595 lines
25 KiB
C++
595 lines
25 KiB
C++
/*
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Copyright (c) 2013-2014 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 <chrono>
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#include <string>
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#include "util/luaref.h"
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#include "util/sstream.h"
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#include "util/interrupt.h"
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#include "util/lazy_list_fn.h"
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#include "kernel/instantiate.h"
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#include "kernel/replace_visitor.h"
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#include "library/kernel_bindings.h"
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#include "library/tactic/tactic.h"
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#include "library/io_state_stream.h"
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namespace lean {
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tactic tactic01(std::function<optional<proof_state>(environment const &, io_state const & ios, proof_state const &)> f) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
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return mk_proof_state_seq([=]() {
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auto r = f(env, ios, s);
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if (r)
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return some(mk_pair(*r, proof_state_seq()));
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else
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return proof_state_seq::maybe_pair();
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});
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});
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}
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tactic tactic1(std::function<proof_state(environment const &, io_state const & ios, proof_state const &)> f) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
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return mk_proof_state_seq([=]() {
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auto r = f(env, ios, s);
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return some(mk_pair(r, proof_state_seq()));
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});
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});
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}
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tactic id_tactic() {
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return tactic1([](environment const &, io_state const &, proof_state const & s) -> proof_state { return s; });
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}
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tactic fail_tactic() {
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return tactic([](environment const &, io_state const &, proof_state const &) -> proof_state_seq { return proof_state_seq(); });
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}
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tactic now_tactic() {
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return tactic01([](environment const &, io_state const &, proof_state const & s) -> optional<proof_state> {
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if (!empty(s.get_goals()))
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return none_proof_state();
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else
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return some(s);
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});
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}
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tactic cond(proof_state_pred p, tactic const & t1, tactic const & t2) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return mk_proof_state_seq([=]() {
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if (p(env, ios, s)) {
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return t1(env, ios, s).pull();
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} else {
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return t2(env, ios, s).pull();
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}
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});
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});
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}
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tactic trace_tactic(std::string const & msg) {
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return tactic1([=](environment const &, io_state const & ios, proof_state const & s) -> proof_state {
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ios.get_diagnostic_channel() << msg << "\n";
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ios.get_diagnostic_channel().get_stream().flush();
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return s;
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});
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}
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tactic trace_tactic(sstream const & msg) {
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return trace_tactic(msg.str());
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}
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tactic trace_tactic(char const * msg) {
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return trace_tactic(std::string(msg));
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}
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tactic trace_state_tactic() {
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return tactic1([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state {
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diagnostic(env, ios) << s << endl;
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ios.get_diagnostic_channel().get_stream().flush();
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return s;
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});
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}
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tactic suppress_trace(tactic const & t) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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io_state new_ios(ios);
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std::shared_ptr<output_channel> out(std::make_shared<string_output_channel>());
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new_ios.set_diagnostic_channel(out);
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return t(env, new_ios, s);
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});
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}
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tactic then(tactic const & t1, tactic const & t2) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s1) -> proof_state_seq {
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return map_append(t1(env, ios, s1), [=](proof_state const & s2) {
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check_interrupted();
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return t2(env, ios, s2);
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}, "THEN tactical");
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});
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}
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tactic orelse(tactic const & t1, tactic const & t2) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return orelse(t1(env, ios, s), t2(env, ios, s), "ORELSE tactical");
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});
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}
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tactic using_params(tactic const & t, options const & opts) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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io_state new_ios(ios);
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new_ios.set_options(join(opts, ios.get_options()));
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return t(env, new_ios, s);
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});
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}
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tactic try_for(tactic const & t, unsigned ms, unsigned check_ms) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return timeout(t(env, ios, s), ms, check_ms);
