notation_cmd.cpp

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#include <utility>
#include <limits>
#include <string>
#include "util/sstream.h"
#include "util/utf8.h"
#include "kernel/abstract.h"
#include "kernel/replace_fn.h"
#include "library/scoped_ext.h"
#include "library/explicit.h"
#include "library/num.h"
#include "library/aliases.h"
#include "library/constants.h"
#include "library/typed_expr.h"
#include "library/vm/vm_nat.h"
#include "frontends/lean/parser.h"
#include "frontends/lean/tokens.h"
#include "frontends/lean/util.h"
#include "frontends/lean/decl_attributes.h"

namespace lean {
static std::string parse_symbol(parser & p, ast_data & parent, char const * msg) {
    name n;
    name type = p.curr_is_quoted_symbol() ? "quoted" : "ident";
    if (p.curr_is_identifier() || p.curr_is_quoted_symbol()) {
        n = p.get_name_val();
    } else if (p.curr_is_keyword()) {
        n = p.get_token_info().value();
    } else {
        throw parser_error(msg, p.pos());
    }
    auto s = n.to_string_unescaped();
    parent.push(p.new_ast(type, p.pos(), s).m_id);
    p.next();
    return s;
}

static pair<ast_id, unsigned> parse_precedence_core(parser & p) {
    auto pos = p.pos();
    if (p.curr_is_numeral()) {
        return p.parse_small_nat();
    } else {
        environment env = p.env();
        options opts = p.get_options();
        env = open_prec_aliases(env);
        parser::local_scope scope(p, env);
        expr pre_val = p.parse_expr(get_max_prec());
        auto expr_id = p.new_ast("expr", pos).push(p.get_id(pre_val)).m_id;
        expr nat = mk_constant(get_nat_name());
        pre_val  = mk_typed_expr(nat, pre_val);
        expr val = p.elaborate("notation", list<expr>(), pre_val).first;
        vm_obj p = eval_closed_expr(env, opts, "_precedence", nat, val, pos);
        if (optional<unsigned> _p = try_to_unsigned(p)) {
            return {expr_id, *_p};
        } else {
            throw parser_error("invalid 'precedence', argument does not evaluate to a small numeral", pos);
        }
    }
}

static pair<ast_id, optional<unsigned>> parse_optional_precedence(parser & p) {
    if (p.curr_is_token(get_colon_tk())) {
        p.next();
        pair<ast_id, optional<unsigned>> r;
        std::tie(r.first, r.second) = parse_precedence_core(p);
        return r;
    } else {
        return {0, optional<unsigned>()};
    }
}

static pair<ast_id, unsigned> parse_precedence(parser & p) {
    return parse_precedence_core(p);
}

LEAN_THREAD_VALUE(bool, g_allow_local, false);

static void check_notation_expr(expr const & e, pos_info const & pos) {
    if (!g_allow_local && (has_local(e) || has_param_univ(e)))
        throw parser_error("invalid notation declaration, contains reference to local variables", pos);
}

enum class mixfix_kind { infixl, infixr, postfix, prefix };

using notation::mk_expr_action;
using notation::mk_binder_action;
using notation::mk_binders_action;
using notation::mk_exprs_action;
using notation::mk_scoped_expr_action;
using notation::mk_skip_action;
using notation::transition;
using notation::action;

static char const * g_forbidden_tokens[] = {"@", nullptr};

void check_not_forbidden(char const * tk) {
    auto it = g_forbidden_tokens;
    while (*it) {
        if (strcmp(*it, tk) == 0)
            throw exception(sstream() << "invalid token `" << tk << "`, it is reserved");
        ++it;
    }
}

static optional<unsigned> get_precedence(environment const & env, char const * tk) {
    return get_expr_precedence(get_token_table(env), tk);
}

void check_notation_name(environment const & env, notation_entry_group grp,
    const pos_info & pos, name const & name, bool was_anon) {
    if (grp == notation_entry_group::Reserve || !has_notation(env, name)) return;
    if (was_anon)
        throw parser_error(sstream() <<
            "invalid notation: notation already declared. Consider using 'notation (name := ...)'", pos);
    else
        throw parser_error(sstream() <<
            "invalid notation: notation '" << name << "' already declared", pos);
}

static pair<ast_id, name> parse_optional_name(parser & p) {
    if (!p.curr_is_token(get_lparen_tk())) return {0, {}};
    p.next();
    auto tk = p.check_id_next("invalid notation declaration, expected 'name'");
    if (tk.second != get_name_tk())
        p.maybe_throw_error({"invalid notation declaration, expected 'name'", p.get_ast(tk.first).m_start});
    p.check_token_next(get_assign_tk(), "invalid notation declaration, expected ':='");
    auto r = p.check_id_next("invalid notation declaration, expected identifier");
    p.check_token_next(get_rparen_tk(), "invalid notation declaration, expected ')'");
    return r;
}

