for all quantifier in Z3

问题:

I would like to see an example of C-API Z3_mk_forall_const() in Z3.

I am trying to encode -

(define-fun max_integ ((x Int) (y Int)) Int      (ite (< x y) y x))  

What I tried is following, but I get type error

#include <stdio.h> #include <stdlib.h> #include <z3.h>   void error_handler(Z3_context c, Z3_error_code e) {     printf("Error code: %d\n", e);     printf("Error msg : %s\n", Z3_get_error_msg(e));     exit(0); }  Z3_context mk_context_custom(Z3_config cfg, Z3_error_handler err) {     Z3_context ctx;      Z3_set_param_value(cfg, "MODEL", "true");     ctx = Z3_mk_context(cfg);     Z3_set_error_handler(ctx, err);      return ctx; }  Z3_context mk_context() {     Z3_config  cfg;     Z3_context ctx;     cfg = Z3_mk_config();     ctx = mk_context_custom(cfg, error_handler);     Z3_del_config(cfg);     return ctx; }  Z3_ast mk_var(Z3_context ctx, const char * name, Z3_sort ty)   {     Z3_symbol   s  = Z3_mk_string_symbol(ctx, name);     return Z3_mk_const(ctx, s, ty);  }  Z3_ast mk_int_var(Z3_context ctx, const char * name) {     Z3_sort ty = Z3_mk_int_sort(ctx);     return mk_var(ctx, name, ty); }  int main() {     Z3_context      ctx;     Z3_func_decl    f;     Z3_sort         int_sort;     Z3_symbol       f_name;     Z3_ast xVar, yVar;     Z3_app bound[2];     Z3_ast implication;     Z3_sort       f_domain[2];      // Make context.     ctx = mk_context();      int_sort    = Z3_mk_int_sort(ctx);     f_name      = Z3_mk_string_symbol(ctx, "max_integer");     f_domain[0] = int_sort;     f_domain[1] = int_sort;     f = Z3_mk_func_decl(ctx, f_name, 2, f_domain, int_sort);      xVar = mk_int_var(ctx, "x");     yVar = mk_int_var(ctx, "y");      bound[0] = (Z3_app)xVar;     bound[1] = (Z3_app)yVar;      implication = Z3_mk_ite(ctx, Z3_mk_lt(ctx, xVar, yVar), xVar, yVar);      Z3_mk_forall_const(ctx, 0, 2, bound, 0, 0, implication);      // Delete the context.     Z3_del_context(ctx);      return 0; } 

回答1:

You are getting a type error because implication is an integer expression. The argument of a forall expression must be a Boolean expression. I'm assuming you are trying to create the formula

(forall ((x Int) (y Int)) (= (max_int x y) (ite (< y x) x y))) 

Here is the modified example. Note that I also modified Z3_mk_lt(ctx, xVar, yVar) to Z3_mk_lt(ctx, yVar, xVar). Otherwise, you would be defining the min function.

int main() {     Z3_context      ctx;     Z3_func_decl    f;     Z3_sort         int_sort;     Z3_symbol       f_name;     Z3_ast xVar, yVar;     Z3_app bound[2];     Z3_ast ite;     Z3_sort f_domain[2];     Z3_ast f_app;     Z3_ast eq;     Z3_ast q;      // Make context.     ctx = mk_context();      int_sort    = Z3_mk_int_sort(ctx);     f_name      = Z3_mk_string_symbol(ctx, "max_integer");     f_domain[0] = int_sort;     f_domain[1] = int_sort;     f = Z3_mk_func_decl(ctx, f_name, 2, f_domain, int_sort);      xVar = mk_int_var(ctx, "x");     yVar = mk_int_var(ctx, "y");      bound[0] = (Z3_app)xVar;     bound[1] = (Z3_app)yVar;      // Create the application f(x, y)     { Z3_ast args[2] = {xVar, yVar};        f_app = Z3_mk_app(ctx, f, 2, args);     }      // Create the expression ite(y < x, x, y)     ite = Z3_mk_ite(ctx, Z3_mk_lt(ctx, yVar, xVar), xVar, yVar);      // Create the equality     eq = Z3_mk_eq(ctx, f_app, ite);      // Create quantifier     q = Z3_mk_forall_const(ctx, 0, 2, bound, 0, 0, eq);      printf("%s\n", Z3_ast_to_string(ctx, q));      // Delete the context.     Z3_del_context(ctx);      return 0; } 

文章来源: for all quantifier in Z3