template <class Z> MY_INLINE RStarTree<Z>::~RStarTree() { if ( myRoot != NULL ) { //Go through and get all the children in a list. DLIList <RStarTreeNode<Z>*> to_delete; to_list(to_delete, myRoot); int ii; for(ii = to_delete.size(); ii > 0; ii-- ) delete to_delete.pop(); delete myRoot; } }
/// Extract indexes from an argument of the form `var_name[index1 index2...]`. /// /// Inputs: /// indexes: the list to insert the new indexes into /// src: The source string to parse. This must be a var spec of the form "var[...]" /// /// Returns: /// The total number of indexes parsed, or -1 on error. If any indexes were found the `src` string /// is modified to omit the index expression leaving just the var name. static int parse_index(std::vector<long> &indexes, wchar_t *src, int scope, io_streams_t &streams, const environment_t &vars) { wchar_t *p = std::wcschr(src, L'['); if (!p) return 0; // no slices so nothing for us to do *p = L'\0'; // split the var name from the indexes/slices p++; auto var_str = vars.get(src, scope); wcstring_list_t var; if (var_str) var_str->to_list(var); int count = 0; while (*p != L']') { const wchar_t *end; long l_ind = fish_wcstol(p, &end); if (errno > 0) { // ignore errno == -1 meaning the int did not end with a '\0' streams.err.append_format(_(L"%ls: Invalid index starting at '%ls'\n"), L"set", src); return -1; } p = (wchar_t *)end; // Convert negative index to a positive index. if (l_ind < 0) l_ind = var.size() + l_ind + 1; if (*p == L'.' && *(p + 1) == L'.') { p += 2; long l_ind2 = fish_wcstol(p, &end); if (errno > 0) { // ignore errno == -1 meaning the int did not end with a '\0' return -1; } p = (wchar_t *)end; // Convert negative index to a positive index. if (l_ind2 < 0) l_ind2 = var.size() + l_ind2 + 1; int direction = l_ind2 < l_ind ? -1 : 1; for (long jjj = l_ind; jjj * direction <= l_ind2 * direction; jjj += direction) { indexes.push_back(jjj); count++; } } else { indexes.push_back(l_ind); count++; } } return count; }
list<unsigned> fun_info_manager::collect_deps(expr const & type, buffer<expr> const & locals) { buffer<unsigned> deps; for_each(type, [&](expr const & e, unsigned) { if (m_ctx.is_tmp_local(e)) { unsigned idx; for (idx = 0; idx < locals.size(); idx++) if (locals[idx] == e) break; if (idx < locals.size() && std::find(deps.begin(), deps.end(), idx) == deps.end()) deps.push_back(idx); } return has_local(e); // continue the search only if e has locals }); std::sort(deps.begin(), deps.end()); return to_list(deps); }
optional<constraints> try_instance(name const & inst) { environment const & env = m_C->env(); if (auto decl = env.find(inst)) { name_generator & ngen = m_C->m_ngen; buffer<level> ls_buffer; unsigned num_univ_ps = decl->get_num_univ_params(); for (unsigned i = 0; i < num_univ_ps; i++) ls_buffer.push_back(mk_meta_univ(ngen.next())); levels ls = to_list(ls_buffer.begin(), ls_buffer.end()); expr inst_cnst = copy_tag(m_meta, mk_constant(inst, ls)); expr inst_type = instantiate_type_univ_params(*decl, ls); return try_instance(inst_cnst, inst_type); } else { return optional<constraints>(); } }
template <class Z> MY_INLINE void RStarTree<Z>::to_list(DLIList <RStarTreeNode<Z>*> &member_list, RStarTreeNode<Z> *top) { //Get the children of the top into the list. int ii; RStarTreeNode <Z> *curr_node; for ( ii = 0; ii < top->num_children(); ii++ ) { curr_node = top->get_child(ii); member_list.append(curr_node); //don't go below the bottom level... if ( curr_node->get_leaf_level() == 0 ) continue; to_list(member_list, curr_node); } return; }
