feat(library): add unifier module skeleton
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
37bee8c852
commit
bf8f3318d8
5 changed files with 478 additions and 1 deletions
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@ -3,7 +3,8 @@ add_library(library deep_copy.cpp expr_lt.cpp io_state.cpp occurs.cpp
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resolve_macro.cpp kernel_serializer.cpp max_sharing.cpp
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normalize.cpp shared_environment.cpp module.cpp coercion.cpp
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private.cpp placeholder.cpp aliases.cpp level_names.cpp
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update_declaration.cpp choice.cpp scoped_ext.cpp locals.cpp)
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update_declaration.cpp choice.cpp scoped_ext.cpp locals.cpp
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unifier.cpp)
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# hop_match.cpp)
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target_link_libraries(library ${LEAN_LIBS})
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346
src/library/unifier.cpp
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346
src/library/unifier.cpp
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@ -0,0 +1,346 @@
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/*
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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 <utility>
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#include "util/luaref.h"
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#include "util/lazy_list_fn.h"
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#include "kernel/for_each_fn.h"
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#include "kernel/abstract.h"
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#include "kernel/type_checker.h"
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#include "library/unifier.h"
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#include "library/kernel_bindings.h"
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namespace lean {
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static std::pair<unify_status, substitution> unify_simple_core(substitution const & s, expr const & lhs, expr const & rhs,
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justification const & j) {
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lean_assert(is_meta(lhs));
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buffer<expr> args;
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expr const & m = get_app_args(lhs, args);
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lean_assert(is_metavar(m));
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for (auto it = args.begin(); it != args.end(); it++) {
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if (!is_local(*it) || std::find(args.begin(), it, *it) != it)
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return mk_pair(unify_status::Unsupported, s);
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}
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if (is_meta(rhs) && get_app_fn(rhs) == m)
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return mk_pair(unify_status::Unsupported, s);
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bool failed = false;
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for_each(rhs, [&](expr const & e, unsigned) {
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if (failed)
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return false;
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if (is_local(e) && std::find(args.begin(), args.end(), e) == args.end()) {
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// right-hand-side contains variable that is not in the scope
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// of metavariable.
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failed = true;
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return false;
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}
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if (is_metavar(e) && e == m) {
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// occurs-check failed
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failed = true;
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return false;
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}
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// we only need to continue exploring e if it contains
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// metavariables and/or local constants.
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return has_metavar(e) || has_local(e);
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});
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if (failed)
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return mk_pair(unify_status::Failed, s);
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expr v = abstract_locals(rhs, args.size(), args.data());
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unsigned i = args.size();
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while (i > 0) {
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--i;
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v = mk_lambda(local_pp_name(args[i]), mlocal_type(args[i]), v);
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}
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return mk_pair(unify_status::Solved, s.assign(mlocal_name(m), v, j));
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}
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std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j) {
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if (lhs == rhs)
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return mk_pair(unify_status::Solved, s);
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else if (!has_metavar(lhs) && !has_metavar(rhs))
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return mk_pair(unify_status::Failed, s);
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else if (is_meta(lhs))
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return unify_simple_core(s, lhs, rhs, j);
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else if (is_meta(rhs))
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return unify_simple_core(s, rhs, lhs, j);
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else
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return mk_pair(unify_status::Unsupported, s);
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}
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std::pair<unify_status, substitution> unify_simple_core(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
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lean_assert(is_meta(lhs));
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bool contains = false;
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for_each(rhs, [&](level const & l) {
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if (contains)
