Using ProB with Z3


The current nightly versions of ProB can make use of Z3 as an alternate way of solving constraints.

How to use Z3 within ProB

One can start a REPL (Read-Eval-Print-Loop) by starting probcli with the '-repl' command line option. Any predicate preceded with :z3 will be solved by Z3. The full integration of Z3 and ProB’s kernel can be enabled by setting the corresponding preference by passing

-p SMT SUPPORTED INTERPRETER TRUE

on the command line.

How to install Z3 for ProB

First of all, download a nightly build of ProB from the Downloads page. To connect Z3 to ProB you also need the proper extension. For Linux and Mac OS, the extension is build by on our infrastructure and ships with the regular ProB download. For Windows, you can download it from the following URLs:

and place it in the "lib" folder of the ProB nightly build.

In addition to ProB, you need to install Z3 by downloading it from Z3's GitHub page. Currently, ProB is linked against the stable release 4.4.1 of Z3. Inside the zip file you will find a folder called "bin" with the z3 binary and the belonging libraries inside.

These libraries have to be made available to ProB. On Linux or Mac, this can either be done by placing them in an appropriate folder (like /usr/lib or /usr/local/lib) or by setting an environmental variable (like LD_LIBRARY_PATH on Linux or DYLD_LIBRARY_PATH on Mac). On Windows, you can place z3.dll in the main folder of the ProB distribution, i. e., on the same level as the lib directory, not inside it. If the libraries can not be loaded, ProB will answer with "solver_not_available" when Z3 is queried.

What can be translated

Currently, the Z3 translation is unable to cope with the following constructs:

  • Strings
  • Generalised union, generalised intersection
  • Generalised concatenation
  • Permutation
  • Iteration and Closure
  • Projection

When using Z3 alone, the solver will report "unsupported_type_or_expression" if it can not handle parts of a constraint.

When used together with ProB, everything Z3 can not be coped with will be handled by ProB alone automatically.

Examples

Using the repl, one can try out different examples.

First an example which can be solved by Z3 and not by ProB:

>>> X<Y & Y<X
% Timeout when posting constraint:
% kernel_objects:(_981727#>0)
### Warning: enumerating X : INTEGER : inf:sup ---> -1:3
Existentially Quantified Predicate over X,Y is UNKNOWN
[FALSE with ** ENUMERATION WARNING **]

Using the Z3 translation it can be solved:

>>> :z3 X<Y & Y<X
PREDICATE is FALSE

Now an example which can be solved by ProB’s own solver:

>>> (2|->4):{y|#x.(y=(x|->x+2))}
PREDICATE is TRUE

This one cannot be solved by Z3:

>>> :z3 (2|->4):{y|#x.(y=(x|->x+2))}
PREDICATE is UNKNOWN: solver_answered_unknown

Here an example that shows that Z3 can be used to solve constraints and obtain solutions for the open variables:

>>> :z3 {x} /\ {y} /= {} & x:1000000..20000000 & y>=0 & y<2000000
PREDICATE is TRUE
Solution:
      x = 1000000
      y = 1000000

More details

A paper describing the integration of ProB and Z3 has been submitted to iFM 2016. You can download the