/* 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 #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/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: (?m_1 ...) (?m_2 ... ) ... (?m_k ...), 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 & metas) { buffer 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 & cs, bool add_meta, subgoals_action_kind subgoals_action) { goals const & gs = s.get_goals(); if (empty(gs)) 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 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 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(), 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 dcs = tc->is_def_eq(t, e_t); if (!dcs.first) 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 meta_lst = to_list(metas.begin(), metas.end()); return map2(rseq, [=](pair 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 (subgoals_action != IgnoreSubgoals) { buffer 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 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)) return proof_state_seq(); proof_state_seq r; goal g = head(gs); buffer hs; get_app_args(g.get_meta(), hs); for (expr const & h : hs) { r = append(r, apply_tactic_core(env, ios, 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)) return proof_state_seq(); goal const & g = head(gs); name_generator ngen = s.get_ngen(); expr new_e; buffer cs; auto ecs = elab(g, ngen.mk_child(), e, 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; } }