level mk_max(buffer<level> const & args) {
lean_assert(!args.empty());
unsigned nargs = args.size();
if (nargs == 1) {
return args[0];
} else {
lean_assert(nargs >= 2);
level r = mk_max(args[nargs-2], args[nargs-1]);
unsigned i = nargs-2;
while (i > 0) {
--i;
r = mk_max(args[i], r);
}
return r;
}
}
level update_max(level const & l, level const & new_lhs, level const & new_rhs) {
if (is_eqp(to_max_core(l).m_lhs, new_lhs) && is_eqp(to_max_core(l).m_rhs, new_rhs))
return l;
else if (is_max(l))
return mk_max(new_lhs, new_rhs);
else
return mk_imax(new_lhs, new_rhs);
}
level mk_imax(level const & l1, level const & l2) {
if (is_not_zero(l2))
return mk_max(l1, l2);
else if (is_zero(l2))
return l2; // imax u 0 = 0 for any u
else if (is_zero(l1))
return l2; // imax 0 u = u for any u
else if (l1 == l2)
return l1; // imax u u = u
else
return cache(level(new level_max_core(true, l1, l2)));
}
br_status float_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * const * args, expr_ref & result) {
br_status st = BR_FAILED;
SASSERT(f->get_family_id() == get_fid());
switch (f->get_decl_kind()) {
case OP_TO_FLOAT: st = mk_to_fp(f, num_args, args, result); break;
case OP_FLOAT_ADD: SASSERT(num_args == 3); st = mk_add(args[0], args[1], args[2], result); break;
case OP_FLOAT_SUB: SASSERT(num_args == 3); st = mk_sub(args[0], args[1], args[2], result); break;
case OP_FLOAT_NEG: SASSERT(num_args == 1); st = mk_neg(args[0], result); break;
case OP_FLOAT_MUL: SASSERT(num_args == 3); st = mk_mul(args[0], args[1], args[2], result); break;
case OP_FLOAT_DIV: SASSERT(num_args == 3); st = mk_div(args[0], args[1], args[2], result); break;
case OP_FLOAT_REM: SASSERT(num_args == 2); st = mk_rem(args[0], args[1], result); break;
case OP_FLOAT_ABS: SASSERT(num_args == 1); st = mk_abs(args[0], result); break;
case OP_FLOAT_MIN: SASSERT(num_args == 2); st = mk_min(args[0], args[1], result); break;
case OP_FLOAT_MAX: SASSERT(num_args == 2); st = mk_max(args[0], args[1], result); break;
case OP_FLOAT_FMA: SASSERT(num_args == 4); st = mk_fma(args[0], args[1], args[2], args[3], result); break;
case OP_FLOAT_SQRT: SASSERT(num_args == 2); st = mk_sqrt(args[0], args[1], result); break;
case OP_FLOAT_ROUND_TO_INTEGRAL: SASSERT(num_args == 2); st = mk_round(args[0], args[1], result); break;
case OP_FLOAT_EQ: SASSERT(num_args == 2); st = mk_float_eq(args[0], args[1], result); break;
case OP_FLOAT_LT: SASSERT(num_args == 2); st = mk_lt(args[0], args[1], result); break;
case OP_FLOAT_GT: SASSERT(num_args == 2); st = mk_gt(args[0], args[1], result); break;
case OP_FLOAT_LE: SASSERT(num_args == 2); st = mk_le(args[0], args[1], result); break;
case OP_FLOAT_GE: SASSERT(num_args == 2); st = mk_ge(args[0], args[1], result); break;
case OP_FLOAT_IS_ZERO: SASSERT(num_args == 1); st = mk_is_zero(args[0], result); break;
case OP_FLOAT_IS_NZERO: SASSERT(num_args == 1); st = mk_is_nzero(args[0], result); break;
case OP_FLOAT_IS_PZERO: SASSERT(num_args == 1); st = mk_is_pzero(args[0], result); break;
case OP_FLOAT_IS_NAN: SASSERT(num_args == 1); st = mk_is_nan(args[0], result); break;
case OP_FLOAT_IS_INF: SASSERT(num_args == 1); st = mk_is_inf(args[0], result); break;
case OP_FLOAT_IS_NORMAL: SASSERT(num_args == 1); st = mk_is_normal(args[0], result); break;
