lean_univ mk_one() {
lean_exception ex;
lean_univ zero, one;
check(lean_univ_mk_zero(&zero, &ex));
check(lean_univ_mk_succ(zero, &one, &ex));
lean_univ_del(zero);
return one;
}
void test_inductive() {
// declare list type
lean_exception ex = 0;
lean_env env = mk_env();
lean_name l_name = mk_name("l");
lean_univ l = mk_uparam("l");
lean_univ one = mk_one();
lean_univ m1l = mk_max(one, l);
lean_expr Typel = mk_sort(l);
lean_expr Typem1l = mk_sort(m1l);
lean_expr list_type = mk_pi("A", Typel, Typem1l);
lean_name list_name = mk_name("list");
lean_expr list = mk_const("list", l);
lean_expr v0 = mk_var(0);
// nil : Pi (A : Type.{l}), list.{l} A
lean_expr list_v0 = mk_app(list, v0);
lean_expr nil_type = mk_pi("A", Typel, list_v0);
lean_expr nil = mk_local("nil", nil_type);
// cons : Pi (A : Type.{l}), A -> list.{l} A -> list.{l} A
lean_expr v1 = mk_var(1);
lean_expr v2 = mk_var(2);
lean_expr list_v2 = mk_app(list, v2);
lean_expr list_v1 = mk_app(list, v1);
lean_expr cons_type1 = mk_pi("tail", list_v1, list_v2);
lean_expr cons_type2 = mk_pi("head", v0, cons_type1);
lean_expr cons_type = mk_pi("A", Typel, cons_type2);
lean_expr cons = mk_local("cons", cons_type);
//
lean_list_expr cs1, cs2, list_cs;
lean_inductive_type list_ind_type;
lean_list_inductive_type li1, list_ind_types;
lean_list_name ls1, ls;
lean_inductive_decl list_decl;
lean_env new_env;
check(lean_list_name_mk_nil(&ls1, &ex));
check(lean_list_name_mk_cons(l_name, ls1, &ls, &ex));
check(lean_list_expr_mk_nil(&cs1, &ex));
check(lean_list_expr_mk_cons(nil, cs1, &cs2, &ex));
check(lean_list_expr_mk_cons(cons, cs2, &list_cs, &ex));
check(lean_inductive_type_mk(list_name, list_type, list_cs, &list_ind_type, &ex));
check(lean_list_inductive_type_mk_nil(&li1, &ex));
check(lean_list_inductive_type_mk_cons(list_ind_type, li1, &list_ind_types, &ex));
check(lean_inductive_decl_mk(ls, 1, list_ind_types, &list_decl, &ex));
check(lean_env_add_inductive(env, list_decl, &new_env, &ex));
{
unsigned n;
lean_inductive_decl d;
lean_name cons_name = mk_name("cons");
lean_name r_name;
lean_list_inductive_type types;
check(lean_env_get_inductive_type_num_indices(new_env, list_name, &n, &ex) && n == 0);
check(lean_env_get_inductive_type_num_minor_premises(new_env, list_name, &n, &ex) && n == 2);
check(!lean_env_is_inductive_type(env, list_name, &d, &ex));
check(lean_env_is_inductive_type(new_env, list_name, &d, &ex));
check(lean_inductive_decl_get_num_params(d, &n, &ex) && n == 1);
check(lean_inductive_decl_get_types(d, &types, &ex));
check(lean_list_inductive_type_is_cons(types));
check(lean_env_is_constructor(new_env, cons_name, &r_name, &ex) && lean_name_eq(list_name, r_name));
lean_inductive_decl_del(d);
lean_name_del(cons_name);
lean_name_del(r_name);
}
lean_env_del(env);
lean_name_del(list_name);