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});
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}
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tactic append(tactic const & t1, tactic const & t2) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return append(t1(env, ios, s), t2(env, ios, s), "APPEND tactical");
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});
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}
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tactic interleave(tactic const & t1, tactic const & t2) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return interleave(t1(env, ios, s), t2(env, ios, s), "INTERLEAVE tactical");
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});
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}
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tactic par(tactic const & t1, tactic const & t2, unsigned check_ms) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return par(t1(env, ios, s), t2(env, ios, s), check_ms);
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});
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}
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tactic repeat(tactic const & t) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s1) -> proof_state_seq {
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return repeat(s1, [=](proof_state const & s2) {
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return t(env, ios, s2);
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}, "REPEAT tactical");
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});
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}
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tactic repeat_at_most(tactic const & t, unsigned k) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s1) -> proof_state_seq {
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return repeat_at_most(s1, [=](proof_state const & s2) {
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return t(env, ios, s2);
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}, k, "REPEAT_AT_MOST tactical");
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});
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}
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tactic take(tactic const & t, unsigned k) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return take(k, t(env, ios, s));
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});
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}
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tactic assumption_tactic() {
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return tactic01([](environment const &, io_state const &, proof_state const & s) -> optional<proof_state> {
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list<std::pair<name, expr>> proofs;
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goals new_gs = map_goals(s, [&](name const & gname, goal const & g) -> optional<goal> {
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expr const & c = g.get_conclusion();
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optional<expr> pr;
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for (auto const & p : g.get_hypotheses()) {
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check_interrupted();
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if (mlocal_type(p.first) == c) {
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pr = p.first;
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break;
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}
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}
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if (pr) {
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proofs.emplace_front(gname, *pr);
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return optional<goal>();
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} else {
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return some(g);
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}
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});
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if (empty(proofs))
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return none_proof_state();
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return some(proof_state(s, new_gs, add_proofs(s.get_pb(), proofs)));
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});
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}
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tactic beta_tactic() {
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return tactic01([=](environment const &, io_state const &, proof_state const & s) -> optional<proof_state> {
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bool reduced = false;
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goals new_gs = map_goals(s, [&](name const &, goal const & g) -> optional<goal> {
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hypotheses new_hs = map(g.get_hypotheses(), [&](hypothesis const & h) {
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expr new_h = update_mlocal(h.first, beta_reduce(mlocal_type(h.first)));
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if (new_h != h.first)
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reduced = true;
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return hypothesis(new_h, h.second);
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});
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expr const & c = g.get_conclusion();
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expr new_c = beta_reduce(c);
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if (new_c != c)
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reduced = true;
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return some(goal(new_hs, new_c));
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});
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return reduced ? some(proof_state(s, new_gs)) : none_proof_state();
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});
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}
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proof_state_seq focus_core(tactic const & t, name const & gname, environment const & env, io_state const & ios, proof_state const & s) {
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for (auto const & p : s.get_goals()) {
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if (p.first == gname) {
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proof_builder pb = proof_builder([=](proof_map const & m, substitution const &) -> expr { return find(m, gname); });
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cex_builder cb = mk_cex_builder_for(gname);
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proof_state new_s(s, goals(p), pb, cb); // new state with singleton goal
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return map(t(env, ios, new_s), [=](proof_state const & s2) {
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// we have to put back the goals that were not selected
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list<std::pair<name, name>> renamed_goals;
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goals new_gs = map_append(s.get_goals(), [&](std::pair<name, goal> const & p) {
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if (p.first == gname) {
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name_set used_names;
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s.get_goal_names(used_names);
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used_names.erase(gname);
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return map(s2.get_goals(), [&](std::pair<name, goal> const & p2) -> std::pair<name, goal> {
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name uname = mk_unique(used_names, p2.first);
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used_names.insert(uname);
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renamed_goals.emplace_front(p2.first, uname);
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return mk_pair(uname, p2.second);
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});
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} else {
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return goals(p);
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}
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});
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proof_builder pb1 = s.get_pb();