static auto parse_mixfix_notation(parser & p, ast_data & parent, mixfix_kind k, bool overload, notation_entry_group grp, bool parse_only,
                                  unsigned priority)
-> pair<notation_entry, optional<token_entry>> {
    bool explicit_pp = p.curr_is_quoted_symbol();
    auto name = parse_optional_name(p);
    parent.push(name.first);
    pos_info tk_pos = p.pos();
    std::string pp_tk = parse_symbol(p, parent, "invalid notation declaration, quoted symbol or identifier expected");
    std::string tk = utf8_trim(pp_tk);
    char const * tks = tk.c_str();
    check_not_forbidden(tks);
    environment const & env = p.env();
    optional<token_entry> new_token;
    optional<unsigned> prec;

    optional<parse_table> reserved_pt;
    optional<transition> reserved_transition;
    optional<action> reserved_action;
    if (grp == notation_entry_group::Main) {
        if (k == mixfix_kind::prefix) {
            if (auto ls = get_reserved_nud_table(p.env()).find(tks)) {
                // Remark: we are ignoring multiple actions in the reserved notation table
                reserved_pt     = head(ls).second;
                reserved_transition = head(ls).first;
                reserved_action = reserved_transition->get_action();
            }
        } else {
            if (auto ls = get_reserved_led_table(p.env()).find(tks)) {
                // Remark: we are ignoring multiple actions in the reserved notation table
                reserved_pt     = head(ls).second;
                reserved_transition = head(ls).first;
                reserved_action = reserved_transition->get_action();
            }
        }
    }

    pos_info prec_pos;
    ast_id prec_id = 0;
    if (p.curr_is_token(get_colon_tk())) {
        p.next();
        prec_pos = p.pos();
        std::tie(prec_id, prec) = parse_precedence(p);
    }
    parent.push(prec_id);

    if (prec && k == mixfix_kind::infixr && *prec == 0)
        throw parser_error("invalid infixr declaration, precedence must be greater than zero", prec_pos);

    if (!prec) {
        if (reserved_action && k == mixfix_kind::prefix && reserved_action->kind() == notation::action_kind::Expr) {
            lean_assert(grp == notation_entry_group::Main);
            prec = reserved_action->rbp();
        } else if (reserved_action && k == mixfix_kind::infixr && reserved_action->kind() == notation::action_kind::Expr) {
            lean_assert(grp == notation_entry_group::Main);
            prec = reserved_action->rbp();
        } else {
            prec = get_precedence(env, tk.c_str());
            if (prec && k == mixfix_kind::infixr)
                prec = *prec - 1;
        }
    } else {
        auto old_prec = get_precedence(env, tk.c_str());
        if (!old_prec || k != mixfix_kind::prefix)
            new_token = mk_token_entry(tk.c_str(), *prec);
        if (k == mixfix_kind::infixr)
            prec = *prec - 1;
    }

    if (!prec) {
        lean_assert(!reserved_pt);
        throw parser_error("invalid notation declaration, precedence was not provided, "
                           "and it is not set for the given symbol, "
                           "solution: use the 'precedence' command", tk_pos);
    }

    unsigned _prec = 0;
    if (prec) _prec = *prec; // this is a hack to fix an incorrect warning produced by clang++ on OSX

    if (!g_allow_local && reserved_action) {
        switch (k) {
        case mixfix_kind::infixl:
            if (reserved_action->kind() != notation::action_kind::Expr || reserved_action->rbp() != _prec)
                throw parser_error("invalid infixl declaration, declaration conflicts with reserved notation", tk_pos);
            break;
        case mixfix_kind::infixr:
            if (reserved_action->kind() != notation::action_kind::Expr || reserved_action->rbp() != _prec)
                throw parser_error("invalid infixr declaration, declaration conflicts with reserved notation", tk_pos);
            break;
        case mixfix_kind::postfix:
            if (reserved_action->kind() != notation::action_kind::Skip)
                throw parser_error("invalid postfix declaration, declaration conflicts with reserved notation", tk_pos);
            break;
        case mixfix_kind::prefix:
            if (reserved_action->kind() != notation::action_kind::Expr || reserved_action->rbp() != _prec)
                throw parser_error("invalid prefix declaration, declaration conflicts with reserved notation", tk_pos);
            break;
        }
    }

    if (reserved_action && !explicit_pp)
        pp_tk = reserved_transition->get_pp_token().to_string_unescaped();