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return false;
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if (l == lhs) {
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// occurs-check failed
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contains = true;
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return false;
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}
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return true;
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});
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if (contains) {
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if (is_succ(rhs))
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return mk_pair(unify_status::Failed, s);
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else
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return mk_pair(unify_status::Unsupported, s);
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}
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return mk_pair(unify_status::Solved, s.assign(meta_id(lhs), rhs, j));
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}
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std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
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if (lhs == rhs)
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return mk_pair(unify_status::Solved, s);
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else if (!has_meta(lhs) && !has_meta(rhs))
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return mk_pair(unify_status::Failed, s);
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else if (is_meta(lhs))
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return unify_simple_core(s, lhs, rhs, j);
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else if (is_meta(rhs))
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return unify_simple_core(s, rhs, lhs, j);
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else if (is_succ(lhs) && is_succ(rhs))
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return unify_simple(s, succ_of(lhs), succ_of(rhs), j);
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else
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return mk_pair(unify_status::Unsupported, s);
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}
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std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c) {
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if (is_eq_cnstr(c))
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return unify_simple(s, cnstr_lhs_expr(c), cnstr_rhs_expr(c), c.get_justification());
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else if (is_level_cnstr(c))
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return unify_simple(s, cnstr_lhs_level(c), cnstr_rhs_level(c), c.get_justification());
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else
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return mk_pair(unify_status::Unsupported, s);
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}
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struct unifier_fn {
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environment m_env;
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name_generator m_ngen;
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substitution m_subst;
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unifier_plugin m_plugin;
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bool m_use_exception;
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unifier_fn(environment const & env, unsigned /* num_cs */, constraint const * /* cs */,
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name_generator const & ngen, substitution const & s, unifier_plugin const & p,
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bool use_exception):
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m_env(env), m_ngen(ngen), m_subst(s), m_plugin(p), m_use_exception(use_exception) {
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}
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optional<substitution> next() {
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// TODO(Leo)
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return optional<substitution>();
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}
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};
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lazy_list<substitution> unify(std::shared_ptr<unifier_fn> const & u) {
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return mk_lazy_list<substitution>([=]() {
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auto s = u->next();
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if (s)
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return some(mk_pair(*s, unify(u)));
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else
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return lazy_list<substitution>::maybe_pair();
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});
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}
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lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
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unifier_plugin const & p, bool use_exception) {
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return unify(std::make_shared<unifier_fn>(env, num_cs, cs, ngen, substitution(), p, use_exception));
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}
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lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
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bool use_exception) {
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return unify(env, num_cs, cs, ngen, [](constraint const &, name_generator const &) { return lazy_list<constraints>(); }, use_exception);
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}
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lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen, unifier_plugin const & p) {
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substitution s;
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buffer<constraint> cs;
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name_generator new_ngen(ngen);
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bool failed = false;
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type_checker tc(env, new_ngen.mk_child(), [&](constraint const & c) {
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if (!failed) {
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auto r = unify_simple(s, c);
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switch (r.first) {
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case unify_status::Solved:
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s = r.second; break;
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case unify_status::Failed:
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failed = true; break;
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case unify_status::Unsupported:
