379 lines
16 KiB
C++
379 lines
16 KiB
C++
/*
|
|
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 "util/sstream.h"
|
|
#include "util/name_map.h"
|
|
#include "kernel/replace_fn.h"
|
|
#include "kernel/type_checker.h"
|
|
#include "kernel/instantiate.h"
|
|
#include "kernel/inductive/inductive.h"
|
|
#include "kernel/free_vars.h"
|
|
#include "library/scoped_ext.h"
|
|
#include "library/locals.h"
|
|
#include "library/placeholder.h"
|
|
#include "library/aliases.h"
|
|
#include "library/explicit.h"
|
|
#include "frontends/lean/decl_cmds.h"
|
|
#include "frontends/lean/util.h"
|
|
#include "frontends/lean/parser.h"
|
|
|
|
namespace lean {
|
|
static name g_assign(":=");
|
|
static name g_with("with");
|
|
static name g_colon(":");
|
|
static name g_bar("|");
|
|
static name g_lcurly("{");
|
|
static name g_rcurly("}");
|
|
|
|
using inductive::intro_rule;
|
|
using inductive::inductive_decl;
|
|
using inductive::inductive_decl_name;
|
|
using inductive::inductive_decl_type;
|
|
using inductive::inductive_decl_intros;
|
|
using inductive::intro_rule_name;
|
|
using inductive::intro_rule_type;
|
|
|
|
// Make sure that every inductive datatype (in decls) occurring in \c type has
|
|
// the universe levels \c lvl_params and section parameters \c section_params
|
|
static expr fix_inductive_occs(expr const & type, buffer<inductive_decl> const & decls,
|
|
buffer<name> const & lvl_params, buffer<expr> const & section_params) {
|
|
return replace(type, [&](expr const & e, unsigned) {
|
|
if (!is_constant(e))
|
|
return none_expr();
|
|
if (!std::any_of(decls.begin(), decls.end(),
|
|
[&](inductive_decl const & d) { return const_name(e) == inductive_decl_name(d); }))
|
|
return none_expr();
|
|
// found target
|
|
levels ls = const_levels(e);
|
|
unsigned n = length(ls);
|
|
if (n < lvl_params.size()) {
|
|
unsigned i = lvl_params.size() - n;
|
|
while (i > 0) {
|
|
--i;
|
|
ls = cons(mk_param_univ(lvl_params[i]), ls);
|
|
}
|
|
}
|
|
expr r = update_constant(e, ls);
|
|
for (unsigned i = 0; i < section_params.size(); i++)
|
|
r = mk_app(r, section_params[i]);
|
|
return some_expr(r);
|
|
});
|
|
}
|
|
|
|
static level mk_result_level(bool impredicative, buffer<level> const & ls) {
|
|
if (ls.empty()) {
|
|
return impredicative ? mk_level_one() : mk_level_zero();
|
|
} else {
|
|
level r = ls[0];
|
|
for (unsigned i = 1; i < ls.size(); i++)
|
|
r = mk_max(r, ls[i]);
|
|
if (is_not_zero(r))
|
|
return r;
|
|
else
|
|
return impredicative ? mk_max(r, mk_level_one()) : r;
|
|
}
|
|
}
|
|
|
|
static expr update_result_sort(type_checker & tc, expr t, level const & l) {
|
|
t = tc.whnf(t);
|
|
if (is_pi(t)) {
|
|
return update_binding(t, binding_domain(t), update_result_sort(tc, binding_body(t), l));
|
|
} else if (is_sort(t)) {
|
|
return update_sort(t, l);
|
|
} else {
|
|
lean_unreachable();
|
|
}
|
|
}
|
|
|
|
/** \brief Return the universe level of the given inductive datatype declaration. */
|
|
level get_datatype_result_level(type_checker & tc, inductive_decl const & d) {
|
|
expr d_t = tc.whnf(inductive_decl_type(d));
|
|
while (is_pi(d_t)) {
|
|
d_t = tc.whnf(binding_body(d_t));
|
|
}
|
|
if (!is_sort(d_t)) {
|
|
std::cout << "ERROR: " << inductive_decl_type(d) << "\n";
|
|
throw exception(sstream() << "invalid inductive datatype '" << inductive_decl_name(d) << "', "
|
|
"resultant type is not a sort");
|
|
}
|
|
return sort_level(d_t);
|
|
}
|
|
|
|
/** \brief Return true if \c u occurs in \c l */
|
|
bool occurs(level const & u, level const & l) {
|
|
bool found = false;
|
|
for_each(l, [&](level const & l) {
|
|
if (found) return false;
|
|
if (l == u) { found = true; return false; }
|
|
return true;
|
|
});
|
|
return found;
|
|
}
|
|
|
|
static name g_tmp_prefix = name::mk_internal_unique_name();
|
|
/**
|
|
\brief Given a type \c t for an introduction rule, store the universe of the types of non-parameters in \c ls.
