1053 lines
45 KiB
C++
1053 lines
45 KiB
C++
/*
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <algorithm>
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#include "util/sstream.h"
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#include "kernel/type_checker.h"
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#include "kernel/abstract.h"
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#include "kernel/replace_fn.h"
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#include "kernel/for_each_fn.h"
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#include "library/scoped_ext.h"
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#include "library/aliases.h"
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#include "library/num.h"
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#include "library/private.h"
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#include "library/normalize.h"
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#include "library/protected.h"
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#include "library/placeholder.h"
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#include "library/locals.h"
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#include "library/explicit.h"
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#include "library/reducible.h"
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#include "library/coercion.h"
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#include "library/class.h"
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#include "library/unfold_macros.h"
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#include "library/definitional/equations.h"
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#include "frontends/lean/parser.h"
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#include "frontends/lean/util.h"
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#include "frontends/lean/tokens.h"
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namespace lean {
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static environment declare_universe(parser & p, environment env, name const & n, bool local) {
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if (in_context(env) || local) {
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p.add_local_level(n, mk_param_univ(n), local);
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} else {
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name const & ns = get_namespace(env);
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name full_n = ns + n;
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env = module::add_universe(env, full_n);
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if (!ns.is_anonymous())
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env = add_level_alias(env, n, full_n);
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}
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return env;
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}
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static environment universes_cmd_core(parser & p, bool local) {
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if (!p.curr_is_identifier())
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throw parser_error("invalid 'universes' command, identifier expected", p.pos());
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environment env = p.env();
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while (p.curr_is_identifier()) {
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name n = p.get_name_val();
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p.next();
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env = declare_universe(p, env, n, local);
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}
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return env;
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}
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static environment universe_cmd(parser & p) {
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if (p.curr_is_token(get_variables_tk())) {
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p.next();
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return universes_cmd_core(p, true);
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} else {
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bool local = false;
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if (p.curr_is_token(get_variable_tk())) {
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p.next();
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local = true;
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}
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name n = p.check_id_next("invalid 'universe' command, identifier expected");
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return declare_universe(p, p.env(), n, local);
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}
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}
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static environment universes_cmd(parser & p) {
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return universes_cmd_core(p, false);
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}
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bool parse_univ_params(parser & p, buffer<name> & ps) {
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if (p.curr_is_token(get_llevel_curly_tk())) {
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p.next();
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while (!p.curr_is_token(get_rcurly_tk())) {
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name l = p.check_id_next("invalid universe parameter, identifier expected");
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p.add_local_level(l, mk_param_univ(l));
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ps.push_back(l);
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}
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p.next();
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return true;
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} else{
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return false;
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}
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}
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void update_univ_parameters(buffer<name> & ls_buffer, name_set const & found, parser const & p) {
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unsigned old_sz = ls_buffer.size();
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found.for_each([&](name const & n) {
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if (std::find(ls_buffer.begin(), ls_buffer.begin() + old_sz, n) == ls_buffer.begin() + old_sz)
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ls_buffer.push_back(n);
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});
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std::sort(ls_buffer.begin(), ls_buffer.end(), [&](name const & n1, name const & n2) {
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return p.get_local_level_index(n1) < p.get_local_level_index(n2);
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});
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}
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enum class variable_kind { Constant, Parameter, Variable, Axiom };
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static void check_parameter_type(parser & p, name const & n, expr const & type, pos_info const & pos) {
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for_each(type, [&](expr const & e, unsigned) {
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if (is_local(e) && p.is_local_variable(e))
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throw parser_error(sstream() << "invalid parameter declaration '" << n << "', it depends on " <<
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"variable '" << local_pp_name(e) << "'", pos);
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return true;
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});
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}
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static environment declare_var(parser & p, environment env,
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name const & n, level_param_names const & ls, expr const & type,
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variable_kind k, optional<binder_info> const & _bi, pos_info const & pos) {
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binder_info bi;
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if (_bi) bi = *_bi;
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if (k == variable_kind::Parameter || k == variable_kind::Variable) {
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if (k == variable_kind::Parameter) {
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check_in_context_or_section(p);
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check_parameter_type(p, n, type, pos);
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}
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if (p.get_local(n))
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throw parser_error(sstream() << "invalid parameter/variable declaration, '"
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<< n << "' has already been declared", pos);
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name u = p.mk_fresh_name();
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expr l = p.save_pos(mk_local(u, n, type, bi), pos);
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if (k == variable_kind::Parameter)
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p.add_parameter(n, l);
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else
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p.add_local_expr(n, l, k == variable_kind::Variable);
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return env;
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} else {
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lean_assert(k == variable_kind::Constant || k == variable_kind::Axiom);
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name const & ns = get_namespace(env);
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name full_n = ns + n;
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expr new_type = unfold_untrusted_macros(env, type);
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if (k == variable_kind::Axiom) {
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env = module::add(env, check(env, mk_axiom(full_n, ls, new_type)));
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p.add_decl_index(full_n, pos, get_axiom_tk(), new_type);
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} else {
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env = module::add(env, check(env, mk_constant_assumption(full_n, ls, new_type)));
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p.add_decl_index(full_n, pos, get_variable_tk(), new_type);
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}
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if (!ns.is_anonymous())
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env = add_expr_alias(env, n, full_n);
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return env;
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}
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}
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/** \brief If we are in a section, then add the new local levels to it. */
