feat(kernel/level): new universe level datastructure for universe level polymorphism
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
1b6b33b3f5
commit
9f93b5d97e
5 changed files with 550 additions and 313 deletions
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@ -245,7 +245,7 @@ set(EXTRA_LIBS ${LEAN_LIBS} ${EXTRA_LIBS})
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add_subdirectory(tests/util)
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add_subdirectory(tests/util/numerics)
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add_subdirectory(tests/util/interval)
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# add_subdirectory(tests/kernel)
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add_subdirectory(tests/kernel)
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# add_subdirectory(tests/library)
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# add_subdirectory(tests/library/rewriter)
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# add_subdirectory(tests/library/tactic)
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@ -5,63 +5,215 @@ 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 <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/object_serializer.h"
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#include "kernel/level.h"
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namespace lean {
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/** \brief Base class for representing universe level cells. */
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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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level_cell(level_kind k):m_rc(1), m_kind(k) {}
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unsigned m_hash;
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level_cell(level_kind k, unsigned h):m_rc(1), m_kind(k), m_hash(h) {}
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};
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/** \brief Cell for universe variables. */
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struct level_uvar : public level_cell {
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name m_name;
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level_uvar(name const & n):level_cell(level_kind::UVar), m_name(n) {}
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unsigned hash(level const & l) { return to_cell(l).m_hash; }
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level_kind kind(level const & l) { return to_cell(l).m_kind; }
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struct level_composite : public level_cell {
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unsigned m_depth;
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unsigned m_param_range;
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unsigned m_meta_range;
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level_composite(level_kind k, unsigned h, unsigned d, unsigned r1, unsigned r2):
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level_cell(k, h), m_depth(d), m_param_range(r1), m_meta_range(r2) {}
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};
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/** \brief Cell for representing the universe <tt>l + k</tt>, where \c l is a level and \c k a unsigned integer. */
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struct level_lift : public level_cell {
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level m_l;
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unsigned m_k;
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level_lift(level const & l, unsigned k):level_cell(level_kind::Lift), m_l(l), m_k(k) {}
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};
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/** \brief Cell for representing the universe <tt>max l_1 ... l_n</tt>, where <tt>n == m_size</tt>. */
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struct level_max : public level_cell {
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unsigned m_size;
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level m_levels[0];
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level_max(unsigned sz, level const * ls):level_cell(level_kind::Max), m_size(sz) {
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for (unsigned i = 0; i < m_size; i++)
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new (m_levels + i) level(ls[i]);
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}
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~level_max() {
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for (unsigned i = 0; i < m_size; i++)
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(m_levels+i)->~level();
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}
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level const * begin_levels() const { return m_levels; }
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level const * end_levels() const { return m_levels + m_size; }
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};
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level_uvar * to_uvar(level_cell * c) { return static_cast<level_uvar*>(c); }
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level_lift * to_lift(level_cell * c) { return static_cast<level_lift*>(c); }
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level_max * to_max(level_cell * c) { return static_cast<level_max*>(c); }
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void level_cell::dealloc() {
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switch (m_kind) {
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case level_kind::UVar: delete to_uvar(this); break;
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case level_kind::Lift: delete to_lift(this); break;
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case level_kind::Max: static_cast<level_max*>(this)->~level_max(); delete[] reinterpret_cast<char*>(this); break;
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static 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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default:
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return false;
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}
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}
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static name g_bot_name("bot");
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level::level(): m_ptr(new level_uvar(g_bot_name)) { lean_assert_eq(uvar_name(*this), name("bot")); }
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level::level(name const & n): m_ptr(new level_uvar(n)) {}
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level::level(level const & l, unsigned k):m_ptr(new level_lift(l, k)) { lean_assert(is_uvar(l)); }
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level::level(level_cell * ptr): m_ptr(ptr) { lean_assert(m_ptr->get_rc() == 1); }
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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, get_param_range(l), get_meta_range(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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std::max(get_param_range(l1), get_param_range(l2)),
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std::max(get_meta_range(l1), get_meta_range(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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unsigned m_id;
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level_param_core(bool is_param, unsigned id):
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level_cell(is_param ? level_kind::Param : level_kind::Meta, hash(id, 11u)),
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m_id(id) {}
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};
