lean2/src/library/tactic/apply_tactic.cpp
2015-03-12 14:52:41 -07:00

268 lines
11 KiB
C++

/*
Copyright (c) 2013-2014 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/lazy_list_fn.h"
#include "util/sstream.h"
#include "util/name_map.h"
#include "util/sexpr/option_declarations.h"
#include "kernel/for_each_fn.h"
#include "kernel/replace_fn.h"
#include "kernel/instantiate.h"
#include "kernel/abstract.h"
#include "kernel/error_msgs.h"
#include "kernel/type_checker.h"
#include "library/reducible.h"
#include "library/kernel_bindings.h"
#include "library/unifier.h"
#include "library/occurs.h"
#include "library/constants.h"
#include "library/metavar_closure.h"
#include "library/type_util.h"
#include "library/local_context.h"
#include "library/tactic/expr_to_tactic.h"
#include "library/tactic/apply_tactic.h"
#include "library/tactic/class_instance_synth.h"
#ifndef LEAN_DEFAULT_APPLY_CLASS_INSTANCE
#define LEAN_DEFAULT_APPLY_CLASS_INSTANCE true
#endif
namespace lean {
static name * g_apply_class_instance = nullptr;
bool get_apply_class_instance(options const & opts) {
return opts.get_bool(*g_apply_class_instance, LEAN_DEFAULT_APPLY_CLASS_INSTANCE);
}
/**
\brief Given a sequence metas: <tt>(?m_1 ...) (?m_2 ... ) ... (?m_k ...)</tt>,
we say ?m_i is "redundant" if it occurs in the type of some ?m_j.
This procedure removes from metas any redundant element.
*/
static void remove_redundant_metas(buffer<expr> & metas) {
buffer<expr> mvars;
for (expr const & m : metas)
mvars.push_back(get_app_fn(m));
unsigned k = 0;
for (unsigned i = 0; i < metas.size(); i++) {
bool found = false;
for (unsigned j = 0; j < metas.size(); j++) {
if (j != i) {
if (occurs(mvars[i], mlocal_type(mvars[j]))) {
found = true;
break;
}
}
}
if (!found) {
metas[k] = metas[i];
k++;
}
}
metas.shrink(k);
}
enum subgoals_action_kind { IgnoreSubgoals, AddRevSubgoals, AddSubgoals, AddAllSubgoals };
static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s,
expr const & _e, buffer<constraint> & cs,
bool add_meta, subgoals_action_kind subgoals_action) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
bool class_inst = get_apply_class_instance(ios.get_options());
name_generator ngen = s.get_ngen();
bool relax_opaque = s.relax_main_opaque();
std::shared_ptr<type_checker> tc(mk_type_checker(env, ngen.mk_child(), relax_opaque));
goal g = head(gs);
goals tail_gs = tail(gs);
expr t = g.get_type();
expr e = _e;
auto e_t_cs = tc->infer(e);
e_t_cs.second.linearize(cs);
expr e_t = e_t_cs.first;
buffer<expr> metas;
local_context ctx;
bool initialized_ctx = false;
unifier_config cfg(ios.get_options());
if (add_meta) {
// unsigned num_t = get_expect_num_args(*tc, t);
unsigned num_e_t = get_expect_num_args(*tc, e_t);
// Remark: we used to add (num_e_t - num_t) arguments.
// This would allow us to handle (A -> B) without using intros,
// but it was preventing us from solving other problems
for (unsigned i = 0; i < num_e_t; i++) {
auto e_t_cs = tc->whnf(e_t);
e_t_cs.second.linearize(cs);
e_t = e_t_cs.first;
expr meta;
if (class_inst && binding_info(e_t).is_inst_implicit()) {
if (!initialized_ctx) {
ctx = g.to_local_context();
initialized_ctx = true;
}
bool use_local_insts = true;
bool is_strict = false;
auto mc = mk_class_instance_elaborator(
env, ios, ctx, ngen.next(), optional<name>(),
relax_opaque, use_local_insts, is_strict,
some_expr(binding_domain(e_t)), e.get_tag(), cfg, nullptr);
meta = mc.first;
cs.push_back(mc.second);
} else {
meta = g.mk_meta(ngen.next(), binding_domain(e_t));
}
e = mk_app(e, meta);
e_t = instantiate(binding_body(e_t), meta);
metas.push_back(meta);
}
}
metavar_closure cls(t);
cls.mk_constraints(s.get_subst(), justification(), relax_opaque);
pair<bool, constraint_seq> dcs = tc->is_def_eq(t, e_t);
if (!dcs.first) {
throw_tactic_exception_if_enabled(s, [=](formatter const & fmt) {
format r = format("invalid 'apply' tactic, failed to unify");
r += pp_indent_expr(fmt, t);
r += compose(line(), format("with"));
r += pp_indent_expr(fmt, e_t);
return r;
});
return proof_state_seq();
}
dcs.second.linearize(cs);
unify_result_seq rseq = unify(env, cs.size(), cs.data(), ngen.mk_child(), s.get_subst(), cfg);
list<expr> meta_lst = to_list(metas.begin(), metas.end());
return map2<proof_state>(rseq, [=](pair<substitution, constraints> const & p) -> proof_state {
substitution const & subst = p.first;
constraints const & postponed = p.second;
name_generator new_ngen(ngen);
substitution new_subst = subst;
expr new_e = new_subst.instantiate_all(e);
assign(new_subst, g, new_e);
goals new_gs = tail_gs;
if (subgoals_action != IgnoreSubgoals) {
buffer<expr> metas;
for (auto m : meta_lst) {
if (!new_subst.is_assigned(get_app_fn(m)))
metas.push_back(m);
}
if (subgoals_action == AddRevSubgoals) {
for (unsigned i = 0; i < metas.size(); i++)
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
} else {
lean_assert(subgoals_action == AddSubgoals || subgoals_action == AddAllSubgoals);
if (subgoals_action == AddSubgoals)
remove_redundant_metas(metas);
unsigned i = metas.size();
while (i > 0) {
--i;
new_gs = cons(goal(metas[i], new_subst.instantiate_all(tc->infer(metas[i]).first)), new_gs);
}
}
}
return proof_state(s, new_gs, new_subst, new_ngen, postponed);
});
}
static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s, expr const & e,
bool add_meta, subgoals_action_kind subgoals_action) {
buffer<constraint> cs;
return apply_tactic_core(env, ios, s, e, cs, add_meta, subgoals_action);
}
tactic eassumption_tactic() {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
proof_state new_s = s.update_report_failure(false);
proof_state_seq r;
goal g = head(gs);
buffer<expr> hs;
get_app_args(g.get_meta(), hs);
for (expr const & h : hs) {
r = append(r, apply_tactic_core(env, ios, new_s, h, false, IgnoreSubgoals));
}
return r;
});
}
tactic apply_tactic_core(elaborate_fn const & elab, expr const & e, subgoals_action_kind k) {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs)) {
throw_no_goal_if_enabled(s);
return proof_state_seq();
}
goal const & g = head(gs);
name_generator ngen = s.get_ngen();
expr new_e;
buffer<constraint> cs;
auto ecs = elab(g, ngen.mk_child(), e, none_expr(), false);
new_e = ecs.first;
to_buffer(ecs.second, cs);
to_buffer(s.get_postponed(), cs);
proof_state new_s(s, ngen, constraints());
return apply_tactic_core(env, ios, new_s, new_e, cs, true, k);
});
}
tactic apply_tactic(elaborate_fn const & elab, expr const & e) {
return apply_tactic_core(elab, e, AddSubgoals);
}
tactic fapply_tactic(elaborate_fn const & elab, expr const & e) {
return apply_tactic_core(elab, e, AddAllSubgoals);
}
tactic rapply_tactic(elaborate_fn const & elab, expr const & e) {
return apply_tactic_core(elab, e, AddRevSubgoals);
}
int mk_eassumption_tactic(lua_State * L) { return push_tactic(L, eassumption_tactic()); }
void open_apply_tactic(lua_State * L) {
SET_GLOBAL_FUN(mk_eassumption_tactic, "eassumption_tac");
}
void initialize_apply_tactic() {
g_apply_class_instance = new name{"apply", "class_instance"};
register_bool_option(*g_apply_class_instance, LEAN_DEFAULT_APPLY_CLASS_INSTANCE,
"(apply tactic) if true apply tactic uses class-instances "
"resolution for instance implicit arguments");
register_tac(get_tactic_apply_name(),
[](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
check_tactic_expr(app_arg(e), "invalid 'apply' tactic, invalid argument");
return apply_tactic(fn, get_tactic_expr_expr(app_arg(e)));
});
register_tac(get_tactic_rapply_name(),
[](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
check_tactic_expr(app_arg(e), "invalid 'rapply' tactic, invalid argument");
return rapply_tactic(fn, get_tactic_expr_expr(app_arg(e)));
});
register_tac(get_tactic_fapply_name(),
[](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
check_tactic_expr(app_arg(e), "invalid 'fapply' tactic, invalid argument");
return fapply_tactic(fn, get_tactic_expr_expr(app_arg(e)));
});
register_simple_tac(get_tactic_eassumption_name(),
[]() { return eassumption_tactic(); });
}
void finalize_apply_tactic() {
delete g_apply_class_instance;
}
}