Question

I am interested in testing the “practical” impact of the decision/instantiation procedure (its implementation inclusive) discussed in [1].

I need:

1) A “tool” that take an SMT benchmark and returns a (possibly complete) instantiated version of it, applying the strategy. If this is not possible,

2) The Z3 version implementing this strategy and an option for switching it on and off.

Can you help me on that?

[1] Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories

Answer 1

As far as I know, there is no tool that will return the instantiated version of an SMT benchmark.
Z3 instantiates the quantifiers on-demand using Model-Based Quantifier Instantiation (MBQI) described on Section 6 of [1]. The actual loop in the latest Z3 is more complicated that the one described on this section.

Here are some notes on how to enable/disable the MBQI module.

• First, we should disable automatic configuration using the command

(set-option :auto-config false)

• Z3 4.x uses MBQI and E-Matching for handling quantifiers. We should use the commands for disabling both of them:

(set-option :ematching false)
(set-option :mbqi false)

• To enable them, we should use:

(set-option :ematching true)
(set-option :mbqi true)

With these options you can check the effect of MBQI and E-Matching in different problems. Note that, if we use only E-matching, then Z3 will return unknown for any satisfiable problem that contains quantifiers.

The MBQI module is implemented in the files src/smt/smt_model_finder.cpp and src/smt/smt_model_checker.cpp. The file src/smt/smt_model_finder.cpp is essentially converting a model produced for the quantifier-free formulas in a model that may potentially satisfy the universally quantified formulas. Note that the class auf_solver is the one that actually “solves” the set constraints and “builds” the projection functions described in [1].

If we want to trace the actual instances generated by the MBQI module, we can modify the method void model_checker::assert_new_instances() at src/smt/smt_model_checker.cpp. Note that these method already has some tracing commands sending data to tout (trace output). We can replace tout with std::cout to get the information on the standard output.
For example, if we add the following piece of code, then whenever a universal quantifier q is instantiated (by the MBQI module) with some bindings, Z3 will display the information in the standard output:

std::cout << "[New-instance]\n" << mk_pp(q, m_manager) << "\n";
std::cout << "[Bindings]\n";
for (unsigned i = 0; i < num_decls; i++) {
    expr * b = inst->m_bindings[i];
    std::cout << mk_pp(b, m_manager) << "\n";
}
std::cout << "[End-New-Instance]\n";