/// Erase a variable. static int builtin_set_erase(const wchar_t *cmd, set_cmd_opts_t &opts, int argc, wchar_t **argv, parser_t &parser, io_streams_t &streams) { if (argc != 1) { streams.err.append_format(BUILTIN_ERR_ARG_COUNT2, cmd, L"--erase", 1, argc); builtin_print_error_trailer(parser, streams.err, cmd); return STATUS_CMD_ERROR; } int scope = compute_scope(opts); // calculate the variable scope based on the provided options wchar_t *dest = argv[0]; std::vector<long> indexes; int idx_count = parse_index(indexes, dest, scope, streams, parser.vars()); if (idx_count == -1) { builtin_print_error_trailer(parser, streams.err, cmd); return STATUS_CMD_ERROR; } int retval; if (!valid_var_name(dest)) { streams.err.append_format(BUILTIN_ERR_VARNAME, cmd, dest); builtin_print_error_trailer(parser, streams.err, cmd); return STATUS_INVALID_ARGS; } if (idx_count == 0) { // unset the var retval = parser.vars().remove(dest, scope); // When a non-existent-variable is unset, return ENV_NOT_FOUND as $status // but do not emit any errors at the console as a compromise between user // friendliness and correctness. if (retval != ENV_NOT_FOUND) { handle_env_return(retval, cmd, dest, streams); } } else { // remove just the specified indexes of the var const auto dest_var = parser.vars().get(dest, scope); if (!dest_var) return STATUS_CMD_ERROR; wcstring_list_t result; dest_var->to_list(result); erase_values(result, indexes); retval = env_set_reporting_errors(cmd, dest, scope, result, streams, parser.vars()); } if (retval != STATUS_CMD_OK) return retval; return check_global_scope_exists(cmd, opts, dest, streams, parser.vars()); }
expr extract(expr const & e) { lean_assert(is_nested_declaration(e)); expr const & d = visit(get_nested_declaration_arg(e)); name new_name = mk_name_for(e); name new_real_name = get_namespace(m_env) + new_name; collected_locals locals; collect_locals(d, locals); buffer<name> uparams; collect_univ_params(d).to_buffer(uparams); expr new_value = Fun(locals.get_collected(), d); expr new_type = m_tc.infer(new_value).first; level_param_names new_ps = to_list(uparams); levels ls = param_names_to_levels(new_ps); m_env = module::add(m_env, check(m_env, mk_definition(m_env, new_real_name, new_ps, new_type, new_value))); if (new_name != new_real_name) m_env = add_expr_alias_rec(m_env, new_name, new_real_name); decl_attributes const & attrs = get_nested_declaration_attributes(e); m_env = attrs.apply(m_env, m_ios, new_real_name, get_namespace(m_env)); return mk_app(mk_constant(new_real_name, ls), locals.get_collected()); }
simp_rule_sets add_core(type_checker & tc, simp_rule_sets const & s, name const & id, levels const & univ_metas, expr const & e, expr const & h) { list<expr_pair> ceqvs = to_ceqvs(tc, e, h); environment const & env = tc.env(); simp_rule_sets new_s = s; for (expr_pair const & p : ceqvs) { expr new_e = p.first; expr new_h = p.second; bool is_perm = is_permutation_ceqv(env, new_e); buffer<expr> metas; unsigned idx = 0; while (is_pi(new_e)) { expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(new_e)); idx++; metas.push_back(mvar); new_e = instantiate(binding_body(new_e), mvar); } expr rel, lhs, rhs; if (is_simp_relation(env, new_e, rel, lhs, rhs) && is_constant(rel)) { new_s.insert(const_name(rel), simp_rule(id, univ_metas, to_list(metas), lhs, rhs, new_h, is_perm)); } } return new_s; }