    bool is_nud = k == mixfix_kind::prefix;
    list<transition> ts;
    switch (k) {
    case mixfix_kind::infixl:
        ts = to_list(transition(tks, mk_expr_action(*prec), pp_tk));
        break;
    case mixfix_kind::infixr:
        ts = to_list(transition(tks, mk_expr_action(*prec), pp_tk));
        break;
    case mixfix_kind::postfix:
        ts = to_list(transition(tks, mk_skip_action(), pp_tk));
        break;
    case mixfix_kind::prefix:
        ts = to_list(transition(tks, mk_expr_action(*prec), pp_tk));
        break;
    }
    expr e;
    if (grp == notation_entry_group::Reserve) {
        // reserve notation commands do not have a denotation
        parent.push(0);
        e = mk_Prop();
        if (p.curr_is_token(get_assign_tk()))
            throw parser_error("invalid reserve notation, found `:=`", p.pos());
    } else {
        p.check_token_next(get_assign_tk(), "invalid notation declaration, ':=' expected");
        auto f_pos = p.pos();
        expr f     = p.parse_expr();
        check_notation_expr(f, f_pos);
        parent.push(p.get_id(f));
        switch (k) {
        case mixfix_kind::infixl:
#if defined(__GNUC__) && !defined(__CLANG__)
#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
#endif
            e = mk_app(f, Var(1), Var(0));
            break;
        case mixfix_kind::infixr:
            e = mk_app(f, Var(1), Var(0));
            break;
        case mixfix_kind::postfix:
            e = mk_app(f, Var(0));
            break;
        case mixfix_kind::prefix:
            e = mk_app(f, Var(0));
            break;
        }
    }
    notation_entry entry(is_nud, ts, e, overload, priority, grp, parse_only, name.second);
    check_notation_name(p.env(), grp, tk_pos, entry.get_name(), name.second.is_anonymous());
    return mk_pair(entry, new_token);
}

static notation_entry parse_mixfix_notation(parser & p, ast_data & data, mixfix_kind k, bool overload, notation_entry_group grp,
                                            buffer<token_entry> & new_tokens, bool parse_only, unsigned priority) {
    auto nt = parse_mixfix_notation(p, data, k, overload, grp, parse_only, priority);
    if (nt.second)
        new_tokens.push_back(*nt.second);
    return nt.first;
}

static name parse_quoted_symbol_or_token(parser & p, ast_data & data, buffer<token_entry> & new_tokens, bool & used_default) {
    used_default = false;
    auto& sym = p.new_ast("sym", p.pos());
    data.push(sym.m_id);
    if (p.curr_is_quoted_symbol()) {
        environment const & env = p.env();
        auto pp_tk = p.get_name_val();
        sym.push(p.new_ast("quoted", p.pos(), pp_tk).m_id);
        auto tks   = utf8_trim(pp_tk.to_string_unescaped());
        auto tkcs  = tks.c_str();
        check_not_forbidden(tkcs);
        p.next();
        ast_id prec_id = 0;
        if (p.curr_is_token(get_colon_tk())) {
            p.next();
            unsigned prec;
            std::tie(prec_id, prec) = parse_precedence(p);
            new_tokens.push_back(mk_token_entry(tkcs, prec));
        } else if (!get_precedence(env, tkcs)) {
            new_tokens.push_back(mk_token_entry(tkcs, LEAN_DEFAULT_PRECEDENCE));
            used_default = true;
        }
        sym.push(prec_id);
        return pp_tk;
    } else if (p.curr_is_keyword()) {
        auto tk = p.get_token_info().token();
        check_not_forbidden(tk.to_string_unescaped().c_str());
        sym.push(p.new_ast("ident", p.pos(), tk).m_id).push(0);
        p.next();
        return tk;
    } else {
        throw parser_error("invalid notation declaration, symbol expected", p.pos());
    }
}

static name parse_quoted_symbol_or_token(parser & p, ast_data & data, buffer<token_entry> & new_tokens) {
    bool dummy;
    return parse_quoted_symbol_or_token(p, data, new_tokens, dummy);
}

static pair<ast_id, expr> parse_notation_expr(parser & p, buffer<expr> const & locals) {
    auto pos = p.pos();
    expr r = p.parse_expr();
    ast_id id = p.get_id(r);
    r = abstract(r, locals.size(), locals.data());
    check_notation_expr(r, pos);
    return {id, r};
}

static ast_id parse_notation_local(parser & p, buffer<expr> & locals) {
    if (p.curr_is_identifier()) {
        name n = p.get_name_val();
        ast_id id = p.new_ast("ident", p.pos(), n).m_id;
        p.next();
        expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
        expr l = mk_local(n, local_type); // remark: the type doesn't matter
        p.add_local(l);
        locals.push_back(l);
        return id;
    } else {
        throw parser_error("invalid notation declaration, identifier expected", p.pos());
    }
}

static unsigned get_precedence(environment const & env, buffer<token_entry> const & new_tokens, name const & token) {
    std::string token_str = token.to_string_unescaped();
    for (auto const & e : new_tokens) {
        if (e.m_token == token_str)
            return *e.m_prec;
    }
    auto prec = get_expr_precedence(get_token_table(env), token_str.c_str());
    if (prec)
        return *prec;
    else
        return 0;
}

