constraint mk_class_instance_cnstr(std::shared_ptr<class_instance_context> const & C, local_context const & ctx, expr const & m, unsigned depth) {
    environment const & env = C->env();
    justification j         = mk_failed_to_synthesize_jst(env, m);
    auto choice_fn = [=](expr const & meta, expr const & meta_type, substitution const &, name_generator const &) {
        if (auto cls_name_it = is_ext_class(C->tc(), meta_type)) {
            name cls_name = *cls_name_it;
            list<expr> const & ctx_lst = ctx.get_data();
            list<expr> local_insts;
            if (C->use_local_instances())
                local_insts = get_local_instances(C->tc(), ctx_lst, cls_name);
            list<name>  insts = get_class_instances(env, cls_name);
            if (empty(local_insts) && empty(insts))
                return lazy_list<constraints>(); // nothing to be done
            // we are always strict with placeholders associated with classes
            return choose(std::make_shared<class_instance_elaborator>(C, ctx, meta, meta_type, local_insts, insts, j, depth));
        } else {
            // do nothing, type is not a class...
            return lazy_list<constraints>(constraints());
        }
    };
    bool owner      = false;
    bool relax      = C->m_relax;
    return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Basic),
                           owner, j, relax);
}
/** \brief Given a term <tt>a : a_type</tt>, and a metavariable \c m, creates a constraint
    that considers coercions from a_type to the type assigned to \c m. */
constraint mk_coercion_cnstr(type_checker & from_tc, type_checker & to_tc, coercion_info_manager & infom,
                             expr const & m, expr const & a, expr const & a_type,
                             justification const & j, unsigned delay_factor, bool lift_coe) {
    auto choice_fn = [=, &from_tc, &to_tc, &infom](expr const & meta, expr const & d_type, substitution const & s) {
        expr          new_a_type;
        justification new_a_type_jst;
        if (is_meta(a_type)) {
            auto p = substitution(s).instantiate_metavars(a_type);
            new_a_type     = p.first;
            new_a_type_jst = p.second;
        } else {
            new_a_type     = a_type;
        }
        if (is_meta(new_a_type)) {
            if (delay_factor < to_delay_factor(cnstr_group::DelayedChoice)) {
                // postpone...
                return lazy_list<constraints>(constraints(mk_coercion_cnstr(from_tc, to_tc, infom, m, a, a_type, justification(),
                                                                            delay_factor+1, lift_coe)));
            } else {
                // giveup...
                return lazy_list<constraints>(constraints(mk_eq_cnstr(meta, a, justification())));
            }
        }
        constraint_seq cs;
        new_a_type = from_tc.whnf(new_a_type, cs);
        if ((lift_coe && is_pi_meta(d_type)) || (!lift_coe && is_meta(d_type))) {
            // case-split
            buffer<expr> locals;
            expr it_from = new_a_type;
            expr it_to   = d_type;
            while (is_pi(it_from) && is_pi(it_to)) {
                expr dom_from = binding_domain(it_from);
                expr dom_to   = binding_domain(it_to);
                if (!from_tc.is_def_eq(dom_from, dom_to, justification(), cs))
                    return lazy_list<constraints>();
                expr local = mk_local(mk_fresh_name(), binding_name(it_from), dom_from, binder_info());
                locals.push_back(local);
                it_from  = instantiate(binding_body(it_from), local);
                it_to    = instantiate(binding_body(it_to), local);
            }
            buffer<expr> alts;
            get_coercions_from(from_tc.env(), it_from, alts);
            expr fn_a;
            if (!locals.empty())
                fn_a = mk_local(mk_fresh_name(), "f", new_a_type, binder_info());
            buffer<constraints> choices;
            buffer<expr> coes;
            // first alternative: no coercion
            constraint_seq cs1 = cs + mk_eq_cnstr(meta, a, justification());
            choices.push_back(cs1.to_list());
            unsigned i = alts.size();
            while (i > 0) {
                --i;
                expr coe = alts[i];
                if (!locals.empty())
                    coe = Fun(fn_a, Fun(locals, mk_app(coe, mk_app(fn_a, locals))));
                expr new_a = copy_tag(a, mk_app(coe, a));
                coes.push_back(coe);
                constraint_seq csi = cs + mk_eq_cnstr(meta, new_a, new_a_type_jst);
                choices.push_back(csi.to_list());
            }
            return choose(std::make_shared<coercion_elaborator>(infom, meta,
                                                                to_list(choices.begin(), choices.end()),
                                                                to_list(coes.begin(), coes.end())));
        } else {
            list<expr> coes    = get_coercions_from_to(from_tc, to_tc, new_a_type, d_type, cs, lift_coe);
            if (is_nil(coes)) {
                expr new_a = a;
                infom.erase_coercion_info(a);
                cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
                return lazy_list<constraints>(cs.to_list());
            } else if (is_nil(tail(coes))) {
                expr new_a = copy_tag(a, mk_app(head(coes), a));
                infom.save_coercion_info(a, new_a);
                cs += mk_eq_cnstr(meta, new_a, new_a_type_jst);
                return lazy_list<constraints>(cs.to_list());
            } else {
                list<constraints> choices = map2<constraints>(coes, [&](expr const & coe) {
                        expr new_a   = copy_tag(a, mk_app(coe, a));
                        constraint c = mk_eq_cnstr(meta, new_a, new_a_type_jst);
                        return (cs + c).to_list();
                    });
                return choose(std::make_shared<coercion_elaborator>(infom, meta, choices, coes, false));
            }
        }
    };
    return mk_choice_cnstr(m, choice_fn, delay_factor, true, j);
}
/** \brief Create a "choice" constraint that postpones the resolution of a calc proof step.