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static bool is_param_core(level const & l) { return is_param(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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unsigned param_id(level const & l) { lean_assert(is_param(l)); return to_param_core(l).m_id; }
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unsigned meta_id(level const & l) { lean_assert(is_meta(l)); return to_param_core(l).m_id; }
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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::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::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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unsigned get_param_range(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Meta:
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return 0;
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case level_kind::Param:
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return to_param_core(l).m_id + 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_param_range;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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unsigned get_meta_range(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param:
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return 0;
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case level_kind::Meta:
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return to_param_core(l).m_id + 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_param_range;
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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::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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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
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return level(new level_max_core(false, l1, l2));
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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;
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else if (l1 == l2)
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return l1;
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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(unsigned i) {
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return level(new level_param_core(true, i));
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}
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level mk_meta_univ(unsigned i) {
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return level(new level_param_core(false, i));
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}
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static level g_zero(new level_cell(level_kind::Zero, 7u));
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static level g_one(mk_succ(g_zero));
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level const & mk_level_zero() { return g_zero; }
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level const & mk_level_one() { return g_one; }
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level::level():level(g_zero) {}
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level::level(level_cell * ptr):m_ptr(ptr) { lean_assert(m_ptr->get_rc() == 1); }
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level::level(level const & s):
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m_ptr(s.m_ptr) {
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if (m_ptr)
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@ -75,196 +227,88 @@ level::~level() {
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if (m_ptr)
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m_ptr->dec_ref();
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}
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level to_level(level_cell * c) { return level(c); }
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level_cell * to_cell(level const & l) { return l.m_ptr; }
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level_max * to_max(level const & l) { return to_max(to_cell(l)); }
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unsigned level::hash() const {
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switch (m_ptr->m_kind) {
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case level_kind::UVar: return to_uvar(m_ptr)->m_name.hash();
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case level_kind::Lift: return ::lean::hash(to_lift(m_ptr)->m_l.hash(), to_lift(m_ptr)->m_k);
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case level_kind::Max: return ::lean::hash(to_max(m_ptr)->m_size, [&](unsigned i) { return to_max(m_ptr)->m_levels[i].hash(); });
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}
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return 0;
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}
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bool level::is_bottom() const {
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return is_uvar(*this) && uvar_name(*this) == g_bot_name;
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}
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level max_core(unsigned sz, level const * ls) {
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char * mem = new char[sizeof(level_max) + sz*sizeof(level)];
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return to_level(new (mem) level_max(sz, ls));
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}
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level const & _lift_of(level const & l) { return is_lift(l) ? lift_of(l) : l; }
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unsigned _lift_offset(level const & l) { return is_lift(l) ? lift_offset(l) : 0; }
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void push_back(buffer<level> & ls, level const & l) {
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if (l.is_bottom())
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return;
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for (unsigned i = 0; i < ls.size(); i++) {
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if (_lift_of(ls[i]) == _lift_of(l)) {
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if (_lift_offset(ls[i]) < _lift_offset(l))
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ls[i] = l;
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return;
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}
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}
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ls.push_back(l);
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}
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level max_core(unsigned sz1, level const * ls1, unsigned sz2, level const * ls2) {
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buffer<level> new_lvls;
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std::for_each(ls1, ls1 + sz1, [&](level const & l) { push_back(new_lvls, l); });
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std::for_each(ls2, ls2 + sz2, [&](level const & l) { push_back(new_lvls, l); });
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unsigned sz = new_lvls.size();
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if (sz == 0)
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return level();
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else if (sz == 1)
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return new_lvls[0];
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else
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return max_core(new_lvls.size(), new_lvls.data());
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}
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level max_core(level const & l1, level const & l2) { return max_core(1, &l1, 1, &l2); }
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level max_core(level const & l1, level_max * l2) { return max_core(1, &l1, l2->m_size, l2->m_levels); }