|
|
|
|
\remark aux_u is an temporary universe used for inductive decls. It should be ignored.
|
|
*/
|
|
static void accumulate_levels(type_checker & tc, expr t, unsigned num_params, level const & aux_u, buffer<level> & ls) {
|
|
name_generator ngen(g_tmp_prefix);
|
|
unsigned i = 0;
|
|
while (is_pi(t)) {
|
|
if (i >= num_params) {
|
|
expr s = tc.ensure_type(binding_domain(t));
|
|
level l = sort_level(s);
|
|
if (l == aux_u) {
|
|
// ignore, this is the auxiliary level
|
|
} else if (occurs(aux_u, l)) {
|
|
throw exception("failed to infer inductive datatype resultant universe, provide the universe levels explicitly");
|
|
} else if (std::find(ls.begin(), ls.end(), l) == ls.end()) {
|
|
ls.push_back(l);
|
|
}
|
|
}
|
|
t = instantiate(binding_body(t), mk_local(ngen.next(), binding_name(t), binding_domain(t), binding_info(t)));
|
|
i++;
|
|
}
|
|
}
|
|
|
|
void throw_all_or_nothing() {
|
|
throw exception("invalid mutually recursive datatype declaration, "
|
|
"if the universe level of one type is provided, then all of them should be");
|
|
}
|
|
|
|
static void elaborate_inductive(buffer<inductive_decl> & decls, level_param_names const & lvls, unsigned num_params, parser & p) {
|
|
// temporary environment used during elaboration
|
|
environment env = p.env();
|
|
// add fake universe level
|
|
name u_name(g_tmp_prefix, "u");
|
|
env = env.add_universe(u_name);
|
|
level u = mk_global_univ(u_name);
|
|
std::unique_ptr<type_checker> tc(new type_checker(env));
|
|
bool infer_result_universe = false;
|
|
unsigned first = true;
|
|
// elaborate inductive datatype types, and declare them in temporary environment.
|
|
for (inductive_decl & d : decls) {
|
|
level l = get_datatype_result_level(*tc, d);
|
|
expr t = inductive_decl_type(d);
|
|
if (is_placeholder(l)) {
|
|
if (first)
|
|
infer_result_universe = true;
|
|
else if (!infer_result_universe)
|
|
throw_all_or_nothing();
|
|
t = update_result_sort(*tc, t, u);
|
|
} else if (!first && infer_result_universe) {
|
|
throw_all_or_nothing();
|
|
}
|
|
t = p.elaborate(env, t);
|
|
env = env.add(check(env, mk_var_decl(inductive_decl_name(d), lvls, t)));
|
|
d = inductive_decl(inductive_decl_name(d), t, inductive_decl_intros(d));
|
|
first = false;
|
|
}
|
|
tc.reset(new type_checker(env));
|
|
buffer<level> r_lvls; // used for inferring the universe level of resultant datatypes.
|
|
// elaborate introduction rules using temporary environment
|
|
for (inductive_decl & d : decls) {
|
|
buffer<intro_rule> intros;
|
|
for (intro_rule const & ir : inductive_decl_intros(d)) {
|
|
expr t = p.elaborate(env, intro_rule_type(ir));
|
|
if (infer_result_universe)
|
|
accumulate_levels(*tc, t, num_params, u, r_lvls);
|
|
intros.push_back(intro_rule(intro_rule_name(ir), t));
|
|
}
|
|
d = inductive_decl(inductive_decl_name(d), inductive_decl_type(d), to_list(intros.begin(), intros.end()));
|
|
}
|
|
if (infer_result_universe) {
|
|
level r_lvl = normalize(mk_result_level(env.impredicative(), r_lvls));
|
|
for (inductive_decl & d : decls) {
|
|
expr t = inductive_decl_type(d);
|
|
t = update_result_sort(*tc, t, r_lvl);
|
|
d = inductive_decl(inductive_decl_name(d), t, inductive_decl_intros(d));
|
|
}
|
|
}
|
|
}
|
|
|
|
static environment create_alias(environment const & env, name const & full_id, name const & id, levels const & section_leves,
|
|
buffer<expr> const & section_params, parser & p) {
|
|
if (in_section(env)) {
|
|
expr r = mk_explicit(mk_constant(full_id, section_leves));
|
|
for (unsigned i = 0; i < section_params.size(); i++)
|
|
r = mk_app(r, section_params[i]);
|
|
p.add_local_expr(id, r);
|
|
return env;
|
|
} else if (full_id != id) {
|
|
return add_alias(env, id, mk_constant(full_id));
|
|
} else {
|
|
return env;
|
|
}
|
|
}
|
|
|
|
environment inductive_cmd(parser & p) {
|
|
parser::no_undef_id_error_scope err_scope(p);
|
|
environment env = p.env();
|
|
name const & ns = get_namespace(env);
|
|
bool first = true;
|
|
buffer<name> ls_buffer;
|
|
name_map<name> id_to_short_id;
|
|
// store intro rule name that are markes for relaxed implicit argument inference.