    By delaying it, we can perform quick fixes such as:
      - adding symmetry
      - adding !
      - adding subst
*/
constraint mk_calc_proof_cnstr(environment const & env, options const & opts,
                               old_local_context const & _ctx, expr const & m, expr const & _e,
                               constraint_seq const & cs, unifier_config const & cfg,
                               info_manager * im, update_type_info_fn const & fn) {
    justification j         = mk_failed_to_synthesize_jst(env, m);
    auto choice_fn = [=](expr const & meta, expr const & _meta_type, substitution const & _s) {
        old_local_context ctx = _ctx;
        expr e            = _e;
        substitution s    = _s;
        expr meta_type    = _meta_type;
        type_checker_ptr tc = mk_type_checker(env);
        constraint_seq new_cs = cs;
        expr e_type = tc->infer(e, new_cs);
        e_type      = s.instantiate(e_type);
        tag g       = e.get_tag();
        bool calc_assistant = get_elaborator_calc_assistant(opts);

        if (calc_assistant) {
            // add '!' is needed
            while (is_norm_pi(*tc, e_type, new_cs)) {
                binder_info bi = binding_info(e_type);
                if (!bi.is_implicit() && !bi.is_inst_implicit()) {
                    if (!has_free_var(binding_body(e_type), 0)) {
                        // if the rest of the type does not reference argument,
                        // then we also stop consuming arguments
                        break;
                    }
                }
                expr imp_arg = ctx.mk_meta(some_expr(binding_domain(e_type)), g);
                e            = mk_app(e, imp_arg, g);
                e_type       = instantiate(binding_body(e_type), imp_arg);
            }
            if (im)
                fn(e);
        }
        e_type = head_beta_reduce(e_type);

        expr const & meta_type_fn = get_app_fn(meta_type);
        expr const & e_type_fn    = get_app_fn(e_type);
        if (is_constant(meta_type_fn) && (!is_constant(e_type_fn) || const_name(e_type_fn) != const_name(meta_type_fn))) {
            // try to make sure meta_type and e_type have the same head symbol
            if (!try_normalize_to_head(env, const_name(meta_type_fn), e_type, new_cs) &&
                is_constant(e_type_fn)) {
                try_normalize_to_head(env, const_name(e_type_fn), meta_type, new_cs);
            }
        }

