smt_astt
smt_convt::overflow_cast(const expr2tc &expr)
{
// If in integer mode, this is completely pointless. Return false.
if (int_encoding)
return mk_smt_bool(false);
const overflow_cast2t &ocast = to_overflow_cast2t(expr);
unsigned int width = ocast.operand->type->get_width();
unsigned int bits = ocast.bits;
smt_sortt boolsort = boolean_sort;
if (ocast.bits >= width || ocast.bits == 0) {
std::cerr << "SMT conversion: overflow-typecast got wrong number of bits"
<< std::endl;
abort();
}
// Basically: if it's positive in the first place, ensure all the top bits
// are zero. If neg, then all the top are 1's /and/ the next bit, so that
// it's considered negative in the next interpretation.
constant_int2tc zero(ocast.operand->type, BigInt(0));
lessthan2tc isnegexpr(ocast.operand, zero);
smt_astt isneg = convert_ast(isnegexpr);
smt_astt orig_val = convert_ast(ocast.operand);
// Difference bits
unsigned int pos_zero_bits = width - bits;
unsigned int neg_one_bits = (width - bits) + 1;
smt_sortt pos_zero_bits_sort =
mk_sort(SMT_SORT_BV, pos_zero_bits, false);
smt_sortt neg_one_bits_sort =
mk_sort(SMT_SORT_BV, neg_one_bits, false);
smt_astt pos_bits = mk_smt_bvint(BigInt(0), false, pos_zero_bits);
smt_astt neg_bits = mk_smt_bvint(BigInt((1 << neg_one_bits) - 1),
false, neg_one_bits);
smt_astt pos_sel = mk_extract(orig_val, width - 1,
width - pos_zero_bits,
pos_zero_bits_sort);
smt_astt neg_sel = mk_extract(orig_val, width - 1,
width - neg_one_bits,
neg_one_bits_sort);
smt_astt pos_eq = mk_func_app(boolsort, SMT_FUNC_EQ, pos_bits, pos_sel);
smt_astt neg_eq = mk_func_app(boolsort, SMT_FUNC_EQ, neg_bits, neg_sel);
// isneg -> neg_eq, !isneg -> pos_eq
smt_astt notisneg = mk_func_app(boolsort, SMT_FUNC_NOT, &isneg, 1);
smt_astt c1 = mk_func_app(boolsort, SMT_FUNC_IMPLIES, isneg, neg_eq);
smt_astt c2 = mk_func_app(boolsort, SMT_FUNC_IMPLIES, notisneg, pos_eq);
smt_astt nooverflow = mk_func_app(boolsort, SMT_FUNC_AND, c1, c2);
return mk_func_app(boolsort, SMT_FUNC_NOT, &nooverflow, 1);
}
sort * array_decl_plugin::mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters) {
if (k == _SET_SORT) {
if (num_parameters != 1) {
m_manager->raise_exception("invalid array sort definition, invalid number of parameters");
return 0;
}
parameter params[2] = { parameters[0], parameter(m_manager->mk_bool_sort()) };
return mk_sort(ARRAY_SORT, 2, params);
}
SASSERT(k == ARRAY_SORT);
if (num_parameters < 2) {
m_manager->raise_exception("invalid array sort definition, invalid number of parameters");
return 0;
}
for (unsigned i = 0; i < num_parameters; i++) {
if (!parameters[i].is_ast() || !is_sort(parameters[i].get_ast())) {
m_manager->raise_exception("invalid array sort definition, parameter is not a sort");
return 0;
}
}
sort * range = to_sort(parameters[num_parameters - 1].get_ast());
TRACE("array_decl_plugin_bug", tout << mk_pp(range, *m_manager) << "\n";);
smt_astt
smt_convt::overflow_arith(const expr2tc &expr)
{
// If in integer mode, this is completely pointless. Return false.
