This article provides a simple example using Z3 bindings in C to demonstrate how to solve equations. Z3 is an open-source theorem prover developed by Microsoft Research. Using C bindings, users can take advantage of Z3's powerful solving capabilities wrapped in a familiar programming language.
Prerequisites
Before proceeding, ensure you have the Z3 library installed on your system. You can download it from the official GitHub repository. Additionally, allocate a C compiler such as GCC or Clang.
Key Concepts
Utilizing Z3 bindings for C involves the following steps:
- Inclusion of the Z3 library header.
- Initialization of the Z3 context.
- Declaration of Z3 expressions (variables).
- Definition of a solver within the context.
- Assertion of equations/constraints.
- Querying for satisfiability.
- Printing model information if the query is satisfiable.
- Disposal of context.
Inclusion of the Z3 library header
To begin, include the Z3 library header file in your C source code. By default, the header is located at:
#include
Initialization of the Z3 context
Initiate the Z3 context by invoking the z3_context function:
Z3_context ctx = z3_context_new();
Declaration of Z3 expressions (variables)
Declare variables (expressions) using the z3_mk_int_var function:
Z3_ast x = z3_mk_int_var(ctx, "x");
Z3_ast y = z3_mk_int_var(ctx, "y");
Definition of a solver within the context
Create a solver with the z3_solver function:
Z3_solver s = z3_solver_new(ctx);
Assertion of equations/constraints
Assert equations or constraints using the z3_solver_assert function:
Z3_lbool status = z3_solver_assert_cnstr(s, z3_mk_eq(ctx, z3_mk_add(ctx, x, y), z3_mk_int(ctx, 5)));
Querying for satisfiability
Check satisfiability with the z3_solver_check function:
status = z3_solver_check(s, 0);
Printing model information if the query is satisfiable
Obtain model information if satisfiable with the z3_solver_get_model function and display values using the z3_model_get_const_interp:
if (status == Z3_L_TRUE) {
Z3_model m = z3_solver_get_model(s);
Z3_ast v1 = z3_model_get_const_interp(m, x);
Z3_ast v2 = z3_model_get_const_interp(m, y);
printf("x = “%d”, y = “%d”
", z3_get_int_value(ctx, v1),
z3_get_int_value(ctx, v2));
z3_model_decref(m);
}
Disposal of context
Eliminate objects using z3_del_context:
z3_del_context(ctx);
Simple Example
The following Z3 binding C program illustrates solving a system of equations:
#include <stdio.h>
#include <z3.h>
int main(void) {
Z3_context ctx;
Z3_solver s;
Z3_ast x, y;
Z3_lbool status;
ctx = z3_context_new();
x = z3_mk_int_var(ctx, "x");
y = z3_mk_int_var(ctx, "y");
s = z3_solver_new(ctx);
// Assert equations
status = z3_solver_assert_cnstr(s, z3_mk_eq(ctx, z3_mk_add(ctx, x, y), z3_mk_int(ctx, 5)));
status = z3_solver_assert_cnstr(s, z3_mk_eq(ctx, z3_mk_sub(ctx, x, y), z3_mk_int(ctx, 3)));
// Check satisfiability
status = z3_solver_check(s, 0);
if (status == Z3_L_TRUE) {
Z3_model m = z3_solver_get_model(s);
Z3_ast v1 = z3_model_get_const_interp(m, x);
Z3_ast v2 = z3_model_get_const_interp(m, y);
printf("x = “%d”, y = “%d”
", z3_get_int_value(ctx, v1),
z3_get_int_value(ctx, v2));
z3_model_decref(m);
}
// Dispose objects
z3_del_context(ctx);
return 0;
}
This article underscored a simple example using Z3 bindings in C to solve equations. By leveraging the Z3 library and C, users can take advantage of powerful solving capabilities while integrating these features into their C-based projects.
References
- Z3Prover on GitHub
- Programming with Z3 by Nikolaj Bjørner (Microsoft Research) and Leonardo de Moura (Microsoft Research)