C++ expr::kind方法代码示例

    expr visit(expr const & e) {
        switch (e.kind()) {
        case expr_kind::Sort:  case expr_kind::Constant:
        case expr_kind::Var:   case expr_kind::Meta:
        case expr_kind::Local:
            return e;
        default:
            break;
        }

        check_system("unfold macros");
        auto it = m_cache.find(e);
        if (it != m_cache.end())
            return it->second;

        switch (e.kind()) {
        case expr_kind::Sort:  case expr_kind::Constant:
        case expr_kind::Var:   case expr_kind::Meta:
        case expr_kind::Local:
            lean_unreachable();
        case expr_kind::Macro:
            return save_result(e, visit_macro(e));
        case expr_kind::App:
            return save_result(e, visit_app(e));
        case expr_kind::Lambda: case expr_kind::Pi:
            return save_result(e, visit_binding(e));
        }
        lean_unreachable();
    }

bool is_lt(expr const & a, expr const & b, bool use_hash) {
    if (is_eqp(a, b))                    return false;
    unsigned wa = get_weight(a);
    unsigned wb = get_weight(b);
    if (wa < wb)                         return true;
    if (wa > wb)                         return false;
    if (a.kind() != b.kind())            return a.kind() < b.kind();
    if (use_hash) {
        if (a.hash() < b.hash())         return true;
        if (a.hash() > b.hash())         return false;
    }
    if (a == b)                          return false;
    switch (a.kind()) {
    case expr_kind::Var:
        return var_idx(a) < var_idx(b);
    case expr_kind::Constant:
        if (const_name(a) != const_name(b))
            return const_name(a) < const_name(b);
        else
            return is_lt(const_levels(a), const_levels(b), use_hash);
    case expr_kind::App:
        if (app_fn(a) != app_fn(b))
            return is_lt(app_fn(a), app_fn(b), use_hash);
        else
            return is_lt(app_arg(a), app_arg(b), use_hash);
    case expr_kind::Lambda: case expr_kind::Pi:
        if (binding_domain(a) != binding_domain(b))
            return is_lt(binding_domain(a), binding_domain(b), use_hash);
        else
            return is_lt(binding_body(a), binding_body(b), use_hash);
    case expr_kind::Let:
        if (let_type(a) != let_type(b))
            return is_lt(let_type(a), let_type(b), use_hash);
        else if (let_value(a) != let_value(b))
            return is_lt(let_value(a), let_value(b), use_hash);
        else
            return is_lt(let_body(a), let_body(b), use_hash);
    case expr_kind::Sort:
        return is_lt(sort_level(a), sort_level(b), use_hash);
    case expr_kind::Local: case expr_kind::Meta:
        if (mlocal_name(a) != mlocal_name(b))
            return mlocal_name(a) < mlocal_name(b);
        else
            return is_lt(mlocal_type(a), mlocal_type(b), use_hash);
    case expr_kind::Macro:
        if (macro_def(a) != macro_def(b))
            return macro_def(a) < macro_def(b);
        if (macro_num_args(a) != macro_num_args(b))
            return macro_num_args(a) < macro_num_args(b);
        for (unsigned i = 0; i < macro_num_args(a); i++) {
            if (macro_arg(a, i) != macro_arg(b, i))
                return is_lt(macro_arg(a, i), macro_arg(b, i), use_hash);
        }
        return false;
    }
    lean_unreachable(); // LCOV_EXCL_LINE
}