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cs.push_back(c); break;
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}
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}
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});
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if (!tc.is_def_eq(lhs, rhs) || failed) {
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return lazy_list<substitution>();
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} else if (cs.empty()) {
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return lazy_list<substitution>(s);
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} else {
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return unify(std::make_shared<unifier_fn>(env, cs.size(), cs.data(), ngen, s, p, false));
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}
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}
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lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen) {
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return unify(env, lhs, rhs, ngen, [](constraint const &, name_generator const &) { return lazy_list<constraints>(); });
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}
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static int unify_simple(lua_State * L) {
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int nargs = lua_gettop(L);
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std::pair<unify_status, substitution> r;
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if (nargs == 2)
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r = unify_simple(to_substitution(L, 1), to_constraint(L, 2));
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else if (nargs == 3 && is_expr(L, 2))
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r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), justification());
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else if (nargs == 3 && is_level(L, 2))
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r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), justification());
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else if (is_expr(L, 2))
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r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), to_justification(L, 4));
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else
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r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), to_justification(L, 4));
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push_integer(L, static_cast<unsigned>(r.first));
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push_substitution(L, r.second);
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return 2;
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}
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typedef lazy_list<substitution> substitution_seq;
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DECL_UDATA(substitution_seq)
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static const struct luaL_Reg substitution_seq_m[] = {
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{"__gc", substitution_seq_gc},
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{0, 0}
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};
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static int substitution_seq_next(lua_State * L) {
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substitution_seq seq = to_substitution_seq(L, lua_upvalueindex(1));
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substitution_seq::maybe_pair p;
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p = seq.pull();
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if (p) {
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push_substitution_seq(L, p->second);
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lua_replace(L, lua_upvalueindex(1));
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push_substitution(L, p->first);
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} else {
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lua_pushnil(L);
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}
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return 1;
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}
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static int push_substitution_seq_it(lua_State * L, substitution_seq const & seq) {
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push_substitution_seq(L, seq);
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lua_pushcclosure(L, &safe_function<substitution_seq_next>, 1); // create closure with 1 upvalue
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return 1;
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}
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static void to_constraint_buffer(lua_State * L, int idx, buffer<constraint> & cs) {
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luaL_checktype(L, idx, LUA_TTABLE);
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lua_pushvalue(L, idx); // put table on top of the stack
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int n = objlen(L, idx);
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for (int i = 1; i <= n; i++) {
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lua_rawgeti(L, -1, i);
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cs.push_back(to_constraint(L, -1));
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lua_pop(L, 1);
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}
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lua_pop(L, 1);
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}
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static constraints to_constraints(lua_State * L, int idx) {
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buffer<constraint> cs;
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to_constraint_buffer(L, idx, cs);
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return to_list(cs.begin(), cs.end());
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}
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static unifier_plugin to_unifier_plugin(lua_State * L, int idx) {
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luaL_checktype(L, idx, LUA_TFUNCTION); // user-fun
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luaref f(L, idx);
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return unifier_plugin([=](constraint const & c, name_generator const & ngen) {
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lua_State * L = f.get_state();
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f.push();
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push_constraint(L, c);
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push_name_generator(L, ngen);
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pcall(L, 2, 1, 0);
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lazy_list<constraints> r;
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if (is_constraint(L, -1)) {
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// single constraint
