% File: crypto.pro for xsolve3 dir
% Type: Prolog source
% Date: F09
% Created By: Bryan Kern

% load necessary files

:- ['gv.pro'].
:- ['combosets.pro'].

% random crypto problem generation

establishCryptoProblemParameters :-
   declare(lo,0),
   declare(hi,15).

% generate a random crypto problem

generateRandomCryptoNumber(R) :-
   valueOf(lo,Lo),
   valueOf(hi,Hi),
   Hip is Hi + 1,
   random(Lo,Hip,R).

generateRandomCryptoProblem :-
   generateRandomCryptoNumber(N1),
   generateRandomCryptoNumber(N2),
   generateRandomCryptoNumber(N3),
   generateRandomCryptoNumber(N4),
   generateRandomCryptoNumber(N5),
   generateRandomCryptoNumber(G),
   addCryptoProblemToKB(N1,N2,N3,N4,N5,G).

addCryptoProblemToKB(N1,N2,N3,N4,N5,G) :-
   retract(problem(_,_)),
   assert(problem(numbers(N1,N2,N3,N4,N5),goal(G))).
addCryptoProblemToKB(N1,N2,N3,N4,N5,G) :-
   assert(problem(numbers(N1,N2,N3,N4,N5),goal(G))).

% display a crypto problem - assuming that it has been internalized

displayProblem :-
   problem(numbers(N1,N2,N3,N4,N5),goal(G)),
     write('Problem: numbers = {'),
     write(N1),write(','),
     write(N2),write(','),
     write(N3),write(','),
     write(N4),write(','),
     write(N5),write('} and goal = '),
     write(G),nl.

% internalize the problem

internalizeProblem :-
  problem(numbers(N1,N2,N3,N4,N5),goal(G)),
  eraseProblemBindings,
  eraseProblem,
  eraseSolution,
  assert(problem(numbers(N1,N2,N3,N4,N5),goal(G))),
  assert(binding(n1,N1)),
  assert(binding(n2,N2)),
  assert(binding(n3,N3)),
  assert(binding(n4,N4)),
  assert(binding(n5,N5)),
  assert(binding(g,G)).

eraseProblem :-
  retract(problem(_,_)),
  fail.
eraseProblem.

eraseSolution :-
  retract(solution(_)),
  fail.
eraseSolution.

eraseProblemBindings :-
  retract(binding(n1,_)),
  retract(binding(n2,_)),
  retract(binding(n3,_)),
  retract(binding(n4,_)),
  retract(binding(n5,_)),
  retract(binding(g,_)),
  fail.
eraseProblemBindings.

% solve the problem decompositionally -- assuming internalization

solveProblemDecompositionally :-
  problem(numbers(N1,N2,N3,N4,N5),goal(G)),
  crypto(N1,N2,N3,N4,N5,G,Expression),
  assert(solution(Expression)).

% crypto problem solving

crypto(N1,N2,Goal,ex(N1, +, N2)) :- Goal is (N1 + N2).
crypto(N1,N2,Goal,ex(N1, *, N2)) :- Goal is (N1 * N2).
crypto(N1,N2,Goal,ex(N1, -, N2)) :- Goal is (N1 - N2).
crypto(N1,N2,Goal,ex(N1, -, N2)) :- Goal is (N2 - N1).
crypto(N1,N2,Goal,ex(N1, /, N2)) :- N2 > 0, Goal is (N1 / N2).
crypto(N1,N2,Goal,ex(N1, /, N2)) :- N1 > 0, Goal is (N2 / N1).

crypto(N1,N2,N3,G,Expr) :-
  combos(set(N1,N2,N3), combo(A,B), extra(C)),
  crypto(A,B,SG,SGE),
  crypto(C,SG,G,UGE),
  substitute(SGE,SG,UGE,Expr).

crypto(N1,N2,N3,N4,G,Expr) :-
  combos(set(N1,N2,N3,N4), combo(A,B), extras(C,D)),
  crypto(A,B,SG,SGE),
  crypto(C,D,SG,G,UGE),
  substitute(SGE,SG,UGE,Expr).

crypto(N1,N2,N3,N4,N5,G,Expr) :-
  combos(set(N1,N2,N3,N4,N5), combo(A,B), extras(C,D,E)),
  crypto(A,B,SG,SGE),
  crypto(C,D,E,SG,G,UGE),
  substitute(SGE,SG,UGE,Expr).

% key substitution code

substitute(New,Old,ex(Old,O,Z), ex(New,O,Z)).
substitute(New,Old,ex(X,O,Old), ex(X,O,New)).
substitute(New,Old,ex(X,O,Z), ex(Q,O,Z)) :-
  substitute(New,Old,X,Q).
substitute(New,Old,ex(X,O,Z), ex(X,O,Q)) :- 
  substitute(New,Old,Z,Q).

% display the solution -- assuming that it has been solved

displaySolution :-
  write('Solution: '),
  solution(S),
  displayResult(S),
  nl.
displaySolution.

% display the result -- assuming the problem has been "solved"

displayResult(ex(A,O,B)) :-
  number(A),number(B),
  write('('),write(A),write(' '),write(O), write(B),write(')').
displayResult(ex(A,O,B)) :-
  number(A),B = ex(A1,O1,B1),
  write('('),write(A),write(O),write(' '),
  displayResult(ex(A1,O1,B1)),write(')').
displayResult(ex(A,O,B)) :-
  number(B),A = ex(A1,O1,B1),
  write('('),displayResult(ex(A1,O1,B1)),write(' '),write(O),write(' '),
  write(B),write(')').
displayResult(ex(A,O,B)) :-
  A = ex(A1,O1,B1),B  = ex(A2,O2,B2),
  write('('),displayResult(ex(A1,O1,B1)),write(' '),write(O),write(' '),
  displayResult(ex(A2,O2,B2)),write(')').

% demo!

demo :- 
  generateRandomCryptoProblem,
  internalizeProblem,
  displayProblem,
  solveProblemDecompositionally,
  displaySolution.

% establish a particular crypto problem

establishCryptoProblem(numbers(N1,N2,N3,N4,N5),goal(G)) :-
  addCryptoProblemToKB(N1,N2,N3,N4,N5,G).

% crypto problem solver

solve(numbers(N1,N2,N3,N4,N5),goal(G)) :-
  establishCryptoProblem(numbers(N1,N2,N3,N4,N5),goal(G)),
  internalizeProblem,
  displayProblem,
  solveProblemDecompositionally,
  displaySolution.

% initialization

:- establishCryptoProblemParameters.