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level max_core(level_max * l1, level const & l2) { return max_core(l1->m_size, l1->m_levels, 1, &l2); }
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level max_core(level_max * l1, level_max * l2) { return max_core(l1->m_size, l1->m_levels, l2->m_size, l2->m_levels); }
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level max(level const & l1, level const & l2) {
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if (is_max(l1)) {
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if (is_max(l2))
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return max_core(to_max(l1), to_max(l2));
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else
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return max_core(to_max(l1), l2);
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} else {
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if (is_max(l2))
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return max_core(l1, to_max(l2));
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else
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return max_core(l1, l2);
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}
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}
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level operator+(level const & l, unsigned k) {
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switch (kind(l)) {
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case level_kind::UVar: return level(l, k);
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case level_kind::Lift: return level(lift_of(l), safe_add(lift_offset(l), k));
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case level_kind::Max: {
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buffer<level> new_lvls;
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for (unsigned i = 0; i < max_size(l); i++)
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new_lvls.push_back(max_level(l, i) + k);
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return max_core(new_lvls.size(), new_lvls.data());
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}}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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level_kind kind (level const & l) { lean_assert(l.m_ptr); return l.m_ptr->m_kind; }
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name const & uvar_name (level const & l) { lean_assert(is_uvar(l)); return static_cast<level_uvar*>(l.m_ptr)->m_name; }
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level const & lift_of (level const & l) { lean_assert(is_lift(l)); return static_cast<level_lift*>(l.m_ptr)->m_l; }
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unsigned lift_offset(level const & l) { lean_assert(is_lift(l)); return static_cast<level_lift*>(l.m_ptr)->m_k; }
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unsigned max_size (level const & l) { lean_assert(is_max(l)); return static_cast<level_max*>(l.m_ptr)->m_size; }
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level const & max_level (level const & l, unsigned i) { lean_assert(is_max(l)); return static_cast<level_max*>(l.m_ptr)->m_levels[i]; }
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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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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::UVar: return uvar_name(l1) == uvar_name(l2);
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case level_kind::Lift: return lift_of(l1) == lift_of(l2) && lift_offset(l1) == lift_offset(l2);
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case level_kind::Max:
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if (max_size(l1) == max_size(l2)) {
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for (unsigned i = 0; i < max_size(l1); i++)
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if (max_level(l1, i) != max_level(l2, i))
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return false;
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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::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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to_composite(l1).m_param_range != to_composite(l2).m_param_range ||
|
||||
to_composite(l1).m_meta_range != to_composite(l2).m_meta_range)
|
||||
return false;
|
||||
break;
|
||||
}
|
||||
switch (kind(l1)) {
|
||||
case level_kind::Zero: case level_kind::Param: case level_kind::Meta:
|
||||
lean_unreachable(); // LCOV_EXCL_LINE
|
||||
case level_kind::Max: case level_kind::IMax:
|
||||
return
|
||||
to_max_core(l1).m_lhs == to_max_core(l2).m_lhs &&
|
||||
to_max_core(l1).m_rhs == to_max_core(l2).m_rhs;
|
||||
case level_kind::Succ:
|
||||
if (is_explicit(l1) != is_explicit(l2)) {
|
||||
return false;
|
||||
} else if (is_explicit(l1)) {
|
||||
lean_assert(get_depth(l1) == get_depth(l2));
|
||||
// the depths are equal, then l1 and l2 must be the same universe
|
||||
return true;
|
||||
} else {
|
||||
return false;
|
||||
return succ_of(l1) == succ_of(l2);
|
||||
}
|
||||
}
|
||||
lean_unreachable(); // LCOV_EXCL_LINE
|
||||
}
|
||||
|
||||
bool operator<(level const & l1, level const & l2) {
|
||||
if (kind(l1) != kind(l2)) return kind(l1) < kind(l2);
|
||||
switch (kind(l1)) {
|
||||
case level_kind::UVar: return uvar_name(l1) < uvar_name(l2);
|
||||
case level_kind::Lift:
|
||||
if (lift_of(l1) != lift_of(l2))
|
||||
return lift_of(l1) < lift_of(l2);
|
||||
else
|
||||
return lift_offset(l1) < lift_offset(l2);
|
||||
case level_kind::Max:
|
||||
if (max_size(l1) != max_size(l2))
|
||||
return max_size(l1) < max_size(l2);
|
||||
for (unsigned i = 0; i < max_size(l1); i++)
|
||||
if (max_level(l1, i) != max_level(l2, i))
|
||||
return max_level(l1, i) < max_level(l2, i);
|
||||
bool is_not_zero(level const & l) {
|
||||
switch (kind(l)) {
|
||||
case level_kind::Zero: case level_kind::Param: case level_kind::Meta:
|
||||
return false;
|
||||
}
|
||||
lean_unreachable(); // LCOV_EXCL_LINE
|
||||
}
|
||||
|
||||
std::ostream & operator<<(std::ostream & out, level const & l) {
|
||||
switch (kind(l)) {
|
||||
case level_kind::UVar: out << uvar_name(l); return out;
|
||||
case level_kind::Lift:
|
||||
if (lift_of(l).is_bottom())
|
||||
out << lift_offset(l);
|
||||
else
|
||||
out << lift_of(l) << "+" << lift_offset(l);
|
||||
return out;
|
||||
case level_kind::Succ:
|
||||
return true;
|
||||
case level_kind::Max:
|
||||
out << "(max";
|
||||
for (unsigned i = 0; i < max_size(l); i++)
|
||||
out << " " << max_level(l, i);
|
||||
out << ")";
|
||||
return out;
|
||||
return is_not_zero(max_lhs(l)) || is_not_zero(max_rhs(l));
|
||||
case level_kind::IMax:
|
||||
return is_not_zero(imax_rhs(l));
|
||||
}
|
||||
return out;
|
||||
}
|
||||
|
||||
format pp(level const & l, bool unicode) {
|
||||
switch (kind(l)) {
|
||||
case level_kind::UVar:
|
||||
if (l.is_bottom())
|
||||
return format(0);
|
||||
else
|
||||
return pp(uvar_name(l));
|
||||
case level_kind::Lift:
|
||||
if (lift_of(l).is_bottom())
|
||||
return format(lift_offset(l));
|
||||
else
|
||||
return format{pp(lift_of(l), unicode), format("+"), format(lift_offset(l))};
|
||||
case level_kind::Max: {
|
||||
if (unicode) {
|
||||
format r = pp(max_level(l, 0), unicode);
|
||||
for (unsigned i = 1; i < max_size(l); i++) {
|
||||
r += format{space(), format("\u2294"), line()};
|
||||
r += pp(max_level(l, i), unicode);
|
||||
}
|
||||
return group(r);
|
||||
} else {
|
||||
format r = format("max");
|
||||
for (unsigned i = 0; i < max_size(l); i++)
|
||||
r += format{line(), pp(max_level(l, i), unicode)};
|
||||
return paren(r);
|
||||
}
|
||||
}}
|
||||
lean_unreachable(); // LCOV_EXCL_LINE
|
||||
}
|
||||
|
||||
format pp(level const & l, options const & opts) {
|
||||
return pp(l, get_pp_unicode(opts));
|
||||
// Monotonic total order on universe level terms.