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static void update_local_levels(parser & p, level_param_names const & new_ls, bool is_variable) {
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for (auto const & l : new_ls)
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p.add_local_level(l, mk_param_univ(l), is_variable);
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}
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optional<binder_info> parse_binder_info(parser & p, variable_kind k) {
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optional<binder_info> bi = p.parse_optional_binder_info();
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if (bi && k != variable_kind::Parameter && k != variable_kind::Variable)
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parser_error("invalid binder annotation, it can only be used to declare variables/parameters", p.pos());
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return bi;
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}
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static void check_variable_kind(parser & p, variable_kind k) {
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if (in_context(p.env())) {
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if (k == variable_kind::Axiom || k == variable_kind::Constant)
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throw parser_error("invalid declaration, 'constant/axiom' cannot be used in contexts",
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p.pos());
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} else if (!in_section(p.env()) && !in_context(p.env()) && k == variable_kind::Parameter) {
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throw parser_error("invalid declaration, 'parameter/hypothesis/conjecture' "
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"can only be used in contexts and sections", p.pos());
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}
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}
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static environment variable_cmd_core(parser & p, variable_kind k) {
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check_variable_kind(p, k);
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auto pos = p.pos();
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optional<binder_info> bi = parse_binder_info(p, k);
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name n = p.check_id_next("invalid declaration, identifier expected");
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buffer<name> ls_buffer;
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if (p.curr_is_token(get_llevel_curly_tk()) && (k == variable_kind::Parameter || k == variable_kind::Variable))
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throw parser_error("invalid declaration, only constants/axioms can be universe polymorphic", p.pos());
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optional<parser::local_scope> scope1;
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if (k == variable_kind::Constant || k == variable_kind::Axiom)
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scope1.emplace(p);
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parse_univ_params(p, ls_buffer);
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expr type;
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if (!p.curr_is_token(get_colon_tk())) {
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buffer<expr> ps;
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unsigned rbp = 0;
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auto lenv = p.parse_binders(ps, rbp);
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p.check_token_next(get_colon_tk(), "invalid declaration, ':' expected");
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type = p.parse_scoped_expr(ps, lenv);
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type = Pi(ps, type, p);
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} else {
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p.next();
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type = p.parse_expr();
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}
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p.parse_close_binder_info(bi);
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level_param_names ls;
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if (ls_buffer.empty()) {
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ls = to_level_param_names(collect_univ_params(type));
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} else {
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update_univ_parameters(ls_buffer, collect_univ_params(type), p);
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ls = to_list(ls_buffer.begin(), ls_buffer.end());
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}
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level_param_names new_ls;
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list<expr> ctx = p.locals_to_context();
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std::tie(type, new_ls) = p.elaborate_type(type, ctx);
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if (k == variable_kind::Variable || k == variable_kind::Parameter)
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update_local_levels(p, new_ls, k == variable_kind::Variable);
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return declare_var(p, p.env(), n, append(ls, new_ls), type, k, bi, pos);
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}
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static environment variable_cmd(parser & p) {
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return variable_cmd_core(p, variable_kind::Variable);
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}
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static environment axiom_cmd(parser & p) {
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return variable_cmd_core(p, variable_kind::Axiom);
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}
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static environment constant_cmd(parser & p) {
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return variable_cmd_core(p, variable_kind::Constant);
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}
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static environment parameter_cmd(parser & p) {
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return variable_cmd_core(p, variable_kind::Parameter);
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}
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static environment variables_cmd_core(parser & p, variable_kind k) {
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check_variable_kind(p, k);
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auto pos = p.pos();
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environment env = p.env();
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while (true) {
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optional<binder_info> bi = parse_binder_info(p, k);
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buffer<name> ids;
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while (!p.curr_is_token(get_colon_tk())) {
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name id = p.check_id_next("invalid parameters declaration, identifier expected");
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ids.push_back(id);
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}
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p.next();
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optional<parser::local_scope> scope1;
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if (k == variable_kind::Constant || k == variable_kind::Axiom)
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scope1.emplace(p);
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expr type = p.parse_expr();
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p.parse_close_binder_info(bi);
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level_param_names ls = to_level_param_names(collect_univ_params(type));
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list<expr> ctx = p.locals_to_context();
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for (auto id : ids) {
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// Hack: to make sure we get different universe parameters for each parameter.
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// Alternative: elaborate once and copy types replacing universes in new_ls.
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level_param_names new_ls;
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expr new_type;
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std::tie(new_type, new_ls) = p.elaborate_type(type, ctx);
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if (k == variable_kind::Variable || k == variable_kind::Parameter)
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update_local_levels(p, new_ls, k == variable_kind::Variable);
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new_ls = append(ls, new_ls);
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env = declare_var(p, env, id, new_ls, new_type, k, bi, pos);
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}
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if (!p.curr_is_token(get_lparen_tk()) && !p.curr_is_token(get_lcurly_tk()) &&
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!p.curr_is_token(get_ldcurly_tk()) && !p.curr_is_token(get_lbracket_tk()))
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break;
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}
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return env;
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}
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static environment variables_cmd(parser & p) {
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return variables_cmd_core(p, variable_kind::Variable);
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}
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static environment parameters_cmd(parser & p) {
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return variables_cmd_core(p, variable_kind::Parameter);
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}
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static environment constants_cmd(parser & p) {
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return variables_cmd_core(p, variable_kind::Constant);
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}
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struct decl_attributes {
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bool m_def_only; // if true only definition attributes are allowed
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bool m_is_instance;
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bool m_is_coercion;
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bool m_is_reducible;
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bool m_is_irreducible;
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bool m_is_class;
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bool m_has_multiple_instances;
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optional<unsigned> m_priority;
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decl_attributes(bool def_only = true):m_priority() {
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m_def_only = def_only;