|
|
name_set relaxed_implicit_inference;
|
|
unsigned num_params = 0;
|
|
bool explicit_levels = false;
|
|
buffer<inductive_decl> decls;
|
|
while (true) {
|
|
parser::local_scope l_scope(p);
|
|
auto id_pos = p.pos();
|
|
name id = p.check_id_next("invalid inductive declaration, identifier expected");
|
|
check_atomic(id);
|
|
name full_id = ns + id;
|
|
id_to_short_id.insert(full_id, id);
|
|
buffer<name> curr_ls_buffer;
|
|
expr type;
|
|
optional<parser::param_universe_scope> pu_scope;
|
|
if (parse_univ_params(p, curr_ls_buffer)) {
|
|
if (first) {
|
|
explicit_levels = true;
|
|
ls_buffer.append(curr_ls_buffer);
|
|
} else if (!explicit_levels) {
|
|
throw parser_error("invalid mutually recursive declaration, "
|
|
"explicit universe levels were not provided for previous inductive types in this declaration",
|
|
id_pos);
|
|
} else if (curr_ls_buffer.size() != ls_buffer.size()) {
|
|
throw parser_error("invalid mutually recursive declaration, "
|
|
"all inductive types must have the same number of universe paramaters", id_pos);
|
|
} else {
|
|
for (unsigned i = 0; i < ls_buffer.size(); i++) {
|
|
if (curr_ls_buffer[i] != ls_buffer[i])
|
|
throw parser_error("invalid mutually recursive inductive declaration, "
|
|
"all inductive types must have the same universe paramaters", id_pos);
|
|
}
|
|
}
|
|
} else {
|
|
if (first) {
|
|
explicit_levels = false;
|
|
} else if (explicit_levels) {
|
|
throw parser_error("invalid mutually recursive declaration, "
|
|
"explicit universe levels were provided for previous inductive types in this declaration",
|
|
id_pos);
|
|
}
|
|
// initialize param_universe_scope, we are using implicit universe levels
|
|
pu_scope.emplace(p);
|
|
}
|
|
buffer<expr> ps;
|
|
local_environment lenv = env;
|
|
auto params_pos = p.pos();
|
|
if (!p.curr_is_token(g_colon)) {
|
|
lenv = p.parse_binders(ps);
|
|
p.check_token_next(g_colon, "invalid inductive declaration, ':' expected");
|
|
{
|
|
parser::placeholder_universe_scope place_scope(p);
|
|
type = p.parse_scoped_expr(ps, lenv);
|
|
}
|
|
type = p.pi_abstract(ps, type);
|
|
} else {
|
|
p.next();
|
|
parser::placeholder_universe_scope place_scope(p);
|
|
type = p.parse_scoped_expr(ps, lenv);
|
|
}
|
|
// check if number of parameters
|
|
if (first) {
|
|
num_params = ps.size();
|
|
} else {
|
|
// mutually recursive declaration checks
|
|
if (num_params != ps.size()) {
|
|
throw parser_error("invalid mutually recursive inductive declaration, "
|
|
"all inductive types must have the same number of arguments",
|
|
params_pos);
|
|
}
|
|
}
|
|
// parse introduction rules
|
|
p.check_token_next(g_assign, "invalid inductive declaration, ':=' expected");
|
|
buffer<intro_rule> intros;
|
|
while (p.curr_is_token(g_bar)) {
|
|
p.next();
|
|
name intro_id = p.check_id_next("invalid introduction rule, identifier expected");
|
|
check_atomic(intro_id);
|
|
name full_intro_id = ns + intro_id;
|
|
id_to_short_id.insert(full_intro_id, intro_id);
|
|
bool strict = true;
|
|
if (p.curr_is_token(g_lcurly)) {
|
|
p.next();
|
|
p.check_token_next(g_rcurly, "invalid introduction rule, '}' expected");
|
|
strict = false;
|
|
relaxed_implicit_inference.insert(full_intro_id);
|
|
}
|
|
p.check_token_next(g_colon, "invalid introduction rule, ':' expected");
|
|
expr intro_type = p.parse_scoped_expr(ps, lenv);
|
|
intro_type = p.pi_abstract(ps, intro_type);
|
|
intro_type = infer_implicit(intro_type, ps.size(), strict);
|
|
intros.push_back(intro_rule(full_intro_id, intro_type));
|
|
}
|
|
decls.push_back(inductive_decl(full_id, type, to_list(intros.begin(), intros.end())));
|
|
if (!p.curr_is_token(g_with))
|
|
break;
|
|
p.next();
|
|
first = false;
|
|
}
|
|
// Collect (section) locals occurring in inductive_decls, and abstract them
|
|
// using these additional parameters.