lean_name_del(l_name);
lean_univ_del(l);
lean_univ_del(one);
lean_univ_del(m1l);
lean_expr_del(Typel);
lean_expr_del(Typem1l);
lean_expr_del(list_type);
lean_expr_del(list);
lean_expr_del(v0);
lean_expr_del(list_v0);
lean_expr_del(nil_type);
lean_expr_del(nil);
lean_expr_del(v1);
lean_expr_del(v2);
lean_expr_del(list_v2);
lean_expr_del(list_v1);
lean_expr_del(cons_type1);
lean_expr_del(cons_type2);
lean_expr_del(cons_type);
lean_expr_del(cons);
lean_list_expr_del(cs1);
lean_list_expr_del(cs2);
lean_list_expr_del(list_cs);
lean_inductive_type_del(list_ind_type);
lean_list_inductive_type_del(li1);
lean_list_inductive_type_del(list_ind_types);
lean_list_name_del(ls1);
lean_list_name_del(ls);
lean_inductive_decl_del(list_decl);
lean_env_del(new_env);
}
void test_id() {
lean_exception ex;
lean_univ l = mk_uparam("l");
lean_env env = mk_env();
lean_expr v0 = mk_var(0);
lean_expr v1 = mk_var(1);
lean_expr AA = mk_pi("a", v0, v1);
lean_expr Type = mk_sort(l);
lean_expr id_type = mk_pi("A", Type, AA);
lean_expr f = mk_lambda("a", v0, v0);
lean_expr id_val = mk_lambda("A", Type, f);
lean_name l_name = mk_name("l");
lean_list_name id_ps = mk_unary_name_list(l_name);
lean_decl id_def = mk_def("id", id_ps, id_type, id_val);
lean_name id_name = mk_name("id");
lean_cert_decl id_cert_def;
lean_env new_env;
lean_univ zero, one;
lean_bool is_lt;
check(lean_expr_lt(f, id_val, &is_lt, &ex) && is_lt);
check(lean_expr_lt(id_val, f, &is_lt, &ex) && !is_lt);
printf("id type: ");
print_expr(id_type);
printf("id value: ");
print_expr(id_val);
printf("-------\n");
/* type check definition */
check(lean_decl_check(env, id_def, &id_cert_def, &ex));
/* add certified definition to environment */
check(lean_env_add(env, id_cert_def, &new_env, &ex));
check(!lean_env_contains_decl(env, id_name));
check(lean_env_contains_decl(new_env, id_name));
check(lean_env_for_each_decl(new_env, print_decl_and_del, &ex));
check(lean_univ_mk_zero(&zero, &ex));
check(lean_univ_mk_succ(zero, &one, &ex));
check(lean_univ_lt(zero, one, &is_lt, &ex) && is_lt);
check(lean_univ_lt(one, zero, &is_lt, &ex) && !is_lt);
{
lean_type_checker tc;
lean_expr T0 = mk_sort(zero);
lean_expr T1 = mk_sort(one);
lean_expr id1 = mk_const("id", one);
lean_expr id1T1, id1T1T0;
lean_expr n1;
lean_cnstr_seq s1;
check(lean_expr_mk_app(id1, T1, &id1T1, &ex));
check(lean_expr_mk_app(id1T1, T0, &id1T1T0, &ex));
check(lean_type_checker_mk(new_env, &tc, &ex));
printf("WHNF test\n");
print_expr(id1T1T0);
check(lean_type_checker_whnf(tc, id1T1T0, &n1, &s1, &ex));
printf("=====>\n");
print_expr(n1);
lean_expr_del(n1);
lean_cnstr_seq_del(s1);
printf("Infer type test\n");
print_expr(id1T1);
check(lean_type_checker_infer(tc, id1T1, &n1, &s1, &ex));
printf("=====>\n");
print_expr(n1);
lean_expr_del(n1);
lean_cnstr_seq_del(s1);