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m_is_instance = false;
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m_is_coercion = false;
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m_is_reducible = false;
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m_is_irreducible = false;
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m_is_class = false;
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m_has_multiple_instances = false;
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}
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optional<unsigned> parse_instance_priority(parser & p) {
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if (p.curr_is_token(get_priority_tk())) {
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p.next();
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auto pos = p.pos();
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environment env = open_priority_aliases(open_num_notation(p.env()));
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parser::local_scope scope(p, env);
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expr val = p.parse_expr();
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val = normalize(p.env(), val);
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if (optional<mpz> mpz_val = to_num(val)) {
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if (!mpz_val->is_unsigned_int())
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throw parser_error("invalid 'priority', argument does not fit in a machine integer", pos);
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p.check_token_next(get_rbracket_tk(), "invalid 'priority', ']' expected");
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return optional<unsigned>(mpz_val->get_unsigned_int());
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} else {
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throw parser_error("invalid 'priority', argument does not evaluate to a numeral", pos);
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}
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} else {
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return optional<unsigned>();
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}
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}
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void parse(parser & p) {
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while (true) {
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auto pos = p.pos();
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if (p.curr_is_token(get_instance_tk())) {
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m_is_instance = true;
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p.next();
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} else if (p.curr_is_token(get_coercion_tk())) {
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auto pos = p.pos();
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p.next();
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if (in_context(p.env()))
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throw parser_error("invalid '[coercion]' attribute, coercions cannot be defined in contexts", pos);
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m_is_coercion = true;
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} else if (p.curr_is_token(get_reducible_tk())) {
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if (m_is_irreducible)
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throw parser_error("invalid '[reducible]' attribute, '[irreducible]' was already provided", pos);
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m_is_reducible = true;
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p.next();
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} else if (p.curr_is_token(get_irreducible_tk())) {
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if (m_is_reducible)
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throw parser_error("invalid '[irreducible]' attribute, '[reducible]' was already provided", pos);
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m_is_irreducible = true;
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p.next();
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} else if (p.curr_is_token(get_class_tk())) {
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if (m_def_only)
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throw parser_error("invalid '[class]' attribute, definitions cannot be marked as classes", pos);
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m_is_class = true;
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p.next();
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} else if (p.curr_is_token(get_multiple_instances_tk())) {
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if (m_def_only)
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throw parser_error("invalid '[multiple-instances]' attribute, only classes can have this attribute", pos);
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m_has_multiple_instances = true;
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p.next();
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} else if (auto it = parse_instance_priority(p)) {
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m_priority = *it;
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if (!m_is_instance)
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throw parser_error("invalid '[priority]' attribute, declaration must be marked as an '[instance]'", pos);
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} else {
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break;
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}
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}
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}
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environment apply(environment env, io_state const & ios, name const & d, bool persistent) {
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if (m_is_instance) {
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if (m_priority) {
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#if defined(__GNUC__) && !defined(__CLANG__)
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#pragma GCC diagnostic ignored "-Wmaybe-uninitialized"
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#endif
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env = add_instance(env, d, *m_priority, persistent);
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} else {
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env = add_instance(env, d, persistent);
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}
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}
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if (m_is_coercion)
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env = add_coercion(env, d, ios, persistent);
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if (m_is_reducible)
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env = set_reducible(env, d, reducible_status::On, persistent);
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if (m_is_irreducible)
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env = set_reducible(env, d, reducible_status::Off, persistent);
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if (m_is_class)
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env = add_class(env, d, persistent);
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if (m_has_multiple_instances)
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env = mark_multiple_instances(env, d, persistent);
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return env;
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}
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};
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static void check_end_of_theorem(parser const & p) {
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if (!p.curr_is_command_like())
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throw parser_error("':=', '.', command, script, or end-of-file expected", p.pos());
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}
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static void erase_local_binder_info(buffer<expr> & ps) {
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for (expr & p : ps)
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p = update_local(p, binder_info());
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}
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static bool is_curr_with_or_comma(parser & p) {
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return p.curr_is_token(get_with_tk()) || p.curr_is_token(get_comma_tk());
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}
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/**
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For convenience, the left-hand-side of a recursive equation may contain
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undeclared variables.
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We use parser::undef_id_to_local_scope to force the parser to create a local constant for
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each undefined identifier.
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This method validates occurrences of these variables. They can only occur as an application
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or macro argument.
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*/
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static void validate_equation_lhs(parser const & p, expr const & lhs, buffer<expr> const & locals) {
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if (is_app(lhs)) {
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validate_equation_lhs(p, app_fn(lhs), locals);
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validate_equation_lhs(p, app_arg(lhs), locals);
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} else if (is_macro(lhs)) {
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for (unsigned i = 0; i < macro_num_args(lhs); i++)
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validate_equation_lhs(p, macro_arg(lhs, i), locals);
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} else if (!is_local(lhs)) {
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for_each(lhs, [&](expr const & e, unsigned) {
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if (is_local(e) &&
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std::any_of(locals.begin(), locals.end(), [&](expr const & local) {
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return mlocal_name(e) == mlocal_name(local);
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})) {
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throw parser_error(sstream() << "invalid occurrence of variable '" << mlocal_name(lhs) <<
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"' in the left-hand-side of recursive equation", p.pos_of(lhs));
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}
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return has_local(e);
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});
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}
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}
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/**
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\brief Merge multiple occurrences of a variable in the left-hand-side of a recursive equation.
