examples/simple_vc_quant_cxx.cpp

   1 /*********************                                                        */
   2 /*! \file simple_vc_quant_cxx.cpp
   3  ** \verbatim
   4  ** Top contributors (to current version):
   5  **   Andrew Reynolds
   6  ** This file is part of the CVC4 project.
   7  ** Copyright (c) 2009-2019 by the authors listed in the file AUTHORS
   8  ** in the top-level source directory) and their institutional affiliations.
   9  ** All rights reserved.  See the file COPYING in the top-level source
  10  ** directory for licensing information.\endverbatim
  11  **
  12  ** \brief A simple demonstration of the C++ interface for quantifiers
  13  **
  14  ** A simple demonstration of the C++ interface for quantifiers.
  15  **/
  16
  17 #include <iostream>
  18
  19 #include <cvc4/cvc4.h>
  20
  21 using namespace std;
  22 using namespace CVC4;
  23
  24 int main() {
  25   ExprManager em;
  26   SmtEngine smt(&em);
  27
  28   // Prove that the following is unsatisfiable:
  29   //   forall x. P( x ) ^ ~P( 5 )
  30
  31   Type integer = em.integerType();
  32   Type boolean = em.booleanType();
  33   Type integerPredicate = em.mkFunctionType(integer, boolean);
  34
  35   Expr p = em.mkVar("P", integerPredicate);
  36   Expr x = em.mkBoundVar("x", integer);
  37
  38   // make forall x. P( x )
  39   Expr var_list = em.mkExpr(kind::BOUND_VAR_LIST, x);
  40   Expr px = em.mkExpr(kind::APPLY_UF, p, x);
  41   Expr quantpospx = em.mkExpr(kind::FORALL, var_list, px);
  42   cout << "Made expression : " << quantpospx << endl;
  43
  44   //make ~P( 5 )
  45   Expr five = em.mkConst(Rational(5));
  46   Expr pfive = em.mkExpr(kind::APPLY_UF, p, five);
  47   Expr negpfive = em.mkExpr(kind::NOT, pfive);
  48   cout << "Made expression : " << negpfive << endl;
  49
  50   Expr formula = em.mkExpr(kind::AND, quantpospx, negpfive);
  51
  52   smt.assertFormula(formula);
  53
  54   cout << "Checking SAT after asserting " << formula << " to CVC4." << endl;
  55   cout << "CVC4 should report unsat." << endl;
  56   cout << "Result from CVC4 is: " << smt.checkSat() << endl;
  57
  58
  59   SmtEngine smtp(&em);
  60
  61   // this version has a pattern e.g. in smt2 syntax (forall ((x Int)) (! (P x ) :pattern ((P x))))
  62   Expr pattern = em.mkExpr(kind::INST_PATTERN, px);
  63   Expr pattern_list = em.mkExpr(kind::INST_PATTERN_LIST, pattern);
  64   Expr quantpospx_pattern = em.mkExpr(kind::FORALL, var_list, px, pattern_list);
  65   cout << "Made expression : " << quantpospx_pattern << endl;
  66
  67   Expr formula_pattern = em.mkExpr(kind::AND, quantpospx_pattern, negpfive);
  68
  69   smtp.assertFormula(formula_pattern);
  70
  71   cout << "Checking SAT after asserting " << formula_pattern << " to CVC4." << endl;
  72   cout << "CVC4 should report unsat." << endl;
  73   cout << "Result from CVC4 is: " << smtp.checkSat() << endl;
  74
  75
  76   return 0;
  77 }