case OP_FLOAT_IS_SUBNORMAL: SASSERT(num_args == 1); st = mk_is_subnormal(args[0], result); break;
case OP_FLOAT_IS_NEGATIVE: SASSERT(num_args == 1); st = mk_is_negative(args[0], result); break;
case OP_FLOAT_IS_POSITIVE: SASSERT(num_args == 1); st = mk_is_positive(args[0], result); break;
case OP_FLOAT_TO_IEEE_BV: SASSERT(num_args == 1); st = mk_to_ieee_bv(args[0], result); break;
case OP_FLOAT_FP: SASSERT(num_args == 3); st = mk_fp(args[0], args[1], args[2], result); break;
case OP_FLOAT_TO_UBV: SASSERT(num_args == 2); st = mk_to_ubv(args[0], args[1], result); break;
case OP_FLOAT_TO_SBV: SASSERT(num_args == 2); st = mk_to_sbv(args[0], args[1], result); break;
case OP_FLOAT_TO_REAL: SASSERT(num_args == 1); st = mk_to_real(args[0], result); break;
}
return st;
}
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);
}
static environment mk_brec_on(environment const & env, name const & n, bool ind) {
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));
// declaration below_decl = env.get(name(n, ind ? "ibelow" : "below"));
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 rlvl;
level_param_names blps;
levels blvls; // universe level parameters of brec_on/binduction_on
// The arguments of brec_on (binduction_on) 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;
if (ind) {
// we are eliminating to Prop
blps = tail(lps);
blvls = lvls;
rlvl = mk_level_zero();
ref_type = instantiate_univ_param(rec_decl.get_type(), param_id(lvl), mk_level_zero());
} else if (is_reflexive) {
blps = lps;
blvls = cons(lvl, lvls);
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);
// inner_prod, inner_prod_intro, pr1, pr2 do not use the same universe levels for
// reflective datatypes.
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
blps = lps;
blvls = cons(lvl, lvls);
rlvl = mk_max(mk_level_one(), lvl);
ref_type = rec_decl.get_type();
}
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 brec_on/binduction_on 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]));
}
// add indices and major premise
for (unsigned i = nparams + ntypeformers + nminors; i < ref_args.size(); i++)
args.push_back(ref_args[i]);
// create below terms (one per datatype)
// (below.{lvls} params type-formers)
// Remark: it also creates the result type
buffer<expr> belows;
expr result_type;
unsigned k = 0;
for (auto const & decl : std::get<2>(decls)) {
name const & n1 = inductive::inductive_decl_name(decl);
if (n1 == n) {
result_type = ref_args[nparams + k];
for (unsigned i = nparams + ntypeformers + nminors; i < ref_args.size(); i++)
result_type = mk_app(result_type, ref_args[i]);
}
k++;
name bname = name(n1, ind ? "ibelow" : "below");
expr below = mk_constant(bname, blvls);
for (unsigned i = 0; i < nparams; i++)
below = mk_app(below, ref_args[i]);
for (unsigned i = nparams; i < nparams + ntypeformers; i++)
below = mk_app(below, ref_args[i]);
belows.push_back(below);
}
// create functionals (one for each type former)
// Pi idxs t, below idxs t -> C idxs t
buffer<expr> Fs;
name F_name("F");
for (unsigned i = nparams, j = 0; i < nparams + ntypeformers; i++, j++) {
expr const & C = ref_args[i];
buffer<expr> F_args;
to_telescope(ngen, mlocal_type(C), F_args);
expr F_result = mk_app(C, F_args);
expr F_below = mk_app(belows[j], F_args);
F_args.push_back(mk_local(ngen.next(), "f", F_below, binder_info()));
