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TODO.md

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+- Demo doing graph colouring program 
+    - Explain graph colouring
+- Goal is to learn how to learn
+    - Manual too
+    - Small examples
+    - Hypothesize and test
+    - No one "right" way to model a problem
+        - Less complicated is generally better
+- First: direct example (color_prim.lp)
+    - Show basic grounding
+        - Uncomment vertex: we're missing some
+        - Uncomment arc to make the graph symmetric (undirected)
+
+    - Show basic solving and disjunctive rule
+        - Ground it first.
+        - We have dupes
+- Ferry problem
+    - Explain time
+
+
+
+
+
+CLPFD

asp/1.lp

@@ -1,6 +0,0 @@
-% Graph colouring
-
-%#show color/2.   
-
-%{ color(X,1..n) } = 1 :- vertex(X).
-%:- arc(X,Y), color(X,C), color(Y,C).

asp/clp.pl

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+:- use_module(library(clpfd)).
+
+vertex(1).
+vertex(2).
+vertex(3).
+link(1, 2).
+link(1, 3).
+link(2, 3).
+
+arc(X, Y) :- link(X, Y).
+arc(X, Y) :- link(Y, X).
+
+coloring(Colors) :- 
+    findall(V, vertex(V), Vertices),
+    length(Vertices, N),
+    same_length(Colors, Vertices),
+    Colors ins 0..N, % At most N different colors
+    maplist(constrain1(Vertices, Colors), Vertices, Colors),
+    sum(Colors, #=, Sum),
+    labeling([min(Sum)], [Sum | Colors]).
+
+constrain1(Vertices, Colors, Vertex, Color) :-
+    maplist(constrain2(Vertex, Color), Vertices, Colors).
+constrain2(V1, C1, V2, C2) :-
+    arc(V1, V2), !,
+    C1 #\= C2.
+constrain2(_, _, _, _).

asp/color.lp

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+arc(1, (2; 3)).
+arc(2, 3).
+
+% Collect the vertices
+vertex(X) :- arc(X, _).
+
+% Symmetry (undirected graph)
+arc(X, Y) :- arc(Y, X).
+
+% Representation 1:
+% #show red/1. #show green/1. #show blue/1.
+% red(Vertex), green(Vertex), blue(Vertex) :- vertex(Vertex).
+% % Remove the dupes
+% :- red(V1), red(V2), V1 != V2.
+% :- green(V1), green(V2), V1 != V2.
+% :- blue(V1), blue(V2), V1 != V2.
+% Remove the adjacent edges with same color
+% :- arc(X, Y), red(X), red(Y).
+% :- arc(X, Y), green(X), green(Y).
+% :- arc(X, Y), blue(X), blue(Y).
+
+
+% Representation 2:
+% #const n = 6.
+
+% #show color/2.   
+
+% { color(X,1..n) } = 1 :- vertex(X).
+% :- arc(X,Y), color(X,C), color(Y,C).
+
+
+
+

asp/ferry.lp

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+% Initially, there are cars at various locations, and there is a
+% ferry at some location. The ferry can only transport one car at
+% a time and the goal is to transport all cars to their
+% destinations. No paralell actions are allowed.
+
+#show board/3.
+#show move/4.
+#show unboard/3.
+%#show at/3.
+%#show in/3.
+%#show moving/3.
+
+
+time(0..steps).
+
+% Clingo processes "safe programs": any variable occuring in a
+% negative literal of rule r must appear in a positive atom in the body of r.
+%
+% There is nothing wrong to use domains predicates. One may first write
+% these predicates and then comment the unnessary ones out (as shown).
+% Nothing wrong to leave them there.
+% Not all of them can be removed, specially when there is a possibility
+% a variable can be instantiated (during grounding) to something unintended.
+% You may discover this during debugging using the "#show" diretive.
+
+
+% actions
+{board(Car,Loc,T)} :-
+        car(Car),
+%       location(Loc), time(T),
+        empty(ferry,T),
+        at(Car,Loc,T),
+        at(ferry,Loc,T),
+        not moving(ferry,Loc,T),
+        not goal(T).
+
+{unboard(Car,Loc,T)} :-
+        car(Car),
+%       location(Loc), time(T),
+        in(ferry,Car,T),
+        at(ferry,Loc,T),
+        not moving(ferry,Loc,T),
+        not goal(T).
+
+{move(ferry,From,To,T)} :-
+%       car(Car),location(From), time(T),
+        location(To),
+        at(ferry,From,T),
+        From != To,
+        not goal(T).
+
+moving(ferry,From,T):-     % irrelevant of where ferry moves to
+%       location(From),location(Loc), time(T),
+        at(ferry,From,T),
+        move(ferry,From,Loc,T).
+
+% Below is the wrong code to define empty: it says if there exists
+% a Car not in ferry, then ferry is empty.
+%
+% empty(ferry,T):-
+%       car(Car), time(T),
+%       not in(ferry,Car,T).
+
+empty(ferry,T):- time(T), not occupied(ferry,T).
+occupied(ferry,T) :- in(_,_,T).
+
+
+%fluents
+in(ferry,Car,T+1):-   %an action causes a property to hold
+%       car(Car), location(Loc), time(T),
+        at(ferry,Loc,T),
+        board(Car,Loc,T).
+
+in(ferry,Car,T+1):-
+%       car(Car),
+        time(T),
+        in(ferry,Car,T),
+        not affected0(Car,T).
+
+affected0(Car,T) :-
+%       time(T), car(Car), location(Loc),
+        unboard(Car,Loc,T).
+
+% !!! Cannot replace the above by below - it says that
+% Car is in ferry at T+1 if at T there is a location Loc
+% s.t. Car is not unboarded - not intended!
+%
+% in(ferry,Car,T+1):-
+%        car(Car), time(T),
+%        in(ferry,Car,T),
+%        not unboard(Car,Loc,T).
+
+at(ferry,Loc,T+1):-
+%       car(Car), location(Loc), time(T),
+        at(ferry,Loc,T),
+        board(Car,Loc,T).
+
+at(ferry,Loc,T+1):-
+%       car(Car), location(Loc), time(T),
+        at(ferry,Loc,T),
+        unboard(Car,Loc,T).
+
+at(ferry,Loc,T+1):-
+%       location(Loc),
+        time(T),
+        at(ferry,Loc,T), %if we don't have tis line, what could happen?
+                         %A: ferry can be everywhere
+        not moving(ferry,Loc,T).
+
+at(ferry,To,T+1):-
+%       location(To),location(From),
+        time(T),
+        at(ferry,From,T),
+        move(ferry,From,To,T).
+
+at(Car,Loc,T+1):-
+        car(Car),  % not commented out - don't want Car instantied to ferry
+%       location(Loc), time(T),
+        unboard(Car,Loc,T).
+
+at(Car,Loc,T+1):-    %frame axiom
+        car(Car), location(Loc), time(T),
+        at(Car,Loc,T),
+        not board(Car,Loc,T).
+
+goal(T+1):-  time(T), goal(T).
+     %once goal is achieved, goal(T) is true for all T > k.
+
+goal :- time(T), goal(T).
+:- not goal.
+
+
+% The code above works for the input file, ferryIn0.lp and ferryIn1.lp,
+% but not ferryIn2.lp.
+%
+% Discover what is wrong. Consider adding the following constraints:
+% 
+% 1. ferry cannot be moved to two different locations at the same time
+% 2. it's not possible to board different cars at the same time and same location. 
+
+
+
+
+