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proof_builder pb2 = s2.get_pb();
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proof_builder new_pb = proof_builder(
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[=](proof_map const & m, substitution const & a) -> expr {
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proof_map m1(m); // map for pb1
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proof_map m2; // map for pb2
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for (auto p : renamed_goals) {
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m2.insert(p.first, find(m, p.second));
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m1.erase(p.first);
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}
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m1.insert(gname, pb2(m2, a));
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return pb1(m1, a);
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});
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cex_builder cb1 = s.get_cb();
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cex_builder cb2 = s2.get_cb();
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cex_builder new_cb = cex_builder(
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[=](name const & n, optional<counterexample> const & cex, substitution const & a) -> counterexample {
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for (auto p : renamed_goals) {
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if (p.second == n)
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return cb2(p.first, cex, a);
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}
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return cb1(n, cex, a);
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});
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return proof_state(s2, new_gs, new_pb, new_cb);
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});
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}
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}
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return proof_state_seq(); // tactic is not applicable
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}
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tactic focus(tactic const & t, name const & gname) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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return focus_core(t, gname, env, ios, s);
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});
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}
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tactic focus(tactic const & t, int i) {
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return tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
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if (optional<name> n = s.get_ith_goal_name(i))
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return focus_core(t, *n, env, ios, s);
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else
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return proof_state_seq();
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});
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}
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class unfold_core_fn : public replace_visitor {
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protected:
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bool m_unfolded;
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virtual expr visit_app(expr const & e) {
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expr const & f = get_app_fn(e);
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if (is_constant(f)) {
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expr new_f = visit(f);
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bool modified = new_f != f;
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buffer<expr> new_args;
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get_app_args(e, new_args);
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for (unsigned i = 0; i < new_args.size(); i++) {
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expr arg = new_args[i];
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new_args[i] = visit(arg);
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if (!modified && new_args[i] != arg)
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modified = true;
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}
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if (is_lambda(new_f)) {
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std::reverse(new_args.begin(), new_args.end());
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return apply_beta(new_f, new_args.size(), new_args.data());
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} else if (modified) {
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return mk_app(new_f, new_args);
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} else {
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return e;
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}
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} else {
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return replace_visitor::visit_app(e);
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}
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}
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public:
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unfold_core_fn():m_unfolded(false) {}
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bool unfolded() const { return m_unfolded; }
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};
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class unfold_fn : public unfold_core_fn {
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protected:
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name const & m_name;
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level_param_names const & m_ps;
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expr const & m_def;
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virtual expr visit_constant(expr const & c) {
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if (const_name(c) == m_name) {
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m_unfolded = true;
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return instantiate_params(m_def, m_ps, const_levels(c));
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} else {
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return c;
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}
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}
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public:
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unfold_fn(name const & n, level_param_names const & ps, expr const & d):m_name(n), m_ps(ps), m_def(d) {}
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};
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class unfold_all_fn : public unfold_core_fn {
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protected:
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environment m_env;
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virtual expr visit_constant(expr const & c) {
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optional<declaration> d = m_env.find(const_name(c));
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if (d && d->is_definition() && (!d->is_opaque() || d->get_module_idx() == 0)) {
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m_unfolded = true;
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return instantiate_params(d->get_value(), d->get_univ_params(), const_levels(c));
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} else {
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return c;
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}
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}
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public:
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unfold_all_fn(environment const & env):m_env(env) {}
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};
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optional<proof_state> unfold_tactic_core(unfold_core_fn & fn, proof_state const & s) {
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goals new_gs = map_goals(s, [&](name const &, goal const & g) -> optional<goal> {
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hypotheses new_hs = map(g.get_hypotheses(), [&](hypothesis const & h) {
