Brown, Clark, Jones and Smith are 4 substantial citizens who serve their community as achitect, banker, doctor and lawyer, though not necessarily respectively. Brown, who is more conservative than Jones but more liberal than Smith, is a better golfer than the men who are YOUNGER than he is and has a larger income than the men who are OLDER than Clark. The banker, who earns more than the architect, is neither the youngest nor the oldest.
The doctor, who is a poorer golfer than the lawyer, is less conservative than the architect. As might be expected, the oldest man is the most conservative and has the largest income, and the youngest man is the best golfer. What is each man's profession?
when I try to launch the code, I get the error:
ERROR: >/2: Arguments are not sufficiently instantiated
The code is:
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% We represent each "person" with a six-tuple of the form
%
% [ name , profession , age , income , politics , golf ranking ]
%
% where name is either brown, clark, jones, or smith
% profession is either banker, lawyer, doctor, or architect
% age is a range 1 .. 4, with 1 being the youngest and 4 the oldest
% income is a range 1 .. 4, with 1 being the least and 4 the most
% politics is a range 1 .. 4, with 1 being conservative, 4 liberal
% golf ranking is a range 1 .. 4, 1 for the best rank, 4 for the worst
%
solutions(L) :- L = [ [brown, _, _, _, _, _], [clark, _, _, _, _, _],
[jones, _, _, _, _, _], [smith, _, _, _, _, _] ],
clue1(L),
clue2(L),
clue3(L),
clue4(L),
constrained_profession(L),
constrained_age(L),
constrained_income(L),
constrained_politics(L),
constrained_golf_rank(L).
%
% clue #1
% brown, who is more conservateive than jones but
% more liberal than smith, is a better golfer than
% the men who are younger than he is and has a larger
% income than the men who are older than clark
%
clue1(L) :- member(P1,L), member(P2,L), member(P3,L),
P1 = [brown, _, A1, _, L1, G1],
P2 = [jones, _, _, _, L2, _],
P3 = [smith, _, _, _, L3, _],
liberaler( P2, P1 ),
liberaler( P1, P3 ),
not( clue1_helper_a(L) ),
not( clue1_helper_b(L) ).
% for all men younger than brown he is a better golfer ===>
% it is not the case that there exists a man younger than brown
% such that brown is not a better golfer than him.
% The "is not the case" is taken care of in clue1.
clue1_helper_a(L) :- member(P1,L), P1 = [brown, _, A1, _, L1, G1],
member(PU,L), PU = [_, _, AU, _, _, GU],
younger(PU,P1),
not(golfier(P1, PU)).
% for all men older than clark, brown makes more money than they do ===>
% it is not the case that there exists a man older than clark such that
% brown does not make more money than him.
% The "is not the case" is taken care of in clue1.
clue1_helper_b(L) :- member(P1,L), P1 = [brown, _, _, _, _, _],
member(P2,L), P2 = [clark, _, _, _, _, _],
member(PU,L), PU = [_, _, _, _, _, _],
younger(P2,PU),
not(richer(P1, PU)).
%
% clue #2
% the banker, who earns more than the archiect, is
% neither the youngest nor the oldest
%
clue2(L) :- member(P1,L), member(P2,L),
P1 = [_, banker, A1, I1, _, _],
P2 = [_, architect, _, I2, _, _],
richer(P1,P2),
not( A1 = 1 ),
not( A1 = 4 ).
%
% clue #3
% the doctor, who is a pooer golfer than the lawyer, is
% less conservative than the architect.
%
clue3(L) :- member(P1, L), member(P2, L), member(P3,L),
P1 = [_,doctor, _, _, L1, G1],
P2 = [_,lawyer, _, _, _, G2],
P3 = [_,architect, _, _, L3, _],
golfier(P2,P1),
liberaler(P1,P3).
%
% clue #4
% as might be expected, the oldest man is the most
% conservative and has the largest income, and the
% youngest man is the best golfer.
clue4(L) :- member(P1,L), member(P2,L),
P1 = [_, _, 4, 4, 1, _],
P2 = [_, _, 1, _, _, 1].
%
% relations
%
younger(X,Y) :- X = [_, _, AX, _, _, _], Y = [_, _, AY, _, _, _], AX < AY.
liberaler(X,Y) :- X = [_, _, _, _, LX, _], Y = [_, _, _, _, LY, _], LX > LY.
golfier(X,Y) :- X = [_, _, _, _, _, GX], Y = [_, _, _, _, _, GY], GX < GY.
richer(X,Y) :- X = [_, _, _, IX, _, _], Y = [_, _, _, IY, _, _], IX > IY.
%
% constraints
%
constrained_profession(L) :-
member(P1,L), member(P2,L), member(P3,L), member(P4,L),
P1 = [_, banker, _, _, _, _],
P2 = [_, lawyer, _, _, _, _],
P3 = [_, doctor, _, _, _, _],
P4 = [_, architect, _, _, _, _].
constrained_age(L) :-
member(P1,L), member(P2,L), member(P3,L), member(P4,L),
P1 = [_, _, 1, _, _, _],
P2 = [_, _, 2, _, _, _],
P3 = [_, _, 3, _, _, _],
P4 = [_, _, 4, _, _, _].
constrained_income(L) :-
member(P1,L), member(P2,L), member(P3,L), member(P4,L),
P1 = [_, _, _, 1, _, _],
P2 = [_, _, _, 2, _, _],
P3 = [_, _, _, 3, _, _],
P4 = [_, _, _, 4, _, _].
constrained_politics(L) :-
member(P1,L), member(P2,L), member(P3,L), member(P4,L),
P1 = [_, _, _, _, 1, _],
P2 = [_, _, _, _, 2, _],
P3 = [_, _, _, _, 3, _],
P4 = [_, _, _, _, 4, _].
constrained_golf_rank(L) :-
member(P1,L), member(P2,L), member(P3,L), member(P4,L),
P1 = [_, _, _, _, _, 1],
P2 = [_, _, _, _, _, 2],
P3 = [_, _, _, _, _, 3],
P4 = [_, _, _, _, _, 4].
% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The built-in predicate (>)/2 is a so-called moded predicate. This means that you can only use it in very specific circumstances. It is not a true relation that you can use in all directions.
To reason more generally over integers, use your Prolog system's CLP(FD) constraints instead.
For example, in GNU Prolog, it suffices to simply replace (>)/2 by (#>)/2 to reason over integers more declaratively.
In other Prolog systems, you may currently need to import a dedicated library. For example, in SICStus Prolog, you need to add the directive:
:- use_module(library(clpfd)).
to your program.
If you do this, and then use the following slightly modified definitions of your predicates:
younger(X,Y) :- X = [_, _, AX, _, _, _], Y = [_, _, AY, _, _, _], AX #< AY. liberaler(X,Y) :- X = [_, _, _, _, LX, _], Y = [_, _, _, _, LY, _], LX #> LY. golfier(X,Y) :- X = [_, _, _, _, _, GX], Y = [_, _, _, _, _, GY], GX #< GY. richer(X,Y) :- X = [_, _, _, IX, _, _], Y = [_, _, _, IY, _, _], IX #> IY.
The the example query runs without errors:
?- solutions(L). false.
However, as you see, your formulation is currently too specific: Not a single solution is found.
Consider filing a separate question to see how you can debug such issues.