added a simple API example example showing how to use the bit-vector theory.

1 files changed, 113 insertions, 0 deletions

diff --git a/examples/api/bitvectors.cpp b/examples/api/bitvectors.cpp
new file mode 100644
index 000000000..080ddf243
--- /dev/null
+++ b/examples/api/bitvectors.cpp
@@ -0,0 +1,113 @@
+/*********************                                                        */
+/*! \file bitvector.cpp
+ ** \verbatim
+ ** Original author: lianah
+ ** Major contributors: none
+ ** Minor contributors (to current version): none
+ ** This file is part of the CVC4 prototype.
+ ** Copyright (c) 2009, 2010, 2011  The Analysis of Computer Systems Group (ACSys)
+ ** Courant Institute of Mathematical Sciences
+ ** New York University
+ ** See the file COPYING in the top-level source directory for licensing
+ ** information.\endverbatim
+ **
+ ** \brief A simple demonstration of the solving capabilities of the CVC4
+ ** bit-vector solver. 
+ **
+ **/
+
+#include <iostream>
+
+//#include <cvc4/cvc4.h> // use this after CVC4 is properly installed
+#include "smt/smt_engine.h"
+
+using namespace std;
+using namespace CVC4;
+
+int main() {
+  ExprManager em;
+  SmtEngine smt(&em);
+  smt.setOption("incremental", true); // Enable incremental solving
+
+  // The following example has been adapted from the book A Hacker's Delight by
+  // Henry S. Warren.
+  //
+  // Given a variable x that can only have two values, a or b. We want to
+  // assign to x a value other than the current one. The straightforward code
+  // to do that is:
+  //
+  //(0) if (x == a ) x = b;
+  //    else x = a;
+  //
+  // Two more efficient yet equivalent methods are:
+  // 
+  //(1) x = a ⊕ b ⊕ x; 
+  //
+  //(2) x = a + b - x;
+  //
+  // We will use CVC4 to prove that the three pieces of code above are all
+  // equivalent by encoding the problem in the bit-vector theory. 
+  
+  // Creating a bit-vector type of width 32
+  Type bitvector32 = em.mkBitVectorType(32);
+
+  // Variables
+  Expr x = em.mkVar("x", bitvector32);
+  Expr a = em.mkVar("a", bitvector32);
+  Expr b = em.mkVar("b", bitvector32);
+
+  // First encode the assumption that x must be equal to a or b
+  Expr x_eq_a = em.mkExpr(kind::EQUAL, x, a); 
+  Expr x_eq_b = em.mkExpr(kind::EQUAL, x, b);
+  Expr assumption = em.mkExpr(kind::OR, x_eq_a, x_eq_b); 
+
+  // Assert the assumption
+  smt.assertFormula(assumption); 
+  
+  // Introduce a new variable for the new value of x after assignment. 
+  Expr new_x = em.mkVar("new_x", bitvector32); // x after executing code (0) 
+  Expr new_x_ = em.mkVar("new_x_", bitvector32); // x after exectuing code (1) or (2)
+
+  // Encoding code (0)
+  // new_x = x == a ? b : a; 
+  Expr ite = em.mkExpr(kind::ITE, x_eq_a, b, a); 
+  Expr assignment0 = em.mkExpr(kind::EQUAL, new_x, ite); 
+
+  // Assert the encoding of code (0)
+  cout << "Asserting " << assignment0 << " to CVC4 " << endl; 
+  smt.assertFormula(assignment0);
+  cout << "Pushing a new context." << endl;
+  smt.push();
+  
+  // Encoding code (1)
+  // new_x_ = a xor b xor x
+  Expr a_xor_b_xor_x = em.mkExpr(kind::BITVECTOR_XOR, a, b, x); 
+  Expr assignment1 = em.mkExpr(kind::EQUAL, new_x_, a_xor_b_xor_x);
+
+  // Assert encoding to CVC4 in current context; 
+  cout << "Asserting " << assignment1 << " to CVC4 " << endl; 
+  smt.assertFormula(assignment1);
+  Expr new_x_eq_new_x_ = em.mkExpr(kind::EQUAL, new_x, new_x_);
+
+  cout << " Querying: " << new_x_eq_new_x_ << endl;
+  cout << " Expect valid. " << endl; 
+  cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl; 
+  cout << " Popping context. " << endl;
+  smt.pop();
+
+  // Encoding code (2)
+  // new_x_ = a + b - x
+  Expr a_plus_b = em.mkExpr(kind::BITVECTOR_PLUS, a, b); 
+  Expr a_plus_b_minus_x = em.mkExpr(kind::BITVECTOR_SUB, a_plus_b, x); 
+  Expr assignment2 = em.mkExpr(kind::EQUAL, new_x_, a_plus_b_minus_x);
+  
+  // Assert encoding to CVC4 in current context; 
+  cout << "Asserting " << assignment2 << " to CVC4 " << endl; 
+  smt.assertFormula(assignment1);
+
+  cout << " Querying: " << new_x_eq_new_x_ << endl;
+  cout << " Expect valid. " << endl; 
+  cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl; 
+  
+  return 0;
+}