示例#1
6
tactic clear_tactic(name const & n) {
    auto fn = [=](environment const &, io_state const &, proof_state const & _s) -> optional<proof_state> {
        if (!_s.get_goals()) {
            throw_no_goal_if_enabled(_s);
            return none_proof_state();
        }
        proof_state s    = apply_substitution(_s);
        goals const & gs = s.get_goals();
        goal  g          = head(gs);
        goals tail_gs    = tail(gs);
        if (auto p = g.find_hyp(n)) {
            expr const & h = p->first;
            unsigned i     = p->second;
            buffer<expr> hyps;
            g.get_hyps(hyps);
            hyps.erase(hyps.size() - i - 1);
            if (depends_on(g.get_type(), h)) {
                throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, conclusion depends on '"
                                                  << n << "'");
                return none_proof_state();
            }
            if (auto h2 = depends_on(i, hyps.end() - i, h)) {
                throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, hypothesis '" << *h2
                                                  << "' depends on '" << n << "'");
                return none_proof_state();
            }
            name_generator ngen = s.get_ngen();
            expr new_type = g.get_type();
            expr new_meta = mk_app(mk_metavar(ngen.next(), Pi(hyps, new_type)), hyps);
            goal new_g(new_meta, new_type);
            substitution new_subst = s.get_subst();
            assign(new_subst, g, new_meta);
            proof_state new_s(s, goals(new_g, tail_gs), new_subst, ngen);
            return some_proof_state(new_s);
        } else {
            throw_tactic_exception_if_enabled(s, sstream() << "invalid 'clear' tactic, goal does not have a hypothesis "
                                              << " named '" << n << "'");
            return none_proof_state();
        }
    };
    return tactic01(fn);
}
示例#2
0
tactic revert_tactic(name const & n) {
    auto fn = [=](environment const &, io_state const &, proof_state const & s) -> optional<proof_state> {
        goals const & gs = s.get_goals();
        if (empty(gs)) {
            throw_no_goal_if_enabled(s);
            return none_proof_state();
        }
        goal  g          = head(gs);
        goals tail_gs    = tail(gs);
        if (auto p = g.find_hyp(n)) {
            expr const & h = p->first;
            unsigned i     = p->second;
            buffer<expr> hyps;
            g.get_hyps(hyps);
            hyps.erase(hyps.size() - i - 1);
            if (optional<expr> other_h = depends_on(i, hyps.end() - i, h)) {
                throw_tactic_exception_if_enabled(s, sstream() << "invalid 'revert' tactic, hypothesis '" << local_pp_name(*other_h)
                                                  << "' depends on '" << local_pp_name(h) << "'");
                return none_proof_state(); // other hypotheses depend on h
            }
            name_generator ngen = s.get_ngen();
            expr new_type = Pi(h, g.get_type());
            expr new_meta = mk_app(mk_metavar(ngen.next(), Pi(hyps, new_type)), hyps);
            goal new_g(new_meta, new_type);
            substitution new_subst = s.get_subst();
            assign(new_subst, g, mk_app(new_meta, h));
            proof_state new_s(s, goals(new_g, tail_gs), new_subst, ngen);
            return some_proof_state(new_s);
        } else {
            throw_tactic_exception_if_enabled(s, sstream() << "invalid 'revert' tactic, unknown hypothesis '" << n << "'");
            return none_proof_state();
        }
    };
    return tactic01(fn);
}
示例#3
0
tactic change_goal_tactic(elaborate_fn const & elab, expr const & e) {
    return tactic([=](environment const & env, io_state const & ios, proof_state const & s) {
            proof_state new_s = s;
            goals const & gs  = new_s.get_goals();
            if (!gs) {
                throw_no_goal_if_enabled(s);
                return proof_state_seq();
            }
            expr t            = head(gs).get_type();
            bool report_unassigned = true;
            if (auto new_e = elaborate_with_respect_to(env, ios, elab, new_s, e, none_expr(), report_unassigned)) {
                goals const & gs    = new_s.get_goals();
                goal const & g      = head(gs);
                substitution subst  = new_s.get_subst();
                auto tc             = mk_type_checker(env);
                constraint_seq cs;
                if (tc->is_def_eq(t, *new_e, justification(), cs)) {
                    if (cs) {
                        unifier_config cfg(ios.get_options());
                        buffer<constraint> cs_buf;
                        cs.linearize(cs_buf);
                        to_buffer(new_s.get_postponed(), cs_buf);
                        unify_result_seq rseq = unify(env, cs_buf.size(), cs_buf.data(), subst, cfg);
                        return map2<proof_state>(rseq, [=](pair<substitution, constraints> const & p) -> proof_state {
                                substitution const & subst    = p.first;
                                constraints const & postponed = p.second;
                                substitution new_subst = subst;
                                expr final_e = new_subst.instantiate_all(*new_e);
                                expr M       = g.mk_meta(mk_fresh_name(), final_e);
                                goal new_g(M, final_e);
                                assign(new_subst, g, M);
                                return proof_state(new_s, cons(new_g, tail(gs)), new_subst, postponed);
                            });
                    }
                    expr M   = g.mk_meta(mk_fresh_name(), *new_e);
                    goal new_g(M, *new_e);
                    assign(subst, g, M);
                    return proof_state_seq(proof_state(new_s, cons(new_g, tail(gs)), subst));
                } else {
                    throw_tactic_exception_if_enabled(new_s, [=](formatter const & fmt) {
                            format r = format("invalid 'change' tactic, the given type");
                            r += pp_indent_expr(fmt, *new_e);
                            r += compose(line(), format("does not match the goal type"));
                            r += pp_indent_expr(fmt, t);
                            return r;
                        });
                    return proof_state_seq();
                }
            }
            return proof_state_seq();
        });
}
示例#4
0
static proof_state_seq apply_tactic_core(environment const & env, io_state const & ios, proof_state const & s,
                                         expr const & _e, buffer<constraint> & cs,
                                         add_meta_kind add_meta, subgoals_action_kind subgoals_action,
                                         optional<unifier_kind> const & uk = optional<unifier_kind>()) {
    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();
    std::shared_ptr<type_checker> tc(mk_type_checker(env, ngen.mk_child()));
    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 (uk)
        cfg.m_kind = *uk;
    if (add_meta != DoNotAdd) {
        unsigned num_e_t = get_expect_num_args(*tc, e_t);
        if (add_meta == AddDiff) {
            unsigned num_t   = get_expect_num_args(*tc, t);
            if (num_t <= num_e_t)
                num_e_t -= num_t;
            else
                num_e_t = 0;
        } else {
            lean_assert(add_meta == AddAll);
        }
        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>(),
                    use_local_insts, is_strict,
                    some_expr(head_beta_reduce(binding_domain(e_t))), e.get_tag(), cfg, nullptr);
                meta    = mc.first;
                cs.push_back(mc.second);
            } else {
                meta  = g.mk_meta(ngen.next(), head_beta_reduce(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());
    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);
        });
}