if (int_encoding)
return mk_smt_bool(false);
const overflow2t &overflow = to_overflow2t(expr);
const arith_2ops &opers = static_cast<const arith_2ops &>(*overflow.operand);
assert(opers.side_1->type == opers.side_2->type);
constant_int2tc zero(opers.side_1->type, BigInt(0));
lessthan2tc op1neg(opers.side_1, zero);
lessthan2tc op2neg(opers.side_2, zero);
equality2tc op1iszero(opers.side_1, zero);
equality2tc op2iszero(opers.side_2, zero);
or2tc containszero(op1iszero, op2iszero);
// Guess whether we're performing a signed or unsigned comparison.
bool is_signed = (is_signedbv_type(opers.side_1) ||
is_signedbv_type(opers.side_2));
if (is_add2t(overflow.operand)) {
if (is_signed) {
// Two cases: pos/pos, and neg/neg, which can over and underflow resp.
// In pos/neg cases, no overflow or underflow is possible, for any value.
constant_int2tc zero(opers.side_1->type, BigInt(0));
lessthan2tc op1pos(zero, opers.side_1);
lessthan2tc op2pos(zero, opers.side_2);
and2tc both_pos(op1pos, op2pos);
not2tc negop1(op1pos);
not2tc negop2(op2pos);
and2tc both_neg(negop1, negop2);
implies2tc nooverflow(both_pos,
greaterthanequal2tc(overflow.operand, zero));
implies2tc nounderflow(both_neg,
lessthanequal2tc(overflow.operand, zero));
return convert_ast(not2tc(and2tc(nooverflow, nounderflow)));
} else {
// Just ensure the result is >= both operands.
greaterthanequal2tc ge1(overflow.operand, opers.side_1);
greaterthanequal2tc ge2(overflow.operand, opers.side_2);
and2tc res(ge1, ge2);
not2tc inv(res);
return convert_ast(inv);
}
} else if (is_sub2t(overflow.operand)) {
if (is_signed) {
// Convert to be an addition
neg2tc negop2(opers.side_2->type, opers.side_2);
add2tc anadd(opers.side_1->type, opers.side_1, negop2);
expr2tc add_overflows(new overflow2t(anadd));
// Corner case: subtracting MIN_INT from many things overflows. The result
// should always be positive.
constant_int2tc zero(opers.side_1->type, BigInt(0));
uint64_t topbit = 1ULL << (opers.side_1->type->get_width() - 1);
constant_int2tc min_int(opers.side_1->type, BigInt(topbit));
equality2tc is_min_int(min_int, opers.side_2);
implies2tc imp(is_min_int, greaterthan2tc(overflow.operand, zero));
return convert_ast(or2tc(add_overflows, is_min_int));
} else {
// Just ensure the result is >= the operands.
lessthanequal2tc le1(overflow.operand, opers.side_1);
lessthanequal2tc le2(overflow.operand, opers.side_2);
and2tc res(le1, le2);
not2tc inv(res);
return convert_ast(inv);
}
} else {
assert(is_mul2t(overflow.operand) && "unexpected overflow_arith operand");
// Zero extend; multiply; Make a decision based on the top half.
unsigned int sz = zero->type->get_width();
smt_sortt boolsort = boolean_sort;
smt_sortt normalsort = mk_sort(SMT_SORT_BV, sz, false);
smt_sortt bigsort = mk_sort(SMT_SORT_BV, sz * 2, false);
// All one bit vector is tricky, might be 64 bits wide for all we know.
constant_int2tc allonesexpr(zero->type, BigInt((sz == 64)
? 0xFFFFFFFFFFFFFFFFULL
: ((1ULL << sz) - 1)));
smt_astt allonesvector = convert_ast(allonesexpr);
smt_astt arg1_ext, arg2_ext;
if (is_signed) {
// sign extend top bits.