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\see validate_equation_lhs
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*/
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static expr merge_equation_lhs_vars(expr const & lhs, buffer<expr> & locals) {
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expr_map<expr> m;
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unsigned j = 0;
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for (unsigned i = 0; i < locals.size(); i++) {
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unsigned k;
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for (k = 0; k < i; k++) {
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if (mlocal_name(locals[k]) == mlocal_name(locals[i])) {
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m.insert(mk_pair(locals[i], locals[k]));
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break;
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}
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}
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if (k == i) {
|
|
locals[j] = locals[i];
|
|
j++;
|
|
}
|
|
}
|
|
if (j == locals.size())
|
|
return lhs;
|
|
locals.shrink(j);
|
|
return replace(lhs, [&](expr const & e) {
|
|
if (!has_local(e))
|
|
return some_expr(e);
|
|
if (is_local(e)) {
|
|
auto it = m.find(e);
|
|
if (it != m.end())
|
|
return some_expr(it->second);
|
|
}
|
|
return none_expr();
|
|
});
|
|
}
|
|
|
|
static void throw_invalid_equation_lhs(name const & n, pos_info const & p) {
|
|
throw parser_error(sstream() << "invalid recursive equation, head symbol '"
|
|
<< n << "' in the left-hand-side does not correspond to function(s) being defined", p);
|
|
}
|
|
|
|
expr parse_equations(parser & p, name const & n, expr const & type, buffer<name> & auxs,
|
|
optional<local_environment> const & lenv, buffer<expr> const & ps,
|
|
pos_info const & def_pos) {
|
|
buffer<expr> eqns;
|
|
buffer<expr> fns;
|
|
{
|
|
parser::local_scope scope1(p, lenv);
|
|
for (expr const & param : ps)
|
|
p.add_local(param);
|
|
lean_assert(is_curr_with_or_comma(p));
|
|
fns.push_back(mk_local(n, type));
|
|
if (p.curr_is_token(get_with_tk())) {
|
|
while (p.curr_is_token(get_with_tk())) {
|
|
p.next();
|
|
auto pos = p.pos();
|
|
name g_name = p.check_id_next("invalid declaration, identifier expected");
|
|
p.check_token_next(get_colon_tk(), "invalid declaration, ':' expected");
|
|
expr g_type = p.parse_expr();
|
|
expr g = p.save_pos(mk_local(g_name, g_type), pos);
|
|
auxs.push_back(g_name);
|
|
fns.push_back(g);
|
|
}
|
|
}
|
|
p.check_token_next(get_comma_tk(), "invalid declaration, ',' expected");
|
|
for (expr const & fn : fns)
|
|
p.add_local(fn);
|
|
while (true) {
|
|
expr lhs;
|
|
unsigned prev_num_undef_ids = p.get_num_undef_ids();
|
|
buffer<expr> locals;
|
|
{
|
|
parser::undef_id_to_local_scope scope2(p);
|
|
auto lhs_pos = p.pos();
|
|
lhs = p.parse_expr();
|
|
expr lhs_fn = get_app_fn(lhs);
|
|
if (is_explicit(lhs_fn))
|
|
lhs_fn = get_explicit_arg(lhs_fn);
|
|
if (is_constant(lhs_fn))
|
|
throw_invalid_equation_lhs(const_name(lhs_fn), lhs_pos);
|
|
if (is_local(lhs_fn) && std::all_of(fns.begin(), fns.end(), [&](expr const & fn) { return fn != lhs_fn; }))
|
|
throw_invalid_equation_lhs(local_pp_name(lhs_fn), lhs_pos);
|
|
if (!is_local(lhs_fn))
|
|
throw parser_error("invalid recursive equation, head symbol in left-hand-side is not a constant", lhs_pos);
|
|
unsigned num_undef_ids = p.get_num_undef_ids();
|
|
for (unsigned i = prev_num_undef_ids; i < num_undef_ids; i++) {
|
|
locals.push_back(p.get_undef_id(i));
|
|
}
|
|
}
|
|
validate_equation_lhs(p, lhs, locals);
|
|
lhs = merge_equation_lhs_vars(lhs, locals);
|
|
auto assign_pos = p.pos();
|
|
p.check_token_next(get_assign_tk(), "invalid declaration, ':=' expected");
|
|
{
|
|
parser::local_scope scope2(p);
|
|
for (expr const & local : locals)
|
|
p.add_local(local);
|
|
expr rhs = p.parse_expr();
|
|
eqns.push_back(Fun(fns, Fun(locals, p.save_pos(mk_equation(lhs, rhs), assign_pos), p)));
|
|
}
|
|
if (!p.curr_is_token(get_comma_tk()))
|
|
break;
|
|
p.next();
|
|
}
|
|
}
|
|
if (p.curr_is_token(get_wf_tk())) {
|
|
auto pos = p.pos();
|
|
p.next();
|
|
expr R = p.save_pos(mk_expr_placeholder(), pos);
|
|
expr Hwf = p.parse_expr();
|
|
return p.save_pos(mk_equations(fns.size(), eqns.size(), eqns.data(), R, Hwf), def_pos);
|
|
} else {
|
|
return p.save_pos(mk_equations(fns.size(), eqns.size(), eqns.data()), def_pos);
|
|
}
|
|
}
|
|
|
|
/** \brief Use equations compiler infrastructure to implement match-with */
|
|
expr parse_match(parser & p, unsigned, expr const *, pos_info const & pos) {
|
|
expr t = p.parse_expr();
|
|
p.check_token_next(get_with_tk(), "invalid 'match' expression, 'with' expected");
|
|
buffer<expr> eqns;
|
|
expr fn = mk_local(p.mk_fresh_name(), "match", mk_expr_placeholder(), binder_info());
|
|
while (true) {
|
|
expr lhs;
|
|
unsigned prev_num_undef_ids = p.get_num_undef_ids();
|
|
buffer<expr> locals;
|
|
{
|
|
parser::undef_id_to_local_scope scope2(p);
|
|
auto lhs_pos = p.pos();
|
|
lhs = p.parse_expr();
|
|
lhs = p.mk_app(fn, lhs, lhs_pos);
|
|
unsigned num_undef_ids = p.get_num_undef_ids();
|
|
for (unsigned i = prev_num_undef_ids; i < num_undef_ids; i++) {
|
|
locals.push_back(p.get_undef_id(i));
|
|
}
|
|
}
|
|
validate_equation_lhs(p, lhs, locals);
|
|
lhs = merge_equation_lhs_vars(lhs, locals);
|
|
auto assign_pos = p.pos();
|
|
p.check_token_next(get_assign_tk(), "invalid 'match' expression, ':=' expected");
|
|
{
|
|
parser::local_scope scope2(p);
|
|
for (expr const & local : locals)
|
|
p.add_local(local);
|
|
expr rhs = p.parse_expr();
|
|
eqns.push_back(Fun(fn, Fun(locals, p.save_pos(mk_equation(lhs, rhs), assign_pos), p)));
|
|
}
|
|
if (!p.curr_is_token(get_comma_tk()))
|
|
break;
|
|
p.next();
|
|
}
|
|
p.check_token_next(get_end_tk(), "invalid 'match' expression, 'end' expected");
|
|
expr f = p.save_pos(mk_equations(1, eqns.size(), eqns.data()), pos);
|
|
return p.mk_app(f, t, pos);
|
|
}
|
|
|
|
// An Lean example is not really a definition, but we use the definition infrastructure to simulate it.