vm_obj to_obj(buffer<level> const & ls) { return to_obj(to_list(ls)); }
constraints mk_constraints(constraint const & c, buffer<constraint> const & cs) { return cons(c, to_list(cs.begin(), cs.end())); }
/** \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); }
environment mk_projections(environment const & env, name const & n, buffer<name> const & proj_names, implicit_infer_kind infer_k, bool inst_implicit) { // Given an inductive datatype C A (where A represent parameters) // intro : Pi A (x_1 : B_1[A]) (x_2 : B_2[A, x_1]) ..., C A // // we generate projections of the form // proj_i A (c : C A) : B_i[A, (proj_1 A n), ..., (proj_{i-1} A n)] // C.rec A (fun (x : C A), B_i[A, ...]) (fun (x_1 ... x_n), x_i) c auto p = get_nparam_intro_rule(env, n); name_generator ngen; unsigned nparams = p.first; inductive::intro_rule intro = p.second; expr intro_type = inductive::intro_rule_type(intro); name rec_name = inductive::get_elim_name(n); declaration ind_decl = env.get(n); if (env.impredicative() && is_prop(ind_decl.get_type())) throw exception(sstream() << "projection generation, '" << n << "' is a proposition"); declaration rec_decl = env.get(rec_name); level_param_names lvl_params = ind_decl.get_univ_params(); levels lvls = param_names_to_levels(lvl_params); buffer<expr> params; // datatype parameters for (unsigned i = 0; i < nparams; i++) { if (!is_pi(intro_type)) throw_ill_formed(n); expr param = mk_local(ngen.next(), binding_name(intro_type), binding_domain(intro_type), binder_info()); intro_type = instantiate(binding_body(intro_type), param); params.push_back(param); } expr C_A = mk_app(mk_constant(n, lvls), params); binder_info c_bi = inst_implicit ? mk_inst_implicit_binder_info() : binder_info(); expr c = mk_local(ngen.next(), name("c"), C_A, c_bi); buffer<expr> intro_type_args; // arguments that are not parameters expr it = intro_type; while (is_pi(it)) { expr local = mk_local(ngen.next(), binding_name(it), binding_domain(it), binding_info(it)); intro_type_args.push_back(local); it = instantiate(binding_body(it), local); } buffer<expr> projs; // projections generated so far unsigned i = 0; environment new_env = env; for (name const & proj_name : proj_names) { if (!is_pi(intro_type)) throw exception(sstream() << "generating projection '" << proj_name << "', '" << n << "' does not have sufficient data"); expr result_type = binding_domain(intro_type); buffer<expr> proj_args; proj_args.append(params); proj_args.push_back(c); expr type_former = Fun(c, result_type); expr minor_premise = Fun(intro_type_args, mk_var(intro_type_args.size() - i - 1)); expr major_premise = c; type_checker tc(new_env); level l = sort_level(tc.ensure_sort(tc.infer(result_type).first).first); levels rec_lvls = append(to_list(l), lvls); expr rec = mk_constant(rec_name, rec_lvls); buffer<expr> rec_args; rec_args.append(params); rec_args.push_back(type_former); rec_args.push_back(minor_premise); rec_args.push_back(major_premise); expr rec_app = mk_app(rec, rec_args); expr proj_type = Pi(proj_args, result_type); proj_type = infer_implicit_params(proj_type, nparams, infer_k); expr proj_val = Fun(proj_args, rec_app); bool opaque = false; bool use_conv_opt = false; declaration new_d = mk_definition(env, proj_name, lvl_params, proj_type, proj_val, opaque, rec_decl.get_module_idx(), use_conv_opt); new_env = module::add(new_env, check(new_env, new_d)); new_env = set_reducible(new_env, proj_name, reducible_status::Reducible); new_env = add_unfold_c_hint(new_env, proj_name, nparams); new_env = save_projection_info(new_env, proj_name, inductive::intro_rule_name(intro), nparams, i, inst_implicit); expr proj = mk_app(mk_app(mk_constant(proj_name, lvls), params), c); intro_type = instantiate(binding_body(intro_type), proj); i++; } return new_env; }