arg1_ext = convert_ast(opers.side_1);
arg1_ext = convert_sign_ext(arg1_ext, bigsort, sz - 1, sz);
arg2_ext = convert_ast(opers.side_2);
arg2_ext = convert_sign_ext(arg2_ext, bigsort, sz - 1, sz);
} else {
// Zero extend the top parts
arg1_ext = convert_ast(opers.side_1);
arg1_ext = convert_zero_ext(arg1_ext, bigsort, sz);
arg2_ext = convert_ast(opers.side_2);
arg2_ext = convert_zero_ext(arg2_ext, bigsort, sz);
}
smt_astt result = mk_func_app(bigsort, SMT_FUNC_BVMUL, arg1_ext, arg2_ext);
// Extract top half.
smt_astt toppart = mk_extract(result, (sz * 2) - 1, sz, normalsort);
if (is_signed) {
// It should either be zero or all one's; which depends on what
// configuration of signs it had. If both pos / both neg, then the top
// should all be zeros, otherwise all ones. Implement with xor.
smt_astt op1neg_ast = convert_ast(op1neg);
smt_astt op2neg_ast = convert_ast(op2neg);
smt_astt allonescond =
mk_func_app(boolsort, SMT_FUNC_XOR, op1neg_ast, op2neg_ast);
smt_astt zerovector = convert_ast(zero);
smt_astt initial_switch =
mk_func_app(normalsort, SMT_FUNC_ITE, allonescond,
allonesvector, zerovector);
// either value being zero means the top must be zero.
smt_astt contains_zero_ast = convert_ast(containszero);
smt_astt second_switch = mk_func_app(normalsort, SMT_FUNC_ITE,
contains_zero_ast,
zerovector,
initial_switch);
smt_astt is_eq =
mk_func_app(boolsort, SMT_FUNC_EQ, second_switch, toppart);
return mk_func_app(boolsort, SMT_FUNC_NOT, &is_eq, 1);
} else {
// It should be zero; if not, overflow
smt_astt iseq =
mk_func_app(boolsort, SMT_FUNC_EQ, toppart, convert_ast(zero));
return mk_func_app(boolsort, SMT_FUNC_NOT, &iseq, 1);
}
}
return NULL;
}
static environment mk_below(environment const & env, name const & n, bool ibelow) {
if (!is_recursive_datatype(env, n))
return env;
if (is_inductive_predicate(env, n))
return env;
inductive::inductive_decls decls = *inductive::is_inductive_decl(env, n);
type_checker tc(env);
name_generator ngen;
unsigned nparams = std::get<1>(decls);
declaration ind_decl = env.get(n);
declaration rec_decl = env.get(inductive::get_elim_name(n));
unsigned nindices = *inductive::get_num_indices(env, n);
unsigned nminors = *inductive::get_num_minor_premises(env, n);
unsigned ntypeformers = length(std::get<2>(decls));
level_param_names lps = rec_decl.get_univ_params();
bool is_reflexive = is_reflexive_datatype(tc, n);
level lvl = mk_param_univ(head(lps));
levels lvls = param_names_to_levels(tail(lps));
level_param_names blvls; // universe level parameters of ibelow/below
level rlvl; // universe level of the resultant type
// The arguments of below (ibelow) are the ones in the recursor - minor premises.
// The universe we map to is also different (l+1 for below of reflexive types) and (0 fo ibelow).