expr F_type = Pi(F_args, F_result);
expr F = mk_local(ngen.next(), F_name.append_after(j+1), F_type, binder_info());
Fs.push_back(F);
args.push_back(F);
}
// We define brec_on/binduction_on using the recursor for this type
levels rec_lvls = cons(rlvl, lvls);
expr rec = mk_constant(rec_decl.get_name(), rec_lvls);
// add parameters to rec
for (unsigned i = 0; i < nparams; i++)
rec = mk_app(rec, ref_args[i]);
// add type formers to rec
// Pi indices t, prod (C ... t) (below ... t)
for (unsigned i = nparams, j = 0; i < nparams + ntypeformers; i++, j++) {
expr const & C = ref_args[i];
buffer<expr> C_args;
to_telescope(ngen, mlocal_type(C), C_args);
expr C_t = mk_app(C, C_args);
expr below_t = mk_app(belows[j], C_args);
expr prod = mk_prod(tc, C_t, below_t, ind);
rec = mk_app(rec, Fun(C_args, prod));
}
// add minor premises to rec
for (unsigned i = nparams + ntypeformers, j = 0; i < nparams + ntypeformers + nminors; i++, j++) {
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> 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 (auto k = is_typeformer_app(typeformer_names, minor_arg_type)) {
buffer<expr> C_args;
get_app_args(minor_arg_type, C_args);
expr new_minor_arg_type = mk_prod(tc, minor_arg_type, mk_app(belows[*k], C_args), ind);
minor_arg = update_mlocal(minor_arg, Pi(minor_arg_args, new_minor_arg_type));
if (minor_arg_args.empty()) {
pairs.push_back(minor_arg);
} else {
expr r = mk_app(minor_arg, minor_arg_args);
expr r_1 = Fun(minor_arg_args, mk_pr1(tc, r, ind));
expr r_2 = Fun(minor_arg_args, mk_pr2(tc, r, ind));
pairs.push_back(mk_pair(tc, r_1, r_2, ind));
}
}
}
expr b = foldr([&](expr const & a, expr const & b) { return mk_pair(tc, a, b, ind); },
[&]() { return mk_unit_mk(rlvl, ind); },
pairs.size(), pairs.data());
unsigned F_idx = *is_typeformer_app(typeformer_names, minor_type);
expr F = Fs[F_idx];
buffer<expr> F_args;
get_app_args(minor_type, F_args);
F_args.push_back(b);
expr new_arg = mk_pair(tc, mk_app(F, F_args), b, ind);
rec = mk_app(rec, Fun(minor_args, new_arg));
}
// add indices and major to rec
for (unsigned i = nparams + ntypeformers + nminors; i < ref_args.size(); i++)
rec = mk_app(rec, ref_args[i]);
name brec_on_name = name(n, ind ? "binduction_on" : "brec_on");
expr brec_on_type = Pi(args, result_type);
expr brec_on_value = Fun(args, mk_pr1(tc, rec, ind));
bool use_conv_opt = true;
declaration new_d = mk_definition(env, brec_on_name, blps, brec_on_type, brec_on_value,
use_conv_opt);
environment new_env = module::add(env, check(env, new_d));
new_env = set_reducible(new_env, brec_on_name, reducible_status::Reducible);
if (!ind)
new_env = add_unfold_hint(new_env, brec_on_name, nparams + nindices + ntypeformers);
return add_protected(new_env, brec_on_name);
}
br_status fpa_rewriter::mk_app_core(func_decl * f, unsigned num_args, expr * const * args, expr_ref & result) {
br_status st = BR_FAILED;
SASSERT(f->get_family_id() == get_fid());
fpa_op_kind k = (fpa_op_kind)f->get_decl_kind();
switch (k) {
case OP_FPA_RM_NEAREST_TIES_TO_EVEN:
case OP_FPA_RM_NEAREST_TIES_TO_AWAY:
case OP_FPA_RM_TOWARD_POSITIVE:
case OP_FPA_RM_TOWARD_NEGATIVE:
case OP_FPA_RM_TOWARD_ZERO:
SASSERT(num_args == 0); result = m().mk_app(f, (expr * const *)0); st = BR_DONE; break;
case OP_FPA_PLUS_INF:
case OP_FPA_MINUS_INF:
