727 lines
25 KiB
C++
727 lines
25 KiB
C++
/*
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Copyright (c) 2013 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 <utility>
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#include <algorithm>
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#include <vector>
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#include "util/safe_arith.h"
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#include "util/buffer.h"
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#include "util/rc.h"
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#include "util/list.h"
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#include "util/debug.h"
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#include "util/hash.h"
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#include "util/interrupt.h"
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#include "kernel/level.h"
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#include "kernel/environment.h"
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namespace lean {
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level_cell const & to_cell(level const & l) {
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return *l.m_ptr;
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}
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/** \brief Base class for representing universe level terms. */
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struct level_cell {
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void dealloc();
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MK_LEAN_RC()
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level_kind m_kind;
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unsigned m_hash;
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level_cell(level_kind k, unsigned h):m_rc(0), m_kind(k), m_hash(h) {}
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};
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struct level_composite : public level_cell {
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unsigned m_depth;
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unsigned m_has_param:1;
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unsigned m_has_global:1;
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unsigned m_has_meta:1;
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level_composite(level_kind k, unsigned h, unsigned d, bool has_param, bool has_global, bool has_meta):
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level_cell(k, h), m_depth(d), m_has_param(has_param), m_has_global(has_global), m_has_meta(has_meta) {}
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};
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bool is_composite(level const & l) {
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switch (kind(l)) {
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case level_kind::Succ: case level_kind::Max: case level_kind::IMax:
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return true;
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case level_kind::Param: case level_kind::Global: case level_kind::Meta: case level_kind::Zero:
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return false;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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static level_composite const & to_composite(level const & l) {
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lean_assert(is_composite(l));
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return static_cast<level_composite const &>(to_cell(l));
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}
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struct level_succ : public level_composite {
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level m_l;
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bool m_explicit;
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level_succ(level const & l):
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level_composite(level_kind::Succ, hash(hash(l), 17u), get_depth(l) + 1, has_param(l), has_global(l), has_meta(l)),
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m_l(l),
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m_explicit(is_explicit(l)) {}
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};
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level_succ const & to_level_succ(level const & l) { lean_assert(is_succ(l)); return static_cast<level_succ const &>(to_cell(l)); }
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level const & succ_of(level const & l) { return to_level_succ(l).m_l; }
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struct level_max_core : public level_composite {
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level m_lhs;
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level m_rhs;
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level_max_core(bool imax, level const & l1, level const & l2):
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level_composite(imax ? level_kind::IMax : level_kind::Max,
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hash(hash(l1), hash(l2)),
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std::max(get_depth(l1), get_depth(l2)) + 1,
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has_param(l1) || has_param(l2),
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has_global(l1) || has_global(l2),
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has_meta(l1) || has_meta(l2)),
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m_lhs(l1), m_rhs(l2) {
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lean_assert(!is_explicit(l1) || !is_explicit(l2));
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}
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};
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static level_max_core const & to_max_core(level const & l) {
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lean_assert(is_max(l) || is_imax(l));
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return static_cast<level_max_core const &>(to_cell(l));
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}
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level const & max_lhs(level const & l) { lean_assert(is_max(l)); return to_max_core(l).m_lhs; }
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level const & max_rhs(level const & l) { lean_assert(is_max(l)); return to_max_core(l).m_rhs; }
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level const & imax_lhs(level const & l) { lean_assert(is_imax(l)); return to_max_core(l).m_lhs; }
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level const & imax_rhs(level const & l) { lean_assert(is_imax(l)); return to_max_core(l).m_rhs; }
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struct level_param_core : public level_cell {
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name m_id;
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level_param_core(level_kind k, name const & id):
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level_cell(k, hash(id.hash(), static_cast<unsigned>(k))),
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m_id(id) {
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lean_assert(k == level_kind::Meta || k == level_kind::Param || k == level_kind::Global);
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}
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};
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bool is_param_core(level const & l) { return is_param(l) || is_global(l) || is_meta(l); }
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static level_param_core const & to_param_core(level const & l) {
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lean_assert(is_param_core(l));
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return static_cast<level_param_core const &>(to_cell(l));
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}
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name const & param_id(level const & l) { lean_assert(is_param(l)); return to_param_core(l).m_id; }
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name const & global_id(level const & l) { lean_assert(is_global(l)); return to_param_core(l).m_id; }
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name const & meta_id(level const & l) { lean_assert(is_meta(l)); return to_param_core(l).m_id; }
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name const & level_id(level const & l) {
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lean_assert(is_param(l) || is_global(l) || is_meta(l));
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return to_param_core(l).m_id;
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}
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void level_cell::dealloc() {
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switch (m_kind) {
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case level_kind::Succ:
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delete static_cast<level_succ*>(this);
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break;
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case level_kind::Max: case level_kind::IMax:
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delete static_cast<level_max_core*>(this);
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break;
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case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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delete static_cast<level_param_core*>(this);
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break;
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case level_kind::Zero:
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delete this;
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break;
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}
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}
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unsigned get_depth(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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return 1;
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case level_kind::Succ: case level_kind::Max: case level_kind::IMax:
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return to_composite(l).m_depth;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool has_param(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Meta: case level_kind::Global:
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return false;
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case level_kind::Param:
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return true;
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case level_kind::Succ: case level_kind::Max: case level_kind::IMax:
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return to_composite(l).m_has_param;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool has_global(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Meta:
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return false;
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case level_kind::Global:
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return true;
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case level_kind::Succ: case level_kind::Max: case level_kind::IMax:
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return to_composite(l).m_has_param;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool has_meta(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Global:
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return false;
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case level_kind::Meta:
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return true;
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case level_kind::Succ: case level_kind::Max: case level_kind::IMax:
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return to_composite(l).m_has_meta;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool is_explicit(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero:
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return true;
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case level_kind::Param: case level_kind::Global: case level_kind::Meta: case level_kind::Max: case level_kind::IMax:
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return false;
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case level_kind::Succ:
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return to_level_succ(l).m_explicit;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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level mk_succ(level const & l) {
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return level(new level_succ(l));
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}
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/** \brief Convert (succ^k l) into (l, k). If l is not a succ, then return (l, 0) */
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pair<level, unsigned> to_offset(level l) {
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unsigned k = 0;
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while (is_succ(l)) {
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l = succ_of(l);
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k++;
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}
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return mk_pair(l, k);
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}
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unsigned to_explicit(level const & l) {
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lean_assert(is_explicit(l));
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return to_offset(l).second;
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}
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level mk_max(level const & l1, level const & l2) {
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if (is_explicit(l1) && is_explicit(l2)) {
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return get_depth(l1) >= get_depth(l2) ? l1 : l2;
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} else if (l1 == l2) {
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return l1;
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} else if (is_zero(l1)) {
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return l2;
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} else if (is_zero(l2)) {
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return l1;
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} else if (is_max(l2) && (max_lhs(l2) == l1 || max_rhs(l2) == l1)) {
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return l2; // if l2 == (max l1 l'), then max l1 l2 == l2
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} else if (is_max(l1) && (max_lhs(l1) == l2 || max_rhs(l1) == l2)) {
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return l1; // if l1 == (max l2 l'), then max l1 l2 == l1
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} else {
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auto p1 = to_offset(l1);
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auto p2 = to_offset(l2);
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if (p1.first == p2.first) {
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lean_assert(p1.second != p2.second);
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return p1.second > p2.second ? l1 : l2;
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} else {
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return level(new level_max_core(false, l1, l2));
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}
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}
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}
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level mk_imax(level const & l1, level const & l2) {
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if (is_not_zero(l2))
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return mk_max(l1, l2);
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else if (is_zero(l2))
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return l2; // imax u 0 = 0 for any u
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else if (is_zero(l1))
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return l2; // imax 0 u = u for any u
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else if (l1 == l2)
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return l1; // imax u u = u
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else
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return level(new level_max_core(true, l1, l2));
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}
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level mk_param_univ(name const & n) { return level(new level_param_core(level_kind::Param, n)); }
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level mk_global_univ(name const & n) { return level(new level_param_core(level_kind::Global, n)); }
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level mk_meta_univ(name const & n) { return level(new level_param_core(level_kind::Meta, n)); }
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static level * g_level_zero = nullptr;
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static level * g_level_one = nullptr;
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level const & mk_level_zero() { return *g_level_zero; }
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level const & mk_level_one() { return *g_level_one; }
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bool is_one(level const & l) { return l == mk_level_one(); }
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level::level():level(mk_level_zero()) {}
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level::level(level_cell * ptr):m_ptr(ptr) { if (m_ptr) m_ptr->inc_ref(); }
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level::level(level const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
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level::level(level && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
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level::~level() { if (m_ptr) m_ptr->dec_ref(); }
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level & level::operator=(level const & l) { LEAN_COPY_REF(l); }
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level & level::operator=(level&& l) { LEAN_MOVE_REF(l); }
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level_kind level::kind() const { return m_ptr->m_kind; }
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unsigned level::hash() const { return m_ptr->m_hash; }
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bool operator==(level const & l1, level const & l2) {
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if (kind(l1) != kind(l2)) return false;
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if (hash(l1) != hash(l2)) return false;
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if (is_eqp(l1, l2)) return true;
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switch (kind(l1)) {
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case level_kind::Zero:
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return true;
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case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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return to_param_core(l1).m_id == to_param_core(l2).m_id;
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case level_kind::Max: case level_kind::IMax: case level_kind::Succ:
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if (to_composite(l1).m_depth != to_composite(l2).m_depth)
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return false;
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break;
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}
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switch (kind(l1)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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lean_unreachable(); // LCOV_EXCL_LINE
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case level_kind::Max: case level_kind::IMax:
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return
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to_max_core(l1).m_lhs == to_max_core(l2).m_lhs &&
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to_max_core(l1).m_rhs == to_max_core(l2).m_rhs;
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case level_kind::Succ:
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if (is_explicit(l1) != is_explicit(l2)) {
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return false;
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} else if (is_explicit(l1)) {
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lean_assert(get_depth(l1) == get_depth(l2));
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// the depths are equal, then l1 and l2 must be the same universe
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return true;
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} else {
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return succ_of(l1) == succ_of(l2);
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}
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool is_not_zero(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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return false;
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case level_kind::Succ:
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return true;
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case level_kind::Max:
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return is_not_zero(max_lhs(l)) || is_not_zero(max_rhs(l));
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case level_kind::IMax:
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return is_not_zero(imax_rhs(l));
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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// Monotonic total order on universe level terms.
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bool is_lt(level const & a, level const & b, bool use_hash) {
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if (is_eqp(a, b)) return false;
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unsigned da = get_depth(a);
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unsigned db = get_depth(b);
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if (da < db) return true;
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if (da > db) return false;
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if (kind(a) != kind(b)) return kind(a) < kind(b);
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if (use_hash) {
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if (hash(a) < hash(b)) return true;
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if (hash(a) > hash(b)) return false;
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}
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if (a == b) return false;
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switch (kind(a)) {
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case level_kind::Zero:
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lean_unreachable(); // LCOV_EXCL_LINE
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case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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return to_param_core(a).m_id < to_param_core(b).m_id;
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case level_kind::Max: case level_kind::IMax:
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if (to_max_core(a).m_lhs != to_max_core(b).m_lhs)
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return is_lt(to_max_core(a).m_lhs, to_max_core(b).m_lhs, use_hash);
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else
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return is_lt(to_max_core(a).m_rhs, to_max_core(b).m_rhs, use_hash);
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case level_kind::Succ:
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return is_lt(succ_of(a), succ_of(b), use_hash);
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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bool is_lt(levels const & as, levels const & bs, bool use_hash) {
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if (is_nil(as))
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return !is_nil(bs);
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if (is_nil(bs))
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return false;
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if (car(as) == car(bs))
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return is_lt(cdr(as), cdr(bs), use_hash);
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else
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return is_lt(car(as), car(bs), use_hash);
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}
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bool has_param(levels const & ls) { return std::any_of(ls.begin(), ls.end(), [](level const & l) { return has_param(l); }); }
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bool has_global(levels const & ls) { return std::any_of(ls.begin(), ls.end(), [](level const & l) { return has_global(l); }); }
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bool has_meta(levels const & ls) { return std::any_of(ls.begin(), ls.end(), [](level const & l) { return has_meta(l); }); }
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void for_each_level_fn::apply(level const & l) {
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if (!m_f(l))
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return;
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switch (l.kind()) {
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case level_kind::Succ: apply(succ_of(l)); break;
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case level_kind::Max: case level_kind::IMax: apply(to_max_core(l).m_lhs); apply(to_max_core(l).m_rhs); break;