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expr l = update_mlocal(h.first, fn(mlocal_type(h.first)));
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return hypothesis(l, h.second);
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});
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expr new_c = fn(g.get_conclusion());
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return some(goal(new_hs, new_c));
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});
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if (fn.unfolded()) {
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return some(proof_state(s, new_gs));
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} else {
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return none_proof_state();
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}
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}
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tactic unfold_tactic(name const & n) {
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return tactic01([=](environment const & env, io_state const &, proof_state const & s) -> optional<proof_state> {
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optional<declaration> d = env.find(n);
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if (!d || !d->is_definition() || (d->is_opaque() && d->get_module_idx() != 0))
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return none_proof_state(); // tactic failed
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unfold_fn fn(n, d->get_univ_params(), d->get_value());
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return unfold_tactic_core(fn, s);
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});
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}
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tactic unfold_tactic() {
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return tactic01([=](environment const & env, io_state const &, proof_state const & s) -> optional<proof_state> {
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unfold_all_fn fn(env);
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return unfold_tactic_core(fn, s);
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});
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}
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DECL_UDATA(proof_state_seq)
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static const struct luaL_Reg proof_state_seq_m[] = {
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{"__gc", proof_state_seq_gc}, // never throws
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{0, 0}
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};
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static int proof_state_seq_next(lua_State * L) {
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proof_state_seq seq = to_proof_state_seq(L, lua_upvalueindex(1));
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auto p = seq.pull();
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if (p) {
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push_proof_state_seq(L, p->second);
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lua_replace(L, lua_upvalueindex(1));
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push_proof_state(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_proof_state_seq_it(lua_State * L, proof_state_seq const & seq) {
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push_proof_state_seq(L, seq);
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lua_pushcclosure(L, &safe_function<proof_state_seq_next>, 1); // create closure with 1 upvalue
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return 1;
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}
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DECL_UDATA(tactic)
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[[ noreturn ]] void throw_tactic_expected(int i) {
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throw exception(sstream() << "arg #" << i << " must be a tactic or a function that returns a tactic");
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}
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static int tactic_call_core(lua_State * L, tactic t, environment env, io_state ios, proof_state s) {
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return push_proof_state_seq_it(L, t(env, ios, s));
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}
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static int tactic_call(lua_State * L) {
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int nargs = lua_gettop(L);
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tactic t = to_tactic(L, 1);
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environment env = to_environment(L, 2);
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if (nargs == 3)
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return tactic_call_core(L, t, env, get_io_state(L), to_proof_state(L, 3));
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else
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return tactic_call_core(L, t, env, to_io_state(L, 3), to_proof_state(L, 4));
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}
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typedef tactic (*binary_tactic_fn)(tactic const &, tactic const &);
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template<binary_tactic_fn F>
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static int nary_tactic(lua_State * L) {
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int nargs = lua_gettop(L);
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if (nargs < 2)
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throw exception("tactical expects at least two arguments");
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tactic r = F(to_tactic(L, 1), to_tactic(L, 2));
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for (int i = 3; i <= nargs; i++)
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r = F(r, to_tactic(L, i));
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return push_tactic(L, r);
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}
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static int tactic_then(lua_State * L) { return push_tactic(L, then(to_tactic(L, 1), to_tactic(L, 2))); }
|
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static int tactic_orelse(lua_State * L) { return push_tactic(L, orelse(to_tactic(L, 1), to_tactic(L, 2))); }
|
|
static int tactic_append(lua_State * L) { return push_tactic(L, append(to_tactic(L, 1), to_tactic(L, 2))); }
|
|
static int tactic_interleave(lua_State * L) { return push_tactic(L, interleave(to_tactic(L, 1), to_tactic(L, 2))); }
|
|
static int tactic_par(lua_State * L) { return push_tactic(L, par(to_tactic(L, 1), to_tactic(L, 2))); }
|
|
static int tactic_repeat(lua_State * L) { return push_tactic(L, repeat(to_tactic(L, 1))); }
|
|
static int tactic_repeat1(lua_State * L) { return push_tactic(L, repeat1(to_tactic(L, 1))); }
|
|
static int tactic_repeat_at_most(lua_State * L) { return push_tactic(L, repeat_at_most(to_tactic(L, 1), luaL_checkinteger(L, 2))); }
|
|
static int tactic_take(lua_State * L) { return push_tactic(L, take(to_tactic(L, 1), luaL_checkinteger(L, 2))); }
|
|
static int tactic_determ(lua_State * L) { return push_tactic(L, determ(to_tactic(L, 1))); }
|
|
static int tactic_suppress_trace(lua_State * L) { return push_tactic(L, suppress_trace(to_tactic(L, 1))); }
|
|
static int tactic_try_for(lua_State * L) { return push_tactic(L, try_for(to_tactic(L, 1), luaL_checkinteger(L, 2))); }
|
|
static int tactic_using_params(lua_State * L) { return push_tactic(L, using_params(to_tactic(L, 1), to_options(L, 2))); }
|
|
static int tactic_try(lua_State * L) { return push_tactic(L, orelse(to_tactic(L, 1), id_tactic())); }
|
|
static int tactic_focus(lua_State * L) {
|
|
int nargs = lua_gettop(L);
|
|
if (nargs == 1)
|
|
return push_tactic(L, focus(to_tactic(L, 1)));
|
|
else if (lua_isnumber(L, 2))
|
|
return push_tactic(L, focus(to_tactic(L, 1), lua_tointeger(L, 2)));
|
|
else
|
|
return push_tactic(L, focus(to_tactic(L, 1), to_name_ext(L, 2)));
|
|
}
|
|
static int mk_lua_tactic01(lua_State * L) {
|
|
luaL_checktype(L, 1, LUA_TFUNCTION); // user-fun
|
|
luaref ref(L, 1);
|
|
tactic t = tactic01([=](environment const & env, io_state const & ios, proof_state const & s) -> optional<proof_state> {
|
|
ref.push(); // push user-fun on the stack
|
|
push_environment(L, env); // push args...