case OP_FPA_NAN:
case OP_FPA_PLUS_ZERO:
case OP_FPA_MINUS_ZERO:
SASSERT(num_args == 0); result = m().mk_app(f, (expr * const *)0); st = BR_DONE; break;
case OP_FPA_NUM:
SASSERT(num_args == 0); result = m().mk_app(f, (expr * const *)0); st = BR_DONE; break;
case OP_FPA_ADD: SASSERT(num_args == 3); st = mk_add(args[0], args[1], args[2], result); break;
case OP_FPA_SUB: SASSERT(num_args == 3); st = mk_sub(args[0], args[1], args[2], result); break;
case OP_FPA_NEG: SASSERT(num_args == 1); st = mk_neg(args[0], result); break;
case OP_FPA_MUL: SASSERT(num_args == 3); st = mk_mul(args[0], args[1], args[2], result); break;
case OP_FPA_DIV: SASSERT(num_args == 3); st = mk_div(args[0], args[1], args[2], result); break;
case OP_FPA_REM: SASSERT(num_args == 2); st = mk_rem(args[0], args[1], result); break;
case OP_FPA_ABS: SASSERT(num_args == 1); st = mk_abs(args[0], result); break;
case OP_FPA_MIN: SASSERT(num_args == 2); st = mk_min(args[0], args[1], result); break;
case OP_FPA_MAX: SASSERT(num_args == 2); st = mk_max(args[0], args[1], result); break;
case OP_FPA_FMA: SASSERT(num_args == 4); st = mk_fma(args[0], args[1], args[2], args[3], result); break;
case OP_FPA_SQRT: SASSERT(num_args == 2); st = mk_sqrt(args[0], args[1], result); break;
case OP_FPA_ROUND_TO_INTEGRAL: SASSERT(num_args == 2); st = mk_round_to_integral(args[0], args[1], result); break;
case OP_FPA_EQ: SASSERT(num_args == 2); st = mk_float_eq(args[0], args[1], result); break;
case OP_FPA_LT: SASSERT(num_args == 2); st = mk_lt(args[0], args[1], result); break;
case OP_FPA_GT: SASSERT(num_args == 2); st = mk_gt(args[0], args[1], result); break;
case OP_FPA_LE: SASSERT(num_args == 2); st = mk_le(args[0], args[1], result); break;
case OP_FPA_GE: SASSERT(num_args == 2); st = mk_ge(args[0], args[1], result); break;
case OP_FPA_IS_ZERO: SASSERT(num_args == 1); st = mk_is_zero(args[0], result); break;
case OP_FPA_IS_NAN: SASSERT(num_args == 1); st = mk_is_nan(args[0], result); break;
case OP_FPA_IS_INF: SASSERT(num_args == 1); st = mk_is_inf(args[0], result); break;
case OP_FPA_IS_NORMAL: SASSERT(num_args == 1); st = mk_is_normal(args[0], result); break;
case OP_FPA_IS_SUBNORMAL: SASSERT(num_args == 1); st = mk_is_subnormal(args[0], result); break;
case OP_FPA_IS_NEGATIVE: SASSERT(num_args == 1); st = mk_is_negative(args[0], result); break;
case OP_FPA_IS_POSITIVE: SASSERT(num_args == 1); st = mk_is_positive(args[0], result); break;
case OP_FPA_FP: SASSERT(num_args == 3); st = mk_fp(args[0], args[1], args[2], result); break;
case OP_FPA_TO_FP: st = mk_to_fp(f, num_args, args, result); break;
case OP_FPA_TO_FP_UNSIGNED: SASSERT(num_args == 2); st = mk_to_fp_unsigned(f, args[0], args[1], result); break;
case OP_FPA_TO_UBV: SASSERT(num_args == 2); st = mk_to_ubv(f, args[0], args[1], result); break;
case OP_FPA_TO_SBV: SASSERT(num_args == 2); st = mk_to_sbv(f, args[0], args[1], result); break;
case OP_FPA_TO_IEEE_BV: SASSERT(num_args == 1); st = mk_to_ieee_bv(f, args[0], result); break;
case OP_FPA_TO_REAL: SASSERT(num_args == 1); st = mk_to_real(args[0], result); break;
case OP_FPA_INTERNAL_MIN_I:
case OP_FPA_INTERNAL_MAX_I:
case OP_FPA_INTERNAL_MIN_UNSPECIFIED:
case OP_FPA_INTERNAL_MAX_UNSPECIFIED:
SASSERT(num_args == 2); st = BR_FAILED; break;
case OP_FPA_INTERNAL_RM:
