lean2/src/library/unifier.cpp

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/*
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 "util/luaref.h"
#include "util/lazy_list_fn.h"
#include "kernel/for_each_fn.h"
#include "kernel/abstract.h"
#include "kernel/type_checker.h"
#include "library/unifier.h"
#include "library/kernel_bindings.h"
namespace lean {
static std::pair<unify_status, substitution> unify_simple_core(substitution const & s, expr const & lhs, expr const & rhs,
justification const & j) {
lean_assert(is_meta(lhs));
buffer<expr> args;
expr const & m = get_app_args(lhs, args);
lean_assert(is_metavar(m));
for (auto it = args.begin(); it != args.end(); it++) {
if (!is_local(*it) || std::find(args.begin(), it, *it) != it)
return mk_pair(unify_status::Unsupported, s);
}
if (is_meta(rhs) && get_app_fn(rhs) == m)
return mk_pair(unify_status::Unsupported, s);
bool failed = false;
for_each(rhs, [&](expr const & e, unsigned) {
if (failed)
return false;
if (is_local(e) && std::find(args.begin(), args.end(), e) == args.end()) {
// right-hand-side contains variable that is not in the scope
// of metavariable.
failed = true;
return false;
}
if (is_metavar(e) && e == m) {
// occurs-check failed
failed = true;
return false;
}
// we only need to continue exploring e if it contains
// metavariables and/or local constants.
return has_metavar(e) || has_local(e);
});
if (failed)
return mk_pair(unify_status::Failed, s);
expr v = abstract_locals(rhs, args.size(), args.data());
unsigned i = args.size();
while (i > 0) {
--i;
v = mk_lambda(local_pp_name(args[i]), mlocal_type(args[i]), v);
}
return mk_pair(unify_status::Solved, s.assign(mlocal_name(m), v, j));
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j) {
if (lhs == rhs)
return mk_pair(unify_status::Solved, s);
else if (!has_metavar(lhs) && !has_metavar(rhs))
return mk_pair(unify_status::Failed, s);
else if (is_meta(lhs))
return unify_simple_core(s, lhs, rhs, j);
else if (is_meta(rhs))
return unify_simple_core(s, rhs, lhs, j);
else
return mk_pair(unify_status::Unsupported, s);
}
std::pair<unify_status, substitution> unify_simple_core(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
lean_assert(is_meta(lhs));
bool contains = false;
for_each(rhs, [&](level const & l) {
if (contains)
return false;
if (l == lhs) {
// occurs-check failed
contains = true;
return false;
}
return true;
});
if (contains) {
if (is_succ(rhs))
return mk_pair(unify_status::Failed, s);
else
return mk_pair(unify_status::Unsupported, s);
}
return mk_pair(unify_status::Solved, s.assign(meta_id(lhs), rhs, j));
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
if (lhs == rhs)
return mk_pair(unify_status::Solved, s);
else if (!has_meta(lhs) && !has_meta(rhs))
return mk_pair(unify_status::Failed, s);
else if (is_meta(lhs))
return unify_simple_core(s, lhs, rhs, j);
else if (is_meta(rhs))
return unify_simple_core(s, rhs, lhs, j);
else if (is_succ(lhs) && is_succ(rhs))
return unify_simple(s, succ_of(lhs), succ_of(rhs), j);
else
return mk_pair(unify_status::Unsupported, s);
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c) {
if (is_eq_cnstr(c))
return unify_simple(s, cnstr_lhs_expr(c), cnstr_rhs_expr(c), c.get_justification());
else if (is_level_cnstr(c))
return unify_simple(s, cnstr_lhs_level(c), cnstr_rhs_level(c), c.get_justification());
else
return mk_pair(unify_status::Unsupported, s);
}
struct unifier_fn {
environment m_env;
name_generator m_ngen;
substitution m_subst;
unifier_plugin m_plugin;
bool m_use_exception;
unifier_fn(environment const & env, unsigned /* num_cs */, constraint const * /* cs */,
name_generator const & ngen, substitution const & s, unifier_plugin const & p,
bool use_exception):
m_env(env), m_ngen(ngen), m_subst(s), m_plugin(p), m_use_exception(use_exception) {
}
optional<substitution> next() {
// TODO(Leo)
return optional<substitution>();
}
};
lazy_list<substitution> unify(std::shared_ptr<unifier_fn> const & u) {
return mk_lazy_list<substitution>([=]() {
auto s = u->next();
if (s)
return some(mk_pair(*s, unify(u)));
else
return lazy_list<substitution>::maybe_pair();
});
}
lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
unifier_plugin const & p, bool use_exception) {
return unify(std::make_shared<unifier_fn>(env, num_cs, cs, ngen, substitution(), p, use_exception));
}
lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
bool use_exception) {
return unify(env, num_cs, cs, ngen, [](constraint const &, name_generator const &) { return lazy_list<constraints>(); }, use_exception);
}
lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen, unifier_plugin const & p) {
substitution s;
buffer<constraint> cs;
name_generator new_ngen(ngen);
bool failed = false;
type_checker tc(env, new_ngen.mk_child(), [&](constraint const & c) {
if (!failed) {
auto r = unify_simple(s, c);
switch (r.first) {
case unify_status::Solved:
s = r.second; break;
case unify_status::Failed:
failed = true; break;
case unify_status::Unsupported:
cs.push_back(c); break;
}
}
});
if (!tc.is_def_eq(lhs, rhs) || failed) {
return lazy_list<substitution>();
} else if (cs.empty()) {