|
|
enum def_cmd_kind { Theorem, Definition, Example };
|
|
|
|
class definition_cmd_fn {
|
|
parser & m_p;
|
|
environment m_env;
|
|
def_cmd_kind m_kind;
|
|
bool m_is_opaque;
|
|
bool m_is_private;
|
|
bool m_is_protected;
|
|
pos_info m_pos;
|
|
|
|
name m_name;
|
|
decl_attributes m_attributes;
|
|
name m_real_name; // real name for this declaration
|
|
buffer<name> m_ls_buffer;
|
|
buffer<name> m_aux_decls; // user provided names for aux_decls
|
|
buffer<name> m_real_aux_names; // real names for aux_decls
|
|
buffer<expr> m_aux_types; // types of auxiliary decls
|
|
expr m_type;
|
|
expr m_value;
|
|
level_param_names m_ls;
|
|
pos_info m_end_pos;
|
|
|
|
expr m_pre_type;
|
|
expr m_pre_value;
|
|
|
|
bool is_definition() const { return m_kind == Definition; }
|
|
unsigned start_line() const { return m_pos.first; }
|
|
unsigned end_line() const { return m_end_pos.first; }
|
|
|
|
void parse_name() {
|
|
if (m_kind == Example)
|
|
m_name = m_p.mk_fresh_name();
|
|
else
|
|
m_name = m_p.check_id_next("invalid declaration, identifier expected");
|
|
}
|
|
|
|
void parse_type_value() {
|
|
// Parse universe parameters
|
|
parser::local_scope scope1(m_p);
|
|
parse_univ_params(m_p, m_ls_buffer);
|
|
|
|
// Parse modifiers
|
|
m_attributes.parse(m_p);
|
|
|
|
if (m_p.curr_is_token(get_assign_tk())) {
|
|
auto pos = m_p.pos();
|
|
m_p.next();
|
|
m_type = m_p.save_pos(mk_expr_placeholder(), pos);
|
|
m_value = m_p.parse_expr();
|
|
} else if (m_p.curr_is_token(get_colon_tk())) {
|
|
m_p.next();
|
|
auto pos = m_p.pos();
|
|
m_type = m_p.parse_expr();
|
|
if (is_curr_with_or_comma(m_p)) {
|
|
m_value = parse_equations(m_p, m_name, m_type, m_aux_decls, optional<local_environment>(), buffer<expr>(), m_pos);
|
|
} else if (!is_definition() && !m_p.curr_is_token(get_assign_tk())) {
|
|
check_end_of_theorem(m_p);
|
|
m_value = m_p.save_pos(mk_expr_placeholder(), pos);
|
|
} else {
|
|
m_p.check_token_next(get_assign_tk(), "invalid declaration, ':=' expected");
|
|
m_value = m_p.save_pos(m_p.parse_expr(), pos);
|
|
}
|
|
} else {
|
|
buffer<expr> ps;
|
|
optional<local_environment> lenv;
|
|
bool last_block_delimited = false;
|
|
lenv = m_p.parse_binders(ps, last_block_delimited);
|
|
auto pos = m_p.pos();
|
|
if (m_p.curr_is_token(get_colon_tk())) {
|
|
m_p.next();
|
|
m_type = m_p.parse_scoped_expr(ps, *lenv);
|
|
if (is_curr_with_or_comma(m_p)) {
|
|
m_value = parse_equations(m_p, m_name, m_type, m_aux_decls, lenv, ps, m_pos);
|
|
} else if (!is_definition() && !m_p.curr_is_token(get_assign_tk())) {
|
|
check_end_of_theorem(m_p);
|
|
m_value = m_p.save_pos(mk_expr_placeholder(), pos);
|
|
} else {
|
|
m_p.check_token_next(get_assign_tk(), "invalid declaration, ':=' expected");
|
|
m_value = m_p.parse_scoped_expr(ps, *lenv);
|
|
}
|
|
} else {
|
|
if (!last_block_delimited && !ps.empty() &&
|
|
!is_placeholder(mlocal_type(ps.back()))) {
|
|
throw parser_error("invalid declaration, ambiguous parameter declaration, "
|
|
"(solution: put parentheses around parameters)",
|
|
pos);
|
|
}
|
|
m_type = m_p.save_pos(mk_expr_placeholder(), m_p.pos());
|
|
m_p.check_token_next(get_assign_tk(), "invalid declaration, ':=' expected");
|
|
m_value = m_p.parse_scoped_expr(ps, *lenv);
|
|
}
|
|
m_type = Pi(ps, m_type, m_p);
|
|
erase_local_binder_info(ps);
|
|
m_value = Fun(ps, m_value, m_p);
|
|
}
|
|
m_end_pos = m_p.pos();
|
|
}
|
|
|
|
void mk_real_name() {
|
|
if (m_is_private) {
|
|
unsigned h = hash(m_pos.first, m_pos.second);
|
|
auto env_n = add_private_name(m_env, m_name, optional<unsigned>(h));
|
|
m_env = env_n.first;
|
|
m_real_name = env_n.second;
|
|
for (name const & aux : m_aux_decls) {
|
|
auto env_n = add_private_name(m_env, aux, optional<unsigned>(h));
|
|
m_env = env_n.first;
|
|
m_real_aux_names.push_back(env_n.second);
|
|
}
|
|
} else {
|
|
name const & ns = get_namespace(m_env);
|
|
m_real_name = ns + m_name;
|
|
for (name const & aux : m_aux_decls)
|
|
m_real_aux_names.push_back(ns + aux);
|
|
}
|
|
}
|
|
|
|
void parse() {
|
|
parse_name();
|
|
parse_type_value();
|
|
if (m_p.used_sorry())
|
|
m_p.declare_sorry();
|
|
m_env = m_p.env();
|
|
mk_real_name();
|
|
}
|
|
|
|
void process_locals() {
|
|
if (m_p.has_locals()) {
|
|
buffer<expr> locals;
|
|
collect_locals(m_type, m_value, m_p, locals);
|
|
m_type = Pi_as_is(locals, m_type, m_p);
|
|
buffer<expr> new_locals;
|
|
new_locals.append(locals);
|
|
erase_local_binder_info(new_locals);
|
|
m_value = Fun_as_is(new_locals, m_value, m_p);
|
|
auto ps = collect_univ_params_ignoring_tactics(m_type);
|
|
ps = collect_univ_params_ignoring_tactics(m_value, ps);
|
|
update_univ_parameters(m_ls_buffer, ps, m_p);
|
|
remove_local_vars(m_p, locals);
|
|
m_ls = to_list(m_ls_buffer.begin(), m_ls_buffer.end());
|
|
levels local_ls = collect_local_nonvar_levels(m_p, m_ls);
|
|
local_ls = remove_local_vars(m_p, local_ls);
|
|
if (!locals.empty()) {
|
|
expr ref = mk_local_ref(m_real_name, local_ls, locals);
|
|
m_p.add_local_expr(m_name, ref);
|
|
} else if (local_ls) {
|
|
expr ref = mk_constant(m_real_name, local_ls);
|
|
m_p.add_local_expr(m_name, ref);
|
|
}
|
|
} else {
|
|
update_univ_parameters(m_ls_buffer, collect_univ_params(m_value, collect_univ_params(m_type)), m_p);
|
|
m_ls = to_list(m_ls_buffer.begin(), m_ls_buffer.end());
|
|
}
|
|
}
|
|
|
|
bool try_cache() {
|
|
// We don't cache examples.