|
||||
bool is_lt(level const & a, level const & b) {
|
||||
if (is_eqp(a, b)) return false;
|
||||
unsigned da = get_depth(a);
|
||||
unsigned db = get_depth(b);
|
||||
if (da < db) return true;
|
||||
if (da > db) return false;
|
||||
if (kind(a) != kind(b)) return kind(a) < kind(b);
|
||||
if (hash(a) < hash(b)) return true;
|
||||
if (hash(a) > hash(b)) return false;
|
||||
if (a == b) return false;
|
||||
switch (kind(a)) {
|
||||
case level_kind::Zero:
|
||||
return false;
|
||||
case level_kind::Param: case level_kind::Meta:
|
||||
return to_param_core(a).m_id < to_param_core(b).m_id;
|
||||
case level_kind::Max: case level_kind::IMax:
|
||||
if (to_max_core(a).m_lhs != to_max_core(b).m_lhs)
|
||||
return is_lt(to_max_core(a).m_lhs, to_max_core(b).m_lhs);
|
||||
else
|
||||
return is_lt(to_max_core(a).m_rhs, to_max_core(b).m_rhs);
|
||||
case level_kind::Succ:
|
||||
return is_lt(succ_of(a), succ_of(b));
|
||||
}
|
||||
lean_unreachable(); // LCOV_EXCL_LINE
|
||||
}
|
||||
|
||||
level max(std::initializer_list<level> const & l) {
|
||||
if (l.size() == 1)
|
||||
return *(l.begin());
|
||||
return max_core(l.size(), l.begin());
|
||||
}
|
||||
|
||||
|
||||
class level_serializer : public object_serializer<level, level::ptr_hash, level::ptr_eq> {
|
||||
typedef object_serializer<level, level::ptr_hash, level::ptr_eq> super;
|
||||
public:
|
||||
|
|
@ -274,17 +318,17 @@ public:
|
|||
auto k = kind(l);
|
||||
s << static_cast<char>(k);
|
||||
switch (k) {
|
||||
case level_kind::UVar:
|
||||
s << uvar_name(l);
|
||||
case level_kind::Zero:
|
||||
break;
|
||||
case level_kind::Lift:
|
||||
s << lift_offset(l);
|
||||
write(lift_of(l));
|
||||
case level_kind::Param: case level_kind::Meta:
|
||||
s << to_param_core(l).m_id;
|
||||
break;
|
||||
case level_kind::Max:
|
||||
s << max_size(l);
|
||||
for (unsigned i = 0; i < max_size(l); i++)
|
||||
write(max_level(l, i));
|
||||
case level_kind::Max: case level_kind::IMax:
|
||||
write(to_max_core(l).m_lhs);
|
||||
write(to_max_core(l).m_rhs);
|
||||
break;
|
||||
case level_kind::Succ:
|
||||
write(succ_of(l));
|
||||
break;
|
||||
}
|
||||
});
|
||||
|
|
@ -299,20 +343,27 @@ public:
|
|||
deserializer & d = get_owner();
|
||||
auto k = static_cast<level_kind>(d.read_char());
|
||||
switch (k) {
|
||||
case level_kind::UVar:
|
||||
return level(read_name(d));
|
||||
case level_kind::Lift: {
|
||||
unsigned offset = d.read_unsigned();
|
||||
return read() + offset;
|
||||
case level_kind::Zero:
|
||||
return mk_level_zero();
|
||||
case level_kind::Param: {
|
||||
unsigned id = d.read_unsigned();
|
||||
return mk_param_univ(id);
|
||||
}
|
||||
case level_kind::Meta: {
|
||||
unsigned id = d.read_unsigned();
|
||||
return mk_meta_univ(id);
|
||||
}
|
||||
case level_kind::Max: {
|
||||
buffer<level> lvls;
|
||||
unsigned num = d.read_unsigned();
|
||||
for (unsigned i = 0; i < num; i++) {
|
||||
lvls.push_back(read());
|
||||
}
|
||||
return max_core(lvls.size(), lvls.data());
|
||||
}}
|
||||
level lhs = read();
|
||||
return mk_max(lhs, read());
|
||||
}
|
||||
case level_kind::IMax: {
|
||||
level lhs = read();
|
||||
return mk_imax(lhs, read());
|
||||
}
|
||||
case level_kind::Succ:
|
||||
return mk_succ(read());
|
||||
}
|
||||
throw_corrupted_file();
|
||||
});
|
||||
}
|
||||
|
|
@ -322,10 +373,15 @@ struct level_sd {
|
|||
unsigned m_s_extid;
|
||||
unsigned m_d_extid;
|
||||
level_sd() {
|
||||
m_s_extid = serializer::register_extension([](){ return std::unique_ptr<serializer::extension>(new level_serializer()); });
|
||||
m_d_extid = deserializer::register_extension([](){ return std::unique_ptr<deserializer::extension>(new level_deserializer()); });
|
||||
m_s_extid = serializer::register_extension([](){
|
||||
return std::unique_ptr<serializer::extension>(new level_serializer());
|
||||
});
|
||||
m_d_extid = deserializer::register_extension([](){