static action parse_action(parser & p, ast_data & parent, name const & prev_token, unsigned default_prec,
                           buffer<expr> & locals, buffer<token_entry> & new_tokens) {
    if (p.curr_is_token(get_colon_tk())) {
        p.next();
        if (p.curr_is_numeral() || p.curr_is_token_or_id(get_max_tk())) {
            ast_id id; unsigned prec;
            std::tie(id, prec) = parse_precedence(p);
            parent.push(id);
            return mk_expr_action(prec);
        } else if (p.curr_is_token_or_id(get_prev_tk())) {
            parent.push(p.new_ast(get_prev_tk(), p.pos()).m_id);
            p.next();
            return mk_expr_action(get_precedence(p.env(), new_tokens, prev_token));
        } else if (p.curr_is_token_or_id(get_scoped_tk())) {
            parent.push(p.new_ast(get_scoped_tk(), p.pos()).push(0).push(0).m_id);
            p.next();
            return mk_scoped_expr_action(mk_var(0));
        } else {
            p.check_token_next(get_lparen_tk(), "invalid notation declaration, '(', numeral or 'scoped' expected");
            if (p.curr_is_token_or_id(get_foldl_tk()) || p.curr_is_token_or_id(get_foldr_tk())) {
                bool is_fold_right = p.curr_is_token_or_id(get_foldr_tk());
                auto& fold = p.new_ast(is_fold_right ? get_foldr_tk() : get_foldl_tk(), p.pos());
                parent.push(fold.m_id);
                p.next();
                ast_id id; optional<unsigned> prec;
                std::tie(id, prec) = parse_optional_precedence(p);
                fold.push(id);
                name sep  = parse_quoted_symbol_or_token(p, fold, new_tokens);
                auto& sc = p.new_ast("scope", p.pos());
                fold.push(sc.m_id);
                expr rec;
                {
                    parser::local_scope scope(p);
                    p.check_token_next(get_lparen_tk(), "invalid fold notation argument, '(' expected");
                    sc.push(parse_notation_local(p, locals));
                    sc.push(parse_notation_local(p, locals));
                    p.check_token_next(get_comma_tk(),  "invalid fold notation argument, ',' expected");
                    std::tie(id, rec) = parse_notation_expr(p, locals);
                    sc.push(id);
                    p.check_token_next(get_rparen_tk(), "invalid fold notation argument, ')' expected");
                    locals.pop_back();
                    locals.pop_back();
                }
                optional<expr> ini; id = 0;
                if (!p.curr_is_token(get_rparen_tk()) && !p.curr_is_quoted_symbol())
                    std::tie(id, ini) = parse_notation_expr(p, locals);
                fold.push(id);
                optional<name> terminator;
                if (p.curr_is_token(get_rparen_tk()))
                    fold.push(0);
                else
                    terminator = parse_quoted_symbol_or_token(p, fold, new_tokens);
                p.check_token_next(get_rparen_tk(), "invalid fold notation argument, ')' expected");
                return mk_exprs_action(sep, rec, ini, terminator, is_fold_right, prec ? *prec : 0);
            } else if (p.curr_is_token_or_id(get_scoped_tk())) {
                auto& sc = p.new_ast(get_scoped_tk(), p.pos());
                parent.push(sc.m_id);
                p.next();
                ast_id id; optional<unsigned> prec;
                std::tie(id, prec) = parse_optional_precedence(p);
                sc.push(id);
                auto& sc1 = p.new_ast("scope", p.pos());
                sc.push(sc1.m_id);
                expr rec;
                {
                    parser::local_scope scope(p);
                    sc1.push(parse_notation_local(p, locals));
                    p.check_token_next(get_comma_tk(),  "invalid scoped notation argument, ',' expected");
                    std::tie(id, rec) = parse_notation_expr(p, locals);
                    sc1.push(id);
                    locals.pop_back();
                }
                p.check_token_next(get_rparen_tk(), "invalid scoped notation argument, ')' expected");
                return mk_scoped_expr_action(rec, prec ? *prec : 0);
            } else {
                throw parser_error("invalid notation declaration, 'foldl', 'foldr' or 'scoped' expected", p.pos());
            }
        }
    } else {
        parent.push(0);
        return mk_expr_action(default_prec);
    }
}

/**
   \brief If the action for token \c tk in parse table \c pt is an Expr action,
   then return its precedence. We use this value as the default precedence
   when the user does not provide it. The idea is to minimize conflict with existing
   notation.
*/
static unsigned get_default_prec(optional<parse_table> const & pt, name const & tk) {
    if (!pt)
        return LEAN_DEFAULT_PRECEDENCE;
    if (auto ls = pt->find(tk)) {
        for (auto at : ls) {
            if (at.first.get_action().kind() == notation::action_kind::Expr)
                return at.first.get_action().rbp();
        }
    }
    return LEAN_DEFAULT_PRECEDENCE;
}

/** \brief Given a parsing table a \c pt and transition \c new_trans, if \c new_trans is a
    transition in \c pt, then return the successor table */
static optional<parse_table> find_match(optional<parse_table> const & pt, transition const & new_trans) {
    if (pt) {
        if (auto ls = pt->find(new_trans.get_token())) {
            for (auto at : ls) {
                if (new_trans.get_action().is_equal(at.first.get_action()))
                    return optional<parse_table>(at.second);
            }
        }
    }
    return optional<parse_table>();
}