 bool apply(expr const & a, expr const & b) {
     if (is_eqp(a, b))          return true;
     if (a.hash() != b.hash())  return false;
     if (a.kind() != b.kind())  return false;
     if (is_var(a))             return var_idx(a) == var_idx(b);
     if (m_cache.check(a, b))
         return true;
     switch (a.kind()) {
     case expr_kind::Var:
         lean_unreachable(); // LCOV_EXCL_LINE
     case expr_kind::Constant:
         return
             const_name(a) == const_name(b) &&
             compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
     case expr_kind::Meta:
         return
             mlocal_name(a) == mlocal_name(b) &&
             apply(mlocal_type(a), mlocal_type(b));
     case expr_kind::Local:
         return
             mlocal_name(a) == mlocal_name(b) &&
             apply(mlocal_type(a), mlocal_type(b)) &&
             (!CompareBinderInfo || local_pp_name(a) == local_pp_name(b)) &&
             (!CompareBinderInfo || local_info(a) == local_info(b));
     case expr_kind::App:
         check_system();
         return
             apply(app_fn(a), app_fn(b)) &&
             apply(app_arg(a), app_arg(b));
     case expr_kind::Lambda: case expr_kind::Pi:
         check_system();
         return
             apply(binding_domain(a), binding_domain(b)) &&
             apply(binding_body(a), binding_body(b)) &&
             (!CompareBinderInfo || binding_name(a) == binding_name(b)) &&
             (!CompareBinderInfo || binding_info(a) == binding_info(b));
     case expr_kind::Let:
         check_system();
         return
             apply(let_type(a), let_type(b)) &&
             apply(let_value(a), let_value(b)) &&
             apply(let_body(a), let_body(b)) &&
             (!CompareBinderInfo || let_name(a) == let_name(b));
     case expr_kind::Sort:
         return sort_level(a) == sort_level(b);
     case expr_kind::Macro:
         check_system();
         if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
             return false;
         for (unsigned i = 0; i < macro_num_args(a); i++) {
             if (!apply(macro_arg(a, i), macro_arg(b, i)))
                 return false;
         }
         return true;
     }
     lean_unreachable(); // LCOV_EXCL_LINE
 }

bool expr_eq_fn::apply(expr const & a, expr const & b) {
    if (is_eqp(a, b))          return true;
    if (a.hash() != b.hash())  return false;
    if (a.kind() != b.kind())  return false;
    if (is_var(a))             return var_idx(a) == var_idx(b);
    if (m_counter >= LEAN_EQ_CACHE_THRESHOLD && is_shared(a) && is_shared(b)) {
        auto p = std::make_pair(a.raw(), b.raw());
        if (!m_eq_visited)
            m_eq_visited.reset(new expr_cell_pair_set);
        if (m_eq_visited->find(p) != m_eq_visited->end())
            return true;
        m_eq_visited->insert(p);
    }
    check_system("expression equality test");
    switch (a.kind()) {
    case expr_kind::Var:
        lean_unreachable(); // LCOV_EXCL_LINE
    case expr_kind::Constant:
        return
            const_name(a) == const_name(b) &&
            compare(const_levels(a), const_levels(b), [](level const & l1, level const & l2) { return l1 == l2; });
    case expr_kind::Local: case expr_kind::Meta:
        return
            mlocal_name(a) == mlocal_name(b) &&
            apply(mlocal_type(a), mlocal_type(b));
    case expr_kind::App:
        m_counter++;
        return
            apply(app_fn(a), app_fn(b)) &&
            apply(app_arg(a), app_arg(b));
    case expr_kind::Lambda: case expr_kind::Pi:
        m_counter++;
        return
            apply(binding_domain(a), binding_domain(b)) &&
            apply(binding_body(a), binding_body(b)) &&
            (!m_compare_binder_info || binding_info(a) == binding_info(b));
    case expr_kind::Sort:
        return sort_level(a) == sort_level(b);
    case expr_kind::Macro:
        m_counter++;
        if (macro_def(a) != macro_def(b) || macro_num_args(a) != macro_num_args(b))
            return false;
        for (unsigned i = 0; i < macro_num_args(a); i++) {
            if (!apply(macro_arg(a, i), macro_arg(b, i)))
                return false;
        }
        return true;
    case expr_kind::Let:
        m_counter++;
        return
            apply(let_type(a), let_type(b)) &&
            apply(let_value(a), let_value(b)) &&
            apply(let_body(a), let_body(b));
    }
    lean_unreachable(); // LCOV_EXCL_LINE
}

