lean2/src/library/user_recursors.cpp

332 lines
13 KiB
C++

/*
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include <algorithm>
#include <string>
#include "util/sstream.h"
#include "kernel/inductive/inductive.h"
#include "library/scoped_ext.h"
#include "library/util.h"
#include "library/kernel_serializer.h"
#include "library/user_recursors.h"
namespace lean {
bool recursor_info::is_minor(unsigned pos) const {
if (pos <= get_motive_pos())
return false;
if (get_first_index_pos() <= pos && pos <= m_major_pos)
return false;
return true;
}
recursor_info::recursor_info(name const & r, name const & I, list<unsigned> const & univ_pos,
bool dep_elim, unsigned num_args, unsigned major_pos,
list<optional<unsigned>> const & params_pos, list<unsigned> const & indices_pos,
list<bool> const & produce_motive):
m_recursor(r), m_type_name(I), m_universe_pos(univ_pos), m_dep_elim(dep_elim),
m_num_args(num_args), m_major_pos(major_pos), m_params_pos(params_pos), m_indices_pos(indices_pos),
m_produce_motive(produce_motive) {}
recursor_info::recursor_info() {}
void recursor_info::write(serializer & s) const {
s << m_recursor << m_type_name << m_dep_elim << m_num_args << m_major_pos;
write_list(s, m_universe_pos);
write_list(s, m_params_pos);
write_list(s, m_indices_pos);
write_list(s, m_produce_motive);
}
recursor_info recursor_info::read(deserializer & d) {
recursor_info info;
d >> info.m_recursor >> info.m_type_name >> info.m_dep_elim
>> info.m_num_args >> info.m_major_pos;
info.m_universe_pos = read_list<unsigned>(d);
info.m_params_pos = read_list<optional<unsigned>>(d);
info.m_indices_pos = read_list<unsigned>(d);
info.m_produce_motive = read_list<bool>(d);
return info;
}
static void throw_invalid_motive(expr const & C) {
throw exception(sstream() << "invalid user defined recursor, motive '" << C
<< "' must have a type of the form (C : Pi (i : B A), I A i -> Type), "
"where A is (possibly empty) sequence of bound variables (aka parameters), "
"(i : B A) is a (possibly empty) telescope (aka indices), "
"and I is a constant");
}
recursor_info mk_recursor_info(environment const & env, name const & r, optional<unsigned> const & given_major_pos) {
if (auto I = inductive::is_elim_rule(env, r)) {
if (*inductive::get_num_type_formers(env, *I) > 1)
throw exception(sstream() << "unsupported recursor '" << r << "', it has multiple motives");
unsigned num_univ_params = env.get(*I).get_num_univ_params();
list<unsigned> universe_pos = mk_list_range(0, num_univ_params);
if (env.get(name(*I, "rec")).get_num_univ_params() != num_univ_params)
universe_pos = cons(recursor_info::get_motive_univ_idx(), universe_pos);
unsigned major_pos = *inductive::get_elim_major_idx(env, r);
unsigned num_indices = *inductive::get_num_indices(env, *I);
unsigned num_params = *inductive::get_num_params(env, *I);
unsigned num_minors = *inductive::get_num_minor_premises(env, *I);
unsigned num_args = num_params + 1 /* motive */ + num_minors + num_indices + 1 /* major */;
list<bool> produce_motive;
for (unsigned i = 0; i < num_minors; i++)
produce_motive = cons(true, produce_motive);
list<optional<unsigned>> params_pos = map2<optional<unsigned>>(mk_list_range(0, num_params),
[](unsigned i) { return optional<unsigned>(i); });
list<unsigned> indices_pos = mk_list_range(num_params, num_params + num_indices);
return recursor_info(r, *I, universe_pos, inductive::has_dep_elim(env, *I),
num_args, major_pos, params_pos, indices_pos, produce_motive);
}
declaration d = env.get(r);
type_checker tc(env);
buffer<expr> tele;
expr rtype = to_telescope(tc, d.get_type(), tele);
buffer<expr> C_args;
expr C = get_app_args(rtype, C_args);
if (!is_local(C) || !std::all_of(C_args.begin(), C_args.end(), is_local)) {
throw exception("invalid user defined recursor, result type must be of the form (C t), "
"where C is a bound variable, and t is a (possibly empty) sequence of bound variables");
}
// Compute number of parameters.