/** \brief Lift parse_table::find method to optional<parse_table> */
static list<pair<transition, parse_table>> find_next(optional<parse_table> const & pt, name const & tk) {
    if (pt)
        return pt->find(tk);
    else
        return list<pair<transition, parse_table>>();
}

static pair<ast_id, unsigned> parse_binders_rbp(parser & p) {
    if (p.curr_is_token(get_colon_tk())) {
        p.next();
        return parse_precedence(p);
    } else {
        return {0, 0};
    }
}

static transition parse_transition(parser & p, ast_data & data, optional<parse_table> const & pt, name const & tk,
                                   buffer<expr> & locals, buffer<token_entry> & new_tokens, name const & pp_tk) {
    if (p.curr_is_token_or_id(get_binder_tk())) {
        auto& b = p.new_ast(get_binder_tk(), p.pos());
        p.next();
        ast_id id; unsigned rbp;
        std::tie(id, rbp) = parse_binders_rbp(p);
        data.push(b.push(id).m_id);
        return transition(tk, mk_binder_action(rbp), pp_tk);
    } else if (p.curr_is_token_or_id(get_binders_tk())) {
        auto& b = p.new_ast(get_binders_tk(), p.pos());
        p.next();
        ast_id id; unsigned rbp;
        std::tie(id, rbp) = parse_binders_rbp(p);
        data.push(b.push(id).m_id);
        return transition(tk, mk_binders_action(rbp), pp_tk);
    } else if (p.curr_is_identifier()) {
        unsigned default_prec = get_default_prec(pt, tk);
        name n   = p.get_name_val();
        auto& v = p.new_ast("var", p.pos()).push(p.new_ast("ident", p.pos(), n).m_id);
        data.push(v.m_id);
        p.next();
        action a = parse_action(p, v, tk, default_prec, locals, new_tokens);
        expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
        expr l = mk_local(n, local_type);
        p.add_local(l);
        locals.push_back(l);
        return transition(tk, a, pp_tk);
    } else if (p.curr_is_quoted_symbol() || p.curr_is_keyword() ||
               p.curr_is_token(get_assign_tk()) || p.curr_is_command() || p.curr_is_eof()) {
        return transition(tk, mk_skip_action(), pp_tk);
    } else {
        throw parser_error("invalid notation declaration, quoted-symbol, identifier, "
                           "'binder', 'binders' expected", p.pos());
    }
}