        auto try_alternative = [&](expr const & e, expr const & e_type, constraint_seq fcs, bool conservative) {
            justification new_j = mk_type_mismatch_jst(e, e_type, meta_type);
            if (!tc->is_def_eq(e_type, meta_type, new_j, fcs))
                throw unifier_exception(new_j, s);
            buffer<constraint> cs_buffer;
            fcs.linearize(cs_buffer);
            metavar_closure cls(meta);
            cls.add(meta_type);
            cls.mk_constraints(s, j, cs_buffer);

            unifier_config new_cfg(cfg);
            new_cfg.m_discard      = false;
            new_cfg.m_kind         = conservative ? unifier_kind::Conservative : unifier_kind::Liberal;
            unify_result_seq seq   = unify(env, cs_buffer.size(), cs_buffer.data(), substitution(), new_cfg);
            auto p = seq.pull();
            lean_assert(p);
            substitution new_s     = p->first.first;
            constraints  postponed = map(p->first.second,
                                         [&](constraint const & c) {
                                             // we erase internal justifications
                                             return update_justification(c, j);
                                         });
            expr new_e = new_s.instantiate(e);
            if (conservative && has_expr_metavar_relaxed(new_s.instantiate_all(e)))
                throw_elaborator_exception("solution contains metavariables", e);
            if (im)
                im->instantiate(new_s);
            constraints r = cls.mk_constraints(new_s, j);
            buffer<expr> locals;
            expr mvar  = get_app_args(meta, locals);
            expr val   = Fun(locals, new_e);
            r = cons(mk_eq_cnstr(mvar, val, j), r);
            return append(r, postponed);
        };

        if (!get_elaborator_calc_assistant(opts)) {
            bool conservative = false;
            return try_alternative(e, e_type, new_cs, conservative);
        } else {
            // TODO(Leo): after we have the simplifier and rewriter tactic, we should revise
            // this code. It is "abusing" the higher-order unifier.

            {
                // Try the following possible intrepretations using a "conservative" unification procedure.
                // That is, we only unfold definitions marked as reducible.
                // Assume pr is the proof provided.

                // 1. pr
                bool conservative = true;
                try { return try_alternative(e, e_type, new_cs, conservative); } catch (exception & ex) {}

                // 2. eq.symm pr
                constraint_seq symm_cs = new_cs;
                auto symm  = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
                if (symm) {
                    try { return try_alternative(symm->first, symm->second, symm_cs, conservative); } catch (exception &) {}
                }

                // 3. subst pr (eq.refl lhs)
                constraint_seq subst_cs = new_cs;
                if (auto subst = apply_subst(env, ctx, tc, e, e_type, meta_type, subst_cs, g)) {
                    try { return try_alternative(subst->first, subst->second, subst_cs, conservative); } catch (exception&) {}
                }

                // 4. subst (eq.symm pr) (eq.refl lhs)
                if (symm) {
                    constraint_seq subst_cs = symm_cs;
                    if (auto subst = apply_subst(env, ctx, tc, symm->first, symm->second,
                                                 meta_type, subst_cs, g)) {
                        try { return try_alternative(subst->first, subst->second, subst_cs, conservative); }
                        catch (exception&) {}
                    }
                }
            }

            {
                // Try the following possible insterpretations using the default unification procedure.

                // 1. pr
                bool conservative = false;
                std::unique_ptr<throwable> saved_ex;
                try {
                    return try_alternative(e, e_type, new_cs, conservative);
                } catch (exception & ex) {
                    saved_ex.reset(ex.clone());
                }

                // 2. eq.symm pr
                constraint_seq symm_cs = new_cs;
                auto symm  = apply_symmetry(env, ctx, tc, e, e_type, symm_cs, g);
                if (symm) {
                    try { return try_alternative(symm->first, symm->second, symm_cs, conservative); }
                    catch (exception &) {}
                }

                // We use the exception for the first alternative as the error message
                saved_ex->rethrow();
                lean_unreachable();
            }
        }
    };
    bool owner = false;
    return mk_choice_cnstr(m, choice_fn, to_delay_factor(cnstr_group::Epilogue), owner, j);
}