|
|
push_io_state(L, ios);
|
|
push_proof_state(L, s);
|
|
pcall(L, 3, 1, 0);
|
|
optional<proof_state> r;
|
|
if (is_proof_state(L, -1))
|
|
r = to_proof_state(L, -1);
|
|
lua_pop(L, 1);
|
|
return r;
|
|
});
|
|
return push_tactic(L, t);
|
|
}
|
|
|
|
static int mk_lua_cond_tactic(lua_State * L, tactic t1, tactic t2) {
|
|
luaL_checktype(L, 1, LUA_TFUNCTION); // user-fun
|
|
luaref ref(L, 1);
|
|
tactic t = tactic([=](environment const & env, io_state const & ios, proof_state const & s) -> proof_state_seq {
|
|
return mk_proof_state_seq([=]() {
|
|
ref.push(); // push user-fun on the stack
|
|
push_environment(L, env); // push args...
|
|
push_io_state(L, ios);
|
|
push_proof_state(L, s);
|
|
pcall(L, 3, 1, 0);
|
|
bool cond = lua_toboolean(L, -1);
|
|
lua_pop(L, 1);
|
|
if (cond) {
|
|
return t1(env, ios, s).pull();
|
|
} else {
|
|
return t2(env, ios, s).pull();
|
|
}
|
|
});
|
|
});
|
|
return push_tactic(L, t);
|
|
}
|
|
|
|
static int mk_lua_cond_tactic(lua_State * L) { return mk_lua_cond_tactic(L, to_tactic(L, 2), to_tactic(L, 3)); }
|
|
static int mk_lua_when_tactic(lua_State * L) { return mk_lua_cond_tactic(L, to_tactic(L, 2), id_tactic()); }
|
|
static int mk_id_tactic(lua_State * L) { return push_tactic(L, id_tactic()); }
|
|
static int mk_now_tactic(lua_State * L) { return push_tactic(L, now_tactic()); }
|
|
static int mk_fail_tactic(lua_State * L) { return push_tactic(L, fail_tactic()); }
|
|
static int mk_trace_tactic(lua_State * L) { return push_tactic(L, trace_tactic(luaL_checkstring(L, 1))); }
|
|
static int mk_assumption_tactic(lua_State * L) { return push_tactic(L, assumption_tactic()); }
|
|
static int mk_trace_state_tactic(lua_State * L) { return push_tactic(L, trace_state_tactic()); }
|
|
static int mk_unfold_tactic(lua_State * L) {
|
|
int nargs = lua_gettop(L);
|
|
if (nargs == 0)
|
|
return push_tactic(L, unfold_tactic());
|
|
else
|
|
return push_tactic(L, unfold_tactic(to_name_ext(L, 1)));
|
|
}
|
|
static int mk_beta_tactic(lua_State * L) { return push_tactic(L, beta_tactic()); }
|
|
static const struct luaL_Reg tactic_m[] = {
|
|
{"__gc", tactic_gc}, // never throws
|
|
{"__call", safe_function<tactic_call>},
|
|
{"__concat", safe_function<tactic_then>},
|
|
{"__pow", safe_function<tactic_orelse>},
|
|
{"__add", safe_function<tactic_append>},
|
|
{"then", safe_function<tactic_then>},
|
|
{"orelse", safe_function<tactic_orelse>},
|
|