|
||||
return std::unique_ptr<deserializer::extension>(new level_deserializer());
|
||||
});
|
||||
}
|
||||
};
|
||||
|
||||
static level_sd g_level_sd;
|
||||
|
||||
serializer & operator<<(serializer & s, level const & n) {
|
||||
|
|
@ -336,5 +392,113 @@ serializer & operator<<(serializer & s, level const & n) {
|
|||
level read_level(deserializer & d) {
|
||||
return d.get_extension<level_deserializer>(g_level_sd.m_d_extid).read();
|
||||
}
|
||||
|
||||
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)) {
|
||||
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:
|
||||
out << "l_" << param_id(l); 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, max_lhs(l));
|
||||
// max and imax are right associative
|
||||
while (kind(max_rhs(l)) == kind(l)) {
|
||||
l = max_rhs(l);
|
||||
out << " ";
|
||||
print_child(out, max_lhs(l));
|
||||
}
|
||||
out << " ";
|
||||
print_child(out, max_rhs(l));
|
||||
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)) {
|
||||
return pp(l, unicode, indent);
|
||||
} else {
|
||||
return paren(pp(l, unicode, indent));
|
||||
}
|
||||
}
|
||||
|
||||
static char const * g_sub[10] = {
|
||||
"\u2080", "\u2081", "\u2082", "\u2083", "\u2084", "\u2085", "\u2086", "\u2087", "\u2088", "\u2089"
|
||||
};
|
||||
|
||||
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:
|
||||
if (unicode) {
|
||||
format r = format("ℓ");
|
||||
if (param_id(l) == 0)
|
||||
return r;
|
||||
else if (param_id(l) <= 9)
|
||||
return r + format(g_sub[param_id(l)]);
|
||||
else
|
||||
return r + format{format("_"), format(param_id(l))};
|
||||
} else {
|
||||
return format{format("l_"), format(param_id(l))};
|
||||
}
|
||||
case level_kind::Meta:
|
||||
return format{format("?"), format(meta_id(l))};
|
||||
case level_kind::Succ:
|
||||
return group(compose(format("succ"), nest(indent, compose(line(), pp_child(succ_of(l), unicode, indent)))));
|
||||
case level_kind::Max: case level_kind::IMax: {
|
||||
format r = format(is_max(l) ? "max" : "imax");
|
||||
r += nest(indent, compose(line(), pp_child(max_lhs(l), unicode, indent)));
|
||||
// max and imax are right associative
|
||||
while (kind(max_rhs(l)) == kind(l)) {
|
||||
l = max_rhs(l);
|
||||
r += nest(indent, compose(line(), pp_child(max_lhs(l), unicode, indent)));
|
||||
}
|
||||
r += nest(indent, compose(line(), pp_child(max_rhs(l), 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));
|
||||
}
|
||||
}
|
||||
|
||||
void print(lean::level const & l) { std::cout << l << std::endl; }
|
||||
|
|
|
|||
|
|
@ -8,6 +8,7 @@ Author: Leonardo de Moura
|
|||
#include <iostream>
|
||||
#include <algorithm>
|
||||
#include "util/name.h"
|
||||
#include "util/optional.h"
|
||||
#include "util/serializer.h"
|
||||
#include "util/sexpr/format.h"
|
||||
#include "util/sexpr/options.h"
|
||||
|
|
@ -15,72 +16,118 @@ Author: Leonardo de Moura
|
|||
namespace lean {
|
||||
class environment;
|
||||
struct level_cell;
|
||||
enum class level_kind { UVar, Lift, Max };
|
||||
/**
|
||||
\brief Universe level kinds.
|
||||
|
||||
- Zero : Bool/Prop level. In Lean, Bool == (Type zero)
|
||||
- Succ(l) : successor level
|
||||
- Max(l1, l2) : maximum of two levels
|
||||
- IMax(l1, l2) : IMax(x, zero) = zero for all x
|
||||
IMax(x, succ(y)) = Max(x, succ(y)) for all x, y
|
||||
|
||||
We use IMax to handle Pi-types, and Max for Sigma-types.
|
||||
Their definitions "mirror" the typing rules for Pi and Sigma.
|
||||
|
||||
- Param(i) : A parameter. In Lean, we have universe polymorphic definitions.
|
||||
- Meta(i) : Placeholder. It is the equivalent of a metavariable for universe levels.
|
||||
The elaborator is responsible for replacing Meta with level expressions
|
||||
that do not contain Meta.
|
||||
*/
|
||||
enum class level_kind { Zero, Succ, Max, IMax, Param, Meta };
|
||||
|
||||
/**
|
||||
\brief Universe level.