expr ref_type;
expr Type_result;
if (ibelow) {
// we are eliminating to Prop
blvls = tail(lps);
rlvl = mk_level_zero();
ref_type = instantiate_univ_param(rec_decl.get_type(), param_id(lvl), mk_level_zero());
} else if (is_reflexive) {
blvls = lps;
rlvl = get_datatype_level(ind_decl.get_type());
// if rlvl is of the form (max 1 l), then rlvl <- l
if (is_max(rlvl) && is_one(max_lhs(rlvl)))
rlvl = max_rhs(rlvl);
rlvl = mk_max(mk_succ(lvl), rlvl);
ref_type = instantiate_univ_param(rec_decl.get_type(), param_id(lvl), mk_succ(lvl));
} else {
// we can simplify the universe levels for non-reflexive datatypes
blvls = lps;
rlvl = mk_max(mk_level_one(), lvl);
ref_type = rec_decl.get_type();
}
Type_result = mk_sort(rlvl);
buffer<expr> ref_args;
to_telescope(ngen, ref_type, ref_args);
if (ref_args.size() != nparams + ntypeformers + nminors + nindices + 1)
throw_corrupted(n);
// args contains the below/ibelow arguments
buffer<expr> args;
buffer<name> typeformer_names;
// add parameters and typeformers
for (unsigned i = 0; i < nparams; i++)
args.push_back(ref_args[i]);
for (unsigned i = nparams; i < nparams + ntypeformers; i++) {
args.push_back(ref_args[i]);
typeformer_names.push_back(mlocal_name(ref_args[i]));
}
// we ignore minor premises in below/ibelow
for (unsigned i = nparams + ntypeformers + nminors; i < ref_args.size(); i++)
args.push_back(ref_args[i]);
// We define below/ibelow using the recursor for this type
levels rec_lvls = cons(mk_succ(rlvl), lvls);
expr rec = mk_constant(rec_decl.get_name(), rec_lvls);
for (unsigned i = 0; i < nparams; i++)
rec = mk_app(rec, args[i]);
// add type formers
for (unsigned i = nparams; i < nparams + ntypeformers; i++) {
buffer<expr> targs;
to_telescope(ngen, mlocal_type(args[i]), targs);
rec = mk_app(rec, Fun(targs, Type_result));
}
// add minor premises
for (unsigned i = nparams + ntypeformers; i < nparams + ntypeformers + nminors; i++) {
expr minor = ref_args[i];
expr minor_type = mlocal_type(minor);
buffer<expr> minor_args;
minor_type = to_telescope(ngen, minor_type, minor_args);
buffer<expr> prod_pairs;
for (expr & minor_arg : minor_args) {
buffer<expr> minor_arg_args;
expr minor_arg_type = to_telescope(tc, mlocal_type(minor_arg), minor_arg_args);
if (is_typeformer_app(typeformer_names, minor_arg_type)) {
expr fst = mlocal_type(minor_arg);
minor_arg = update_mlocal(minor_arg, Pi(minor_arg_args, Type_result));
expr snd = Pi(minor_arg_args, mk_app(minor_arg, minor_arg_args));
prod_pairs.push_back(mk_prod(tc, fst, snd, ibelow));
}
}
expr new_arg = foldr([&](expr const & a, expr const & b) { return mk_prod(tc, a, b, ibelow); },
[&]() { return mk_unit(rlvl, ibelow); },
prod_pairs.size(), prod_pairs.data());
rec = mk_app(rec, Fun(minor_args, new_arg));
}
// add indices and major premise
for (unsigned i = nparams + ntypeformers; i < args.size(); i++) {
rec = mk_app(rec, args[i]);
}
name below_name = ibelow ? name{n, "ibelow"} : name{n, "below"};
expr below_type = Pi(args, Type_result);
expr below_value = Fun(args, rec);
bool use_conv_opt = true;
declaration new_d = mk_definition(env, below_name, blvls, below_type, below_value,
use_conv_opt);
environment new_env = module::add(env, check(env, new_d));
new_env = set_reducible(new_env, below_name, reducible_status::Reducible);
if (!ibelow)
new_env = add_unfold_hint(new_env, below_name, nparams + nindices + ntypeformers);
return add_protected(new_env, below_name);
}
expr update_sort(expr const & e, level const & new_level) {
if (!is_eqp(sort_level(e), new_level))
return mk_sort(new_level, e.get_tag());
else
return e;
}
void initialize_expr() {
g_dummy = new expr(mk_constant("__expr_for_default_constructor__"));
g_default_name = new name("a");