|
|
// We don't cache mutually recursive definitions (if this becomes a performance problem, we can fix it).
|
|
if (m_kind != Example &&
|
|
m_p.are_info_lines_valid(start_line(), end_line()) &&
|
|
m_aux_decls.size() == 0) {
|
|
// we only use the cache if the information associated with the line is valid
|
|
if (auto it = m_p.find_cached_definition(m_real_name, m_type, m_value)) {
|
|
optional<certified_declaration> cd;
|
|
try {
|
|
level_param_names c_ls; expr c_type, c_value;
|
|
std::tie(c_ls, c_type, c_value) = *it;
|
|
// cache may have been created using a different trust level
|
|
c_type = unfold_untrusted_macros(m_env, c_type);
|
|
c_value = unfold_untrusted_macros(m_env, c_value);
|
|
if (m_kind == Theorem) {
|
|
cd = check(m_env, mk_theorem(m_real_name, c_ls, c_type, c_value));
|
|
if (!m_p.keep_new_thms()) {
|
|
// discard theorem
|
|
cd = check(m_env, mk_axiom(m_real_name, c_ls, c_type));
|
|
}
|
|
} else {
|
|
cd = check(m_env, mk_definition(m_env, m_real_name, c_ls, c_type, c_value, m_is_opaque));
|
|
}
|
|
if (!m_is_private)
|
|
m_p.add_decl_index(m_real_name, m_pos, m_p.get_cmd_token(), c_type);
|
|
m_env = module::add(m_env, *cd);
|
|
return true;
|
|
} catch (exception&) {}
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
void register_decl(name const & n, name const & real_n, expr const & type) {
|
|
if (m_kind != Example) {
|
|
// TODO(Leo): register aux_decls
|
|
if (!m_is_private)
|
|
m_p.add_decl_index(real_n, m_pos, m_p.get_cmd_token(), type);
|
|
if (m_is_protected)
|
|
m_env = add_protected(m_env, real_n);
|
|
if (n != real_n)
|
|
m_env = add_expr_alias_rec(m_env, n, real_n);
|
|
bool persistent = true;
|
|
m_env = m_attributes.apply(m_env, m_p.ios(), real_n, persistent);
|
|
}
|
|
}
|
|
|
|
void register_decl() {
|
|
register_decl(m_name, m_real_name, m_type);
|
|
for (unsigned i = 0; i < m_aux_decls.size(); i++) {
|
|
register_decl(m_aux_decls[i], m_real_aux_names[i], m_aux_types[i]);
|
|
}
|
|
}
|
|
|
|
// When compiling mutually recursive equations or equations based on well-found recursion,
|
|
// the equations compiler produces a result that combines different definitions.
|
|
// We say the result is "tangled". This method untangles it.
|
|
// The tangled result is of the form
|
|
// Fun (a : A), [equations_result main-value aux-type-1 aux-value-1 ... aux-type-i aux-value-i]
|
|
//
|
|
// The result is the updated value. The auxiliary definitions (type and value) are stored at m_aux_types and aux_values
|
|
expr untangle_definitions(expr const & type, expr const & value, buffer<expr> & aux_values) {
|
|
if (is_lambda(value)) {
|
|
lean_assert(is_pi(type));
|
|
expr r = untangle_definitions(binding_body(type), binding_body(value), aux_values);
|
|
lean_assert(aux_values.size() == m_aux_types.size());
|
|
for (unsigned i = 0; i < aux_values.size(); i++) {
|
|
m_aux_types[i] = mk_pi(binding_name(type), binding_domain(type), m_aux_types[i], binding_info(type));
|
|
aux_values[i] = mk_lambda(binding_name(value), binding_domain(value), aux_values[i], binding_info(value));
|
|
}
|
|
return update_binding(value, binding_domain(value), r);
|
|
} else if (is_equations_result(value)) {
|
|
lean_assert(get_equations_result_size(value) > 1);
|
|
lean_assert(get_equations_result_size(value) % 2 == 1);
|
|
for (unsigned i = 1; i < get_equations_result_size(value); i+=2) {
|
|
m_aux_types.push_back(get_equations_result(value, i));
|
|
aux_values.push_back(get_equations_result(value, i+1));
|
|
}
|
|
return get_equations_result(value, 0);
|
|
} else {
|
|
throw exception("invalid declaration, unexpected result produced by equations compiler");
|
|
}
|
|
}
|
|
|
|
// Elaborate definitions that contain auxiliary ones nested inside.
|
|
// Remark: we do not cache this kind of definition.
