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in(ferry,Car,T),
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not affected0(Car,T).
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affected0(Car,T) :-
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% time(T), car(Car), location(Loc),
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unboard(Car,Loc,T).
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% !!! Cannot replace the above by below - it says that
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% Car is in ferry at T+1 if at T there is a location Loc
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% s.t. Car is not unboarded - not intended!
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%
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% in(ferry,Car,T+1):-
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% car(Car), time(T),
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% in(ferry,Car,T),
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% not unboard(Car,Loc,T).
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at(ferry,Loc,T+1):-
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% car(Car), location(Loc), time(T),
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at(ferry,Loc,T),
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board(Car,Loc,T).
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at(ferry,Loc,T+1):-
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% car(Car), location(Loc), time(T),
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at(ferry,Loc,T),
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unboard(Car,Loc,T).
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at(ferry,Loc,T+1):-
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% location(Loc),
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time(T),
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at(ferry,Loc,T), %if we don't have tis line, what could happen?
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%A: ferry can be everywhere
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not moving(ferry,Loc,T).
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at(ferry,To,T+1):-
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% location(To),location(From),
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time(T),
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at(ferry,From,T),
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move(ferry,From,To,T).
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at(Car,Loc,T+1):-
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car(Car), % not commented out - don't want Car instantied to ferry
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% location(Loc), time(T),
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unboard(Car,Loc,T).
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at(Car,Loc,T+1):- %frame axiom
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car(Car), location(Loc), time(T),
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at(Car,Loc,T),
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not board(Car,Loc,T).
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goal(T+1):- time(T), goal(T).
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%once goal is achieved, goal(T) is true for all T > k.
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goal :- time(T), goal(T).
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:- not goal.
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% The code above works for the input file, ferryIn0.lp and ferryIn1.lp,
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% but not ferryIn2.lp.
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%
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% Discover what is wrong. Consider adding the following constraints:
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%
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% 1. ferry cannot be moved to two different locations at the same time
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% 2. it's not possible to board different cars at the same time and same location.
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