g_Type1 = new expr(mk_sort(mk_level_one()));
g_Prop = new expr(mk_sort(mk_level_zero()));
}
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);
}
optional<environment> mk_no_confusion_type(environment const & env, name const & n) {
optional<inductive::inductive_decls> decls = inductive::is_inductive_decl(env, n);
if (!decls)
throw exception(sstream() << "error in 'no_confusion' generation, '" << n << "' is not an inductive datatype");
if (is_inductive_predicate(env, n))
return optional<environment>(); // type is a proposition
name_generator ngen;
unsigned nparams = std::get<1>(*decls);
declaration ind_decl = env.get(n);
declaration cases_decl = env.get(name(n, "cases_on"));
level_param_names lps = cases_decl.get_univ_params();
level rlvl = mk_param_univ(head(lps));
levels ilvls = param_names_to_levels(tail(lps));
if (length(ilvls) != length(ind_decl.get_univ_params()))
return optional<environment>(); // type does not have only a restricted eliminator
expr ind_type = instantiate_type_univ_params(ind_decl, ilvls);
name eq_name("eq");
name heq_name("heq");
// All inductive datatype parameters and indices are arguments
buffer<expr> args;
ind_type = to_telescope(ngen, ind_type, args, some(mk_implicit_binder_info()));
if (!is_sort(ind_type) || args.size() < nparams)
throw_corrupted(n);
lean_assert(!(env.impredicative() && is_zero(sort_level(ind_type))));
unsigned nindices = args.size() - nparams;
// Create inductive datatype
expr I = mk_app(mk_constant(n, ilvls), args);
// Add (P : Type)
expr P = mk_local(ngen.next(), "P", mk_sort(rlvl), binder_info());
args.push_back(P);
// add v1 and v2 elements of the inductive type
expr v1 = mk_local(ngen.next(), "v1", I, binder_info());
expr v2 = mk_local(ngen.next(), "v2", I, binder_info());
args.push_back(v1);
args.push_back(v2);
expr R = mk_sort(rlvl);
name no_confusion_type_name{n, "no_confusion_type"};
expr no_confusion_type_type = Pi(args, R);
// Create type former
buffer<expr> type_former_args;
for (unsigned i = nparams; i < nparams + nindices; i++)
type_former_args.push_back(args[i]);
type_former_args.push_back(v1);
expr type_former = Fun(type_former_args, R);
// Create cases_on
levels clvls = levels(mk_succ(rlvl), ilvls);
expr cases_on = mk_app(mk_app(mk_constant(cases_decl.get_name(), clvls), nparams, args.data()), type_former);
cases_on = mk_app(cases_on, nindices, args.data() + nparams);
expr cases_on1 = mk_app(cases_on, v1);
expr cases_on2 = mk_app(cases_on, v2);
type_checker tc(env);
expr t1 = tc.infer(cases_on1).first;
expr t2 = tc.infer(cases_on2).first;
buffer<expr> outer_cases_on_args;
unsigned idx1 = 0;
while (is_pi(t1)) {
buffer<expr> minor1_args;
expr minor1 = to_telescope(tc, binding_domain(t1), minor1_args);
expr curr_t2 = t2;
buffer<expr> inner_cases_on_args;
unsigned idx2 = 0;
while (is_pi(curr_t2)) {
buffer<expr> minor2_args;
expr minor2 = to_telescope(tc, binding_domain(curr_t2), minor2_args);
if (idx1 != idx2) {
// infeasible case, constructors do not match
inner_cases_on_args.push_back(Fun(minor2_args, P));
} else {
if (minor1_args.size() != minor2_args.size())
throw_corrupted(n);
buffer<expr> rtype_hyp;
// add equalities
for (unsigned i = 0; i < minor1_args.size(); i++) {
expr lhs = minor1_args[i];
expr rhs = minor2_args[i];
expr lhs_type = mlocal_type(lhs);
expr rhs_type = mlocal_type(rhs);
level l = sort_level(tc.ensure_type(lhs_type).first);
expr h_type;
if (tc.is_def_eq(lhs_type, rhs_type).first) {
h_type = mk_app(mk_constant(eq_name, to_list(l)), lhs_type, lhs, rhs);
} else {
h_type = mk_app(mk_constant(heq_name, to_list(l)), lhs_type, lhs, rhs_type, rhs);
}
rtype_hyp.push_back(mk_local(ngen.next(), local_pp_name(lhs).append_after("_eq"), h_type, binder_info()));