|
||||
*/
|
||||
class level {
|
||||
friend class environment;
|
||||
level_cell * m_ptr;
|
||||
/** \brief Private constructor used by the environment to create a new universe variable named \c n with internal id \c u. */
|
||||
level(level const & l, unsigned k);
|
||||
level(level_cell * ptr);
|
||||
friend level to_level(level_cell * c);
|
||||
friend level_cell * to_cell(level const & l);
|
||||
friend level operator+(level const & l, unsigned k);
|
||||
friend level_cell const & to_cell(level const & l);
|
||||
public:
|
||||
/** \brief Universe 0 */
|
||||
/** \brief Universe zero */
|
||||
level();
|
||||
level(name const & n);
|
||||
level(level_cell * ptr);
|
||||
level(level const & l);
|
||||
level(level&& s);
|
||||
~level();
|
||||
|
||||
unsigned hash() const;
|
||||
|
||||
bool is_bottom() const;
|
||||
|
||||
friend level_kind kind (level const & l);
|
||||
friend name const & uvar_name (level const & l);
|
||||
friend level const & lift_of (level const & l);
|
||||
friend unsigned lift_offset(level const & l);
|
||||
friend unsigned max_size (level const & l);
|
||||
friend level const & max_level (level const & l, unsigned i);
|
||||
|
||||
level & operator=(level const & l);
|
||||
level & operator=(level&& l);
|
||||
|
||||
friend bool operator==(level const & l1, level const & l2);
|
||||
friend bool operator!=(level const & l1, level const & l2) { return !operator==(l1, l2); }
|
||||
friend bool operator<(level const & l1, level const & l2);
|
||||
friend void swap(level & l1, level & l2) { std::swap(l1, l2); }
|
||||
friend bool is_eqp(level const & l1, level const & l2) { return l1.m_ptr == l2.m_ptr; }
|
||||
|
||||
friend std::ostream & operator<<(std::ostream & out, level const & l);
|
||||
friend void swap(level & l1, level & l2) { std::swap(l1, l2); }
|
||||
|
||||
struct ptr_hash { unsigned operator()(level const & n) const { return std::hash<level_cell*>()(n.m_ptr); } };
|
||||
struct ptr_eq { bool operator()(level const & n1, level const & n2) const { return n1.m_ptr == n2.m_ptr; } };
|
||||
};
|
||||
|
||||
level max(level const & l1, level const & l2);
|
||||
level max(std::initializer_list<level> const & l);
|
||||
level operator+(level const & l, unsigned k);
|
||||
level const & mk_level_zero();
|
||||
level const & mk_level_one();
|
||||
level mk_max(level const & l1, level const & l2);
|
||||
level mk_imax(level const & l1, level const & l2);
|
||||
level mk_succ(level const & l);
|
||||
level mk_param_univ(unsigned i);
|
||||
level mk_meta_univ(unsigned i);
|
||||
|
||||
inline bool is_bottom(level const & l) { return l.is_bottom(); }
|
||||
inline bool is_uvar(level const & l) { return kind(l) == level_kind::UVar; }
|
||||
inline bool is_lift(level const & l) { return kind(l) == level_kind::Lift; }
|
||||
inline bool is_max (level const & l) { return kind(l) == level_kind::Max; }
|
||||
bool operator==(level const & l1, level const & l2);
|
||||
inline bool operator!=(level const & l1, level const & l2) { return !operator==(l1, l2); }
|
||||
|
||||
/** \brief Return a */
|
||||
inline level const * max_begin_levels(level const & l) { return &max_level(l, 0); }
|
||||
inline level const * max_end_levels(level const & l) { return max_begin_levels(l) + max_size(l); }
|
||||
/**
|
||||
\brief An arbitrary (monotonic) total order on universe level terms.
|
||||
*/
|
||||
bool is_lt(level const & l1, level const & l2);
|
||||
|
||||
/** \brief Pretty print the given level expression, unicode characters are used if \c unicode is \c true. */
|
||||
format pp(level const & l, bool unicode);
|
||||
/** \brief Pretty print the given level expression using the given configuration options. */
|
||||
format pp(level const & l, options const & opts = options());
|
||||
unsigned hash(level const & l);
|
||||
level_kind kind(level const & l);
|
||||
inline bool is_zero(level const & l) { return kind(l) == level_kind::Zero; }
|
||||
inline bool is_param(level const & l) { return kind(l) == level_kind::Param; }
|
||||
inline bool is_meta(level const & l) { return kind(l) == level_kind::Meta; }
|
||||
inline bool is_succ(level const & l) { return kind(l) == level_kind::Succ; }
|
||||
inline bool is_max(level const & l) { return kind(l) == level_kind::Max; }
|
||||
inline bool is_imax(level const & l) { return kind(l) == level_kind::IMax; }
|
||||
|
||||
unsigned get_depth(level const & l);
|
||||
unsigned get_param_range(level const & l);
|
||||
unsigned get_meta_range(level const & l);
|
||||
|
||||
level const & max_lhs(level const & l);
|
||||
level const & max_rhs(level const & l);
|
||||
level const & imax_lhs(level const & l);
|
||||
level const & imax_rhs(level const & l);
|
||||
level const & succ_of(level const & l);
|
||||
unsigned param_id(level const & l);
|
||||
unsigned meta_id(level const & l);
|
||||
/**
|
||||
\brief Return true iff \c l is an explicit level.