|
|
// This method will also initialize m_aux_types
|
|
void elaborate_multi() {
|
|
lean_assert(!m_aux_decls.empty());
|
|
level_param_names new_ls;
|
|
std::tie(m_type, m_value, new_ls) = m_p.elaborate_definition(m_name, m_type, m_value, m_is_opaque);
|
|
new_ls = append(m_ls, new_ls);
|
|
lean_assert(m_aux_types.empty());
|
|
buffer<expr> aux_values;
|
|
m_value = untangle_definitions(m_type, m_value, aux_values);
|
|
lean_assert(aux_values.size() == m_aux_types.size());
|
|
if (aux_values.size() != m_real_aux_names.size())
|
|
throw exception("invalid declaration, failed to compile auxiliary declarations");
|
|
m_type = unfold_untrusted_macros(m_env, m_type);
|
|
m_value = unfold_untrusted_macros(m_env, m_value);
|
|
for (unsigned i = 0; i < aux_values.size(); i++) {
|
|
m_aux_types[i] = unfold_untrusted_macros(m_env, m_aux_types[i]);
|
|
aux_values[i] = unfold_untrusted_macros(m_env, aux_values[i]);
|
|
}
|
|
if (is_definition()) {
|
|
m_env = module::add(m_env, check(m_env, mk_definition(m_env, m_real_name, new_ls,
|
|
m_type, m_value, m_is_opaque)));
|
|
for (unsigned i = 0; i < aux_values.size(); i++)
|
|
m_env = module::add(m_env, check(m_env, mk_definition(m_env, m_real_aux_names[i], new_ls,
|
|
m_aux_types[i], aux_values[i], m_is_opaque)));
|
|
} else {
|
|
m_env = module::add(m_env, check(m_env, mk_theorem(m_real_name, new_ls, m_type, m_value)));
|
|
for (unsigned i = 0; i < aux_values.size(); i++)
|
|
m_env = module::add(m_env, check(m_env, mk_theorem(m_real_aux_names[i], new_ls,
|
|
m_aux_types[i], aux_values[i])));
|
|
}
|
|
}
|
|
|
|
void elaborate() {
|
|
if (!try_cache()) {
|
|
expr pre_type = m_type;
|
|
expr pre_value = m_value;
|
|
level_param_names new_ls;
|
|
m_p.remove_proof_state_info(m_pos, m_p.pos());
|
|
if (!m_aux_decls.empty()) {
|
|
// TODO(Leo): split equations_result
|
|
elaborate_multi();
|
|
} else if (!is_definition()) {
|
|
// Theorems and Examples
|
|
auto type_pos = m_p.pos_of(m_type);
|
|
bool clear_pre_info = false; // we don't want to clear pre_info data until we process the proof.
|
|
std::tie(m_type, new_ls) = m_p.elaborate_type(m_type, list<expr>(), clear_pre_info);
|
|
check_no_metavar(m_env, m_real_name, m_type, true);
|
|
m_ls = append(m_ls, new_ls);
|
|
m_type = unfold_untrusted_macros(m_env, m_type);
|
|
expr type_as_is = m_p.save_pos(mk_as_is(m_type), type_pos);
|
|
if (!m_p.collecting_info() && m_kind == Theorem && m_p.num_threads() > 1) {
|
|
// Add as axiom, and create a task to prove the theorem.
|
|
// Remark: we don't postpone the "proof" of Examples.
|
|
m_p.add_delayed_theorem(m_env, m_real_name, m_ls, type_as_is, m_value);
|
|
m_env = module::add(m_env, check(m_env, mk_axiom(m_real_name, m_ls, m_type)));
|
|
} else {
|
|
std::tie(m_type, m_value, new_ls) = m_p.elaborate_definition(m_name, type_as_is, m_value, m_is_opaque);
|
|
m_type = unfold_untrusted_macros(m_env, m_type);
|
|
m_value = unfold_untrusted_macros(m_env, m_value);
|
|
new_ls = append(m_ls, new_ls);
|
|
auto cd = check(m_env, mk_theorem(m_real_name, new_ls, m_type, m_value));
|
|
if (m_kind == Theorem) {
|
|
// Remark: we don't keep examples
|
|
if (!m_p.keep_new_thms()) {
|
|
// discard theorem
|
|
cd = check(m_env, mk_axiom(m_real_name, new_ls, m_type));
|
|
}
|
|
m_env = module::add(m_env, cd);
|
|
m_p.cache_definition(m_real_name, pre_type, pre_value, new_ls, m_type, m_value);
|
|
}
|
|
}
|
|
} else {
|
|
std::tie(m_type, m_value, new_ls) = m_p.elaborate_definition(m_name, m_type, m_value, m_is_opaque);
|
|
new_ls = append(m_ls, new_ls);
|
|
m_type = unfold_untrusted_macros(m_env, m_type);
|
|
m_value = unfold_untrusted_macros(m_env, m_value);
|
|
m_env = module::add(m_env, check(m_env, mk_definition(m_env, m_real_name, new_ls,
|
|
m_type, m_value, m_is_opaque)));
|
|
m_p.cache_definition(m_real_name, pre_type, pre_value, new_ls, m_type, m_value);
|
|
}
|
|
}
|
|
}
|
|
|
|
public:
|
|
definition_cmd_fn(parser & p, def_cmd_kind kind, bool is_opaque, bool is_private, bool is_protected):
|
|
m_p(p), m_env(m_p.env()), m_kind(kind), m_is_opaque(is_opaque),
|
|
m_is_private(is_private), m_is_protected(is_protected),
|
|
m_pos(p.pos()) {
|
|
lean_assert(!(!is_definition() && !m_is_opaque));
|
|
lean_assert(!(m_is_private && m_is_protected));
|
|
}
|
|
|
|
environment operator()() {
|
|
parse();
|
|
process_locals();
|
|
elaborate();
|
|
register_decl();
|
|
return m_env;
|
|
}
|
|
};
|
|
|
|
static environment definition_cmd_core(parser & p, def_cmd_kind kind, bool is_opaque, bool is_private, bool is_protected) {
|
|
return definition_cmd_fn(p, kind, is_opaque, is_private, is_protected)();
|
|
}
|
|
static environment definition_cmd(parser & p) {
|
|
return definition_cmd_core(p, Definition, false, false, false);
|
|
}
|
|
static environment opaque_definition_cmd(parser & p) {
|
|
p.check_token_next(get_definition_tk(), "invalid 'opaque' definition, 'definition' expected");
|
|
return definition_cmd_core(p, Definition, true, false, false);
|
|
}
|
|
static environment theorem_cmd(parser & p) {