bool is_lt_no_level_params(expr const & a, expr const & b) {
    if (is_eqp(a, b))                    return false;
    unsigned wa = get_weight(a);
    unsigned wb = get_weight(b);
    if (wa < wb)                         return true;
    if (wa > wb)                         return false;
    if (a.kind() != b.kind())            return a.kind() < b.kind();
    switch (a.kind()) {
    case expr_kind::Var:
        return var_idx(a) < var_idx(b);
    case expr_kind::Constant:
        if (const_name(a) != const_name(b))
            return const_name(a) < const_name(b);
        else
            return is_lt_no_level_params(const_levels(a), const_levels(b));
    case expr_kind::App:
        if (is_lt_no_level_params(app_fn(a), app_fn(b)))
            return true;
        else if (is_lt_no_level_params(app_fn(b), app_fn(a)))
            return false;
        else
            return is_lt_no_level_params(app_arg(a), app_arg(b));
    case expr_kind::Lambda: case expr_kind::Pi:
        if (is_lt_no_level_params(binding_domain(a), binding_domain(b)))
            return true;
        else if (is_lt_no_level_params(binding_domain(b), binding_domain(a)))
            return false;
        else
            return is_lt_no_level_params(binding_body(a), binding_body(b));
    case expr_kind::Sort:
        return is_lt_no_level_params(sort_level(a), sort_level(b));
    case expr_kind::Local: case expr_kind::Meta:
        if (mlocal_name(a) != mlocal_name(b))
            return mlocal_name(a) < mlocal_name(b);
        else
            return is_lt_no_level_params(mlocal_type(a), mlocal_type(b));
    case expr_kind::Macro:
        if (macro_def(a) != macro_def(b))
            return macro_def(a) < macro_def(b);
        if (macro_num_args(a) != macro_num_args(b))
            return macro_num_args(a) < macro_num_args(b);
        for (unsigned i = 0; i < macro_num_args(a); i++) {
            if (is_lt_no_level_params(macro_arg(a, i), macro_arg(b, i)))
                return true;
            else if (is_lt_no_level_params(macro_arg(b, i), macro_arg(a, i)))
                return false;
        }
        return false;
    }
    lean_unreachable();
}

 /** \brief Return true iff all recursive applications in \c e are structurally smaller than \c m_pattern. */
 bool check_rhs(expr const & e) {
     switch (e.kind()) {
     case expr_kind::Var:   case expr_kind::Meta:
     case expr_kind::Local: case expr_kind::Constant:
     case expr_kind::Sort:
         return true;
     case expr_kind::Macro:
         for (unsigned i = 0; i < macro_num_args(e); i++)
             if (!check_rhs(macro_arg(e, i)))
                 return false;
         return true;
     case expr_kind::App: {
         buffer<expr> args;
         expr const & fn = get_app_args(e, args);
         if (!check_rhs(fn))
             return false;
         for (unsigned i = 0; i < args.size(); i++)
             if (!check_rhs(args[i]))
                 return false;
         if (is_local(fn) && mlocal_name(fn) == mlocal_name(m_fn)) {
             /* recusive application */
             if (m_arg_idx < args.size()) {
                 expr const & arg = args[m_arg_idx];
                 /* arg must be structurally smaller than m_pattern */
                 if (!is_lt(arg, m_pattern)) {
                     trace_struct_aux(tout() << "structural recursion on argument #" << (m_arg_idx+1)
                                      << " was not used "
                                      << "for '" << m_fn << "'\nargument #" << (m_arg_idx+1)
                                      << " in the application\n  "
                                      << e << "\nis not structurally smaller than the one occurring in "
                                      << "the equation left-hand-side\n  "
                                      << m_lhs << "\n";);
                     return false;
                 }
             } else {

 expr apply(expr const & a) {
     check_system("max_sharing");
     auto r = m_expr_cache.find(a);
     if (r != m_expr_cache.end())
         return *r;
     expr res;
     switch (a.kind()) {
     case expr_kind::Var:
         res = a;
         break;
     case expr_kind::Constant:
         res = update_constant(a, map(const_levels(a), [&](level const & l) { return apply(l); }));
         break;
     case expr_kind::Sort:
         res = update_sort(a, apply(sort_level(a)));
         break;
     case expr_kind::App:
         res = update_app(a, apply(app_fn(a)), apply(app_arg(a)));
         break;
     case expr_kind::Lambda: case expr_kind::Pi:
         res = update_binding(a, apply(binding_domain(a)), apply(binding_body(a)));
         break;
     case expr_kind::Meta:  case expr_kind::Local:
         res = update_mlocal(a, apply(mlocal_type(a)));
         break;
     case expr_kind::Macro: {
         buffer<expr> new_args;
         for (unsigned i = 0; i < macro_num_args(a); i++)
             new_args.push_back(macro_arg(a, i));
         res = update_macro(a, new_args.size(), new_args.data());
         break;
     }}
     m_expr_cache.insert(res);
     return res;
 }

void forward_branch_extension::index_expr(expr const & e) {
    // TODO(dhs): index the target when it gets updated

    if (auto head_idx = to_head_index(e)) {
        m_index.insert(head_index(e), e);
    }
    switch (e.kind()) {
    case expr_kind::Var:
        lean_unreachable();  // LCOV_EXCL_LINE
    case expr_kind::Local:
    case expr_kind::Meta:
    case expr_kind::Sort:
    case expr_kind::Constant:
    case expr_kind::Macro: // TODO(dhs): do I unfold macros?
        break;
    case expr_kind::Lambda:
    case expr_kind::Pi:
        // TODO(dhs): confirm that I only index quantified-free hypotheses
        break;
    case expr_kind::Let:
        // Let-expressions must be unfolded before invoking this method
        lean_unreachable();
    case expr_kind::App:
        index_expr(app_fn(e));
        index_expr(app_arg(e));
        break;
    }
}

