299 lines
11 KiB
C++
299 lines
11 KiB
C++
/*
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Copyright (c) 2015 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <string>
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#include "util/optional.h"
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#include "util/name.h"
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#include "util/rb_map.h"
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#include "util/sstream.h"
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#include "library/constants.h"
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#include "library/scoped_ext.h"
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#include "library/relation_manager.h"
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namespace lean {
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// Check whether e is of the form (f ...) where f is a constant. If it is return f.
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static name const & get_fn_const(expr const & e, char const * msg) {
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expr const & fn = get_app_fn(e);
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if (!is_constant(fn))
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throw exception(msg);
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return const_name(fn);
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}
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static pair<expr, unsigned> extract_arg_types_core(environment const & env, name const & f, buffer<expr> & arg_types) {
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declaration d = env.get(f);
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expr f_type = d.get_type();
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while (is_pi(f_type)) {
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arg_types.push_back(binding_domain(f_type));
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f_type = binding_body(f_type);
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}
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return mk_pair(f_type, d.get_num_univ_params());
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}
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enum class op_kind { Relation, Subst, Trans, Refl, Symm };
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struct rel_entry {
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op_kind m_kind;
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name m_name;
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rel_entry() {}
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rel_entry(op_kind k, name const & n):m_kind(k), m_name(n) {}
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};
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struct rel_state {
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typedef name_map<refl_info> refl_table;
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typedef name_map<subst_info> subst_table;
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typedef name_map<symm_info> symm_table;
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typedef rb_map<name_pair, trans_info, name_pair_quick_cmp> trans_table;
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typedef name_map<relation_info> rop_table;
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trans_table m_trans_table;
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refl_table m_refl_table;
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subst_table m_subst_table;
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symm_table m_symm_table;
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rop_table m_rop_table;
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rel_state() {}
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bool is_equivalence(name const & rop) const {
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return m_trans_table.contains(mk_pair(rop, rop)) && m_refl_table.contains(rop) && m_symm_table.contains(rop);
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}
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static void throw_invalid_relation(name const & rop) {
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throw exception(sstream() << "invalid binary relation declaration, relation '" << rop
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<< "' must have two explicit parameters");
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}
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void register_rop(environment const & env, name const & rop) {
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if (m_rop_table.contains(rop))
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return;
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declaration const & d = env.get(rop);
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optional<unsigned> lhs_pos;
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optional<unsigned> rhs_pos;
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unsigned i = 0;
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expr type = d.get_type();
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while (is_pi(type)) {
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if (is_explicit(binding_info(type))) {
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if (!lhs_pos) {
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lhs_pos = i;
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} else if (!rhs_pos) {
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rhs_pos = i;
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} else {
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lhs_pos = rhs_pos;
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rhs_pos = i;
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}
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}
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type = binding_body(type);
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i++;
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}
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if (lhs_pos && rhs_pos) {
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m_rop_table.insert(rop, relation_info(i, *lhs_pos, *rhs_pos));
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} else {
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throw_invalid_relation(rop);
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}
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}
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void add_subst(environment const & env, name const & subst) {
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buffer<expr> arg_types;
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auto p = extract_arg_types_core(env, subst, arg_types);
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expr r_type = p.first;
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unsigned nunivs = p.second;
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unsigned nargs = arg_types.size();
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if (nargs < 2)
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throw exception("invalid substitution theorem, it must have at least 2 arguments");
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name const & rop = get_fn_const(arg_types[nargs-2], "invalid substitution theorem, penultimate argument must be an operator application");
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m_subst_table.insert(rop, subst_info(subst, nunivs, nargs));
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}
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void add_refl(environment const & env, name const & refl) {
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buffer<expr> arg_types;
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auto p = extract_arg_types_core(env, refl, arg_types);
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expr r_type = p.first;
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unsigned nunivs = p.second;
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unsigned nargs = arg_types.size();
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if (nargs < 1)
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throw exception("invalid reflexivity rule, it must have at least 1 argument");
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name const & rop = get_fn_const(r_type, "invalid reflexivity rule, result type must be an operator application");
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register_rop(env, rop);
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m_refl_table.insert(rop, refl_info(refl, nunivs, nargs));
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}
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void add_trans(environment const & env, name const & trans) {
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buffer<expr> arg_types;
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auto p = extract_arg_types_core(env, trans, arg_types);
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expr r_type = p.first;
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unsigned nunivs = p.second;
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unsigned nargs = arg_types.size();
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if (nargs < 5)
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throw exception("invalid transitivity rule, it must have at least 5 arguments");
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name const & rop = get_fn_const(r_type, "invalid transitivity rule, result type must be an operator application");
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name const & op1 = get_fn_const(arg_types[nargs-2], "invalid transitivity rule, penultimate argument must be an operator application");
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name const & op2 = get_fn_const(arg_types[nargs-1], "invalid transitivity rule, last argument must be an operator application");
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register_rop(env, rop);
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m_trans_table.insert(name_pair(op1, op2), trans_info(trans, nunivs, nargs, rop));
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}
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void add_symm(environment const & env, name const & symm) {
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buffer<expr> arg_types;
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auto p = extract_arg_types_core(env, symm, arg_types);
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expr r_type = p.first;
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unsigned nunivs = p.second;
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unsigned nargs = arg_types.size();
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if (nargs < 1)
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throw exception("invalid symmetry rule, it must have at least 1 argument");
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name const & rop = get_fn_const(r_type, "invalid symmetry rule, result type must be an operator application");
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register_rop(env, rop);
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m_symm_table.insert(rop, symm_info(symm, nunivs, nargs));
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}
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};
