322 lines
14 KiB
C++
322 lines
14 KiB
C++
/*
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Copyright (c) 2014 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 <utility>
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#include <algorithm>
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#include <vector>
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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/buffer.h"
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#include "util/interrupt.h"
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#include "kernel/environment.h"
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#include "library/module.h"
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#include "library/choice.h"
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#include "library/placeholder.h"
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#include "library/explicit.h"
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#include "frontends/lean/parser.h"
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#include "frontends/lean/util.h"
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namespace lean {
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struct calc_ext : public environment_extension {
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typedef rb_map<name, pair<name, unsigned>, name_quick_cmp> refl_table;
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typedef rb_map<name_pair, std::tuple<name, name, unsigned>, name_pair_quick_cmp> trans_table;
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optional<name> m_subst;
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unsigned m_subst_num_args;
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trans_table m_trans_table;
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refl_table m_refl_table;
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calc_ext():m_subst_num_args(0) {}
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};
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struct calc_ext_reg {
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unsigned m_ext_id;
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calc_ext_reg() { m_ext_id = environment::register_extension(std::make_shared<calc_ext>()); }
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};
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static calc_ext_reg g_ext;
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static calc_ext const & get_extension(environment const & env) {
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return static_cast<calc_ext const &>(env.get_extension(g_ext.m_ext_id));
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}
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static environment update(environment const & env, calc_ext const & ext) {
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return env.update(g_ext.m_ext_id, std::make_shared<calc_ext>(ext));
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}
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static expr extract_arg_types(environment const & env, name const & f, buffer<expr> & arg_types) {
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expr f_type = env.get(f).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 f_type;
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}
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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 std::string g_calc_subst_key("calcs");
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static std::string g_calc_refl_key("calcr");
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static std::string g_calc_trans_key("calct");
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environment add_calc_subst(environment const & env, name const & subst) {
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buffer<expr> arg_types;
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expr r_type = extract_arg_types(env, subst, arg_types);
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unsigned nargs = arg_types.size();
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if (nargs < 2)
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throw exception("invalid calc substitution theorem, it must have at least 2 arguments");
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calc_ext ext = get_extension(env);
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ext.m_subst = subst;
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ext.m_subst_num_args = nargs;
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environment new_env = module::add(env, g_calc_subst_key, [=](serializer & s) {
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s << subst << nargs;
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});
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return update(new_env, ext);
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}
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environment add_calc_refl(environment const & env, name const & refl) {
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buffer<expr> arg_types;
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expr r_type = extract_arg_types(env, refl, arg_types);
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unsigned nargs = arg_types.size();
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if (nargs < 1)
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throw exception("invalid calc reflexivity rule, it must have at least 1 argument");
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name const & rop = get_fn_const(r_type, "invalid calc reflexivity rule, result type must be an operator application");
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calc_ext ext = get_extension(env);
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ext.m_refl_table.insert(rop, mk_pair(refl, nargs));
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environment new_env = module::add(env, g_calc_refl_key, [=](serializer & s) {
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s << rop << refl << nargs;
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});
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return update(new_env, ext);
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}
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environment add_calc_trans(environment const & env, name const & trans) {
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buffer<expr> arg_types;
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expr r_type = extract_arg_types(env, trans, arg_types);
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unsigned nargs = arg_types.size();
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if (nargs < 5)
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throw exception("invalid calc transitivity rule, it must have at least 5 arguments");
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name const & rop = get_fn_const(r_type, "invalid calc transitivity rule, result type must be an operator application");
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name const & op1 = get_fn_const(arg_types[nargs-2], "invalid calc transitivity rule, penultimate argument must be an operator application");
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name const & op2 = get_fn_const(arg_types[nargs-1], "invalid calc transitivity rule, last argument must be an operator application");
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calc_ext ext = get_extension(env);
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ext.m_trans_table.insert(name_pair(op1, op2), std::make_tuple(trans, rop, nargs));
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environment new_env = module::add(env, g_calc_trans_key, [=](serializer & s) {
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s << op1 << op2 << trans << rop << nargs;
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});
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return update(new_env, ext);
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}
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static void calc_subst_reader(deserializer & d, module_idx, shared_environment &,
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std::function<void(asynch_update_fn const &)> &,
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std::function<void(delayed_update_fn const &)> & add_delayed_update) {
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name subst; unsigned nargs;
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d >> subst >> nargs;
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add_delayed_update([=](environment const & env, io_state const &) -> environment {
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calc_ext ext = get_extension(env);
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ext.m_subst = subst;
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ext.m_subst_num_args = nargs;
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return update(env, ext);
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});
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}
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register_module_object_reader_fn g_calc_subst_reader(g_calc_subst_key, calc_subst_reader);
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static void calc_refl_reader(deserializer & d, module_idx, shared_environment &,
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std::function<void(asynch_update_fn const &)> &,
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std::function<void(delayed_update_fn const &)> & add_delayed_update) {
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name rop, refl; unsigned nargs;
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d >> rop >> refl >> nargs;
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add_delayed_update([=](environment const & env, io_state const &) -> environment {
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calc_ext ext = get_extension(env);
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ext.m_refl_table.insert(rop, mk_pair(refl, nargs));
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return update(env, ext);
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});
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}
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register_module_object_reader_fn g_calc_refl_reader(g_calc_refl_key, calc_refl_reader);
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static void calc_trans_reader(deserializer & d, module_idx, shared_environment &,
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std::function<void(asynch_update_fn const &)> &,
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std::function<void(delayed_update_fn const &)> & add_delayed_update) {
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name op1, op2, trans, rop; unsigned nargs;
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d >> op1 >> op2 >> trans >> rop >> nargs;
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add_delayed_update([=](environment const & env, io_state const &) -> environment {
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calc_ext ext = get_extension(env);
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ext.m_trans_table.insert(name_pair(op1, op2), std::make_tuple(trans, rop, nargs));
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return update(env, ext);
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});
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}
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register_module_object_reader_fn g_calc_trans_reader(g_calc_trans_key, calc_trans_reader);
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environment calc_subst_cmd(parser & p) {
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name id = p.check_constant_next("invalid 'calc_subst' command, constant expected");
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return add_calc_subst(p.env(), id);
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}
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environment calc_refl_cmd(parser & p) {
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name id = p.check_constant_next("invalid 'calc_refl' command, constant expected");
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return add_calc_refl(p.env(), id);
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}
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environment calc_trans_cmd(parser & p) {
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name id = p.check_constant_next("invalid 'calc_trans' command, constant expected");
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return add_calc_trans(p.env(), id);
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}
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void register_calc_cmds(cmd_table & r) {
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add_cmd(r, cmd_info("calc_subst", "set the substitution rule that is used by the calculational proof '{...}' notation", calc_subst_cmd));
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add_cmd(r, cmd_info("calc_refl", "set the reflexivity rule for an operator, this command is relevant for the calculational proof '{...}' notation", calc_refl_cmd));
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add_cmd(r, cmd_info("calc_trans", "set the transitivity rule for a pair of operators, this command is relevant for the calculational proof '{...}' notation", calc_trans_cmd));
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}
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typedef std::tuple<name, expr, expr> calc_pred;
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typedef pair<calc_pred, expr> calc_step;
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inline name const & pred_op(calc_pred const & p) { return std::get<0>(p); }
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inline expr const & pred_lhs(calc_pred const & p) { return std::get<1>(p); }
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inline expr const & pred_rhs(calc_pred const & p) { return std::get<2>(p); }
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inline calc_pred const & step_pred(calc_step const & s) { return s.first; }
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inline expr const & step_proof(calc_step const & s) { return s.second; }
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static name g_lcurly("{");
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static name g_rcurly("}");
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static name g_ellipsis("...");
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static name g_colon(":");
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static void decode_expr_core(expr const & e, buffer<calc_pred> & preds) {
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buffer<expr> args;
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expr const & fn = get_app_args(e, args);
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if (!is_constant(fn))
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return;
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unsigned nargs = args.size();
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if (nargs < 2)
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return;
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preds.emplace_back(const_name(fn), args[nargs-2], args[nargs-1]);
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}
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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 void decode_expr(expr const & e, buffer<calc_pred> & preds, pos_info const & pos) {
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preds.clear();
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if (is_choice(e)) {
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for (unsigned i = 0; i < get_num_choices(e); i++)
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decode_expr_core(get_choice(e, i), preds);
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} else {
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decode_expr_core(e, preds);
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}
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if (preds.empty())
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throw parser_error("invalid 'calc' expression, expression must be a function application 'f a_1 ... a_k' "
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"where f is a constant, and k >= 2", pos);
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}
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// Create (op _ _ ... _)
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static expr mk_op_fn(parser & p, name const & op, unsigned num_placeholders, pos_info const & pos) {
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expr r = p.save_pos(mk_explicit(mk_constant(op)), pos);
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while (num_placeholders > 0) {
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num_placeholders--;
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r = p.mk_app(r, p.save_pos(mk_expr_placeholder(), pos), pos);
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}
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return r;
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}
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static void parse_calc_proof(parser & p, buffer<calc_pred> const & preds, std::vector<calc_step> & steps) {
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steps.clear();
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auto pos = p.pos();
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p.check_token_next(g_colon, "invalid 'calc' expression, ':' expected");
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if (p.curr_is_token(g_lcurly)) {
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p.next();
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expr pr = p.parse_expr();
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p.check_token_next(g_rcurly, "invalid 'calc' expression, '}' expected");
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calc_ext const & ext = get_extension(p.env());
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if (!ext.m_subst)
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throw parser_error("invalid 'calc' expression, substitution rule was not defined with calc_subst command", pos);
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for (auto const & pred : preds) {
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auto refl_it = ext.m_refl_table.find(pred_op(pred));
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if (refl_it) {
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expr refl = mk_op_fn(p, refl_it->first, refl_it->second-1, pos);
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expr refl_pr = p.mk_app(refl, pred_lhs(pred), pos);
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expr subst = mk_op_fn(p, *ext.m_subst, ext.m_subst_num_args-2, pos);
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expr subst_pr = p.mk_app({subst, pr, refl_pr}, pos);
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steps.emplace_back(pred, subst_pr);
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}
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}
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if (steps.empty())
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throw parser_error("invalid 'calc' expression, reflexivity rule is not defined for operator", pos);
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} else {
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expr pr = p.parse_expr();
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for (auto const & pred : preds)
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steps.emplace_back(pred, pr);
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}
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}
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/** \brief Collect distinct rhs's */
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static void collect_rhss(std::vector<calc_step> const & steps, buffer<expr> & rhss) {
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rhss.clear();
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for (auto const & step : steps) {
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calc_pred const & pred = step_pred(step);
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expr const & rhs = pred_rhs(pred);
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if (std::find(rhss.begin(), rhss.end(), rhs) == rhss.end())
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rhss.push_back(rhs);
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}
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lean_assert(!rhss.empty());
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}
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static void join(parser & p, std::vector<calc_step> const & steps1, std::vector<calc_step> const & steps2, std::vector<calc_step> & res_steps,
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pos_info const & pos) {
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res_steps.clear();
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calc_ext const & ext = get_extension(p.env());
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for (calc_step const & s1 : steps1) {
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check_interrupted();
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calc_pred const & pred1 = step_pred(s1);
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expr const & pr1 = step_proof(s1);
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for (calc_step const & s2 : steps2) {
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calc_pred const & pred2 = step_pred(s2);
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expr const & pr2 = step_proof(s2);
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if (!is_eqp(pred_rhs(pred1), pred_lhs(pred2)))
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continue;
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auto trans_it = ext.m_trans_table.find(name_pair(pred_op(pred1), pred_op(pred2)));
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if (!trans_it)
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continue;
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expr trans = mk_op_fn(p, std::get<0>(*trans_it), std::get<2>(*trans_it)-5, pos);
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expr trans_pr = p.mk_app({trans, pred_lhs(pred1), pred_rhs(pred1), pred_rhs(pred2), pr1, pr2}, pos);
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res_steps.emplace_back(calc_pred(std::get<1>(*trans_it), pred_lhs(pred1), pred_rhs(pred2)), trans_pr);
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}
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}
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}
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expr parse_calc(parser & p) {
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buffer<calc_pred> preds, new_preds;
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buffer<expr> rhss;
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std::vector<calc_step> steps, new_steps, next_steps;
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auto pos = p.pos();
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decode_expr(p.parse_expr(), preds, pos);
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parse_calc_proof(p, preds, steps);
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expr dummy = mk_expr_placeholder();
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while (p.curr_is_token(g_ellipsis)) {
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pos = p.pos();
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p.next();
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decode_expr(p.parse_led(dummy), preds, pos);
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collect_rhss(steps, rhss);
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new_steps.clear();
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for (auto const & pred : preds) {
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if (is_eqp(pred_lhs(pred), dummy)) {
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for (expr const & rhs : rhss)
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new_preds.emplace_back(pred_op(pred), rhs, pred_rhs(pred));
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}
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}
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if (new_preds.empty())
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throw parser_error("invalid 'calc' expression, invalid expression", pos);
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parse_calc_proof(p, new_preds, new_steps);
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join(p, steps, new_steps, next_steps, pos);
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if (next_steps.empty())
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throw parser_error("invalid 'calc' expression, transitivity rule is not defined for current step", pos);
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steps.swap(next_steps);
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}
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buffer<expr> choices;
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for (auto const & s : steps)
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choices.push_back(step_proof(s));
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return p.save_pos(mk_choice(choices.size(), choices.data()), pos);
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}
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}
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