%deps

:- consult('../gv.pro').
:- consult('../combosets.pro').

%handout

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

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),
  addCryptoProblemToKnowledgeBase(N1,N2,N3,N4,N5,G).

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

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.

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.

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

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

crypto(N1,N2,N3,G,K) :-
  combos(set(N1,N2,N3),combo(A1,A2),extra(A3)),
  crypto(A1,A2,AG,Aex),
  crypto(A3,AG,G,Bex),
  substitute(Aex,AG,Bex,K).

crypto(N1,N2,N3,N4,G,K) :-
  combos(set(N1,N2,N3,N4),combo(A1,A2),extras(A3,A4)),
  crypto(A1,A2,A3,AG,Aex),
  crypto(A4,AG,G,Bex),
  substitute(Aex,AG,Bex,K).
  
crypto(N1,N2,N3,N4,N5,G,K) :-
  combos(set(N1,N2,N3,N4,N5),combo(A1,A2),extras(A3,A4,A5)),
  crypto(A1,A2,A3,AG,Aex),
  crypto(A4,A5,AG,G,Bex),
  substitute(Aex,AG,Bex,K).

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).

%init

:- establishCryptoProblemParameters.