是，Z3的團隊提供了多種方法做同樣的事情。原理上的區別是Z3_mk_forall_const需要使用正常機制定義的常量列表，而Z3_mk_forall需要使用Z3_mk_bound創建的綁定變量列表。
哪種機制更易於使用將取決於您的具體應用。特別是，當我想要建立一個量詞的符號數量很少，數量固定時，在我看來Z3_mk_forall_const會更自然。相反，Z3_mk_forall可能會更自然，因爲量詞中符號的數量可能會有所不同，在這種情況下，生成綁定變量數組是很自然的，您可以使用索引來解決該問題。
還有其他的優點和缺點。例如，看到這個問題： "How to declare constants to use as bound variables in Z3_mk_forall_const?" 在這個問題中，提問者希望避免在他們的全局上下文中引入很多變量，這將是使用Z3_mk_forall_const所必需的。回答者（克里斯托夫）建議使用Z3_mk_forall來代替，但這也不是很理想，因爲對於嵌套量詞，這會導致每個量詞的索引不同。克里斯托夫還透露，在內部，基於Z3_mk_forall_const的方法被翻譯成相當於Z3_mk_forall的東西，所以在引擎蓋下實際上沒有區別。然而，API的差異會給程序員帶來很大的變化。
如果您能夠使用它，那麼在C++ API中還提供了一個（更簡單的）程序員機制。下面是使用實例的三種不同的方法：
// g++ --std=c++11 z3-quantifier-support.cpp -I../src/api/ -I../src/api/c++/ libz3.so
#include <stdio.h>
#include "z3.h"
#include <iostream>
#include "z3++.h"
using namespace z3;
/**
* This is by far the most concise and easiest to use if the C++ API is available to you.
*/
void example_cpp_forall() {
context c;
expr a = c.int_const("a");
expr b = c.int_const("b");
expr x = c.int_const("x");
expr axiom = forall(x, implies(x <= a, x < b));
std::cout << "Result obtained using the C++ API with forall:\n" << axiom << "\n\n";
}
/**
* Example using Z3_mk_forall_const. Not as clean as the C++ example, but this was still
* significantly easier for me to get working than the example using Z3_mk_forall().
*/
void example_c_Z3_mk_forall_const() {
// Get the context
Z3_config cfg;
Z3_context ctx;
cfg = Z3_mk_config();
ctx = Z3_mk_context(cfg);
// Declare integers a, b, and x
Z3_sort I = Z3_mk_int_sort(ctx);
Z3_symbol a_S = Z3_mk_string_symbol(ctx, "a");
Z3_symbol b_S = Z3_mk_string_symbol(ctx, "b");
Z3_symbol x_S = Z3_mk_string_symbol(ctx, "x");
Z3_ast a_A = Z3_mk_const(ctx, a_S, I);
Z3_ast b_A = Z3_mk_const(ctx, b_S, I);
Z3_ast x_A = Z3_mk_const(ctx, x_S, I);
// Build the AST (x <= a) --> (x < b)
Z3_ast x_le_a = Z3_mk_le(ctx, x_A, a_A);
Z3_ast x_lt_b = Z3_mk_lt(ctx, x_A, b_A);
Z3_ast f = Z3_mk_implies(ctx, x_le_a, x_lt_b);
Z3_app vars[] = {(Z3_app) x_A};
Z3_ast axiom = Z3_mk_forall_const(ctx, 0, 1, vars, 0, 0, f);
printf("Result obtained using the C API with Z3_mk_forall_const:\n");
printf("%s\n\n", Z3_ast_to_string(ctx, axiom));
}
/**
* Example using Z3_mk_forall. For the example, this is the most cumbersome.
*/
void example_c_Z3_mk_forall() {
// Get the context
Z3_config cfg;
Z3_context ctx;
cfg = Z3_mk_config();
ctx = Z3_mk_context(cfg);
// Declare integers a and b
Z3_sort I = Z3_mk_int_sort(ctx);
Z3_symbol a_S = Z3_mk_string_symbol(ctx, "a");
Z3_symbol b_S = Z3_mk_string_symbol(ctx, "b");
Z3_ast a_A = Z3_mk_const(ctx, a_S, I);
Z3_ast b_A = Z3_mk_const(ctx, b_S, I);
// Declare bound variables, in this case, just x
Z3_symbol x_S = Z3_mk_string_symbol(ctx, "x");
Z3_ast x_A = Z3_mk_bound(ctx, 0, I);
// Z3_mk_forall requires all names, types, and bound variables to be provided in
// arrays. In this example, where there is only one quantified variable, this seems a
// bit cumbersome. If we were dealing with an varying number of quantified variables,
// then this would seem more reasonable.
const unsigned sz = 1;
const Z3_sort types[] = {I};
const Z3_symbol names[] = {x_S};
const Z3_ast xs[] = {x_A};
// Build the AST (x <= a) --> (x < b)
Z3_ast x_le_a = Z3_mk_le(ctx, x_A, a_A);
Z3_ast x_lt_b = Z3_mk_lt(ctx, x_A, b_A);
Z3_ast f = Z3_mk_implies(ctx, x_le_a, x_lt_b);
// In the Z3 docs for Z3_mk_pattern, the following sentence appears: "If a pattern is
// not provided for a quantifier, then Z3 will automatically compute a set of
// patterns for it." So I tried supplying '0' for the number of patterns, and 'NULL'
// for the list of patterns, and Z3_mk_forall still seems to function.
Z3_ast axiom = Z3_mk_forall(ctx, 0, 0, NULL, sz, types, names, f);
printf("Result obtained using the C API with Z3_mk_forall:\n");
printf("%s\n", Z3_ast_to_string(ctx, axiom));
}
int main() {
example_cpp_forall();
example_c_Z3_mk_forall_const();
example_c_Z3_mk_forall();
}
我也發現了這些問題有所幫助：
在Z3源代碼中提供的示例和註釋也很有幫助，特別是在examples/c/test_capi.c,examples/c++/example.cpp和src/api/z3_api.h中。