|
||||
We say a level l is explicit iff
|
||||
1) l is zero OR
|
||||
2) l = succ(l') and l' is explicit
|
||||
*/
|
||||
bool is_explicit(level const & l);
|
||||
|
||||
/**
|
||||
\brief Return true iff \c l contains placeholder (aka meta parameters).
|
||||
*/
|
||||
inline bool has_meta(level const & l) { return get_meta_range(l) > 0; }
|
||||
|
||||
/**
|
||||
\brief Printer for debugging purposes
|
||||
*/
|
||||
std::ostream & operator<<(std::ostream & out, level const & l);
|
||||
|
||||
/**
|
||||
\brief If the result is true, then forall assignments \c A that assigns all parameters and metavariables occuring
|
||||
in \c l, eval(A, l) != zero.
|
||||
*/
|
||||
bool is_not_zero(level const & l);
|
||||
|
||||
serializer & operator<<(serializer & s, level const & l);
|
||||
level read_level(deserializer & d);
|
||||
inline deserializer & operator>>(deserializer & d, level & l) { l = read_level(d); return d; }
|
||||
|
||||
/** \brief Pretty print the given level expression, unicode characters are used if \c unicode is \c true. */
|
||||
format pp(level l, bool unicode, unsigned indent);
|
||||
/** \brief Pretty print the given level expression using the given configuration options. */
|
||||
format pp(level const & l, options const & opts = options());
|
||||
}
|
||||
void print(lean::level const & l);
|
||||
|
|
|
|||
|
|
@ -1,41 +1,41 @@
|
|||
add_executable(expr expr.cpp)
|
||||
target_link_libraries(expr ${EXTRA_LIBS})
|
||||
add_test(expr ${CMAKE_CURRENT_BINARY_DIR}/expr)
|
||||
add_executable(normalizer normalizer.cpp)
|
||||
target_link_libraries(normalizer ${EXTRA_LIBS})
|
||||
add_test(normalizer ${CMAKE_CURRENT_BINARY_DIR}/normalizer)
|
||||
set_tests_properties(normalizer PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
add_executable(threads threads.cpp)
|
||||
target_link_libraries(threads ${EXTRA_LIBS})
|
||||
add_test(threads ${CMAKE_CURRENT_BINARY_DIR}/threads)
|
||||
set_tests_properties(threads PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
add_executable(free_vars free_vars.cpp)
|
||||
target_link_libraries(free_vars ${EXTRA_LIBS})
|
||||
add_test(free_vars ${CMAKE_CURRENT_BINARY_DIR}/free_vars)
|
||||
# add_executable(expr expr.cpp)
|
||||
# target_link_libraries(expr ${EXTRA_LIBS})
|
||||
# add_test(expr ${CMAKE_CURRENT_BINARY_DIR}/expr)
|
||||
# add_executable(normalizer normalizer.cpp)
|
||||
# target_link_libraries(normalizer ${EXTRA_LIBS})
|
||||
# add_test(normalizer ${CMAKE_CURRENT_BINARY_DIR}/normalizer)
|
||||
# set_tests_properties(normalizer PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
# add_executable(threads threads.cpp)
|
||||
# target_link_libraries(threads ${EXTRA_LIBS})
|
||||
# add_test(threads ${CMAKE_CURRENT_BINARY_DIR}/threads)
|
||||
# set_tests_properties(threads PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
# add_executable(free_vars free_vars.cpp)
|
||||
# target_link_libraries(free_vars ${EXTRA_LIBS})
|
||||
# add_test(free_vars ${CMAKE_CURRENT_BINARY_DIR}/free_vars)
|
||||
add_executable(level level.cpp)
|
||||
target_link_libraries(level ${EXTRA_LIBS})
|
||||
add_test(level ${CMAKE_CURRENT_BINARY_DIR}/level)
|
||||
add_executable(replace replace.cpp)
|
||||
target_link_libraries(replace ${EXTRA_LIBS})
|
||||
add_test(replace ${CMAKE_CURRENT_BINARY_DIR}/replace)
|
||||
add_executable(type_checker type_checker.cpp)
|
||||
target_link_libraries(type_checker ${EXTRA_LIBS})
|
||||
add_test(type_checker ${CMAKE_CURRENT_BINARY_DIR}/type_checker)
|
||||
set_tests_properties(type_checker PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
add_executable(environment environment.cpp)
|
||||
target_link_libraries(environment ${EXTRA_LIBS})
|
||||
add_test(environment ${CMAKE_CURRENT_BINARY_DIR}/environment)
|
||||
set_tests_properties(environment PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
add_executable(occurs occurs.cpp)
|
||||
target_link_libraries(occurs ${EXTRA_LIBS})
|
||||
add_test(occurs ${CMAKE_CURRENT_BINARY_DIR}/occurs)
|
||||
add_executable(metavar metavar.cpp)
|
||||
target_link_libraries(metavar ${EXTRA_LIBS})
|
||||