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case level_kind::Zero: case level_kind::Param:
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case level_kind::Meta: case level_kind::Global: break;
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}
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}
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level replace_level_fn::apply(level const & l) {
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optional<level> r = m_f(l);
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if (r)
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return *r;
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switch (l.kind()) {
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case level_kind::Succ:
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return update_succ(l, apply(succ_of(l)));
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case level_kind::Max: case level_kind::IMax:
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return update_max(l, apply(to_max_core(l).m_lhs), apply(to_max_core(l).m_rhs));
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case level_kind::Zero: case level_kind::Param: case level_kind::Meta: case level_kind::Global:
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return l;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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optional<name> get_undef_param(level const & l, level_param_names const & ps) {
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optional<name> r;
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for_each(l, [&](level const & l) {
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if (!has_param(l) || r)
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return false;
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if (is_param(l) && std::find(ps.begin(), ps.end(), param_id(l)) == ps.end())
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r = param_id(l);
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return true;
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});
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return r;
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}
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optional<name> get_undef_global(level const & l, environment const & env) {
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optional<name> r;
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for_each(l, [&](level const & l) {
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if (!has_global(l) || r)
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return false;
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if (is_global(l) && !env.is_universe(global_id(l)))
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r = global_id(l);
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return true;
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});
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return r;
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}
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level update_succ(level const & l, level const & new_arg) {
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if (is_eqp(succ_of(l), new_arg))
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return l;
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else
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return mk_succ(new_arg);
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}
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level update_max(level const & l, level const & new_lhs, level const & new_rhs) {
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if (is_eqp(to_max_core(l).m_lhs, new_lhs) && is_eqp(to_max_core(l).m_rhs, new_rhs))
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return l;
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else if (is_max(l))
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|
return mk_max(new_lhs, new_rhs);
|
|
else
|
|
return mk_imax(new_lhs, new_rhs);
|
|
}
|
|
|
|
level instantiate(level const & l, level_param_names const & ps, levels const & ls) {
|
|
lean_assert(length(ps) == length(ls));
|
|
return replace(l, [=](level const & l) {
|
|
if (!has_param(l)) {
|
|
return some_level(l);
|
|
} else if (is_param(l)) {
|
|
name const & id = param_id(l);
|
|
list<name> const *it1 = &ps;
|
|
list<level> const * it2 = &ls;
|
|
while (!is_nil(*it1)) {
|
|
if (head(*it1) == id)
|
|
return some_level(head(*it2));
|
|
it1 = &tail(*it1);
|
|
it2 = &tail(*it2);
|
|
}
|
|
return some_level(l);
|
|
} else {
|
|
return none_level();
|
|
}
|
|
});
|
|
}
|
|
|
|
static void print(std::ostream & out, level l);
|
|
|
|
static void print_child(std::ostream & out, level const & l) {
|
|
if (is_explicit(l) || is_param(l) || is_meta(l) || is_global(l)) {
|
|
print(out, l);
|
|
} else {
|
|
out << "(";
|
|
print(out, l);
|
|
out << ")";
|
|
}
|
|
}
|
|
|
|
static void print(std::ostream & out, level l) {
|
|
if (is_explicit(l)) {
|
|
lean_assert(get_depth(l) > 0);
|
|
out << get_depth(l) - 1;
|
|
} else {
|
|
switch (kind(l)) {
|
|
case level_kind::Zero:
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
case level_kind::Param: case level_kind::Global:
|
|
out << to_param_core(l).m_id; break;
|
|
case level_kind::Meta:
|
|
out << "?" << meta_id(l); break;
|
|
case level_kind::Succ:
|
|
out << "succ "; print_child(out, succ_of(l)); break;
|
|
case level_kind::Max: case level_kind::IMax:
|
|
if (is_max(l))
|
|
out << "max ";
|
|
else
|
|
out << "imax ";
|
|
print_child(out, to_max_core(l).m_lhs);
|
|
// max and imax are right associative
|
|
while (kind(to_max_core(l).m_rhs) == kind(l)) {
|
|
l = to_max_core(l).m_rhs;
|
|
out << " ";
|
|
print_child(out, to_max_core(l).m_lhs);
|
|
}
|
|
out << " ";
|
|
print_child(out, to_max_core(l).m_rhs);
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
std::ostream & operator<<(std::ostream & out, level const & l) {
|
|
print(out, l);
|
|
return out;
|
|
}
|
|
|
|
format pp(level l, bool unicode, unsigned indent);
|
|
|
|
static format pp_child(level const & l, bool unicode, unsigned indent) {
|
|
if (is_explicit(l) || is_param(l) || is_meta(l) || is_global(l)) {
|
|
return pp(l, unicode, indent);
|
|
} else {
|
|
return paren(pp(l, unicode, indent));
|
|
}
|
|
}
|
|
|
|
format pp(level l, bool unicode, unsigned indent) {
|
|
if (is_explicit(l)) {
|
|
lean_assert(get_depth(l) > 0);
|
|
return format(get_depth(l) - 1);
|
|
} else {
|
|
switch (kind(l)) {
|
|
case level_kind::Zero:
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