expr mk_structure_instance(expr const & src, buffer<name> const & fns, buffer<expr> const & fvs) { buffer<expr> aux; aux.append(fvs); aux.push_back(src); return mk_structure_instance_core(name(), to_list(fns), aux.size(), aux.data()); }
expr mk_structure_instance(name const & s, buffer<name> const & fns, buffer<expr> const & fvs) { lean_assert(fns.size() == fvs.size()); return mk_structure_instance_core(s, to_list(fns), fvs.size(), fvs.data()); }
optional<environment> mk_no_confusion_type(environment const & env, name const & n) { optional<inductive::inductive_decls> decls = inductive::is_inductive_decl(env, n); if (!decls) throw exception(sstream() << "error in 'no_confusion' generation, '" << n << "' is not an inductive datatype"); if (is_inductive_predicate(env, n)) return optional<environment>(); // type is a proposition name_generator ngen; unsigned nparams = std::get<1>(*decls); declaration ind_decl = env.get(n); declaration cases_decl = env.get(name(n, "cases_on")); level_param_names lps = cases_decl.get_univ_params(); level rlvl = mk_param_univ(head(lps)); levels ilvls = param_names_to_levels(tail(lps)); if (length(ilvls) != length(ind_decl.get_univ_params())) return optional<environment>(); // type does not have only a restricted eliminator expr ind_type = instantiate_type_univ_params(ind_decl, ilvls); name eq_name("eq"); name heq_name("heq"); // All inductive datatype parameters and indices are arguments buffer<expr> args; ind_type = to_telescope(ngen, ind_type, args, some(mk_implicit_binder_info())); if (!is_sort(ind_type) || args.size() < nparams) throw_corrupted(n); lean_assert(!(env.impredicative() && is_zero(sort_level(ind_type)))); unsigned nindices = args.size() - nparams; // Create inductive datatype expr I = mk_app(mk_constant(n, ilvls), args); // Add (P : Type) expr P = mk_local(ngen.next(), "P", mk_sort(rlvl), binder_info()); args.push_back(P); // add v1 and v2 elements of the inductive type expr v1 = mk_local(ngen.next(), "v1", I, binder_info()); expr v2 = mk_local(ngen.next(), "v2", I, binder_info()); args.push_back(v1); args.push_back(v2); expr R = mk_sort(rlvl); name no_confusion_type_name{n, "no_confusion_type"}; expr no_confusion_type_type = Pi(args, R); // Create type former buffer<expr> type_former_args; for (unsigned i = nparams; i < nparams + nindices; i++) type_former_args.push_back(args[i]); type_former_args.push_back(v1); expr type_former = Fun(type_former_args, R); // Create cases_on levels clvls = levels(mk_succ(rlvl), ilvls); expr cases_on = mk_app(mk_app(mk_constant(cases_decl.get_name(), clvls), nparams, args.data()), type_former); cases_on = mk_app(cases_on, nindices, args.data() + nparams); expr cases_on1 = mk_app(cases_on, v1); expr cases_on2 = mk_app(cases_on, v2); type_checker tc(env); expr t1 = tc.infer(cases_on1).first; expr t2 = tc.infer(cases_on2).first; buffer<expr> outer_cases_on_args; unsigned idx1 = 0; while (is_pi(t1)) { buffer<expr> minor1_args; expr minor1 = to_telescope(tc, binding_domain(t1), minor1_args); expr curr_t2 = t2; buffer<expr> inner_cases_on_args; unsigned idx2 = 0; while (is_pi(curr_t2)) { buffer<expr> minor2_args; expr minor2 = to_telescope(tc, binding_domain(curr_t2), minor2_args); if (idx1 != idx2) { // infeasible case, constructors do not match inner_cases_on_args.push_back(Fun(minor2_args, P)); } else { if (minor1_args.size() != minor2_args.size()) throw_corrupted(n); buffer<expr> rtype_hyp; // add equalities for (unsigned i = 0; i < minor1_args.size(); i++) { expr lhs = minor1_args[i]; expr rhs = minor2_args[i]; expr lhs_type = mlocal_type(lhs); expr rhs_type = mlocal_type(rhs); level l = sort_level(tc.ensure_type(lhs_type).first); expr h_type; if (tc.is_def_eq(lhs_type, rhs_type).first) { h_type = mk_app(mk_constant(eq_name, to_list(l)), lhs_type, lhs, rhs); } else { h_type = mk_app(mk_constant(heq_name, to_list(l)), lhs_type, lhs, rhs_type, rhs); } rtype_hyp.push_back(mk_local(ngen.next(), local_pp_name(lhs).append_after("_eq"), h_type, binder_info())); } inner_cases_on_args.push_back(Fun(minor2_args, mk_arrow(Pi(rtype_hyp, P), P))); } idx2++; curr_t2 = binding_body(curr_t2); } outer_cases_on_args.push_back(Fun(minor1_args, mk_app(cases_on2, inner_cases_on_args))); idx1++; t1 = binding_body(t1); } expr no_confusion_type_value = Fun(args, mk_app(cases_on1, outer_cases_on_args)); bool opaque = false; bool use_conv_opt = true; declaration new_d = mk_definition(env, no_confusion_type_name, lps, no_confusion_type_type, no_confusion_type_value, opaque, ind_decl.get_module_idx(), use_conv_opt); environment new_env = module::add(env, check(env, new_d)); return some(add_protected(new_env, no_confusion_type_name)); }
environment mk_no_confusion(environment const & env, name const & n) { optional<environment> env1 = mk_no_confusion_type(env, n); if (!env1) return env; environment new_env = *env1; type_checker tc(new_env); inductive::inductive_decls decls = *inductive::is_inductive_decl(new_env, n); unsigned nparams = std::get<1>(decls); name_generator ngen; declaration no_confusion_type_decl = new_env.get(name{n, "no_confusion_type"}); declaration cases_decl = new_env.get(name(n, "cases_on")); level_param_names lps = no_confusion_type_decl.get_univ_params(); levels ls = param_names_to_levels(lps); expr no_confusion_type_type = instantiate_type_univ_params(no_confusion_type_decl, ls); name eq_name("eq"); name heq_name("heq"); name eq_refl_name{"eq", "refl"}; name heq_refl_name{"heq", "refl"}; buffer<expr> args; expr type = no_confusion_type_type; type = to_telescope(ngen, type, args, some(mk_implicit_binder_info())); lean_assert(args.size() >= nparams + 3); unsigned nindices = args.size() - nparams - 3; // 3 is for P v1 v2 expr range = mk_app(mk_constant(no_confusion_type_decl.get_name(), ls), args); expr P = args[args.size()-3]; expr v1 = args[args.size()-2]; expr v2 = args[args.size()-1]; expr v_type = mlocal_type(v1); level v_lvl = sort_level(tc.ensure_type(v_type).first); expr eq_v = mk_app(mk_constant(eq_name, to_list(v_lvl)), v_type); expr H12 = mk_local(ngen.next(), "H12", mk_app(eq_v, v1, v2), binder_info()); args.push_back(H12); name no_confusion_name{n, "no_confusion"}; expr no_confusion_ty = Pi(args, range); // The gen proof is of the form // (fun H11 : v1 = v1, cases_on Params (fun Indices v1, no_confusion_type Params Indices