layton.prolog

%%  A question is a [[question number,answer], correctness].  
%%  Example:
%%      [[1,a], correct] 
%%  A test is a list of questions.


%% We create a rule that every correct answer is 10 points.
points([_, correct], 10).      points([_, incorrect], 0).

%% Create rules flip solutions and whether or not they are incorrect.
flip(a, b).  flip(correct, incorrect).
flip(b, a).  flip(incorrect, correct).

%% Given a test, calculates the score based on the correctness.
test_score([], 0).
test_score([H|T], Score) :-
  points(H, These_Points),
  test_score(T, Rest_of_Points),
  Score is These_Points + Rest_of_Points.

%% This is the critical rule:  it ensures that all tests are scored
%% by the same answer key.  This way, Prolog won't find a binding that
%% works for each individual test, but for all tests that get bound.
%% Two empty tests naturally follow the same grading criteria:
sensible_scores([], []).

%% We investigate tests recursively:  if both tests have identical heads
%% (e.g. they agree on an answer and its correctness) then the test is
%% 'sensible' (follows a common rubric) as long as the rest of the test does.
sensible_scores([A|T1], [A|T2]) :-
  sensible_scores(T1, T2).

%% If they have the same number but differ in answer, they must also differ
%% in correctness.
sensible_scores([[[A,B],Aye]|T1], [[[A,C],Nay]|T2]) :-
  flip(B, C),
  flip(Aye, Nay),
  sensible_scores(T1, T2).


%% A cheap rule that binds X to Mary's score sheet.  Correctness 
%% is automagically bound by Prolog!
mary_test(X) :-
  X = [ [[1, b], _],
        [[2, b], _],
        [[3, a], _],
        [[4, b], _],
        [[5, a], _],
        [[6, b], _],
        [[7, b], _],
        [[8, a], _],
        [[9, b], _],
        [[10, b], _]].

%% Dan's score sheet.
dan_test(X) :-
  X = [ [[1, b], _],
        [[2, a], _],
        [[3, a], _],
        [[4, a], _],
        [[5, b], _],
        [[6, a], _],
        [[7, b], _],
        [[8, a], _],
        [[9, a], _],
        [[10, a], _]].

%% Lisa's score sheet.
lisa_test(X) :-
  X = [ [[1, b], _],
        [[2, a], _],
        [[3, a], _],
        [[4, a], _],
        [[5, b], _],
        [[6, b], _],
        [[7, b], _],
        [[8, a], _],
        [[9, b], _],
        [[10, a], _]].


%% And Colin's, whose score we don't know.
colin_test(X) :-
  X = [ [[1, b], _],
        [[2, b], _],
        [[3, a], _],
        [[4, a], _],
        [[5, a], _],
        [[6, b], _],
        [[7, b], _],
        [[8, a], _],
        [[9, a], _],
        [[10, a], _]].

%% Finally, the meat!  We bind Lisa, Dan, and Mary to their score sheets.
%% We then use sensible_scores to ensure that their sheets follow the same
%% grading rubric.  Finally, we ensure that this rubric adheres to the scores
%% that Mary, Dan, and Lisa obtained.
test_integrity(X) :-
  lisa_test(Lisa),
  dan_test(Dan),
  mary_test(Mary),
  sensible_scores(Lisa, Dan),
  sensible_scores(Dan, Mary),
  sensible_scores(Mary, X),
  test_score(Mary, 70),
  test_score(Dan, 50),
  test_score(Lisa, 30).
 
%% Finally, we bind Score to what Colin's score is by setting
%% it to his test results, ensuring that his score has the same 
%% answer key as his peers, then calculating the score with that 
%% answer key.
colin_score(Score) :-
  colin_test(X),
  test_integrity(X),
  test_score(X, Score).