C++ environment::get方法代码示例

void get_rec_args(environment const & env, name const & n, buffer<buffer<bool>> & r) {
    lean_assert(inductive::is_inductive_decl(env, n));
    type_checker tc(env);
    name_generator ngen;
    declaration ind_decl   = env.get(n);
    declaration rec_decl   = env.get(inductive::get_elim_name(n));
    unsigned nparams       = *inductive::get_num_params(env, n);
    unsigned nminors       = *inductive::get_num_minor_premises(env, n);
    unsigned ntypeformers  = *inductive::get_num_type_formers(env, n);
    buffer<expr> rec_args;
    to_telescope(ngen, rec_decl.get_type(), rec_args);
    buffer<name> typeformer_names;
    for (unsigned i = nparams; i < nparams + ntypeformers; i++) {
        typeformer_names.push_back(mlocal_name(rec_args[i]));
    }
    lean_assert(typeformer_names.size() == ntypeformers);
    r.clear();
    // add minor premises
    for (unsigned i = nparams + ntypeformers; i < nparams + ntypeformers + nminors; i++) {
        r.push_back(buffer<bool>());
        buffer<bool> & bv = r.back();
        expr minor_type = mlocal_type(rec_args[i]);
        buffer<expr> minor_args;
        to_telescope(ngen, minor_type, minor_args);
        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);
            bv.push_back(is_typeformer_app(typeformer_names, minor_arg_type));
        }
    }
}

json serialize_decl(name const & short_name, name const & long_name, environment const & env, options const & o) {
    declaration const & d = env.get(long_name);
    type_context_old tc(env);
    auto fmter = mk_pretty_formatter_factory()(env, o, tc);
    expr type = d.get_type();
    if (LEAN_COMPLETE_CONSUME_IMPLICIT) {
        while (true) {
            if (!is_pi(type))
                break;
            if (!binding_info(type).is_implicit() && !binding_info(type).is_inst_implicit())
                break;
            std::string q("?");
            q += binding_name(type).to_string();
            expr m = mk_constant(name(q.c_str()));
            type   = instantiate(binding_body(type), m);
        }
    }
    json completion;
    completion["text"] = short_name.to_string();
    interactive_report_type(env, o, type, completion);
    add_source_info(env, long_name, completion);
    if (auto doc = get_doc_string(env, long_name))
        completion["doc"] = *doc;
    return completion;
}

optional<name> get_noncomputable_reason(environment const & env, name const & n) {
    declaration const & d = env.get(n);
    if (!d.is_definition())
        return optional<name>();
    type_checker tc(env);
    if (tc.is_prop(d.get_type()))
        return optional<name>(); // definition is a proposition, then do nothing
    expr const & v = d.get_value();
    auto ext = get_extension(env);
    bool ok  = true;
    /* quick check */
    for_each(v, [&](expr const & e, unsigned) {
            if (!ok) return false; // stop the search
            if (is_constant(e) && is_noncomputable(tc, ext, const_name(e))) {
                ok = false;
            }
            return true;
        });
    if (ok) {
        return optional<name>();
    }
    /* expensive check */
    try {
        get_noncomputable_reason_fn proc(tc);
        proc(v);
        return optional<name>();
    } catch (get_noncomputable_reason_fn::found & r) {
        return optional<name>(r.m_reason);
    }
}

static optional<pair<expr, expr>> mk_op(environment const & env, old_local_context & ctx, type_checker_ptr & tc,
                                        name const & op, unsigned nunivs, unsigned nargs, std::initializer_list<expr> const & explicit_args,
                                        constraint_seq & cs, tag g) {
    levels lvls;
    for (unsigned i = 0; i < nunivs; i++)
        lvls = levels(mk_meta_univ(mk_fresh_name()), lvls);
    expr c = mk_constant(op, lvls);
    expr op_type = instantiate_type_univ_params(env.get(op), lvls);
    buffer<expr> args;
    for (unsigned i = 0; i < nargs; i++) {
        if (!is_pi(op_type))
            return optional<pair<expr, expr>>();
        expr arg = ctx.mk_meta(some_expr(binding_domain(op_type)), g);
        args.push_back(arg);
        op_type  = instantiate(binding_body(op_type), arg);
    }
    expr r = mk_app(c, args, g);
    for (expr const & explicit_arg : explicit_args) {
        if (!is_pi(op_type))
            return optional<pair<expr, expr>>();
        r = mk_app(r, explicit_arg);
        expr type = tc->infer(explicit_arg, cs);
        justification j = mk_app_justification(r, op_type, explicit_arg, type);
        if (!tc->is_def_eq(binding_domain(op_type), type, j, cs))
            return optional<pair<expr, expr>>();
        op_type  = instantiate(binding_body(op_type), explicit_arg);
    }
    return some(mk_pair(r, op_type));
}

 name_set operator()() {
     name_set A;
     name_set Fs = m_relevant;
     // unsigned i = 1;
     while (true) {
         // std::cout << "#" << i << ", p: " << m_p << "\n";
         name_set Rel;
         Fs.for_each([&](name const & F) {
                 name_set used_by = get_used_by_set(m_env, F);
                 used_by.for_each([&](name const & T) {
                         declaration const & T_decl = m_env.get(T);
                         if (A.contains(T))
                             return; // T is already in the result set
                         if (!T_decl.is_theorem() && !T_decl.is_axiom())
                             return; // we only care about axioms and theorems
                         if (ignore_T(T))
                             return; // we ignore private decls
                         double M = get_thm_score(T);
                         // std::cout << T << " : " << M << "\n";
                         if (M < m_p)
                             return; // score is to low
                         Rel.insert(T);
                         A.insert(T);
                     });
             });
         if (Rel.empty())
             break;
         // include symbols of new theorems in m_relevant
         Fs = name_set(); // reset Fs
         Rel.for_each([&](name const & T) {
                 name_set uses = get_use_set(m_env, T);
                 uses.for_each([&](name const & F) {
                         declaration const & F_decl = m_env.get(F);
                         if (F_decl.is_theorem() || F_decl.is_axiom())
                             return; // we ignore theorems occurring in types
                         if (ignore_F(F))
                             return;
                         // if (!m_relevant.contains(F))
                         //    std::cout << "new relevant: " << F << "\n";
                         m_relevant.insert(F);
                         Fs.insert(F);
                     });
             });
         m_p = m_p + (1.0 - m_p) / m_c;
     }
     return A;
 }

static pair<expr, unsigned> extract_arg_types_core(environment const & env, name const & f, buffer<expr> & arg_types) {
    declaration d = env.get(f);
    expr f_type = d.get_type();
    while (is_pi(f_type)) {
        arg_types.push_back(binding_domain(f_type));
        f_type = binding_body(f_type);
    }
    return mk_pair(f_type, length(d.get_univ_params()));
}

unsigned get_constructor_arity(environment const & env, name const & n) {
    declaration d = env.get(n);
    expr e = d.get_type();
    unsigned r = 0;
    while (is_pi(e)) {
        r++;
        e = binding_body(e);
    }
    return r;
}

 void print_axioms(expr const & ex) {
     for_each(ex, [&] (expr const & e, unsigned) {
         if (is_constant(e) && !m_already_printed.count(const_name(e))) {
             auto decl = m_env.get(const_name(e));
             m_already_printed.insert(decl.get_name());
             print_axioms(decl);
             if (decl.is_constant_assumption() && !m_env.is_builtin(decl.get_name()))
                 print_decl(decl);
         }
         return true;
     });
 }

environment mk_rec_on(environment const & env, name const & n) {
    if (!inductive::is_inductive_decl(env, n))
        throw exception(sstream() << "error in 'rec_on' generation, '" << n << "' is not an inductive datatype");
    name rec_on_name(n, "rec_on");
    name_generator ngen;
    declaration rec_decl = env.get(inductive::get_elim_name(n));

    buffer<expr> locals;
    expr rec_type = rec_decl.get_type();
    while (is_pi(rec_type)) {
        expr local = mk_local(ngen.next(), binding_name(rec_type), binding_domain(rec_type), binding_info(rec_type));
        rec_type   = instantiate(binding_body(rec_type), local);
        locals.push_back(local);
    }