|
|
return definition_cmd_core(p, Theorem, true, false, false);
|
|
}
|
|
static environment example_cmd(parser & p) {
|
|
return definition_cmd_core(p, Example, true, false, false);
|
|
}
|
|
static environment private_definition_cmd(parser & p) {
|
|
def_cmd_kind kind = Definition;
|
|
bool is_opaque = false;
|
|
if (p.curr_is_token_or_id(get_opaque_tk())) {
|
|
is_opaque = true;
|
|
p.next();
|
|
p.check_token_next(get_definition_tk(), "invalid 'private' definition, 'definition' expected");
|
|
} else if (p.curr_is_token_or_id(get_definition_tk())) {
|
|
p.next();
|
|
} else if (p.curr_is_token_or_id(get_theorem_tk())) {
|
|
p.next();
|
|
kind = Theorem;
|
|
is_opaque = true;
|
|
} else {
|
|
throw parser_error("invalid 'private' definition/theorem, 'definition' or 'theorem' expected", p.pos());
|
|
}
|
|
return definition_cmd_core(p, kind, is_opaque, true, false);
|
|
}
|
|
static environment protected_definition_cmd(parser & p) {
|
|
def_cmd_kind kind = Definition;
|
|
bool is_opaque = false;
|
|
if (p.curr_is_token_or_id(get_opaque_tk())) {
|
|
is_opaque = true;
|
|
p.next();
|
|
p.check_token_next(get_definition_tk(), "invalid 'protected' definition, 'definition' expected");
|
|
} else if (p.curr_is_token_or_id(get_definition_tk())) {
|
|
p.next();
|
|
} else if (p.curr_is_token_or_id(get_theorem_tk())) {
|
|
p.next();
|
|
kind = Theorem;
|
|
is_opaque = true;
|
|
} else {
|
|
throw parser_error("invalid 'protected' definition/theorem, 'definition' or 'theorem' expected", p.pos());
|
|
}
|
|
return definition_cmd_core(p, kind, is_opaque, false, true);
|
|
}
|
|
|
|
static environment include_cmd_core(parser & p, bool include) {
|
|
if (!p.curr_is_identifier())
|
|
throw parser_error(sstream() << "invalid include/omit command, identifier expected", p.pos());
|
|
while (p.curr_is_identifier()) {
|
|
auto pos = p.pos();
|
|
name n = p.get_name_val();
|
|
p.next();
|
|
if (!p.get_local(n))
|
|
throw parser_error(sstream() << "invalid include/omit command, '" << n << "' is not a parameter/variable", pos);
|
|
if (include) {
|
|
if (p.is_include_variable(n))
|
|
throw parser_error(sstream() << "invalid include command, '" << n << "' has already been included", pos);
|
|
p.include_variable(n);
|
|
} else {
|
|
if (!p.is_include_variable(n))
|
|
throw parser_error(sstream() << "invalid omit command, '" << n << "' has not been included", pos);
|
|
p.omit_variable(n);
|
|
}
|
|
}
|
|
return p.env();
|
|
}
|
|
|
|
static environment include_cmd(parser & p) {
|
|
return include_cmd_core(p, true);
|
|
}
|
|
|
|
static environment omit_cmd(parser & p) {
|
|
return include_cmd_core(p, false);
|
|
}
|
|
|
|
static environment attribute_cmd_core(parser & p, bool persistent) {
|
|
buffer<name> ds;
|
|
name d = p.check_constant_next("invalid 'attribute' command, constant expected");
|
|
ds.push_back(d);
|
|
while (p.curr_is_identifier()) {
|
|
ds.push_back(p.check_constant_next("invalid 'attribute' command, constant expected"));
|
|
}
|
|
bool decl_only = false;
|
|
decl_attributes attributes(decl_only);
|
|
attributes.parse(p);
|
|
environment env = p.env();
|
|
for (name const & d : ds)
|
|
env = attributes.apply(env, p.ios(), d, persistent);
|
|
return env;
|
|
}
|
|
|
|
static environment attribute_cmd(parser & p) {
|
|
return attribute_cmd_core(p, true);
|
|
}
|
|
|
|
environment local_attribute_cmd(parser & p) {
|
|
return attribute_cmd_core(p, false);
|
|
}
|
|
|
|
void register_decl_cmds(cmd_table & r) {
|
|
add_cmd(r, cmd_info("universe", "declare a universe level", universe_cmd));
|
|
add_cmd(r, cmd_info("universes", "declare universe levels", universes_cmd));
|
|
add_cmd(r, cmd_info("variable", "declare a new variable", variable_cmd));
|
|
add_cmd(r, cmd_info("parameter", "declare a new parameter", parameter_cmd));
|
|
add_cmd(r, cmd_info("constant", "declare a new constant (aka top-level variable)", constant_cmd));
|
|
add_cmd(r, cmd_info("axiom", "declare a new axiom", axiom_cmd));
|
|
add_cmd(r, cmd_info("variables", "declare new variables", variables_cmd));
|
|
add_cmd(r, cmd_info("parameters", "declare new parameters", parameters_cmd));
|
|
add_cmd(r, cmd_info("constants", "declare new constants (aka top-level variables)", constants_cmd));
|
|
add_cmd(r, cmd_info("definition", "add new definition", definition_cmd));
|
|
add_cmd(r, cmd_info("example", "add new example", example_cmd));
|
|
add_cmd(r, cmd_info("opaque", "add new opaque definition", opaque_definition_cmd));
|
|
add_cmd(r, cmd_info("private", "add new private definition/theorem", private_definition_cmd));
|
|
add_cmd(r, cmd_info("protected", "add new protected definition/theorem", protected_definition_cmd));
|
|
add_cmd(r, cmd_info("theorem", "add new theorem", theorem_cmd));
|
|
add_cmd(r, cmd_info("include", "force section parameter/variable to be included", include_cmd));
|
|
add_cmd(r, cmd_info("attribute", "set declaration attributes", attribute_cmd));
|
|
add_cmd(r, cmd_info("omit", "undo 'include' command", omit_cmd));
|
|
}
|
|
}
|