// We assume a parameter is anything that occurs before the motive.
unsigned num_params = 0;
for (expr const & x : tele) {
if (mlocal_name(x) == mlocal_name(C))
break;
num_params++;
}
// Locate major premise, and check whether the recursor supports dependent elimination or not.
expr major;
unsigned major_pos = 0;
bool dep_elim;
if (given_major_pos) {
if (*given_major_pos >= tele.size())
throw exception(sstream() << "invalid user defined recursor, invalid major premise position, "
"recursor has only " << tele.size() << "arguments");
major = tele[*given_major_pos];
major_pos = *given_major_pos;
if (!C_args.empty() && tc.is_def_eq(C_args.back(), major).first)
dep_elim = true;
else
dep_elim = false;
} else if (C_args.empty()) {
throw exception(sstream() << "invalid user defined recursor, '" << r << "' does not support dependent elimination, "
<< "and position of the major premise was not specified "
<< "(solution: set attribute '[recursor <pos>]', where <pos> is the position of the major premise)");
} else {
major = C_args.back();
dep_elim = true;
for (expr const & x : tele) {
if (tc.is_def_eq(x, major).first)
break;
major_pos++;
}
}
// Number of indices
unsigned num_indices = C_args.size();
if (dep_elim)
num_indices--; // when we have dependent elimination, the last element is the major premise.
if (major_pos < num_indices)
throw exception(sstream() << "invalid user defined recursor, indices must occur before major premise '"
<< major << "'");
buffer<expr> I_args;
expr I = get_app_args(mlocal_type(major), I_args);
if (!is_constant(I)) {
throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
<< "' must be for the form (I ...), where I is a constant");
}
// Store position of the recursor parameters in the major premise.
buffer<optional<unsigned>> params_pos;
for (unsigned i = 0; i < num_params; i++) {
expr const & A = tele[i];
unsigned j = 0;
for (; j < I_args.size(); j++) {
if (tc.is_def_eq(I_args[j], A).first)
break;
}
if (j == I_args.size()) {
if (local_info(tele[i]).is_inst_implicit()) {
params_pos.push_back(optional<unsigned>());
} else {
throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
<< "' does not contain the recursor parameter '" << A << "'");
}
} else {
params_pos.push_back(optional<unsigned>(j));
}
}
// Store position of the recursor indices in the major premise
buffer<unsigned> indices_pos;
for (unsigned i = major_pos - num_indices; i < major_pos; i++) {
expr const & idx = tele[i];
unsigned j = 0;
for (; j < I_args.size(); j++) {
if (tc.is_def_eq(I_args[j], idx).first)
break;
}
if (j == I_args.size()) {
throw exception(sstream() << "invalid user defined recursor, type of the major premise '" << major
<< "' does not contain the recursor index '" << idx << "'");
}
indices_pos.push_back(j);
}
buffer<expr> C_tele;
expr C_rtype = to_telescope(tc, mlocal_type(C), C_tele);
if (!is_sort(C_rtype) || C_tele.size() != C_args.size()) {
throw_invalid_motive(C);
}
level motive_lvl = sort_level(C_rtype);
// Remark: if we are in the standard environment, then the motive may be a proposition, and be fixed at 0.