// scoped_expr_actions must occur after a Binder/Binders.
static void validate_transitions(bool nud, unsigned num, transition const * ts, expr const & a) {
    unsigned nargs = 0;
    if (!nud)
        nargs++; // led tables have an implicit left argument
    bool found_binder = false;
    for (unsigned i = 0; i < num; i++) {
        action const & a = ts[i].get_action();
        switch (a.kind()) {
        case action_kind::Binder: case action_kind::Binders:
            found_binder = true;
            break;
        case action_kind::Expr: case action_kind::Exprs: case action_kind::Ext: case action_kind::LuaExt:
            nargs++;
            break;
        case action_kind::ScopedExpr:
            if (!found_binder)
                throw exception("invalid notation declaration, a scoped expression must occur after a binder element");
            nargs++;
            break;
        case action_kind::Skip:
            break;
        }
    }
    if (get_free_var_range(a) > nargs)
        throw exception("invalid notation declaration, expression template has more free variables than arguments");
}

expr replace_visitor::visit(expr const & e) {
    check_system("expression replacer");
    bool shared = false;
    if (is_shared(e)) {
        shared = true;
        auto it = m_cache.find(e);
        if (it != m_cache.end())
            return it->second;
    }

    switch (e.kind()) {
    case expr_kind::Sort:      return save_result(e, visit_sort(e), shared);
    case expr_kind::Macro:     return save_result(e, visit_macro(e), shared);
    case expr_kind::Constant:  return save_result(e, visit_constant(e), shared);
    case expr_kind::Var:       return save_result(e, visit_var(e), shared);
    case expr_kind::Meta:      return save_result(e, visit_meta(e), shared);
    case expr_kind::Local:     return save_result(e, visit_local(e), shared);
    case expr_kind::App:       return save_result(e, visit_app(e), shared);
    case expr_kind::Lambda:    return save_result(e, visit_lambda(e), shared);
    case expr_kind::Pi:        return save_result(e, visit_pi(e), shared);
    case expr_kind::Let:       return save_result(e, visit_let(e), shared);
    }

    lean_unreachable(); // LCOV_EXCL_LINE
}

void process(expr e)
{
	if (e.num_args() > 0)
	{
		for (int i = 0; i < e.num_args(); i++)
			process(e.arg(i));
		return;
	}
	if (e.kind() != Z3_APP_AST) return; //not a variable
	VARIBLE_VALUE vv;
	func_decl def = e.decl();
	vv.name = def.name().str();
	if (e.is_bool()) // bool
	{
		if (vv.name == "false" || vv.name == "true") return;
		vv.type = "bool";
		vv.size = 1;
		vv.value = "false";
	}
	else if (e.is_bv()) //bitvector
	{
		sort s = def.range();
		vv.type = "bitvector";
		vv.size = s.bv_size();
		vv.value = "0";
	}
	else // we do not handle other sorts
	{
		std::cout << "we just handle bool or bitvector.\n";
		exit(0);
	}
	defaultSolution.insert(std::make_pair(def.name().str(), vv));
}

unsigned get_weight(expr const & e) {
    switch (e.kind()) {
    case expr_kind::Var:  case expr_kind::Constant: case expr_kind::Sort:
    case expr_kind::Meta: case expr_kind::Local:
        return 1;
    case expr_kind::Lambda: case expr_kind::Pi:  case expr_kind::Macro:
    case expr_kind::App:    case expr_kind::Let:
        return static_cast<expr_composite*>(e.raw())->m_weight;
    }
    lean_unreachable(); // LCOV_EXCL_LINE
}

