define-fun macro & regex in Z3 C++ binding - c++

Question

I'm writing some code that uses Z3 strings to evaluate permissions in ACLs. So far with SMT2 this has been relatively easy. An eg. code of what I'm trying to acheive is:
(declare-const Group String)
(declare-const Resource String)
(define-fun acl1() Bool
(or (and
(= Group "employee")
(str.prefixof "shared/News_" Resource))
(and
(= Group "manager")
(or (str.prefixof "shared/Internal_" Resource)
(str.prefixof "shared/News_" Resource))
)))
(define-fun acl2() Bool
(and (and (str.prefixof "shared/" Resource)
(str.in.re Group re.allchar))
(not (and (str.prefixof "shared/Internal_" Resource)
(= Group "employee")))))
;; perm(acl1) <= perm(acl) iff acl1 => acl2
(define-fun conjecture() Bool
(=> (= acl1 true)
(= acl2 true)))
(assert (not conjecture))
(check-sat)
Reading the z3 c++ bindings, I can't figure out how to stick a z3::function to this yet. So far, assuming that define-fun is just a lisp macro, I have this.
#include <z3++.h>
z3::expr acl1(z3::context& c, z3::expr& G, z3::expr& R)
{
return (((G == c.string_val("employee")) &&
z3::prefixof(c.string_val("shared/News_"), R)) ||
((G == c.string_val("manager")) &&
(z3::prefixof(c.string_val("shared/Internal_"), R) ||
z3::prefixof(c.string_val("shared/News_"), R))));
}
z3::expr acl2(z3::context& c, z3::expr& G, z3::expr& R)
{
return ((z3::prefixof(c.string_val(""), G) &&
z3::prefixof(c.string_val("shared/"), R)) &&
!((G == c.string_val("employee")) &&
(z3::prefixof(c.string_val("shared/Internal"), R))));
}
z3::expr MakeStringFunction(z3::context* c, std::string s) {
z3::sort sort = c->string_sort();
z3::symbol name = c->str_symbol(s.c_str());
return c->constant(name, sort);
}
void acl_eval()
{
z3::context c;
auto Group = MakeStringFunction(&c, "Group");
auto Resource = MakeStringFunction(&c, "Resource");
auto acl1_f = acl1(c, Group, Resource);
auto acl2_f = acl2(c, Group, Resource);
auto conjecture = implies(acl1_f == c.bool_val(true),
acl2_f == c.bool_val(true));
z3::solver s(c);
s.add(!conjecture);
std::cout << s.to_smt2() << std::endl;
switch(s.check()){
case z3::unsat: std::cout<< "Valid Conjecture" << std::endl; break;
case z3::sat: std::cout << "Invalid Conjecture" << std::endl; break;
case z3::unknown: [[fallthrough]]
default:
std::cout << "Unknown" << std::endl;
}
}
int main(){
acl_eval();
return 0;
}
Is this how this is to be done wrt functions in C++ bindings?
while the smt2 code generated by C++ bindings don't exactly look like the other one, I see a whole expr inside an assert with let bindings which kind of does what I want. Additionally, I also want to know if C++ bindings support regex functions like the SMT lib of z3 exposes? I can't find any examples and the docs aren't very clear.

Answer 1

In general, you do not need to create "functions" in SMTLib when you're using the C++ (or any other high-level) API. Instead, you simply write functions in those languages, which generate the required code directly. This does sound confusing at first, but it is the intended use case: SMTLib functions get replaced by functions in the host language. Running them in the host language then produces the necessary syntax trees in the object language; i.e., Z3's internal AST representation. Especially in your case, you do not need any "arguments" passed to these functions, so you shouldn't be creating any at all. So, what you did here is correct.
(Side note: There can be scenarios where you do want to spit out functions in SMTLib. For instance if you want to use uninterpreted functions. Or perhaps you want to use the recursive function definitions, which you cannot really do in the host language. But let's not conflate the matters here. If you do feel you actually do need them, please ask a separate question about that. From your description, I see no reason for them.)
Regarding regular-expression expressions: They're all available in the C++ API, take a look here: https://z3prover.github.io/api/html/z3_09_09_8h_source.html#l03334
In particular, the functions you're looking for are:
in_re: For checking membership
re_full: Regular expression accepting all strings (Somewhat confusingly, SMTLibs allchar is called re_full in the C++ API.)
Hopefully that'll get you started!