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static name * g_rel_name = nullptr;
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static std::string * g_key = nullptr;
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struct rel_config {
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typedef rel_state state;
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typedef rel_entry entry;
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static void add_entry(environment const & env, io_state const &, state & s, entry const & e) {
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switch (e.m_kind) {
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case op_kind::Relation: s.register_rop(env, e.m_name); break;
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case op_kind::Refl: s.add_refl(env, e.m_name); break;
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case op_kind::Subst: s.add_subst(env, e.m_name); break;
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case op_kind::Trans: s.add_trans(env, e.m_name); break;
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case op_kind::Symm: s.add_symm(env, e.m_name); break;
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}
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}
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static name const & get_class_name() {
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return *g_rel_name;
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}
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static std::string const & get_serialization_key() {
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return *g_key;
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}
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static void write_entry(serializer & s, entry const & e) {
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s << static_cast<char>(e.m_kind) << e.m_name;
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}
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static entry read_entry(deserializer & d) {
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entry e;
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char cmd;
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d >> cmd >> e.m_name;
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e.m_kind = static_cast<op_kind>(cmd);
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return e;
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}
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static optional<unsigned> get_fingerprint(entry const &) {
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return optional<unsigned>();
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}
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};
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template class scoped_ext<rel_config>;
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typedef scoped_ext<rel_config> rel_ext;
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environment add_relation(environment const & env, name const & n, bool persistent) {
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return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Relation, n), persistent);
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}
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environment add_subst(environment const & env, name const & n, bool persistent) {
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return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Subst, n), persistent);
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}
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environment add_refl(environment const & env, name const & n, bool persistent) {
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return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Refl, n), persistent);
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}
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environment add_symm(environment const & env, name const & n, bool persistent) {
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return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Symm, n), persistent);
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}
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environment add_trans(environment const & env, name const & n, bool persistent) {
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return rel_ext::add_entry(env, get_dummy_ios(), rel_entry(op_kind::Trans, n), persistent);
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}
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static optional<relation_lemma_info> get_info(name_map<relation_lemma_info> const & table, name const & op) {
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if (auto it = table.find(op)) {
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return optional<relation_lemma_info>(*it);
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} else {
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return optional<relation_lemma_info>();
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}
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}
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optional<refl_info> get_refl_extra_info(environment const & env, name const & op) {
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return get_info(rel_ext::get_state(env).m_refl_table, op);
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}
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optional<subst_info> get_subst_extra_info(environment const & env, name const & op) {
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return get_info(rel_ext::get_state(env).m_subst_table, op);
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}
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optional<symm_info> get_symm_extra_info(environment const & env, name const & op) {
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return get_info(rel_ext::get_state(env).m_symm_table, op);
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}
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optional<trans_info> get_trans_extra_info(environment const & env, name const & op1, name const & op2) {
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if (auto it = rel_ext::get_state(env).m_trans_table.find(mk_pair(op1, op2))) {
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return optional<trans_info>(*it);
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} else {
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return optional<trans_info>();
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}
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}
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bool is_subst_relation(environment const & env, name const & op) {
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return rel_ext::get_state(env).m_subst_table.contains(op);
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}
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optional<name> get_refl_info(environment const & env, name const & op) {
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if (auto it = get_refl_extra_info(env, op))
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return optional<name>(it->m_name);
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else
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return optional<name>();
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}
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optional<name> get_symm_info(environment const & env, name const & op) {
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if (auto it = get_symm_extra_info(env, op))
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return optional<name>(it->m_name);
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else
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return optional<name>();
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}
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optional<name> get_trans_info(environment const & env, name const & op) {
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if (auto it = get_trans_extra_info(env, op, op))
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return optional<name>(it->m_name);
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else
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return optional<name>();
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}
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refl_info_getter mk_refl_info_getter(environment const & env) {
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auto t = rel_ext::get_state(env).m_refl_table;
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return [=](name const & n) { return get_info(t, n); }; // NOLINT
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}
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trans_info_getter mk_trans_info_getter(environment const & env) {
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auto t = rel_ext::get_state(env).m_trans_table;
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return [=](name const & op1, name const & op2) { // NOLINT
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if (auto it = t.find(mk_pair(op1, op2))) {
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return optional<trans_info>(*it);
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} else {
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return optional<trans_info>();
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}
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};
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}
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symm_info_getter mk_symm_info_getter(environment const & env) {
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auto t = rel_ext::get_state(env).m_symm_table;
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return [=](name const & n) { return get_info(t, n); }; // NOLINT
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}
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bool is_equivalence(environment const & env, name const & rop) {
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return rel_ext::get_state(env).is_equivalence(rop);
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}
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relation_info const * get_relation_info(environment const & env, name const & rop) {
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return rel_ext::get_state(env).m_rop_table.find(rop);
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}
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void initialize_relation_manager() {
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g_rel_name = new name("rel");
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g_key = new std::string("rel");
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rel_ext::initialize();
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}
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void finalize_relation_manager() {
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rel_ext::finalize();
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delete g_key;
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delete g_rel_name;
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}
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}
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