P v1 v1) Indices v1 // <for-each case> // (fun H : (equations -> P), H (refl) ... (refl)) // ... // ) // H11 is for creating the generalization expr H11 = mk_local(ngen.next(), "H11", mk_app(eq_v, v1, v1), binder_info()); // Create the type former (fun Indices v1, no_confusion_type Params Indices P v1 v1) buffer<expr> type_former_args; for (unsigned i = nparams; i < nparams + nindices; i++) type_former_args.push_back(args[i]); type_former_args.push_back(v1); buffer<expr> no_confusion_type_args; for (unsigned i = 0; i < nparams + nindices; i++) no_confusion_type_args.push_back(args[i]); no_confusion_type_args.push_back(P); no_confusion_type_args.push_back(v1); no_confusion_type_args.push_back(v1); expr no_confusion_type_app = mk_app(mk_constant(no_confusion_type_decl.get_name(), ls), no_confusion_type_args); expr type_former = Fun(type_former_args, no_confusion_type_app); // create cases_on levels clvls = ls; expr cases_on = mk_app(mk_app(mk_constant(cases_decl.get_name(), clvls), nparams, args.data()), type_former); cases_on = mk_app(mk_app(cases_on, nindices, args.data() + nparams), v1); expr cot = tc.infer(cases_on).first; while (is_pi(cot)) { buffer<expr> minor_args; expr minor = to_telescope(tc, binding_domain(cot), minor_args); lean_assert(!minor_args.empty()); expr H = minor_args.back(); expr Ht = mlocal_type(H); buffer<expr> refl_args; while (is_pi(Ht)) { buffer<expr> eq_args; expr eq_fn = get_app_args(binding_domain(Ht), eq_args); if (const_name(eq_fn) == eq_name) { refl_args.push_back(mk_app(mk_constant(eq_refl_name, const_levels(eq_fn)), eq_args[0], eq_args[1])); } else { refl_args.push_back(mk_app(mk_constant(heq_refl_name, const_levels(eq_fn)), eq_args[0], eq_args[1])); } Ht = binding_body(Ht); } expr pr = mk_app(H, refl_args); cases_on = mk_app(cases_on, Fun(minor_args, pr)); cot = binding_body(cot); } expr gen = Fun(H11, cases_on); // Now, we use gen to build the final proof using eq.rec // // eq.rec InductiveType v1 (fun (a : InductiveType), v1 = a -> no_confusion_type Params Indices v1 a) gen v2 H12 H12 // name eq_rec_name{"eq", "rec"}; expr eq_rec = mk_app(mk_constant(eq_rec_name, {head(ls), v_lvl}), v_type, v1); // create eq_rec type_former // (fun (a : InductiveType), v1 = a -> no_confusion_type Params Indices v1 a) expr a = mk_local(ngen.next(), "a", v_type, binder_info()); expr H1a = mk_local(ngen.next(), "H1a", mk_app(eq_v, v1, a), binder_info()); // reusing no_confusion_type_args... we just replace the last argument with a no_confusion_type_args.pop_back(); no_confusion_type_args.push_back(a); expr no_confusion_type_app_1a = mk_app(mk_constant(no_confusion_type_decl.get_name(), ls), no_confusion_type_args); expr rec_type_former = Fun(a, Pi(H1a, no_confusion_type_app_1a)); // finalize eq_rec eq_rec = mk_app(mk_app(eq_rec, rec_type_former, gen, v2, H12), H12); // expr no_confusion_val = Fun(args, eq_rec); bool opaque = false; bool use_conv_opt = true; declaration new_d = mk_definition(new_env, no_confusion_name, lps, no_confusion_ty, no_confusion_val, opaque, no_confusion_type_decl.get_module_idx(), use_conv_opt); new_env = module::add(new_env, check(new_env, new_d)); return add_protected(new_env, no_confusion_name); }
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); }); }
old_local_context goal::to_local_context() const { buffer<expr> hyps; get_hyps(hyps); std::reverse(hyps.begin(), hyps.end()); return old_local_context(to_list(hyps)); }
vm_obj to_obj(buffer<name> const & ls) { return to_obj(to_list(ls)); }
void add_congr_core(environment const & env, simp_rule_sets & s, name const & n) { declaration const & d = env.get(n); type_checker tc(env); buffer<level> us; unsigned num_univs = d.get_num_univ_params(); for (unsigned i = 0; i < num_univs; i++) { us.push_back(mk_meta_univ(name(*g_prefix, i))); } levels ls = to_list(us); expr pr = mk_constant(n, ls); expr e = instantiate_type_univ_params(d, ls); buffer<bool> explicit_args; buffer<expr> metas; unsigned idx = 0; while (is_pi(e)) { expr mvar = mk_metavar(name(*g_prefix, idx), binding_domain(e)); idx++; explicit_args.push_back(is_explicit(binding_info(e))); metas.push_back(mvar); e = instantiate(binding_body(e), mvar); pr = mk_app(pr, mvar); } expr rel, lhs, rhs; if (!is_simp_relation(env, e, rel, lhs, rhs) || !is_constant(rel)) { throw exception(sstream() << "invalid congruence rule, '" << n << "' resulting type is not of the form t ~ s, where '~' is a transitive and reflexive relation"); } name_set found_mvars; buffer<expr> lhs_args, rhs_args; expr const & lhs_fn = get_app_args(lhs, lhs_args); expr const & rhs_fn = get_app_args(rhs, rhs_args); if (is_constant(lhs_fn)) { if (!is_constant(rhs_fn) || const_name(lhs_fn) != const_name(rhs_fn) || lhs_args.size() != rhs_args.size()) { throw exception(sstream() << "invalid congruence rule, '" << n << "' resulting type is not of the form (" << const_name(lhs_fn) << " ...) " << "~ (" << const_name(lhs_fn) << " ...), where ~ is '" << const_name(rel) << "'"); } for (expr const & lhs_arg : lhs_args) { if (is_sort(lhs_arg)) continue; if (!is_metavar(lhs_arg) || found_mvars.contains(mlocal_name(lhs_arg))) { throw exception(sstream() << "invalid congruence rule, '" << n << "' the left-hand-side of the congruence resulting type must be of the form (" << const_name(lhs_fn) << " x_1 ... x_n), where each x_i is a distinct variable or a sort"); } found_mvars.insert(mlocal_name(lhs_arg)); } } else if (is_binding(lhs)) { if (lhs.kind() != rhs.kind()) { throw exception(sstream() << "invalid congruence rule, '" << n << "' kinds of the left-hand-side and right-hand-side of " << "the congruence resulting type do not match"); } if (!is_valid_congr_rule_binding_lhs(lhs, found_mvars)) { throw exception(sstream() << "invalid congruence rule, '" << n << "' left-hand-side of the congruence resulting type must " << "be of the form (fun/Pi (x : A), B x)"); } } else { throw exception(sstream() << "invalid congruence rule, '" << n << "' left-hand-side is not an application nor a binding"); } buffer<expr> congr_hyps; lean_assert(metas.size() == explicit_args.size()); for (unsigned i = 0; i < metas.size(); i++) { expr const & mvar = metas[i]; if (explicit_args[i] && !found_mvars.contains(mlocal_name(mvar))) { buffer<expr> locals; expr type = mlocal_type(mvar); while (is_pi(type)) { expr local = mk_local(tc.mk_fresh_name(), binding_domain(type)); locals.push_back(local); type = instantiate(binding_body(type), local); } expr h_rel, h_lhs, h_rhs; if (!is_simp_relation(env, type, h_rel, h_lhs, h_rhs) || !is_constant(h_rel)) continue; unsigned j = 0; for (expr const & local : locals) { j++; if (!only_found_mvars(mlocal_type(local), found_mvars)) { throw exception(sstream() << "invalid congruence rule, '" << n << "' argument #" << j << " of parameter #" << (i+1) << " contains " << "unresolved parameters"); } } if (!only_found_mvars(h_lhs, found_mvars)) { throw exception(sstream() << "invalid congruence rule, '" << n << "' argument #" << (i+1) << " is not a valid hypothesis, the left-hand-side contains " << "unresolved parameters"); } if (!is_valid_congr_hyp_rhs(h_rhs, found_mvars)) { throw exception(sstream() << "invalid congruence rule, '" << n << "' argument #" << (i+1) << " is not a valid hypothesis, the right-hand-side must be " << "of the form (m l_1 ... l_n) where m is parameter that was not " << "'assigned/resolved' yet and l_i's are locals"); } found_mvars.insert(mlocal_name(mvar)); congr_hyps.push_back(mvar); } } congr_rule rule(n, ls, to_list(metas), lhs, rhs, pr, to_list(congr_hyps)); s.insert(const_name(rel), rule); }
void decl_attributes::parse(parser & p) { buffer<char const *> attr_tokens; get_attribute_tokens(attr_tokens); while (true) { auto pos = p.pos(); if (auto it = parse_priority(p)) { m_prio = *it; bool has_prio_attr = false; for (auto const & entry : m_entries) { if (get_attribute_kind(entry.m_attr.c_str()) == attribute_kind::Prioritized) { has_prio_attr = true; break; } } if (!has_prio_attr) { throw parser_error("invalid '[priority]' attribute, declaration has not been marked with a prioritized attribute", pos); } } else if (p.curr_is_token(get_parsing_only_tk())) { if (!m_is_abbrev) throw parser_error("invalid '[parsing_only]' attribute, only abbreviations can be " "marked as '[parsing_only]'", pos); m_parsing_only = true; p.next(); } else { bool found = false; for (char const * tk : attr_tokens) { if (p.curr_is_token(tk)) { p.next(); char const * attr = get_attribute_from_token(tk); for (auto const & entry : m_entries) { if (are_incompatible(entry.m_attr.c_str(), attr)) { throw parser_error(sstream() << "invalid attribute [" << attr << "], declaration was already marked with [" << entry.m_attr << "]", pos); } } switch (get_attribute_kind(attr)) { case attribute_kind::Default: case attribute_kind::Prioritized: m_entries = cons(entry(attr), m_entries); break; case attribute_kind::Parametric: { unsigned v = p.parse_small_nat(); if (v == 0) throw parser_error("invalid attribute parameter, value must be positive", pos); p.check_token_next(get_rbracket_tk(), "invalid attribute, ']' expected"); m_entries = cons(entry(attr, v-1), m_entries); break; } case attribute_kind::OptParametric: if (!p.curr_is_token(get_rbracket_tk())) { unsigned v = p.parse_small_nat(); if (v == 0) throw parser_error("invalid attribute parameter, value must be positive", pos); p.check_token_next(get_rbracket_tk(), "invalid attribute, ']' expected"); m_entries = cons(entry(attr, v-1), m_entries); } else { p.check_token_next(get_rbracket_tk(), "invalid attribute, ']' expected"); m_entries = cons(entry(attr), m_entries); } break; case attribute_kind::MultiParametric: { buffer<unsigned> vs; while (true) { unsigned v = p.parse_small_nat(); if (v == 0) throw parser_error("invalid attribute parameter, value must be positive", pos); vs.push_back(v-1); if (p.curr_is_token(get_rbracket_tk())) break; } p.next(); m_entries = cons(entry(attr, to_list(vs)), m_entries); break; } } found = true; break; } } if (!found) break; } } }
list<expr> goal::to_context() const { buffer<expr> locals; get_app_rev_args(m_meta, locals); return to_list(locals.begin(), locals.end()); }
vm_obj to_obj(buffer<expr> const & ls) { return to_obj(to_list(ls)); }