}
inner_cases_on_args.push_back(Fun(minor2_args, mk_arrow(Pi(rtype_hyp, P), P)));
}
idx2++;
curr_t2 = binding_body(curr_t2);
}
outer_cases_on_args.push_back(Fun(minor1_args, mk_app(cases_on2, inner_cases_on_args)));
idx1++;
t1 = binding_body(t1);
}
expr no_confusion_type_value = Fun(args, mk_app(cases_on1, outer_cases_on_args));
bool opaque = false;
bool use_conv_opt = true;
declaration new_d = mk_definition(env, no_confusion_type_name, lps, no_confusion_type_type, no_confusion_type_value,
opaque, ind_decl.get_module_idx(), use_conv_opt);
environment new_env = module::add(env, check(env, new_d));
return some(add_protected(new_env, no_confusion_type_name));
}
smt_astt
smt_convt::convert_byte_update(const expr2tc &expr)
{
const byte_update2t &data = to_byte_update2t(expr);
assert(is_scalar_type(data.source_value) && "Byte update only works on "
"scalar variables now");
if (!is_constant_int2t(data.source_offset)) {
expr2tc source = data.source_value;
unsigned int src_width = source->type->get_width();
if (!is_bv_type(source))
source = typecast2tc(get_uint_type(src_width), source);
expr2tc offs = data.source_offset;
// Endian-ness: if we're in non-"native" endian-ness mode, then flip the
// offset distance. The rest of these calculations will still apply.
if (data.big_endian) {
auto data_size = type_byte_size(*source->type);
constant_int2tc data_size_expr(source->type, data_size - 1);
sub2tc sub(source->type, data_size_expr, offs);
offs = sub;
}
if (offs->type->get_width() != src_width)
offs = typecast2tc(get_uint_type(src_width), offs);
expr2tc update = data.update_value;
if (update->type->get_width() != src_width)
update = typecast2tc(get_uint_type(src_width), update);
// The approach: mask, shift and or. XXX, byte order?
// Massively inefficient.
expr2tc eight = constant_int2tc(get_uint_type(src_width), BigInt(8));
expr2tc effs = constant_int2tc(eight->type, BigInt(255));
offs = mul2tc(eight->type, offs, eight);
expr2tc shl = shl2tc(offs->type, effs, offs);
expr2tc noteffs = bitnot2tc(effs->type, shl);
source = bitand2tc(source->type, source, noteffs);
expr2tc shl2 = shl2tc(offs->type, update, offs);
return convert_ast(bitor2tc(offs->type, shl2, source));
}
// We are merging two values: an 8 bit update value, and a larger source
// value that we will have to merge it into. Start off by collecting
// information about the source values and their widths.
assert(is_number_type(data.source_value->type) && "Byte update of unsupported data type");
smt_astt value, src_value;
unsigned int width_op0, width_op2, src_offset;
value = convert_ast(data.update_value);
src_value = convert_ast(data.source_value);
width_op2 = data.update_value->type->get_width();
width_op0 = data.source_value->type->get_width();
src_offset = to_constant_int2t(data.source_offset).constant_value.to_ulong();
// Flip location if we're in big-endian mode
if (data.big_endian) {
unsigned int data_size =
type_byte_size(*data.source_value->type).to_ulong() - 1;
src_offset = data_size - src_offset;
}
if (int_encoding) {
std::cerr << "Can't byte update in integer mode; rerun in bitvector mode"
<< std::endl;
abort();
}
// Assertion some of our assumptions, which broadly mean that we'll only work
// on bytes that are going into non-byte words
assert(width_op2 == 8 && "Can't byte update non-byte operations");
assert(width_op2 != width_op0 && "Can't byte update bytes, sorry");
smt_astt top, middle, bottom;
// Build in three parts: the most significant bits, any in the middle, and
// the bottom, of the reconstructed / merged output. There might not be a
// middle if the update byte is at the top or the bottom.
