Prolog program for preference-based assignments (e.g., papers to students)

assignments.pl

:- use_module(library(clpfd)).
:- use_module(library(aggregate)).

% How to use:
%
% - Add preference(student, paper_id, pref_value) facts for the preferences of all students
%   (see end of file!)
% - student is any kind of value, e.g., strings or atoms
% - paper_id is a numeric identifier starting a 0
% - pref_value is a numeric value. Higher values indicate higher preferences
% - If there are N students, there should be N preference facts for each student
% - Furthermore, there have to be at least N papers
% - For each paper id, optionally add a paper_title(paper_id, title) fact for showing titles,
%   and not ids, in the output
% - Then, call ":- solution(S)" to produce one optimal assignment. If there are multiple
%   optimal assignments, a random optimal assignment is returned.

%%% Assignments and Scores

assignment(A) :- 
  students(Students),
  length(Students, L),
  length(Papers, L),
  term_variables(Papers, Vars),
  all_distinct(Vars),
  papers(AllPapers),
  max_list(AllPapers, M),
  Vars ins 0..M,
  permutation(Papers, PapersPerm),
  permutation(Students, StudentsPerm),
  zip(StudentsPerm, PapersPerm, A).

score([], 0).
score([A|Tl], R) :-
  A = St-Pa,
  preference(St, Pa, Pr),
  score(Tl, Sub),
  R #= Pr + Sub.

%%% Computing a Solution

solution(R) :- 
  aggregate_all(
    max(S, O),
    (
      assignment(A),
      score(A, S),
      maplist([Assgn, Out]>>(
        Assgn = Student-PaperId,
        (
          paper_title(PaperId, PaperTitle),
          Out = Student-PaperTitle
        ) ; Out = Assgn
      ), A, O)
    ),
    R).

%%% Utility Predicates

paper(P) :- preference(_, P, _).
papers(R) :- aggregate_all(set(P), paper(P), R).

student(S) :- preference(S, _, _).
students(R) :- aggregate_all(set(S), student(S), R).

zip(L1, L2, R) :- maplist([A, B, Out]>>(Out = A-B), L1, L2, R).

% Ensures that there is no error if no paper titles are defined
:- discontiguous paper_title/2.
paper_title(-1, "").



%%% DATA %%%

% preference/3: Triples (student, paper_id, preference value)
preference("Dominic", 0, 10).
preference("Dominic", 1, 9).
preference("Dominic", 2, 8).

preference("Alice", 0, 10).
preference("Alice", 1, 8).
preference("Alice", 2, 9).

% paper_title/2: *Optional* definitions of paper titles for IDs
paper_title(0, "QuickSpec").
paper_title(1, "Alhazen").
paper_title(1, "Beginner's Luck").