|
|
name_set used_levels;
|
|
name_set section_locals;
|
|
for (inductive_decl const & d : decls) {
|
|
used_levels = collect_univ_params(inductive_decl_type(d), used_levels);
|
|
section_locals = collect_locals(inductive_decl_type(d), section_locals);
|
|
for (auto const & ir : inductive_decl_intros(d)) {
|
|
used_levels = collect_univ_params(intro_rule_type(ir), used_levels);
|
|
section_locals = collect_locals(intro_rule_type(ir), section_locals);
|
|
}
|
|
}
|
|
update_univ_parameters(ls_buffer, used_levels, p);
|
|
buffer<expr> section_params;
|
|
mk_section_params(section_locals, p, section_params);
|
|
// First, add section_params to inductive types type.
|
|
// We don't update the introduction rules in the first pass, because
|
|
// we will mark all section_params as implicit for them.
|
|
for (inductive_decl & d : decls) {
|
|
d = inductive_decl(inductive_decl_name(d),
|
|
p.pi_abstract(section_params, inductive_decl_type(d)),
|
|
inductive_decl_intros(d));
|
|
}
|
|
// Add section_params to introduction rules type, and also "fix"
|
|
// occurrences of inductive types.
|
|
for (inductive_decl & d : decls) {
|
|
buffer<intro_rule> new_irs;
|
|
for (auto const & ir : inductive_decl_intros(d)) {
|
|
expr type = intro_rule_type(ir);
|
|
type = fix_inductive_occs(type, decls, ls_buffer, section_params);
|
|
type = p.pi_abstract(section_params, type);
|
|
bool strict = relaxed_implicit_inference.contains(intro_rule_name(ir));
|
|
type = infer_implicit(type, section_params.size(), strict);
|
|
new_irs.push_back(intro_rule(intro_rule_name(ir), type));
|
|
}
|
|
d = inductive_decl(inductive_decl_name(d),
|
|
inductive_decl_type(d),
|
|
to_list(new_irs.begin(), new_irs.end()));
|
|
}
|
|
num_params += section_params.size();
|
|
level_param_names ls = to_list(ls_buffer.begin(), ls_buffer.end());
|
|
|
|
elaborate_inductive(decls, ls, num_params, p);
|
|
env = module::add_inductive(env, ls, num_params, to_list(decls.begin(), decls.end()));
|
|
// Create aliases/local refs
|
|
levels section_levels = collect_section_levels(ls, p);
|
|
for (inductive_decl const & d : decls) {
|
|
name const & n = inductive_decl_name(d);
|
|
env = create_alias(env, n, *id_to_short_id.find(n), section_levels, section_params, p);
|
|
env = create_alias(env, n.append_after("_rec"), id_to_short_id.find(n)->append_after("_rec"), section_levels, section_params, p);
|
|
for (intro_rule const & ir : inductive_decl_intros(d)) {
|
|
name const & n = intro_rule_name(ir);
|
|
env = create_alias(env, n, *id_to_short_id.find(n), section_levels, section_params, p);
|
|
}
|
|
}
|
|
return env;
|
|
}
|
|
void register_inductive_cmd(cmd_table & r) {
|
|
add_cmd(r, cmd_info("inductive", "declare an inductive datatype", inductive_cmd));
|
|
}
|
|
}
|