unsigned int top_of_update = (8 * src_offset) + 8;
unsigned int bottom_of_update = (8 * src_offset);
if (top_of_update == width_op0) {
top = value;
} else {
smt_sortt s = mk_sort(SMT_SORT_BV, width_op0 - top_of_update, false);
top = mk_extract(src_value, width_op0 - 1, top_of_update, s);
}
if (top == value) {
middle = NULL;
} else {
middle = value;
}
if (src_offset == 0) {
middle = NULL;
bottom = value;
} else {
smt_sortt s = mk_sort(SMT_SORT_BV, bottom_of_update, false);
bottom = mk_extract(src_value, bottom_of_update - 1, 0, s);
}
// Concatenate the top and bottom, and possible middle, together.
smt_astt concat;
if (middle != NULL) {
smt_sortt s = mk_sort(SMT_SORT_BV, width_op0 - bottom_of_update, false);
concat = mk_func_app(s, SMT_FUNC_CONCAT, top, middle);
} else {
concat = top;
}
return mk_func_app(src_value->sort, SMT_FUNC_CONCAT, concat, bottom);
}
smt_astt
smt_convt::convert_byte_extract(const expr2tc &expr)
{
const byte_extract2t &data = to_byte_extract2t(expr);
assert(is_scalar_type(data.source_value) && "Byte extract now only works on "
"scalar variables");
if (!is_constant_int2t(data.source_offset)) {
expr2tc source = data.source_value;
unsigned int src_width = source->type->get_width();
if (!is_bv_type(source)) {
source = typecast2tc(get_uint_type(src_width), source);
}
// The approach: the argument is now a bitvector. Just shift it the
// appropriate amount, according to the source offset, and select out the
// bottom byte.
expr2tc offs = data.source_offset;
// Endian-ness: if we're in non-"native" endian-ness mode, then flip the
// offset distance. The rest of these calculations will still apply.
if (data.big_endian) {
auto data_size = type_byte_size(*source->type);
constant_int2tc data_size_expr(source->type, data_size - 1);
sub2tc sub(source->type, data_size_expr, offs);
offs = sub;
}
if (offs->type->get_width() != src_width)
// Z3 requires these two arguments to be the same width
offs = typecast2tc(source->type, data.source_offset);
lshr2tc shr(source->type, source, offs);
smt_astt ext = convert_ast(shr);
smt_astt res = mk_extract(ext, 7, 0, convert_sort(get_uint8_type()));
return res;
}
const constant_int2t &intref = to_constant_int2t(data.source_offset);
unsigned width;
width = data.source_value->type->get_width();
uint64_t upper, lower;
if (!data.big_endian) {
upper = ((intref.constant_value.to_long() + 1) * 8) - 1; //((i+1)*w)-1;
lower = intref.constant_value.to_long() * 8; //i*w;
} else {
uint64_t max = width - 1;
upper = max - (intref.constant_value.to_long() * 8); //max-(i*w);
lower = max - ((intref.constant_value.to_long() + 1) * 8 - 1); //max-((i+1)*w-1);
}
smt_astt source = convert_ast(data.source_value);;
if (int_encoding) {
std::cerr << "Refusing to byte extract in integer mode; re-run in "
"bitvector mode" << std::endl;
abort();
} else {
if (is_bv_type(data.source_value)) {
;
} else if (is_fixedbv_type(data.source_value)) {
;
} else if (is_bool_type(data.source_value)) {
// We cdan extract a byte from a bool -- zero or one.
typecast2tc cast(get_uint8_type(), data.source_value);
source = convert_ast(cast);
} else {
std::cerr << "Unrecognized type in operand to byte extract." << std::endl;
data.dump();
abort();
}
unsigned int sort_sz = data.source_value->type->get_width();
if (sort_sz <= upper) {
smt_sortt s = mk_sort(SMT_SORT_BV, 8, false);
return mk_smt_symbol("out_of_bounds_byte_extract", s);
} else {
return mk_extract(source, upper, lower, convert_sort(expr->type));
}
}
}