case level_kind::Param: case level_kind::Global:
|
|
return format(to_param_core(l).m_id);
|
|
case level_kind::Meta:
|
|
return format("?") + format(meta_id(l));
|
|
case level_kind::Succ: {
|
|
auto p = to_offset(l);
|
|
return format{pp_child(p.first, unicode, indent), format("+"), format(p.second)};
|
|
}
|
|
case level_kind::Max: case level_kind::IMax: {
|
|
format r = format(is_max(l) ? "max" : "imax");
|
|
r += nest(indent, compose(line(), pp_child(to_max_core(l).m_lhs, unicode, indent)));
|
|
// max and imax are right associative
|
|
while (kind(to_max_core(l).m_rhs) == kind(l)) {
|
|
l = to_max_core(l).m_rhs;
|
|
r += nest(indent, compose(line(), pp_child(to_max_core(l).m_lhs, unicode, indent)));
|
|
}
|
|
r += nest(indent, compose(line(), pp_child(to_max_core(l).m_rhs, unicode, indent)));
|
|
return group(r);
|
|
}}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
}
|
|
}
|
|
|
|
format pp(level const & l, options const & opts) {
|
|
return pp(l, get_pp_unicode(opts), get_pp_indent(opts));
|
|
}
|
|
|
|
format pp(level const & lhs, level const & rhs, bool unicode, unsigned indent) {
|
|
format leq = unicode ? format("≤") : format("<=");
|
|
return group(pp(lhs, unicode, indent) + space() + leq + line() + pp(rhs, unicode, indent));
|
|
}
|
|
|
|
format pp(level const & lhs, level const & rhs, options const & opts) {
|
|
return pp(lhs, rhs, get_pp_unicode(opts), get_pp_indent(opts));
|
|
}
|
|
|
|
// A total order on level expressions that has the following properties
|
|
// - succ(l) is an immediate successor of l.
|
|
// - zero is the minimal element.
|
|
// This total order is used in the normalization procedure.
|
|
static bool is_norm_lt(level const & a, level const & b) {
|
|
if (is_eqp(a, b)) return false;
|
|
auto p1 = to_offset(a);
|
|
auto p2 = to_offset(b);
|
|
level const & l1 = p1.first;
|
|
level const & l2 = p2.first;
|
|
if (l1 != l2) {
|
|
if (kind(l1) != kind(l2)) return kind(l1) < kind(l2);
|
|
switch (kind(l1)) {
|
|
case level_kind::Zero: case level_kind::Succ:
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
case level_kind::Param: case level_kind::Global: case level_kind::Meta:
|
|
return to_param_core(l1).m_id < to_param_core(l2).m_id;
|
|
case level_kind::Max: case level_kind::IMax:
|
|
if (to_max_core(l1).m_lhs != to_max_core(l2).m_lhs)
|
|
return is_norm_lt(to_max_core(l1).m_lhs, to_max_core(l2).m_lhs);
|
|
else
|
|
return is_norm_lt(to_max_core(l1).m_rhs, to_max_core(l2).m_rhs);
|
|
}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
} else {
|
|
return p1.second < p2.second;
|
|
}
|
|
}
|
|
|
|
void push_max_args(level const & l, buffer<level> & r) {
|
|
if (is_max(l)) {
|
|
push_max_args(max_lhs(l), r);
|
|
push_max_args(max_rhs(l), r);
|
|
} else {
|
|
r.push_back(l);
|
|
}
|
|
}
|
|
|
|
level mk_max(buffer<level> const & args) {
|
|
lean_assert(!args.empty());
|
|
unsigned nargs = args.size();
|
|
if (nargs == 1) {
|
|
return args[0];
|
|
} else {
|
|
lean_assert(nargs >= 2);
|
|
level r = mk_max(args[nargs-2], args[nargs-1]);
|
|
unsigned i = nargs-2;
|
|
while (i > 0) {
|
|
--i;
|
|
r = mk_max(args[i], r);
|
|
}
|
|
return r;
|
|
}
|
|
}
|
|
|
|
level mk_succ(level l, unsigned k) {
|
|
while (k > 0) {
|
|
--k;
|
|
l = mk_succ(l);
|
|
}
|
|
return l;
|
|
}
|
|
|
|
level normalize(level const & l) {
|
|
auto p = to_offset(l);
|
|
level const & r = p.first;
|
|
switch (kind(r)) {
|
|
case level_kind::Succ:
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
case level_kind::Zero: case level_kind::Param:
|
|
case level_kind::Global: case level_kind::Meta:
|
|
return l;
|
|
case level_kind::IMax: {
|
|
auto l1 = normalize(imax_lhs(r));
|
|
auto l2 = normalize(imax_rhs(r));
|
|
if (!is_eqp(l1, imax_lhs(r)) || !is_eqp(l2, imax_rhs(r)))
|
|
return mk_succ(mk_imax(l1, l2), p.second);
|
|
else
|
|
return l;
|
|
}
|
|
case level_kind::Max: {
|
|
buffer<level> todo;
|
|
buffer<level> args;
|
|
push_max_args(r, todo);
|
|
for (level const & a : todo)
|
|
push_max_args(normalize(a), args);
|
|
std::sort(args.begin(), args.end(), is_norm_lt);
|
|
buffer<level> & rargs = todo;
|
|
rargs.clear();
|
|
unsigned i = 0;
|
|
if (is_explicit(args[i])) {
|
|
// find max explicit univierse
|
|
while (i+1 < args.size() && is_explicit(args[i+1]))
|
|
i++;
|
|
lean_assert(is_explicit(args[i]));
|
|
unsigned k = to_offset(args[i]).second;
|
|
// an explicit universe k is subsumed by succ^k(l)
|
|
unsigned j = i+1;
|
|
for (; j < args.size(); j++) {
|
|
if (to_offset(args[j]).second >= k)
|
|
break;
|
|
}
|
|
if (j < args.size()) {
|
|
// explicit universe was subsumed by succ^k'(l) where k' >= k
|
|
i++;
|
|
}
|
|
}
|
|
rargs.push_back(args[i]);
|
|
auto p_prev = to_offset(args[i]);
|
|
i++;
|
|
for (; i < args.size(); i++) {
|
|
auto p_curr = to_offset(args[i]);
|
|
if (p_prev.first == p_curr.first) {
|
|
if (p_prev.second < p_curr.second) {
|
|
p_prev = p_curr;
|
|
rargs.pop_back();
|
|
rargs.push_back(args[i]);
|
|
}
|
|
} else {
|
|
p_prev = p_curr;
|
|
rargs.push_back(args[i]);
|
|
}
|
|
}
|
|
for (level & a : rargs)
|
|
a = mk_succ(a, p.second);
|
|
return mk_max(rargs);
|
|
}}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
}
|
|
|
|
bool is_equivalent(level const & lhs, level const & rhs) {
|
|
check_system("level constraints");
|
|
return lhs == rhs || normalize(lhs) == normalize(rhs);
|
|
}
|
|
|
|
bool is_geq_core(level l1, level l2) {
|
|
if (l1 == l2 || is_zero(l2))
|
|
return true;
|
|
if (is_max(l2))
|
|
return is_geq(l1, max_lhs(l2)) && is_geq(l1, max_rhs(l2));
|
|
if (is_max(l1) && (is_geq(max_lhs(l1), l2) || is_geq(max_rhs(l1), l2)))
|
|
return true;
|
|
if (is_imax(l2))
|
|
return is_geq(l1, imax_lhs(l2)) && is_geq(l1, imax_rhs(l2));
|
|
if (is_imax(l1))
|
|
return is_geq(imax_rhs(l1), l2);
|
|
auto p1 = to_offset(l1);
|
|
auto p2 = to_offset(l2);
|
|
if (p1.first == p2.first || is_zero(p2.first))
|
|
return p1.second >= p2.second;
|
|
if (p1.second == p2.second && p1.second > 0)
|
|
return is_geq(p1.first, p2.first);
|
|
return false;
|
|
}
|
|
bool is_geq(level const & l1, level const & l2) {
|
|
return is_geq_core(normalize(l1), normalize(l2));
|
|
}
|
|
levels param_names_to_levels(level_param_names const & ps) {
|
|
return map2<level>(ps, [](name const & p) { return mk_param_univ(p); });
|
|
}
|
|
|
|
void initialize_level() {
|
|
g_level_zero = new level(new level_cell(level_kind::Zero, 7u));
|
|
g_level_one = new level(mk_succ(mk_level_zero()));
|
|
}
|
|
|
|
void finalize_level() {
|
|
delete g_level_one;
|
|
delete g_level_zero;
|
|
}
|
|
}
|
|
void print(lean::level const & l) { std::cout << l << std::endl; }
|