lean2/src/library/tactic/apply_tactic.cpp

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/*
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 "kernel/for_each_fn.h"
#include "kernel/replace_fn.h"
#include "kernel/instantiate.h"
#include "kernel/abstract.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/metavar_closure.h"
#include "library/type_util.h"
#include "library/tactic/apply_tactic.h"
#include "library/tactic/expr_to_tactic.h"
namespace lean {
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, bool add_subgoals, bool relax_main_opaque) {
goals const & gs = s.get_goals();
if (empty(gs))
return proof_state_seq();
name_generator ngen = s.get_ngen();
std::shared_ptr<type_checker> tc(mk_type_checker(env, ngen.mk_child(), relax_main_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;
if (add_meta) {
unsigned num_t = get_expect_num_args(*tc, t);
unsigned num_e_t = get_expect_num_args(*tc, e_t);
if (num_t > num_e_t)
return proof_state_seq(); // no hope to unify then
for (unsigned i = 0; i < num_e_t - num_t; i++) {
auto e_t_cs = tc->whnf(e_t);
e_t_cs.second.linearize(cs);
e_t = e_t_cs.first;
expr 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_main_opaque);
pair<bool, constraint_seq> dcs = tc->is_def_eq(t, e_t);
if (!dcs.first)
return proof_state_seq();
dcs.second.linearize(cs);
unifier_config cfg(ios.get_options());
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);
expr new_p = g.abstract(new_e);
check_has_no_local(new_p, _e, "apply");
new_subst.assign(g.get_name(), new_p);
goals new_gs = tail_gs;
if (add_subgoals) {
buffer<expr> metas;
for (auto m : meta_lst) {
if (!new_subst.is_assigned(get_app_fn(m)))
metas.push_back(m);
}
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);
}
return proof_state(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, bool add_subgoals, bool relax_main_opaque) {
buffer<constraint> cs;
return apply_tactic_core(env, ios, s, e, cs, add_meta, add_subgoals, relax_main_opaque);
}
tactic eassumption_tactic(bool relax_main_opaque) {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs))
return proof_state_seq();
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, s, h, false, false, relax_main_opaque));
}
return r;
});
}
tactic apply_tactic(elaborate_fn const & elab, expr const & e, bool relax_main_opaque) {
return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs))
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);
new_e = ecs.first;
to_buffer(ecs.second, cs);
to_buffer(s.get_postponed(), cs);
proof_state new_s(s.get_goals(), s.get_subst(), ngen, constraints());
return apply_tactic_core(env, ios, new_s, new_e, cs, true, true, relax_main_opaque);
});
}
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");
}
static name * g_apply_tactic_name = nullptr;
expr mk_apply_tactic_macro(expr const & e) {
return mk_tactic_macro(*g_apply_tactic_name, e);
}
void initialize_apply_tactic() {
g_apply_tactic_name = new name({"tactic", "apply"});
auto fn = [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
check_macro_args(e, 1, "invalid 'apply' tactic, it must have one argument");
return apply_tactic(fn, macro_arg(e, 0));
};
register_tactic_macro(*g_apply_tactic_name, fn);
register_simple_tac(name({"tactic", "eassumption"}),
[]() { return eassumption_tactic(); });
}
void finalize_apply_tactic() {
delete g_apply_tactic_name;
}
}