    // locals order
    //   A C minor_premises indices major-premise

    // new_locals order
    //   A C indices major-premise minor-premises
    buffer<expr> new_locals;
    unsigned idx_major_sz = *inductive::get_num_indices(env, n) + 1;
    unsigned minor_sz     = *inductive::get_num_minor_premises(env, n);
    unsigned AC_sz        = locals.size() - minor_sz - idx_major_sz;
    for (unsigned i = 0; i < AC_sz; i++)
        new_locals.push_back(locals[i]);
    for (unsigned i = 0; i < idx_major_sz; i++)
        new_locals.push_back(locals[AC_sz + minor_sz + i]);
    unsigned rec_on_major_idx = new_locals.size() - 1;
    for (unsigned i = 0; i < minor_sz; i++)
        new_locals.push_back(locals[AC_sz + i]);
    expr rec_on_type = Pi(new_locals, rec_type);

    levels ls = param_names_to_levels(rec_decl.get_univ_params());
    expr rec  = mk_constant(rec_decl.get_name(), ls);
    expr rec_on_val = Fun(new_locals, mk_app(rec, locals));

    bool use_conv_opt = true;
    environment new_env = module::add(env,
                                      check(env, mk_definition(env, rec_on_name, rec_decl.get_univ_params(),
                                                               rec_on_type, rec_on_val, use_conv_opt)));
    new_env = set_reducible(new_env, rec_on_name, reducible_status::Reducible);
    new_env = add_unfold_hint(new_env, rec_on_name, rec_on_major_idx);
    new_env = add_aux_recursor(new_env, rec_on_name);
    return add_protected(new_env, rec_on_name);
}

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]);
//.........这里部分代码省略.........

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()));
//.........这里部分代码省略.........

void info_manager::add_const_info(environment const & env, pos_info pos, name const & full_id) {
    add_identifier_info(pos, full_id);
    add_type_info(pos, env.get(full_id).get_type());
}