unsigned abstract_expr_manager::hash(expr const & e) {
    unsigned h;
    switch (e.kind()) {
    case expr_kind::Constant:
    case expr_kind::Local:
    case expr_kind::Meta:
    case expr_kind::Sort:
    case expr_kind::Var:
    case expr_kind::Macro:
        return e.hash();
    case expr_kind::Lambda:
    case expr_kind::Pi:
        h = hash(binding_domain(e));
        // Remark binding_domain(e) may contain de-bruijn variables.
        // We can instantiate them eagerly as we do here, or lazily.
        // The lazy approach is potentially more efficient, but we would have
        // to use something more sophisticated than an instantiate_rev at expr_kind::App
        m_locals.push_back(instantiate_rev(m_tctx.mk_tmp_local(binding_domain(e)), m_locals.size(), m_locals.data()));
        h = ::lean::hash(h, hash(binding_body(e)));
        m_locals.pop_back();
        return h;
    case expr_kind::Let:
        // Let-expressions must be unfolded before invoking this method
        lean_unreachable();
    case expr_kind::App:
        buffer<expr> args;
        expr const & f     = get_app_args(e, args);
        unsigned prefix_sz = m_congr_lemma_manager.get_specialization_prefix_size(instantiate_rev(f, m_locals.size(), m_locals.data()), args.size());
        expr new_f = e;
        unsigned rest_sz   = args.size() - prefix_sz;
        for (unsigned i = 0; i < rest_sz; i++)
            new_f = app_fn(new_f);
        new_f = instantiate_rev(new_f, m_locals.size(), m_locals.data());
        optional<congr_lemma> congr = m_congr_lemma_manager.mk_congr(new_f, rest_sz);
        h = hash(new_f);
        if (!congr) {
            for (unsigned i = prefix_sz; i < args.size(); i++) {
                h = ::lean::hash(h, hash(args[i]));
            }
        } else {
            lean_assert(length(congr->get_arg_kinds()) == rest_sz);
            unsigned i = prefix_sz;
            for_each(congr->get_arg_kinds(), [&](congr_arg_kind const & c_kind) {
                    if (c_kind != congr_arg_kind::Cast) {
                        h = ::lean::hash(h, hash(args[i]));
                    }
                    i++;
                });
        }
        return h;
    }
    lean_unreachable();
}

static bool is_permutation(expr const & lhs, expr const & rhs, unsigned offset, buffer<optional<unsigned>> & p) {
    if (lhs.kind() != rhs.kind())
        return false;
    switch (lhs.kind()) {
    case expr_kind::Constant: case expr_kind::Sort:
    case expr_kind::Meta: case expr_kind::Local:
        return lhs == rhs;
    case expr_kind::Var:
        if (var_idx(lhs) < offset) {
            return lhs == rhs; // locally bound variable
        } else if (var_idx(lhs) - offset < p.size()) {
            if (p[var_idx(lhs) - offset]) {
                return *(p[var_idx(lhs) - offset]) == var_idx(rhs);
            } else {
                p[var_idx(lhs) - offset] = var_idx(rhs);
                return true;
            }
        } else {
            return lhs == rhs; // free variable
        }
    case expr_kind::Lambda: case expr_kind::Pi:
        return
            is_permutation(binding_domain(lhs), binding_domain(rhs), offset, p) &&
            is_permutation(binding_body(lhs), binding_body(rhs), offset+1, p);
    case expr_kind::App:
        return
            is_permutation(app_fn(lhs), app_fn(rhs), offset, p) &&
            is_permutation(app_arg(lhs), app_arg(rhs), offset, p);
    case expr_kind::Macro:
        if (macro_def(lhs) != macro_def(rhs) ||
            macro_num_args(lhs) != macro_num_args(rhs))
            return false;
        for (unsigned i = 0; i < macro_num_args(lhs); i++) {
            if (!is_permutation(macro_arg(lhs, i), macro_arg(rhs, i), offset, p))
                return false;
        }
        return true;
    }
    lean_unreachable();
}

 expr visit_binding(expr e) {
     expr_kind k = e.kind();
     buffer<expr>  es;
     buffer<expr>  ls;
     while (e.kind() == k) {
         expr d = visit(instantiate_rev(binding_domain(e), ls.size(), ls.data()));
         expr l = mk_local(m_tc.mk_fresh_name(), binding_name(e), d, binding_info(e));
         ls.push_back(l);
         es.push_back(e);
         e = binding_body(e);
     }
     e = visit(instantiate_rev(e, ls.size(), ls.data()));
     expr r = abstract_locals(e, ls.size(), ls.data());
     while (!ls.empty()) {
         expr d = mlocal_type(ls.back());
         ls.pop_back();
         d = abstract_locals(d, ls.size(), ls.data());
         r = update_binding(es.back(), d, r);
         es.pop_back();
     }
     return r;
 }