{"append", safe_function<tactic_append>},
|
|
{"interleave", safe_function<tactic_interleave>},
|
|
{"par", safe_function<tactic_par>},
|
|
{"determ", safe_function<tactic_determ>},
|
|
{"repeat", safe_function<tactic_repeat>},
|
|
{"repeat1", safe_function<tactic_repeat1>},
|
|
{"repeat_at_most", safe_function<tactic_repeat_at_most>},
|
|
{"take", safe_function<tactic_take>},
|
|
{"suppress_trace", safe_function<tactic_suppress_trace>},
|
|
{"try_for", safe_function<tactic_try_for>},
|
|
{"using_params", safe_function<tactic_using_params>},
|
|
{"using", safe_function<tactic_using_params>},
|
|
{"focus", safe_function<tactic_focus>},
|
|
{0, 0}
|
|
};
|
|
|
|
void open_tactic(lua_State * L) {
|
|
luaL_newmetatable(L, proof_state_seq_mt);
|
|
lua_pushvalue(L, -1);
|
|
lua_setfield(L, -2, "__index");
|
|
setfuncs(L, proof_state_seq_m, 0);
|
|
SET_GLOBAL_FUN(proof_state_seq_pred, "is_proof_state_seq");
|
|
|
|
luaL_newmetatable(L, tactic_mt);
|
|
lua_pushvalue(L, -1);
|
|
lua_setfield(L, -2, "__index");
|
|
setfuncs(L, tactic_m, 0);
|
|
|
|
SET_GLOBAL_FUN(tactic_pred, "is_tactic");
|
|
SET_GLOBAL_FUN(mk_trace_tactic, "trace_tac");
|
|
SET_GLOBAL_FUN(mk_id_tactic, "id_tac");
|
|
SET_GLOBAL_FUN(mk_now_tactic, "now_tac");
|
|
SET_GLOBAL_FUN(mk_fail_tactic, "fail_tac");
|
|
SET_GLOBAL_FUN(mk_trace_state_tactic, "show_tac");
|
|
SET_GLOBAL_FUN(mk_assumption_tactic, "assumption_tac");
|
|
SET_GLOBAL_FUN(mk_unfold_tactic, "unfold_tac");
|
|
SET_GLOBAL_FUN(mk_beta_tactic, "beta_tac");
|
|
SET_GLOBAL_FUN(mk_lua_tactic01, "tactic01");
|
|
|
|
// HOL-like tactic names
|
|
SET_GLOBAL_FUN(nary_tactic<then>, "Then");
|
|
SET_GLOBAL_FUN(nary_tactic<orelse>, "OrElse");
|
|
SET_GLOBAL_FUN(nary_tactic<interleave>, "Interleave");
|
|
SET_GLOBAL_FUN(nary_tactic<append>, "Append");
|
|
SET_GLOBAL_FUN(nary_tactic<par>, "Par");
|
|
SET_GLOBAL_FUN(tactic_repeat, "Repeat");
|
|
SET_GLOBAL_FUN(tactic_repeat_at_most, "RepeatAtMost");
|
|
SET_GLOBAL_FUN(tactic_repeat1, "Repeat1");
|
|
SET_GLOBAL_FUN(mk_lua_cond_tactic, "Cond");
|
|
SET_GLOBAL_FUN(mk_lua_when_tactic, "When");
|
|
SET_GLOBAL_FUN(tactic_try, "Try");
|
|
SET_GLOBAL_FUN(tactic_try_for, "TryFor");
|
|
SET_GLOBAL_FUN(tactic_take, "Take");
|
|
SET_GLOBAL_FUN(tactic_using_params, "Using");
|
|
SET_GLOBAL_FUN(tactic_using_params, "UsingParams");
|
|
SET_GLOBAL_FUN(tactic_determ, "Determ");
|
|
SET_GLOBAL_FUN(tactic_focus, "Focus");
|
|
}
|
|
}
|