static notation_entry parse_notation_core(parser & p, ast_data & parent, bool overload, notation_entry_group grp, buffer<token_entry> & new_tokens, bool parse_only,
                                          unsigned priority) {
    buffer<expr>       locals;
    buffer<transition> ts;
    parser::local_scope scope(p);
    bool is_nud = true;
    optional<parse_table> pt;
    optional<parse_table> reserved_pt;
    auto notation_name = parse_optional_name(p);
    parent.push(notation_name.first);
    auto& args = p.new_ast("args", p.pos());
    parent.push(args.m_id);
    if (p.curr_is_numeral()) {
        lean_assert(p.curr_is_numeral());
        mpz num = p.get_num_val().get_numerator();
        args.push(p.new_ast("nat", p.pos(), num.to_string()).m_id);
        p.next();
        p.check_token_next(get_assign_tk(), "invalid numeral notation, `:=` expected");
        auto e_pos = p.pos();
        expr e     = p.parse_expr();
        parent.push(p.get_id(e));
        check_notation_expr(e, e_pos);
        return notation_entry(num, e, overload, parse_only);
    } else if (p.curr_is_identifier()) {
        ast_id id = parse_notation_local(p, locals);
        args.push(p.new_ast("var", p.ast_pos(id)).push(id).push(0).m_id);
        is_nud = false;
        pt = get_led_table(p.env());
        if (grp != notation_entry_group::Reserve)
            reserved_pt = get_reserved_led_table(p.env());
    } else {
        pt = get_nud_table(p.env());
        if (grp != notation_entry_group::Reserve)
            reserved_pt = get_reserved_nud_table(p.env());
    }
    while ((grp != notation_entry_group::Reserve && !p.curr_is_token(get_assign_tk())) ||
           (grp == notation_entry_group::Reserve && !p.curr_is_command() && !p.curr_is_eof())) {
        bool used_default = false;
        name pp_tk = parse_quoted_symbol_or_token(p, args, new_tokens, used_default).to_string_unescaped();
        name tk = utf8_trim(pp_tk.to_string_unescaped());
        if (auto at = find_next(reserved_pt, tk)) {
            // Remark: we are ignoring multiple actions in the reserved notation table
            transition const & trans = head(at).first;
            action const & a = trans.get_action();
            reserved_pt      = head(at).second;
            if (!p.curr_is_quoted_symbol())
                pp_tk = trans.get_pp_token();
            switch (a.kind()) {
            case notation::action_kind::Skip:
                if (!p.curr_is_quoted_symbol() && !p.curr_is_keyword() && !p.curr_is_token(get_assign_tk())) {
                    if (g_allow_local && !p.curr_is_token_or_id(get_binders_tk())) {
                        ts.push_back(parse_transition(p, args, pt, tk, locals, new_tokens, pp_tk));
                        break;
                    }
                    auto pos = p.pos();
                    p.check_token_or_id_next(get_binders_tk(),
                                             "invalid notation declaration, quoted-symbol, keyword or `:=` expected "
                                             "(declaration prefix matches reserved notation)");
                    args.push(p.new_ast(get_binders_tk(), pos).push(0).m_id);
                }
                ts.push_back(transition(tk, a, pp_tk));
                break;
            case notation::action_kind::Binder: {
                if (g_allow_local && !p.curr_is_token_or_id(get_binder_tk())) {
                    ts.push_back(parse_transition(p, args, pt, tk, locals, new_tokens, pp_tk));
                    break;
                }
                auto pos = p.pos();
                p.check_token_or_id_next(get_binder_tk(),
                                         "invalid notation declaration, 'binder' expected "
                                         "(declaration prefix matches reserved notation)");
                args.push(p.new_ast(get_binder_tk(), pos).push(0).m_id);
                ts.push_back(transition(tk, a, pp_tk));
                break;
            }
            case notation::action_kind::Binders: {
                if (g_allow_local && !p.curr_is_token_or_id(get_binders_tk())) {
                    ts.push_back(parse_transition(p, args, pt, tk, locals, new_tokens, pp_tk));
                    break;
                }
                auto pos = p.pos();
                p.check_token_or_id_next(get_binders_tk(),
                                         "invalid notation declaration, 'binders' expected "
                                         "(declaration prefix matches reserved notation)");
                args.push(p.new_ast(get_binders_tk(), pos).push(0).m_id);
                ts.push_back(transition(tk, a, pp_tk));
                break;
            }
            case notation::action_kind::Expr: case notation::action_kind::Exprs: case notation::action_kind::ScopedExpr:
            case notation::action_kind::Ext: {
                if (g_allow_local && !p.curr_is_identifier()) {
                    ts.push_back(parse_transition(p, args, pt, tk, locals, new_tokens, pp_tk));
                    break;
                }
                ast_id id; name n;
                std::tie(id, n) = p.check_id_next("invalid notation declaration, identifier expected "
                                                  "(declaration prefix matches reserved notation)");
                auto& v = p.new_ast("var", p.pos()).push(id);
                args.push(v.m_id);
                if (p.curr_is_token(get_colon_tk())) {
                    if (g_allow_local) {
                        unsigned default_prec = get_default_prec(pt, tk);
                        action a = parse_action(p, v, tk, default_prec, locals, new_tokens);
                        expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
                        expr l = mk_local(n, local_type);
                        p.add_local(l);
                        locals.push_back(l);
                        ts.push_back(transition(tk, a, pp_tk));
                        break;
                    } else {
                        throw parser_error("invalid notation declaration, invalid ':' occurrence "
                                           "(declaration prefix matches reserved notation)", p.pos());
                    }
                } else {
                    v.push(0);
                    expr local_type = mk_Prop(); // type used in notation local declarations, it is irrelevant
                    expr l = mk_local(n, local_type);
                    p.add_local(l);
                    locals.push_back(l);
                    ts.push_back(transition(tk, a, pp_tk));
                    break;
                }
            }}
        } else {
            reserved_pt = optional<parse_table>();
            ts.push_back(parse_transition(p, args, pt, tk, locals, new_tokens, pp_tk));
        }
        // for leading tokens where binding power was not set, we set it to max
        if (is_nud && used_default && ts.size() == 1) {
            lean_assert(!new_tokens.empty());
            new_tokens.back().m_prec = get_max_prec();
        }
        pt = find_match(pt, ts.back());
    }
    expr n;
    if (grp == notation_entry_group::Reserve) {
        // reserve notation commands do not have a denotation
        lean_assert(p.curr_is_command() || p.curr_is_eof());
        parent.push(0);
        expr dummy = mk_Prop(); // any expression without free variables will do
        n = dummy;
    } else {
        lean_assert(p.curr_is_token(get_assign_tk()));
        p.next();
        if (ts.empty())
            throw parser_error("invalid notation declaration, empty notation is not allowed", p.pos());
        ast_id id;
        std::tie(id, n) = parse_notation_expr(p, locals);
        parent.push(id);
    }
    notation_entry entry(is_nud, to_list(ts.begin(), ts.end()), n, overload, priority, grp, parse_only, notation_name.second);
    check_notation_name(p.env(), grp, parent.m_start, entry.get_name(), notation_name.second.is_anonymous());
    return entry;
}

bool curr_is_notation_decl(parser & p) {
    return
        p.curr_is_token(get_infix_tk()) || p.curr_is_token(get_infixl_tk()) || p.curr_is_token(get_infixr_tk()) ||
        p.curr_is_token(get_postfix_tk()) || p.curr_is_token(get_prefix_tk()) || p.curr_is_token(get_notation_tk());
}