lean_type_checker_del(tc);
lean_expr_del(T0);
lean_expr_del(T1);
lean_expr_del(id1);
lean_expr_del(id1T1);
lean_expr_del(id1T1T0);
}
lean_univ_del(l);
lean_env_del(env);
lean_expr_del(v0);
lean_expr_del(v1);
lean_expr_del(Type);
lean_expr_del(AA);
lean_expr_del(id_type);
lean_expr_del(f);
lean_expr_del(id_val);
lean_decl_del(id_def);
lean_list_name_del(id_ps);
lean_name_del(l_name);
lean_cert_decl_del(id_cert_def);
lean_env_del(new_env);
lean_name_del(id_name);
lean_univ_del(zero);
lean_univ_del(one);
}
int main() {
lean_exception ex;
lean_name a, l, U, pp, pp_unicode, rn;
lean_options o1, o2;
lean_univ zero, one, p1, g1, m1, u, n, i, ru;
lean_list_name ln1, ln2;
lean_list_univ lu1, lu2;
char const * s1;
lean_bool r;
check(lean_name_mk_anonymous(&a, &ex));
check(lean_name_mk_str(a, "l_1", &l, &ex));
check(lean_name_mk_str(a, "U", &U, &ex));
check(lean_name_mk_str(a, "pp", &pp, &ex));
check(lean_name_mk_str(pp, "unicode", &pp_unicode, &ex));
check(lean_options_mk_empty(&o1, &ex));
check(lean_options_set_bool(o1, pp_unicode, lean_false, &o2, &ex));
check(lean_univ_mk_zero(&zero, &ex));
check(lean_univ_mk_succ(zero, &one, &ex));
check(lean_univ_mk_param(l, &p1, &ex));
check(lean_univ_mk_global(U, &g1, &ex));
check(lean_univ_mk_max(p1, one, &m1, &ex));
check(lean_univ_mk_succ(m1, &u, &ex));
check(lean_univ_normalize(u, &n, &ex));
check(lean_univ_to_string(n, &s1, &ex));
printf("universe: %s\n", s1);
check(lean_univ_geq(one, zero, &r, &ex) && r);
/* replace l_1 with one in u */
check(lean_list_name_mk_nil(&ln1, &ex));
check(lean_list_name_mk_cons(l, ln1, &ln2, &ex));
check(lean_list_univ_mk_nil(&lu1, &ex));
check(lean_list_univ_mk_cons(one, lu1, &lu2, &ex));
check(lean_univ_instantiate(u, ln2, lu2, &i, &ex));
lean_list_name_del(ln1);
lean_list_name_del(ln2);
lean_list_univ_del(lu1);
lean_list_univ_del(lu2);
lean_string_del(s1);
check(lean_univ_to_string_using(i, o2, &s1, &ex));
printf("universe: %s\n", s1);
check(lean_univ_get_kind(zero) == LEAN_UNIV_ZERO);
check(lean_univ_get_kind(one) == LEAN_UNIV_SUCC);
check(lean_univ_get_kind(n) == LEAN_UNIV_MAX);
check(lean_univ_get_name(g1, &rn, &ex) && lean_name_eq(rn, U));
check(lean_univ_get_max_lhs(m1, &ru, &ex) && lean_univ_eq(ru, p1, &r, &ex) && r);
lean_univ_del(ru);
check(lean_univ_get_max_rhs(m1, &ru, &ex) && lean_univ_eq(ru, one, &r, &ex) && r);
lean_univ_del(ru);
check(lean_univ_get_pred(one, &ru, &ex) && lean_univ_eq(ru, zero, &r, &ex) && r);
lean_univ_del(ru);
lean_name_del(a);
lean_name_del(l);
lean_name_del(U);
lean_name_del(pp);
lean_name_del(pp_unicode);
lean_name_del(rn);
lean_options_del(o1);
lean_options_del(o2);
lean_univ_del(zero);
lean_univ_del(one);
lean_univ_del(p1);
lean_univ_del(g1);
lean_univ_del(m1);
lean_univ_del(u);
lean_univ_del(n);
lean_univ_del(i);
lean_string_del(s1);
return 0;
}