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r = lazy_list<constraints>(constraints(to_constraint(L, -1)));
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} else if (lua_istable(L, -1)) {
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int num = objlen(L, -1);
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if (num == 0) {
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// empty table
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r = lazy_list<constraints>();
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} else {
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lua_rawgeti(L, -1, 1);
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if (is_constraint(L, -1)) {
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// array of constraints case
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lua_pop(L, 1);
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r = lazy_list<constraints>(to_constraints(L, -1));
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} else {
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lua_pop(L, 1);
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buffer<constraints> css;
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// array of array of constraints
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for (int i = 1; i <= num; i++) {
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lua_rawgeti(L, -1, i);
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css.push_back(to_constraints(L, -1));
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lua_pop(L, 1);
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}
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r = to_lazy(to_list(css.begin(), css.end()));
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}
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}
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} else if (lua_isnil(L, -1)) {
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// nil case
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r = lazy_list<constraints>();
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} else {
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throw exception("invalid unifier plugin, the result value must be a constrant, "
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"nil, an array of constraints, or an array of arrays of constraints");
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}
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lua_pop(L, 1);
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return r;
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});
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}
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static name g_tmp_prefix = name::mk_internal_unique_name();
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static int unify(lua_State * L) {
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int nargs = lua_gettop(L);
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lazy_list<substitution> r;
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environment const & env = to_environment(L, 1);
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if (is_expr(L, 2)) {
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if (nargs == 3)
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r = unify(env, to_expr(L, 2), to_expr(L, 3), name_generator(g_tmp_prefix));
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else if (nargs == 4 && is_name_generator(L, 4))
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r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4));
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else if (nargs == 4)
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r = unify(env, to_expr(L, 2), to_expr(L, 3), name_generator(g_tmp_prefix), to_unifier_plugin(L, 4));
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else
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r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4), to_unifier_plugin(L, 5));
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} else {
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buffer<constraint> cs;
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to_constraint_buffer(L, 2, cs);
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if (nargs == 2)
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r = unify(env, cs.size(), cs.data(), name_generator(g_tmp_prefix));
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else if (nargs == 3 && is_name_generator(L, 3))
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r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3));
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else if (nargs == 3)
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r = unify(env, cs.size(), cs.data(), name_generator(g_tmp_prefix), to_unifier_plugin(L, 3));
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else
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r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3), to_unifier_plugin(L, 4));
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}
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return push_substitution_seq_it(L, r);
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}
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void open_unifier(lua_State * L) {
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luaL_newmetatable(L, substitution_seq_mt);
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lua_pushvalue(L, -1);
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lua_setfield(L, -2, "__index");
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setfuncs(L, substitution_seq_m, 0);
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SET_GLOBAL_FUN(substitution_seq_pred, "is_substitution_seq");
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SET_GLOBAL_FUN(unify_simple, "unify_simple");
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SET_GLOBAL_FUN(unify, "unify");
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lua_newtable(L);
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SET_ENUM("Solved", unify_status::Solved);
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SET_ENUM("Failed", unify_status::Failed);
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SET_ENUM("Unsupported", unify_status::Unsupported);
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lua_setglobal(L, "unify_status");
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}
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}
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44
src/library/unifier.h
Normal file
44
src/library/unifier.h
Normal file
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@ -0,0 +1,44 @@
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/*
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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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#pragma once
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#include <utility>
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#include <functional>
