/* 

  Smullyan's Lion and Unicorn problem in Picat.

  From Raymond Smullyans "What is the name of this book?",
  Chapter 4 "Alice in the Forest of Forgetfulness".
  Problems 47, 48, 49, 50.

  Lions lies on Mondays, Tuesdays, and Wednesdays.
  Unicorns lies on Thursdays, Fridays, and Saturdays.

  Solutions:

    problem47
    today = 3 = thu

    problem48
    today = 0 = mon

    problem49

    problem50
    today = 0 = mon
    today = 2 = wed


  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
  _ = findall(_,problem47),
  nl,
  _ = findall(_,problem48),
  nl,
  _ = findall(_,problem49),
  nl,
  _ = findall(_,problem50),
  nl.
  

% 
% Problem 47
% Lion: Yesterday was one of my lying days.
% Unicorn: Yesterday was one of my lying days too.
%
% Solution: Today is Thursday (day 3)
%
problem47 =>
  println("problem47"),
  truth_days(unicorn,Unicorn),
  truth_days(lion,   Lion),

  Today :: 0..6,
  T1 #= 1+Today,
  T2 #= 1+ ((Today-1) mod 7),
  element(T1,Lion,LionWhen),
  element(T2,Lion,LionWhat),
  says(LionWhen, LionWhat #= 0),

  element(T1,Unicorn,UnicornWhen),
  element(T2,Unicorn,UnicornWhat),
  says(UnicornWhen, UnicornWhat #= 0),

  Vars = Today,
  solve(Vars),

  println(today=Today=which_day(Today)),
  fail,
  
  nl.

%
% Problem 48
% Lion: 
%   1) I lied yesterday
%   2) I will lie two days after tomorrow
% 
% Solution: Today is Monday (day 0)
%
problem48 =>
  println("problem48"),
  truth_days(lion,   Lion),

  Today :: 0..6,
  T1 #= 1+Today,
  T2 #= 1+(Today - 1) mod 7,

  
  element(T1,Lion,LionWhen),
  element(T2,Lion,LionWhat), 
  says(LionWhen, LionWhat #= 0),

  T3 #= 1+(Today + 3) mod 7,
  element(T3,Lion,LionWhat2), 
  says(LionWhen, LionWhat2 #= 0),

  Vars = Today,
  solve(Vars),

  println(today=Today=which_day(Today)),
  fail,
  nl.

% Problem 49
% Lion: 
%   1) I lied yesterday
%   2) I will lie again tomorrow
% 
% Solution: On no day is this possible to say.
%
problem49 =>
  println("problem49"),
 
  truth_days(lion,Lion),

  Today :: 0..6,
  
  T1 #= 1+(Today mod 7),
  T2 #= 1+(Today - 1) mod 7,
  element(T1,Lion,LionWhen),
  element(T2,Lion,LionWhat1),
  says(LionWhen, LionWhat1 #= 0),
  
  T3 #= 1+(Today + 1) mod 7,
  element(T3,Lion,LionWhat2),  
  says(LionWhen, LionWhat2 #= 0),

  Vars = Today,
  solve(Vars),

  println(today=Today=which_day(Today)),
  fail,
  nl.

%
% Problem 50
% Lion: I lied yesterday and I will lie again tomorrow
%
% Solution: Today is either Monday or Wednesday.
% 
problem50 =>
  println("problem50"),
 
  truth_days(lion,Lion),

  Today :: 0..6,
  
  T1 #= 1+(Today mod 7),
  T2 #= 1+(Today - 1) mod 7,
  T3 #= 1+(Today + 1) mod 7,  
  element(T1,Lion,LionWhen),
  element(T2,Lion,LionWhat1),
  element(T3,Lion,LionWhat2),    
  says(LionWhen, LionWhat1 #= 0 #/\ LionWhat2 #= 0),

  Vars = Today,
  solve(Vars),

  println(today=Today=which_day(Today)),
  fail,
  nl.


says(When, What) =>
   When #= What.


% Truthfullness of lion and unicorn.
% start week with Monday (day 0)
truth_days(unicorn,[1, 1, 1, 0, 0, 0, 1]).
truth_days(lion,   [0, 0, 0, 1, 1, 1, 1]).

which_day(Day) = Days[Day+1] =>
 Days = [mon,tue,wed,thu,fri,sat,sun].