return lazy_list<substitution>(s);
} else {
return unify(std::make_shared<unifier_fn>(env, cs.size(), cs.data(), ngen, s, p, false));
}
}
lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen) {
return unify(env, lhs, rhs, ngen, [](constraint const &, name_generator const &) { return lazy_list<constraints>(); });
}
static int unify_simple(lua_State * L) {
int nargs = lua_gettop(L);
std::pair<unify_status, substitution> r;
if (nargs == 2)
r = unify_simple(to_substitution(L, 1), to_constraint(L, 2));
else if (nargs == 3 && is_expr(L, 2))
r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), justification());
else if (nargs == 3 && is_level(L, 2))
r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), justification());
else if (is_expr(L, 2))
r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), to_justification(L, 4));
else
r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), to_justification(L, 4));
push_integer(L, static_cast<unsigned>(r.first));
push_substitution(L, r.second);
return 2;
}
typedef lazy_list<substitution> substitution_seq;
DECL_UDATA(substitution_seq)
static const struct luaL_Reg substitution_seq_m[] = {
{"__gc", substitution_seq_gc},
{0, 0}
};
static int substitution_seq_next(lua_State * L) {
substitution_seq seq = to_substitution_seq(L, lua_upvalueindex(1));
substitution_seq::maybe_pair p;
p = seq.pull();
if (p) {
push_substitution_seq(L, p->second);
lua_replace(L, lua_upvalueindex(1));
push_substitution(L, p->first);
} else {
lua_pushnil(L);
}
return 1;
}
static int push_substitution_seq_it(lua_State * L, substitution_seq const & seq) {
push_substitution_seq(L, seq);
lua_pushcclosure(L, &safe_function<substitution_seq_next>, 1); // create closure with 1 upvalue
return 1;
}
static void to_constraint_buffer(lua_State * L, int idx, buffer<constraint> & cs) {
luaL_checktype(L, idx, LUA_TTABLE);
lua_pushvalue(L, idx); // put table on top of the stack
int n = objlen(L, idx);
for (int i = 1; i <= n; i++) {
lua_rawgeti(L, -1, i);
cs.push_back(to_constraint(L, -1));
lua_pop(L, 1);
}
lua_pop(L, 1);
}
static constraints to_constraints(lua_State * L, int idx) {
buffer<constraint> cs;
to_constraint_buffer(L, idx, cs);
return to_list(cs.begin(), cs.end());
}
static unifier_plugin to_unifier_plugin(lua_State * L, int idx) {
luaL_checktype(L, idx, LUA_TFUNCTION); // user-fun
luaref f(L, idx);
return unifier_plugin([=](constraint const & c, name_generator const & ngen) {
lua_State * L = f.get_state();
f.push();
push_constraint(L, c);
push_name_generator(L, ngen);
pcall(L, 2, 1, 0);
lazy_list<constraints> r;
if (is_constraint(L, -1)) {
// single constraint
r = lazy_list<constraints>(constraints(to_constraint(L, -1)));
} else if (lua_istable(L, -1)) {
int num = objlen(L, -1);
if (num == 0) {
// empty table
r = lazy_list<constraints>();
} else {
lua_rawgeti(L, -1, 1);
if (is_constraint(L, -1)) {
// array of constraints case
lua_pop(L, 1);
r = lazy_list<constraints>(to_constraints(L, -1));
} else {
lua_pop(L, 1);
buffer<constraints> css;
// array of array of constraints
for (int i = 1; i <= num; i++) {
lua_rawgeti(L, -1, i);
css.push_back(to_constraints(L, -1));
lua_pop(L, 1);
}
r = to_lazy(to_list(css.begin(), css.end()));
}
}
} else if (lua_isnil(L, -1)) {
// nil case
r = lazy_list<constraints>();
} else {
throw exception("invalid unifier plugin, the result value must be a constrant, "
"nil, an array of constraints, or an array of arrays of constraints");
}
lua_pop(L, 1);
return r;
});
}
static name g_tmp_prefix = name::mk_internal_unique_name();
static int unify(lua_State * L) {
int nargs = lua_gettop(L);
lazy_list<substitution> r;
environment const & env = to_environment(L, 1);
if (is_expr(L, 2)) {
if (nargs == 3)
r = unify(env, to_expr(L, 2), to_expr(L, 3), name_generator(g_tmp_prefix));
else if (nargs == 4 && is_name_generator(L, 4))
r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4));
else if (nargs == 4)
r = unify(env, to_expr(L, 2), to_expr(L, 3), name_generator(g_tmp_prefix), to_unifier_plugin(L, 4));
else
r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4), to_unifier_plugin(L, 5));
} else {
buffer<constraint> cs;
to_constraint_buffer(L, 2, cs);
if (nargs == 2)
r = unify(env, cs.size(), cs.data(), name_generator(g_tmp_prefix));
else if (nargs == 3 && is_name_generator(L, 3))
r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3));
else if (nargs == 3)
r = unify(env, cs.size(), cs.data(), name_generator(g_tmp_prefix), to_unifier_plugin(L, 3));
else
r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3), to_unifier_plugin(L, 4));
}
return push_substitution_seq_it(L, r);
}
void open_unifier(lua_State * L) {
luaL_newmetatable(L, substitution_seq_mt);
lua_pushvalue(L, -1);
lua_setfield(L, -2, "__index");
setfuncs(L, substitution_seq_m, 0);
SET_GLOBAL_FUN(substitution_seq_pred, "is_substitution_seq");
SET_GLOBAL_FUN(unify_simple, "unify_simple");
SET_GLOBAL_FUN(unify, "unify");
lua_newtable(L);
SET_ENUM("Solved", unify_status::Solved);
SET_ENUM("Failed", unify_status::Failed);
SET_ENUM("Unsupported", unify_status::Unsupported);
lua_setglobal(L, "unify_status");
}
}