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#include "util/lua.h"
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#include "util/lazy_list.h"
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#include "util/name_generator.h"
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#include "kernel/constraint.h"
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#include "kernel/environment.h"
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#include "kernel/metavar.h"
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namespace lean {
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enum class unify_status { Solved, Failed, Unsupported };
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/**
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\brief Handle the easy-cases: first-order unification, higher-order patterns, identical terms, and terms without metavariables.
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This function assumes that all assigned metavariables have been substituted.
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*/
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std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j);
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std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j);
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std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c);
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/**
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\brief A unifier_plugin provides a simple way to extend the \c unify procedures.
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Whenever, the default implementation does not know how to solve a constraint, it invokes the plugin.
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The plugin return a lazy_list (stream) of possible solutions. Each "solution" is represented as
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a new list of constraints.
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*/
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typedef std::function<lazy_list<constraints>(constraint const &, name_generator const &)> unifier_plugin;
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lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
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unifier_plugin const & p, bool use_exception = true);
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lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
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bool use_exception = true);
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lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen, unifier_plugin const & p);
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lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen);
|
||||
|
||||
void open_unifier(lua_State * L);
|
||||
}
|
||||
55
tests/lua/unify1.lua
Normal file
55
tests/lua/unify1.lua
Normal file
|
|
@ -0,0 +1,55 @@
|
|||
function test_unify_simple(lhs, rhs, expected)
|
||||
print(tostring(lhs) .. " =?= " .. tostring(rhs) .. ", expected: " .. tostring(expected))
|
||||
r, s = unify_simple(substitution(), lhs, rhs, justification())
|
||||
if r == unify_status.Solved then
|
||||
s:for_each_expr(function(n, v, j)
|
||||
print(" " .. tostring(n) .. " := " .. tostring(v))
|
||||
end)
|
||||
s:for_each_level(function(n, v, j)
|
||||
print(" " .. tostring(n) .. " := " .. tostring(v))
|
||||
end)
|
||||
end
|
||||
assert(r == expected)
|
||||
end
|
||||
|
||||
local f = Const("f")
|
||||
local a = Const("a")
|
||||
local l1 = mk_local("l1", "x", Bool)
|
||||
local l2 = mk_local("l2", "y", Bool)
|
||||
local l3 = mk_local("l3", "z", Bool)
|
||||
local m = mk_metavar("m", Bool)
|
||||
|
||||
test_unify_simple(m(l1, l2), f(f(a, l1), l1), unify_status.Solved)
|
||||
test_unify_simple(m(l1, l2), m(l1, l2), unify_status.Solved)
|
||||
test_unify_simple(m(l1, l2), m(l2, l2), unify_status.Unsupported)
|
||||
test_unify_simple(m(l1, l2), f(f(l2, l1), l1), unify_status.Solved)
|
||||
test_unify_simple(m(l1, a), f(f(a), l1), unify_status.Unsupported)
|
||||
test_unify_simple(f(m, a), f(f(a), l1), unify_status.Unsupported)
|
||||
test_unify_simple(m(l1, l2), f(f(m), l1), unify_status.Failed)
|
||||
test_unify_simple(m(l1, l2), f(f(l3), l1), unify_status.Failed)
|
||||
test_unify_simple(m, f(a), unify_status.Solved)
|
||||
test_unify_simple(f(a), f(a), unify_status.Solved)
|
||||
test_unify_simple(f(a), f(f(a)), unify_status.Failed)
|
||||
test_unify_simple(f(f(a, l1), l1), m(l1, l2), unify_status.Solved)
|
||||
test_unify_simple(m(l1, l1), f(f(l2, l1), l1), unify_status.Unsupported)
|
||||
test_unify_simple(m(l1, l2, l1), f(f(l2, l1), l1), unify_status.Unsupported)
|
||||
test_unify_simple(m(l1, l2), Fun(l3, f(f(a, l1), l3)), unify_status.Solved)
|
||||
|
||||
local zero = level()
|
||||
local one = zero+1
|
||||
local l = mk_param_univ("l")
|
||||
local u = mk_global_univ("u")
|
||||
local m = mk_meta_univ("m")
|
||||
test_unify_simple(m+1, u+1, unify_status.Solved)
|
||||
test_unify_simple(u+1, u+1, unify_status.Solved)
|
||||
test_unify_simple(u+1, m+1, unify_status.Solved)
|
||||
test_unify_simple(m, u+1, unify_status.Solved)
|
||||
test_unify_simple(m, max_univ(u, l), unify_status.Solved)
|
||||
test_unify_simple(max_univ(u, l), max_univ(u, l), unify_status.Solved)
|
||||
test_unify_simple(m+1, m+1, unify_status.Solved)
|
||||
test_unify_simple(l, l+1, unify_status.Failed)
|
||||
test_unify_simple(m, m+1, unify_status.Failed)
|
||||
test_unify_simple(m, max_univ(m, u), unify_status.Unsupported)
|
||||
test_unify_simple(m, max_univ(m, u)+1, unify_status.Failed)
|
||||
test_unify_simple(m+2, m+1, unify_status.Failed)
|
||||
test_unify_simple(u+2, m+1, unify_status.Solved)
|
||||
31
tests/lua/unify2.lua
Normal file
31
tests/lua/unify2.lua
Normal file
|
|
@ -0,0 +1,31 @@
|
|||
function test_unify(env, lhs, rhs, num_s)
|
||||
print(tostring(lhs) .. " =?= " .. tostring(rhs) .. ", expected: " .. tostring(num_s))
|
||||
local ss = unify(env, lhs, rhs)
|
||||
local n = 0
|
||||
for s in ss do
|
||||
print("solution: ")
|
||||
s:for_each_expr(function(n, v, j)
|
||||
print(" " .. tostring(n) .. " := " .. tostring(v))
|
||||
end)
|
||||
s:for_each_level(function(n, v, j)
|
||||
print(" " .. tostring(n) .. " := " .. tostring(v))
|
||||
end)
|
||||
n = n + 1
|
||||
end
|
||||
assert(num_s == n)
|
||||
end
|
||||
|
||||
local env = environment()
|
||||
env = add_decl(env, mk_var_decl("N", Type))
|
||||
local N = Const("N")
|
||||
env = add_decl(env, mk_var_decl("f", mk_arrow(N, N, N)))
|
||||
env = add_decl(env, mk_var_decl("a", N))
|
||||
local f = Const("f")
|
||||
local a = Const("a")
|
||||
local l1 = mk_local("l1", "x", N)
|
||||
local l2 = mk_local("l2", "y", N)
|
||||
local l3 = mk_local("l3", "z", N)
|
||||
local m = mk_metavar("m", mk_arrow(N, N, N))
|
||||
test_unify(env, m(l1, l2), f(f(a, l1), l1), 1)
|
||||
test_unify(env, f(m(l1, l2), l1), f(f(a, l1), l1), 1)
|
||||
test_unify(env, f(m(l1, l2), a), f(f(a, l1), l1), 0)
|
||||
Loading…
Reference in a new issue