// The following pragma is for avoiding gcc bogus warning
if (!is_standard(env) || !is_zero(motive_lvl)) {
if (!is_param(motive_lvl)) {
if (is_standard(env))
throw exception("invalid user defined recursor, "
"motive result sort must be Prop or Type.{l} where l is a universe parameter");
else
throw exception("invalid user defined recursor, "
"motive result sort must be Type.{l} where l is a universe parameter");
}
}
// A universe parameter must occur in the major premise or in the motive
buffer<unsigned> univ_param_pos;
for (name const & p : d.get_univ_params()) {
if (!is_zero(motive_lvl) && param_id(motive_lvl) == p) {
univ_param_pos.push_back(recursor_info::get_motive_univ_idx());
} else {
bool found = false;
unsigned i = 0;
for (level const & l : const_levels(I)) {
if (is_param(l) && param_id(l) == p) {
univ_param_pos.push_back(i);
found = true;
break;
}
i++;
}
if (!found) {
throw exception(sstream() << "invalid user defined recursor, major premise '"
<< major << "' does not contain universe parameter '" << p << "'");
}
}
}
buffer<bool> produce_motive;
unsigned nparams = params_pos.size();
unsigned nindices = indices_pos.size();
for (unsigned i = nparams+1; i < tele.size(); i++) {
if (i < major_pos - nindices || i > major_pos) {
// i is a minor premise
buffer<expr> tmp;
expr res = get_app_fn(to_telescope(tc, mlocal_type(tele[i]), tmp));
if (is_local(res) && mlocal_name(C) == mlocal_name(res)) {
produce_motive.push_back(true);
} else {
produce_motive.push_back(false);
}
}
}
return recursor_info(r, const_name(I), to_list(univ_param_pos), dep_elim, tele.size(), major_pos,
to_list(params_pos), to_list(indices_pos), to_list(produce_motive));
}
struct recursor_state {
name_map<recursor_info> m_recursors;
name_map<list<name>> m_type2recursors;
void insert(recursor_info const & info) {
m_recursors.insert(info.get_name(), info);
if (auto l = m_type2recursors.find(info.get_type_name())) {
m_type2recursors.insert(info.get_type_name(),
cons(info.get_name(),
filter(*l, [&](name const & n) { return n != info.get_name(); })));
} else {
m_type2recursors.insert(info.get_type_name(), to_list(info.get_name()));
}
}
};
static name * g_class_name = nullptr;
static std::string * g_key = nullptr;
struct recursor_config {
typedef recursor_state state;
typedef recursor_info entry;
static void add_entry(environment const &, io_state const &, state & s, entry const & e) {
s.insert(e);
}
static name const & get_class_name() {
return *g_class_name;
}
static std::string const & get_serialization_key() {
return *g_key;
}
static void write_entry(serializer & s, entry const & e) {
e.write(s);
}
static entry read_entry(deserializer & d) {
return recursor_info::read(d);
}
static optional<unsigned> get_fingerprint(entry const & e) {
return some(e.get_name().hash());
}
};
template class scoped_ext<recursor_config>;
typedef scoped_ext<recursor_config> recursor_ext;
environment add_user_recursor(environment const & env, name const & r, optional<unsigned> const & major_pos,
bool persistent) {
if (inductive::is_elim_rule(env, r))
throw exception(sstream() << "invalid user defined recursor, '" << r << "' is a builtin recursor");
recursor_info info = mk_recursor_info(env, r, major_pos);
return recursor_ext::add_entry(env, get_dummy_ios(), info, persistent);
}
recursor_info get_recursor_info(environment const & env, name const & r) {
if (auto info = recursor_ext::get_state(env).m_recursors.find(r))
return *info;
return mk_recursor_info(env, r, optional<unsigned>());
}
list<name> get_recursors_for(environment const & env, name const & I) {
if (auto l = recursor_ext::get_state(env).m_type2recursors.find(I))
return *l;
else
return list<name>();
}
bool is_user_defined_recursor(environment const & env, name const & r) {
return recursor_ext::get_state(env).m_recursors.find(r) != nullptr;
}
has_recursors_pred::has_recursors_pred(environment const & env):
m_type2recursors(recursor_ext::get_state(env).m_type2recursors) {}
void initialize_user_recursors() {
g_class_name = new name("recursor");
g_key = new std::string("urec");
recursor_ext::initialize();
}
void finalize_user_recursors() {
recursor_ext::finalize();
delete g_class_name;
delete g_key;
}
}