static notation_entry parse_notation(parser & p, ast_data & parent, bool overload, notation_entry_group grp, buffer<token_entry> & new_tokens,
                                     bool allow_local) {
    bool parse_only   = false;
    unsigned priority = LEAN_DEFAULT_NOTATION_PRIORITY;
    flet<bool> set_allow_local(g_allow_local, allow_local);
    if (p.curr_is_token(get_infix_tk()) || p.curr_is_token(get_infixl_tk())) {
        p.next();
        return parse_mixfix_notation(p, parent, mixfix_kind::infixl, overload, grp, new_tokens, parse_only, priority);
    } else if (p.curr_is_token(get_infixr_tk())) {
        p.next();
        return parse_mixfix_notation(p, parent, mixfix_kind::infixr, overload, grp, new_tokens, parse_only, priority);
    } else if (p.curr_is_token(get_postfix_tk())) {
        p.next();
        return parse_mixfix_notation(p, parent, mixfix_kind::postfix, overload, grp, new_tokens, parse_only, priority);
    } else if (p.curr_is_token(get_prefix_tk())) {
        p.next();
        return parse_mixfix_notation(p, parent, mixfix_kind::prefix, overload, grp, new_tokens, parse_only, priority);
    } else if (p.curr_is_token(get_notation_tk())) {
        p.next();
        return parse_notation_core(p, parent, overload, grp, new_tokens, parse_only, priority);
    } else {
        throw parser_error("invalid notation, 'infix', 'infixl', 'infixr', 'prefix', "
                           "'postfix' or 'notation' expected", p.pos());
    }
}

notation_entry parse_notation(parser & p, ast_data & parent, bool overload, buffer<token_entry> & new_tokens, bool allow_local) {
    notation_entry_group grp = notation_entry_group::Main;
    return parse_notation(p, parent, overload, grp, new_tokens, allow_local);
}

static char g_reserved_chars[] = {',', 0};

static void check_token(char const * tk) {
    if (!tk || !*tk)
        throw exception("invalid null token");
    if (tk[0] == '(')
        throw exception(sstream() << "invalid token `" << tk << "`, it starts with '('");
    unsigned sz = strlen(tk);
    if (tk[sz-1] == ')')
        throw exception(sstream() << "invalid token `" << tk << "`, it ends with ')'");
    while (tk && *tk) {
        unsigned sz = get_utf8_size(*tk);
        if (sz == 0) {
            throw exception(sstream() << "invalid token `" << tk << "`, contains invalid utf-8 character");
        } else if (sz > 1) {
            // multi-size unicode character
            for (unsigned i = 0; i < sz; i++) {
                if (!*tk)
                    throw exception(sstream() << "invalid token `" << tk << "`, contains invalid utf-8 character");
                ++tk;
            }
        } else {
            auto it = g_reserved_chars;
            while (*it) {
                if (*tk == *it)
                    throw exception(sstream() << "invalid token `" << tk
                                    << "`, it contains reserved character `" << *it << "`");
                ++it;
            }
            ++tk;
        }
    }
}

static environment add_user_token(environment const & env, token_entry const & e, bool persistent) {
    check_token(e.m_token.c_str());
    return add_token(env, e, persistent);
}

static environment add_user_token(environment const & env, char const * val, unsigned prec) {
    check_token(val);
    return add_token(env, val, prec);
}

struct notation_modifiers {
    bool     m_parse_only;
    unsigned m_priority;
    notation_modifiers():m_parse_only(false), m_priority(LEAN_DEFAULT_NOTATION_PRIORITY) {}
    void parse(parser & p, ast_data & parent) {
        auto pos = p.pos();
        decl_attributes attrs;
        parent.push(attrs.parse(p));
        for (auto const & entry : attrs.get_entries()) {
            if (entry.m_attr->get_name() == "parsing_only")
                m_parse_only = true;
            else
                throw parser_error(sstream() << "invalid notation: unexpected attribute ["
                                             << entry.m_attr->get_name() << "]", pos);
        }
        if (attrs.get_priority())
            m_priority = *attrs.get_priority();
    }
};

static environment notation_cmd_core(parser & p, ast_data & parent, ast_id local, bool overload, notation_entry_group grp, bool persistent) {
    notation_modifiers mods;
    parent.push(local);
    mods.parse(p, parent);
    flet<bool> set_allow_local(g_allow_local, !persistent);
    environment env = p.env();
    buffer<token_entry> new_tokens;
    auto ne = parse_notation_core(p, parent, overload, grp, new_tokens, mods.m_parse_only, mods.m_priority);
    for (auto const & te : new_tokens)
        env = add_user_token(env, te, persistent);
    env = add_notation(env, ne, persistent);
    return env;
}

static environment mixfix_cmd(parser & p, ast_data & parent, ast_id local, mixfix_kind k, bool overload, notation_entry_group grp, bool persistent) {
    notation_modifiers mods;
    parent.push(local);
    mods.parse(p, parent);
    flet<bool> set_allow_local(g_allow_local, !persistent);
    auto nt = parse_mixfix_notation(p, parent, k, overload, grp, mods.m_parse_only, mods.m_priority);
    environment env = p.env();
    if (nt.second)
        env = add_user_token(env, *nt.second, persistent);
    env = add_notation(env, nt.first, persistent);
    return env;
}

static environment notation_cmd(parser & p, ast_id & cmd_id) {
    bool overload = true;
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = true;
    return notation_cmd_core(p, p.get_ast(cmd_id), 0, overload, grp, persistent);
}