add_test(metavar ${CMAKE_CURRENT_BINARY_DIR}/metavar)
|
||||
set_tests_properties(metavar PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
add_executable(instantiate instantiate.cpp)
|
||||
target_link_libraries(instantiate ${EXTRA_LIBS})
|
||||
add_test(instantiate ${CMAKE_CURRENT_BINARY_DIR}/instantiate)
|
||||
add_executable(universe_constraints universe_constraints.cpp)
|
||||
target_link_libraries(universe_constraints ${EXTRA_LIBS})
|
||||
add_test(universe_constraints ${CMAKE_CURRENT_BINARY_DIR}/universe_constraints)
|
||||
# add_executable(replace replace.cpp)
|
||||
# target_link_libraries(replace ${EXTRA_LIBS})
|
||||
# add_test(replace ${CMAKE_CURRENT_BINARY_DIR}/replace)
|
||||
# add_executable(type_checker type_checker.cpp)
|
||||
# target_link_libraries(type_checker ${EXTRA_LIBS})
|
||||
# add_test(type_checker ${CMAKE_CURRENT_BINARY_DIR}/type_checker)
|
||||
# set_tests_properties(type_checker PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
# add_executable(environment environment.cpp)
|
||||
# target_link_libraries(environment ${EXTRA_LIBS})
|
||||
# add_test(environment ${CMAKE_CURRENT_BINARY_DIR}/environment)
|
||||
# set_tests_properties(environment PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
# add_executable(occurs occurs.cpp)
|
||||
# target_link_libraries(occurs ${EXTRA_LIBS})
|
||||
# add_test(occurs ${CMAKE_CURRENT_BINARY_DIR}/occurs)
|
||||
# add_executable(metavar metavar.cpp)
|
||||
# target_link_libraries(metavar ${EXTRA_LIBS})
|
||||
# add_test(metavar ${CMAKE_CURRENT_BINARY_DIR}/metavar)
|
||||
# set_tests_properties(metavar PROPERTIES ENVIRONMENT "LEAN_PATH=${LEAN_BINARY_DIR}/shell")
|
||||
# add_executable(instantiate instantiate.cpp)
|
||||
# target_link_libraries(instantiate ${EXTRA_LIBS})
|
||||
# add_test(instantiate ${CMAKE_CURRENT_BINARY_DIR}/instantiate)
|
||||
# add_executable(universe_constraints universe_constraints.cpp)
|
||||
# target_link_libraries(universe_constraints ${EXTRA_LIBS})
|
||||
# add_test(universe_constraints ${CMAKE_CURRENT_BINARY_DIR}/universe_constraints)
|
||||
|
|
|
|||
|
|
@ -7,8 +7,7 @@ Author: Leonardo de Moura
|
|||
#include <locale>
|
||||
#include "util/test.h"
|
||||
#include "util/exception.h"
|
||||
#include "kernel/environment.h"
|
||||
#include "library/printer.h"
|
||||
#include "kernel/level.h"
|
||||
using namespace lean;
|
||||
|
||||
static void check_serializer(level const & l) {
|
||||
|
|
@ -19,10 +18,33 @@ static void check_serializer(level const & l) {
|
|||
deserializer d(in);
|
||||
level l1, l2;
|
||||
d >> l1 >> l2;
|
||||
lean_assert(l == l1);
|
||||
lean_assert(l == l2);
|
||||
lean_assert_eq(l, l1);
|
||||
lean_assert_eq(l, l2);
|
||||
}
|
||||
|
||||
static void tst1() {
|
||||
level zero;
|
||||
level one = mk_succ(zero);
|
||||
level two = mk_succ(one);
|
||||
lean_assert(mk_max(one, two) == two);
|
||||
lean_assert(mk_imax(one, two) == two);
|
||||
lean_assert(mk_imax(two, zero) == zero);
|
||||
check_serializer(two);
|
||||
check_serializer(one);
|
||||
level p = mk_param_univ(0);
|
||||
lean_assert(mk_imax(p, zero) == zero);
|
||||
lean_assert(mk_max(zero, p) == p);
|
||||
lean_assert(mk_max(p, zero) == p);
|
||||
lean_assert(mk_max(p, one) != p);
|
||||
check_serializer(mk_max(p, one));
|
||||
check_serializer(mk_imax(p, one));
|
||||
check_serializer(mk_imax(one, p));
|
||||
check_serializer(mk_imax(mk_succ(p), p));
|
||||
std::cout << pp(mk_max(p, mk_max(mk_succ(mk_param_univ(1)), one))) << "\n";
|
||||
}
|
||||
|
||||
|
||||
#if 0
|
||||
static void tst0() {
|
||||
environment env;
|
||||
lean_assert(env->begin_objects() == env->end_objects());
|
||||
|
|
@ -123,14 +145,18 @@ static void tst5() {
|
|||
std::cout << max(l1, max(l2, l1+1)) << "\n";
|
||||
lean_assert(max(l1, max(l2, l1+1)) == max(l1+1, l2));
|
||||
}
|
||||
#endif
|
||||
|
||||
int main() {
|
||||
save_stack_info();
|
||||
tst1();
|
||||
#if 0
|
||||
tst0();
|
||||
tst1();
|
||||
tst2();
|
||||
tst3();
|
||||
tst4();
|
||||
tst5();
|
||||
#endif
|
||||
return has_violations() ? 1 : 0;
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue