## 0 vs failure

As expected, aggregate_all/3, which uses findall/3, yields 0 if there is nothing:

?- aggregate_all(sum(P),false,Payoff). Payoff = 0.

But aggregate/3, which uses bagof/3, fails if there is nothing:

?- aggregate(sum(P),false,Payoff). false.

## Properly quantifying free variables in the goal of aggregate∕3

Do not forget to properly quantify free variables in the goal of aggregate/3 in the same way as you would do for bagof/3 and setof/3 (using the `X^` notation) or you will get unexpected results:

:- begin_tests(aggregate). test("aggregate all, sum, member-of-list") :- aggregate_all(sum(P),member(P,[1,2,3]),Sum), assertion(Sum == 6). test("aggregate all, sum, key-value of dict") :- aggregate_all(sum(Value),get_dict(_Key,_{a:1,b:2,c:3},Value),Sum), assertion(Sum == 6). test("aggregate all, sum, but no values") :- aggregate_all(sum(P),member(P,[]),Sum), assertion(Sum == 0). test("aggregate, sum, member-of-list") :- aggregate(sum(P),member(P,[1,2,3]),Sum), assertion(Sum == 6). test("aggregate all, sum, key-value of dict, forgot to quantify, thus wrong result and open choicepoint",[nondet]) :- aggregate(sum(Value),get_dict(_Key,_Tag{a:1,b:2,c:3},Value),Sum), assertion(Sum == 1). test("aggregate all, sum, key-value of dict, properly quantified") :- aggregate(sum(Value),Tag^Key^get_dict(Key,Tag{a:1,b:2,c:3},Value),Sum), assertion(Sum == 6). test("aggregate all, sum, key-value of dict, call 'hiding' predicate") :- aggregate(sum(Value),hide(Value),Sum), assertion(Sum == 6). hide(Value) :- get_dict(_Key,_Tag{a:1,b:2,c:3},Value). test("aggregate, sum, but no values", fail) :- aggregate(sum(P),member(P,[]),_Sum). :- end_tests(aggregate).

## Usage example

An example using aggregates to find a worker-task assignment yielding maximum payoff (testing all possibilites):

% -------------------> tasks 1...MaxTask % workers 1..maxWorker payoff_matrix( [ [22, 9,47,24,37,25,25], % | [45,49,38,13, 7,45,50], % | [33,10,10,40,13,25,32], % | [ 6, 5,48,36,36,15, 3] ] ). % V max_task(MaxTask) :- payoff_matrix(M), nth0(0,M,Row), length(Row,MaxTask). max_worker(MaxWorker) :- payoff_matrix(M), length(M,MaxWorker). % What is the Payoff of assigning worker Worker % to task Task? This predicate can also be redone % to generate all Worker/Task combinations though we % don't use it that way. payoff(Worker,Task,Payoff) :- payoff_matrix(M), nth1(Worker,M,Row), nth1(Task,Row,Payoff). % Find the best assignment using aggregate/3 best(WitnessAssignment,MaxPayoff) :- aggregate( max(Payoff,Assignment), gen_assignment(Assignment,Payoff), max(MaxPayoff,WitnessAssignment)). % Backtrackably generate an Assignment. It has the given Payoff gen_assignment(Assignment,Payoff) :- max_task(MaxTask), max_worker(MaxWorker), bagof(X,between(1,MaxTask,X),Tasks), % Tasks now contains the task numbers 1...MaxTask bagof(X,between(1,MaxWorker,X),Workers), % Workers now contains the worker numbers 1...MaxWorkers gen_assignment_2(Tasks,[],Workers,Assignment), aggregate_all(sum(P),member(_{worker:_,task:_,payoff:P},Assignment),Payoff). % Use aggregate_all to not care about free variables % gen_assignment_2(Tasks,TasksPicked,WorkersLeft,Assignment) % % Generate an assignment (a list of dicts, with each dict a worker-task % pairing) by successively (and backtrackably) picking a task for the next % worker from the list of tasks that haven't been assigned yet, % getting the payoff for that worker-task pairing and recursively moving % on to the next worker. gen_assignment_2(Tasks,TasksPicked,[W|Ws],[_{worker:W,task:T,payoff:P}|As]) :- member(T,Tasks), \+ member(T,TasksPicked), payoff(W,T,P), gen_assignment_2(Tasks,[T|TasksPicked],Ws,As). gen_assignment_2(_,_,[],[]).