static environment infixl_cmd(parser & p, ast_id & cmd_id) {
    bool overload = true;
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = true;
    return mixfix_cmd(p, p.get_ast(cmd_id), 0, mixfix_kind::infixl, overload, grp, persistent);
}

static environment infixr_cmd(parser & p, ast_id & cmd_id) {
    bool overload = true;
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = true;
    return mixfix_cmd(p, p.get_ast(cmd_id), 0, mixfix_kind::infixr, overload, grp, persistent);
}

static environment postfix_cmd(parser & p, ast_id & cmd_id) {
    bool overload = true;
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = true;
    return mixfix_cmd(p, p.get_ast(cmd_id), 0, mixfix_kind::postfix, overload, grp, persistent);
}

static environment prefix_cmd(parser & p, ast_id & cmd_id) {
    bool overload = true;
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = true;
    return mixfix_cmd(p, p.get_ast(cmd_id), 0, mixfix_kind::prefix, overload, grp, persistent);
}

// auxiliary procedure used by local_notation_cmd and reserve_cmd
static environment dispatch_notation_cmd(parser & p, ast_data & parent, bool overload, notation_entry_group grp, bool persistent) {
    ast_id id = p.new_ast(parent.m_type, p.pos()).m_id;
    parent.m_type = p.get_token_info().value();
    if (p.curr_is_token(get_notation_tk())) {
        p.next();
        return notation_cmd_core(p, parent, id, overload, grp, persistent);
    } else if (p.curr_is_token(get_infixl_tk())) {
        p.next();
        return mixfix_cmd(p, parent, id, mixfix_kind::infixl, overload, grp, persistent);
    } else if (p.curr_is_token(get_infix_tk())) {
        p.next();
        return mixfix_cmd(p, parent, id, mixfix_kind::infixl, overload, grp, persistent);
    } else if (p.curr_is_token(get_infixr_tk())) {
        p.next();
        return mixfix_cmd(p, parent, id, mixfix_kind::infixr, overload, grp, persistent);
    } else if (p.curr_is_token(get_prefix_tk())) {
        p.next();
        return mixfix_cmd(p, parent, id, mixfix_kind::prefix, overload, grp, persistent);
    } else if (p.curr_is_token(get_postfix_tk())) {
        p.next();
        return mixfix_cmd(p, parent, id, mixfix_kind::postfix, overload, grp, persistent);
    } else {
        throw parser_error("invalid local/reserve notation, 'infix', 'infixl', 'infixr', 'prefix', "
                           "'postfix' or 'notation' expected", p.pos());
    }
}

environment local_notation_cmd(parser & p, ast_id & cmd_id) {
    parser::in_notation_ctx ctx(p);
    bool overload   = false; // REMARK: local notation override global one
    notation_entry_group grp = notation_entry_group::Main;
    bool persistent = false;
    return dispatch_notation_cmd(p, p.get_ast(cmd_id), overload, grp, persistent);
}

static environment reserve_cmd(parser & p, ast_id & cmd_id) {
    parser::in_notation_ctx ctx(p);
    bool overload   = false;
    notation_entry_group grp = notation_entry_group::Reserve;
    bool persistent = true;
    return dispatch_notation_cmd(p, p.get_ast(cmd_id), overload, grp, persistent);
}

static environment precedence_cmd(parser & p, ast_id & cmd_id) {
    auto& data = p.get_ast(cmd_id);
    std::string tk = parse_symbol(p, data, "invalid precedence declaration, quoted symbol or identifier expected");
    p.check_token_next(get_colon_tk(), "invalid precedence declaration, ':' expected");
    ast_id id; unsigned prec;
    std::tie(id, prec) = parse_precedence(p);
    data.push(id);
    return add_user_token(p.env(), tk.c_str(), prec);
}

void register_notation_cmds(cmd_table & r) {
    add_cmd(r, cmd_info("precedence",      "set token left binding power", precedence_cmd));
    add_cmd(r, cmd_info("infixl",          "declare a new infix (left) notation", infixl_cmd));
    add_cmd(r, cmd_info("infix",           "declare a new infix (left) notation", infixl_cmd));
    add_cmd(r, cmd_info("infixr",          "declare a new infix (right) notation", infixr_cmd));
    add_cmd(r, cmd_info("postfix",         "declare a new postfix notation", postfix_cmd));
    add_cmd(r, cmd_info("prefix",          "declare a new prefix notation", prefix_cmd));
    add_cmd(r, cmd_info("notation",        "declare a new notation", notation_cmd));
    add_cmd(r, cmd_info("reserve",         "reserve notation", reserve_cmd));
}

bool is_notation_cmd(name const & n) {
    return
        n == get_infix_tk() || n == get_infixl_tk() || n == get_infixr_tk() || n == get_postfix_tk() ||
        n == get_prefix_tk() || n == get_notation_tk() || n == get_precedence_tk();
}

void initialize_notation_cmd() {
    register_system_attribute(basic_attribute::with_check(
            "parsing_only", "parsing-only notation declaration",
            [](environment const &, name const &, bool) {
                throw exception("invalid '[parsing_only]' attribute, can only be used in notation declarations");
            }));
}
void finalize_notation_cmd() {
}
}