environment mk_projections(environment const & env, name const & n, buffer<name> const & proj_names,
                           implicit_infer_kind infer_k, bool inst_implicit) {
    // Given an inductive datatype C A (where A represent parameters)
    //   intro : Pi A (x_1 : B_1[A]) (x_2 : B_2[A, x_1]) ..., C A
    //
    // we generate projections of the form
    //   proj_i A (c : C A) : B_i[A, (proj_1 A n), ..., (proj_{i-1} A n)]
    //     C.rec A (fun (x : C A), B_i[A, ...]) (fun (x_1 ... x_n), x_i) c
    auto p = get_nparam_intro_rule(env, n);
    name_generator ngen;
    unsigned nparams             = p.first;
    inductive::intro_rule intro  = p.second;
    expr intro_type              = inductive::intro_rule_type(intro);
    name rec_name                = inductive::get_elim_name(n);
    declaration ind_decl         = env.get(n);
    if (env.impredicative() && is_prop(ind_decl.get_type()))
        throw exception(sstream() << "projection generation, '" << n << "' is a proposition");
    declaration rec_decl         = env.get(rec_name);
    level_param_names lvl_params = ind_decl.get_univ_params();
    levels lvls                  = param_names_to_levels(lvl_params);
    buffer<expr> params; // datatype parameters
    for (unsigned i = 0; i < nparams; i++) {
        if (!is_pi(intro_type))
            throw_ill_formed(n);
        expr param = mk_local(ngen.next(), binding_name(intro_type), binding_domain(intro_type), binder_info());
        intro_type = instantiate(binding_body(intro_type), param);
        params.push_back(param);
    }
    expr C_A                     = mk_app(mk_constant(n, lvls), params);
    binder_info c_bi             = inst_implicit ? mk_inst_implicit_binder_info() : binder_info();
    expr c                       = mk_local(ngen.next(), name("c"), C_A, c_bi);
    buffer<expr> intro_type_args; // arguments that are not parameters
    expr it = intro_type;
    while (is_pi(it)) {
        expr local = mk_local(ngen.next(), binding_name(it), binding_domain(it), binding_info(it));
        intro_type_args.push_back(local);
        it = instantiate(binding_body(it), local);
    }
    buffer<expr> projs; // projections generated so far
    unsigned i = 0;
    environment new_env = env;
    for (name const & proj_name : proj_names) {
        if (!is_pi(intro_type))
            throw exception(sstream() << "generating projection '" << proj_name << "', '"
                            << n << "' does not have sufficient data");
        expr result_type   = binding_domain(intro_type);
        buffer<expr> proj_args;
        proj_args.append(params);
        proj_args.push_back(c);
        expr type_former   = Fun(c, result_type);
        expr minor_premise = Fun(intro_type_args, mk_var(intro_type_args.size() - i - 1));
        expr major_premise = c;
        type_checker tc(new_env);
        level l            = sort_level(tc.ensure_sort(tc.infer(result_type).first).first);
        levels rec_lvls    = append(to_list(l), lvls);
        expr rec           = mk_constant(rec_name, rec_lvls);
        buffer<expr> rec_args;
        rec_args.append(params);
        rec_args.push_back(type_former);
        rec_args.push_back(minor_premise);
        rec_args.push_back(major_premise);
        expr rec_app      = mk_app(rec, rec_args);
        expr proj_type    = Pi(proj_args, result_type);
        proj_type         = infer_implicit_params(proj_type, nparams, infer_k);
        expr proj_val     = Fun(proj_args, rec_app);
        bool opaque       = false;
        bool use_conv_opt = false;
        declaration new_d = mk_definition(env, proj_name, lvl_params, proj_type, proj_val,
                                          opaque, rec_decl.get_module_idx(), use_conv_opt);
        new_env = module::add(new_env, check(new_env, new_d));
        new_env = set_reducible(new_env, proj_name, reducible_status::Reducible);
        new_env = add_unfold_c_hint(new_env, proj_name, nparams);
        new_env = save_projection_info(new_env, proj_name, inductive::intro_rule_name(intro), nparams, i, inst_implicit);
        expr proj         = mk_app(mk_app(mk_constant(proj_name, lvls), params), c);
        intro_type        = instantiate(binding_body(intro_type), proj);
        i++;
    }
    return new_env;
}

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,
//.........这里部分代码省略.........