SASSERT(num_args == 1); st = mk_rm(args[0], result); break;
case OP_FPA_INTERNAL_TO_UBV_UNSPECIFIED:
SASSERT(num_args == 0); st = mk_to_ubv_unspecified(f, result); break;
case OP_FPA_INTERNAL_TO_SBV_UNSPECIFIED:
SASSERT(num_args == 0); st = mk_to_sbv_unspecified(f, result); break;
case OP_FPA_INTERNAL_TO_REAL_UNSPECIFIED:
SASSERT(num_args == 0); st = mk_to_real_unspecified(result); break;
case OP_FPA_INTERNAL_BVWRAP:
case OP_FPA_INTERNAL_BVUNWRAP:
st = BR_FAILED;
break;
default:
NOT_IMPLEMENTED_YET();
}
return st;
}
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);
}
vm_obj level_max(vm_obj const & o1, vm_obj const & o2) {
return to_obj(mk_max(to_level(o1), to_level(o2)));
}
unsigned sz = is_signed ? bvsize - 1 : bvsize;
rational max_bound = power(rational(2), sz);
--max_bound;
return Z3_mk_numeral(ctx, max_bound.to_string().c_str(), bv);
}
void test_add(unsigned bvsize, bool is_signed) {
TRACE("no_overflow", tout << "test_add: bvsize = " << bvsize << ", is_signed = " << is_signed << "\n";);
Z3_config cfg = Z3_mk_config();
Z3_context ctx = Z3_mk_context(cfg);
Z3_sort bv = Z3_mk_bv_sort(ctx, bvsize);
Z3_ast min = mk_min(ctx, bv, is_signed);
Z3_ast max = mk_max(ctx, bv, is_signed);
Z3_ast t1;
Z3_ast t2;
Z3_ast test_ovfl;
Z3_ast test_udfl;
t1 = Z3_mk_const(ctx, Z3_mk_string_symbol(ctx,"x"), bv);
t2 = Z3_mk_const(ctx, Z3_mk_string_symbol(ctx,"y"), bv);
test_ovfl = Z3_mk_bvadd_no_overflow(ctx, t1, t2, is_signed);
test_udfl = is_signed ? Z3_mk_bvadd_no_underflow(ctx, t1, t2) : NULL;
Z3_push(ctx);
Z3_assert_cnstr(ctx, Z3_mk_eq(ctx, t1, Z3_mk_numeral(ctx, "0", bv)));
Z3_assert_cnstr(ctx, Z3_mk_eq(ctx, t2, Z3_mk_numeral(ctx, "1", bv)));
TEST_NO_OVERFLOW;
TEST_NO_UNDERFLOW;
level normalize(level const & l) {
auto p = to_offset(l);
level const & r = p.first;
switch (kind(r)) {
case level_kind::Succ:
lean_unreachable(); // LCOV_EXCL_LINE
case level_kind::Zero: case level_kind::Param:
case level_kind::Global: case level_kind::Meta:
return l;
case level_kind::IMax: {
auto l1 = normalize(imax_lhs(r));
auto l2 = normalize(imax_rhs(r));
if (!is_eqp(l1, imax_lhs(r)) || !is_eqp(l2, imax_rhs(r)))
return mk_succ(mk_imax(l1, l2), p.second);
else
return l;
}
case level_kind::Max: {
buffer<level> todo;
buffer<level> args;
push_max_args(r, todo);
for (level const & a : todo)
push_max_args(normalize(a), args);
std::sort(args.begin(), args.end(), is_norm_lt);
buffer<level> & rargs = todo;
rargs.clear();
unsigned i = 0;
if (is_explicit(args[i])) {
// find max explicit univierse
while (i+1 < args.size() && is_explicit(args[i+1]))
i++;
lean_assert(is_explicit(args[i]));
unsigned k = to_offset(args[i]).second;
// an explicit universe k is subsumed by succ^k(l)
unsigned j = i+1;
for (; j < args.size(); j++) {
if (to_offset(args[j]).second >= k)
break;
}
if (j < args.size()) {
// explicit universe was subsumed by succ^k'(l) where k' >= k
i++;
}
}
rargs.push_back(args[i]);
auto p_prev = to_offset(args[i]);
i++;
for (; i < args.size(); i++) {
auto p_curr = to_offset(args[i]);
if (p_prev.first == p_curr.first) {
if (p_prev.second < p_curr.second) {
p_prev = p_curr;
rargs.pop_back();
rargs.push_back(args[i]);
}
} else {
p_prev = p_curr;
rargs.push_back(args[i]);
}
}
for (level & a : rargs)
a = mk_succ(a, p.second);
return mk_max(rargs);
}}
lean_unreachable(); // LCOV_EXCL_LINE
}