void add_congr_core(environment const & env, simp_rule_sets & s, name const & n) {
    declaration const & d = env.get(n);
    type_checker tc(env);
    buffer<level> us;
    unsigned num_univs = d.get_num_univ_params();
    for (unsigned i = 0; i < num_univs; i++) {
        us.push_back(mk_meta_univ(name(*g_prefix, i)));
    }
    levels ls = to_list(us);
    expr pr   = mk_constant(n, ls);
    expr e    = instantiate_type_univ_params(d, ls);
    buffer<bool> explicit_args;
    buffer<expr> metas;
    unsigned idx = 0;
    while (is_pi(e)) {
        expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(e));
        idx++;
        explicit_args.push_back(is_explicit(binding_info(e)));
        metas.push_back(mvar);
        e   = instantiate(binding_body(e), mvar);
        pr  = mk_app(pr, mvar);
    }
    expr rel, lhs, rhs;
    if (!is_simp_relation(env, e, rel, lhs, rhs) || !is_constant(rel)) {
        throw exception(sstream() << "invalid congruence rule, '" << n
                        << "' resulting type is not of the form t ~ s, where '~' is a transitive and reflexive relation");
    }
    name_set found_mvars;
    buffer<expr> lhs_args, rhs_args;
    expr const & lhs_fn = get_app_args(lhs, lhs_args);
    expr const & rhs_fn = get_app_args(rhs, rhs_args);
    if (is_constant(lhs_fn)) {
        if (!is_constant(rhs_fn) || const_name(lhs_fn) != const_name(rhs_fn) || lhs_args.size() != rhs_args.size()) {
            throw exception(sstream() << "invalid congruence rule, '" << n
                            << "' resulting type is not of the form (" << const_name(lhs_fn) << "  ...) "
                            << "~ (" << const_name(lhs_fn) << " ...), where ~ is '" << const_name(rel) << "'");
        }
        for (expr const & lhs_arg : lhs_args) {
            if (is_sort(lhs_arg))
                continue;
            if (!is_metavar(lhs_arg) || found_mvars.contains(mlocal_name(lhs_arg))) {
                throw exception(sstream() << "invalid congruence rule, '" << n
                                << "' the left-hand-side of the congruence resulting type must be of the form ("
                                << const_name(lhs_fn) << " x_1 ... x_n), where each x_i is a distinct variable or a sort");
            }
            found_mvars.insert(mlocal_name(lhs_arg));
        }
    } else if (is_binding(lhs)) {
        if (lhs.kind() != rhs.kind()) {
            throw exception(sstream() << "invalid congruence rule, '" << n
                            << "' kinds of the left-hand-side and right-hand-side of "
                            << "the congruence resulting type do not match");
        }
        if (!is_valid_congr_rule_binding_lhs(lhs, found_mvars)) {
            throw exception(sstream() << "invalid congruence rule, '" << n
                            << "' left-hand-side of the congruence resulting type must "
                            << "be of the form (fun/Pi (x : A), B x)");
        }
    } else {
        throw exception(sstream() << "invalid congruence rule, '" << n
                        << "' left-hand-side is not an application nor a binding");
    }

    buffer<expr> congr_hyps;
    lean_assert(metas.size() == explicit_args.size());
    for (unsigned i = 0; i < metas.size(); i++) {
        expr const & mvar = metas[i];
        if (explicit_args[i] && !found_mvars.contains(mlocal_name(mvar))) {
            buffer<expr> locals;
            expr type = mlocal_type(mvar);
            while (is_pi(type)) {
                expr local = mk_local(tc.mk_fresh_name(), binding_domain(type));
                locals.push_back(local);
                type = instantiate(binding_body(type), local);
            }
            expr h_rel, h_lhs, h_rhs;
            if (!is_simp_relation(env, type, h_rel, h_lhs, h_rhs) || !is_constant(h_rel))
                continue;
            unsigned j = 0;
            for (expr const & local : locals) {
                j++;
                if (!only_found_mvars(mlocal_type(local), found_mvars)) {
                    throw exception(sstream() << "invalid congruence rule, '" << n
                                    << "' argument #" << j << " of parameter #" << (i+1) << " contains "
                                    << "unresolved parameters");
                }
            }
            if (!only_found_mvars(h_lhs, found_mvars)) {
                throw exception(sstream() << "invalid congruence rule, '" << n
                                << "' argument #" << (i+1) << " is not a valid hypothesis, the left-hand-side contains "
                                << "unresolved parameters");
            }
            if (!is_valid_congr_hyp_rhs(h_rhs, found_mvars)) {
                throw exception(sstream() << "invalid congruence rule, '" << n
                                << "' argument #" << (i+1) << " is not a valid hypothesis, the right-hand-side must be "
                                << "of the form (m l_1 ... l_n) where m is parameter that was not "
                                << "'assigned/resolved' yet and l_i's are locals");
            }
            found_mvars.insert(mlocal_name(mvar));
            congr_hyps.push_back(mvar);
//.........这里部分代码省略.........