462 lines
15 KiB
C++
462 lines
15 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 <algorithm>
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#include <vector>
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#include <atomic>
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#include <sstream>
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#include <unordered_map>
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#include "kernel_exception.h"
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#include "environment.h"
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#include "safe_arith.h"
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#include "type_check.h"
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#include "exception.h"
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#include "debug.h"
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namespace lean {
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/**
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\brief Create object for tracking universe variable declarations.
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This object is mainly used for pretty printing.
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*/
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class uvar_declaration : public anonymous_object {
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name m_name;
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level m_level;
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public:
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uvar_declaration(name const & n, level const & l):m_name(n), m_level(l) {}
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virtual ~uvar_declaration() {}
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static char const * g_keyword;
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virtual char const * keyword() const { return g_keyword; }
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virtual format pp(environment const &) const {
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return format{highlight_command(format(keyword())), space(), format(m_name), space(), format("\u2265"), space(), ::lean::pp(m_level)};
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}
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};
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char const * uvar_declaration::g_keyword = "Universe";
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/** \brief Implementation of the Lean environment. */
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struct environment::imp {
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// Remark: only named objects are stored in the dictionary.
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typedef std::unordered_map<name, named_object *, name_hash, name_eq> object_dictionary;
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typedef std::tuple<level, level, int> constraint;
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// Universe variable management
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std::vector<constraint> m_constraints;
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std::vector<level> m_uvars;
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// Children environment management
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std::atomic<unsigned> m_num_children;
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std::shared_ptr<imp> m_parent;
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// Object management
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std::vector<object*> m_objects;
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object_dictionary m_object_dictionary;
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// Expression formatter && locator
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std::shared_ptr<expr_formatter> m_formatter;
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expr_formatter & get_formatter() {
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if (m_formatter) {
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return *m_formatter;
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} else {
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// root environments always have a formatter.
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lean_assert(has_parent());
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return m_parent->get_formatter();
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}
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}
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/**
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\brief Return true iff this environment has children.
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\remark If an environment has children than it cannot be
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updated. That is, it is read-only.
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*/
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bool has_children() const { return m_num_children > 0; }
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void inc_children() { m_num_children++; }
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void dec_children() { m_num_children--; }
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/** \brief Return true iff this environment has a parent environment */
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bool has_parent() const { return m_parent != nullptr; }
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/**
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\brief Return true if u >= v + k is implied by constraints
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\pre is_uvar(u) && is_uvar(v)
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*/
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bool is_implied(level const & u, level const & v, int k) {
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lean_assert(is_uvar(u) && is_uvar(v));
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if (u == v)
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return k <= 0;
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else
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return std::any_of(m_constraints.begin(), m_constraints.end(),
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[&](constraint const & c) { return std::get<0>(c) == u && std::get<1>(c) == v && std::get<2>(c) >= k; });
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}
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/** \brief Return true iff l1 >= l2 + k by asserted universe constraints. */
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bool is_ge(level const & l1, level const & l2, int k) {
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if (l1 == l2)
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return k == 0;
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switch (kind(l2)) {
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case level_kind::UVar:
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switch (kind(l1)) {
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case level_kind::UVar: return is_implied(l1, l2, k);
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case level_kind::Lift: return is_ge(lift_of(l1), l2, safe_sub(k, lift_offset(l1)));
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case level_kind::Max: return std::any_of(max_begin_levels(l1), max_end_levels(l1), [&](level const & l) { return is_ge(l, l2, k); });
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}
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case level_kind::Lift: return is_ge(l1, lift_of(l2), safe_add(k, lift_offset(l2)));
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case level_kind::Max: return std::all_of(max_begin_levels(l2), max_end_levels(l2), [&](level const & l) { return is_ge(l1, l, k); });
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}
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lean_unreachable();
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return false;
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}
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/** \brief Return true iff l1 >= l2 is implied by asserted universe constraints. */
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bool is_ge(level const & l1, level const & l2) {
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if (has_parent())
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return m_parent->is_ge(l1, l2);
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else
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return is_ge(l1, l2, 0);
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}
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/** \brief Add a new universe variable */
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level add_var(name const & n, environment const & env) {
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if (std::any_of(m_uvars.begin(), m_uvars.end(), [&](level const & l){ return uvar_name(l) == n; }))
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throw already_declared_universe_exception(env, n);
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level r(n);
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m_uvars.push_back(r);
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return r;
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}
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/**
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\brief Add basic constraint u >= v + d, and all basic
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constraints implied by transitivity.
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\pre is_uvar(u) && is_uvar(v)
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*/
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void add_constraint(level const & u, level const & v, int d) {
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lean_assert(is_uvar(u) && is_uvar(v));
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if (is_implied(u, v, d))
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return; // redundant
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buffer<constraint> to_add;
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for (constraint const & c : m_constraints) {
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if (std::get<0>(c) == v) {
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level const & l3 = std::get<1>(c);
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int u_l3_d = safe_add(d, std::get<2>(c));
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if (!is_implied(u, l3, u_l3_d))
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to_add.push_back(constraint(u, l3, u_l3_d));
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}
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}
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m_constraints.push_back(constraint(u, v, d));
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for (constraint const & c: to_add) {
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m_constraints.push_back(c);
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}
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}
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/**
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\brief Add all basic constraints implied by n >= l + k
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A basic constraint is a constraint of the form u >= v + k
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where u and v are universe variables.
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*/
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void add_constraints(level const & n, level const & l, int k) {
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lean_assert(is_uvar(n));
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switch (kind(l)) {
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case level_kind::UVar: add_constraint(n, l, k); return;
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case level_kind::Lift: add_constraints(n, lift_of(l), safe_add(k, lift_offset(l))); return;
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case level_kind::Max: std::for_each(max_begin_levels(l), max_end_levels(l), [&](level const & l1) { add_constraints(n, l1, k); }); return;
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}
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lean_unreachable();
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}
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/** \brief Add a new universe variable with constraint n >= l */
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level add_uvar(name const & n, level const & l, environment const & env) {
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if (has_parent())
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throw kernel_exception(env, "invalid universe declaration, universe variables can only be declared in top-level environments");
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if (has_children())
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throw read_only_environment_exception(env);
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level r = add_var(n, env);
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add_constraints(r, l, 0);
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m_objects.push_back(new uvar_declaration(n, l));
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return r;
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}
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/**
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\brief Return the universe variable with given name. Throw an
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exception if the environment and its ancestors do not
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contain a universe variable named \c n.
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*/
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level get_uvar(name const & n, environment const & env) const {
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if (has_parent()) {
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return m_parent->get_uvar(n, env);
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} else {
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auto it = std::find_if(m_uvars.begin(), m_uvars.end(), [&](level const & l) { return uvar_name(l) == n; });
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if (it == m_uvars.end())
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throw unknown_universe_variable_exception(env, n);
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else
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return *it;
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}
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}
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/**
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\brief Initialize the set of universe variables with bottom
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*/
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void init_uvars() {
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m_uvars.push_back(level());
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}
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/** \brief Display universe variable constraints */
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void display_uvars(std::ostream & out) const {
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for (constraint const & c : m_constraints) {
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out << uvar_name(std::get<0>(c)) << " >= " << uvar_name(std::get<1>(c));
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if (std::get<2>(c) >= 0)
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out << " + " << std::get<2>(c);
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out << "\n";
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}
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}
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/** \brief Throw exception if environment or its ancestors already have an object with the given name. */
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void check_name_core(name const & n, environment const & env) {
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if (has_parent())
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m_parent->check_name_core(n, env);
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if (m_object_dictionary.find(n) != m_object_dictionary.end())
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throw already_declared_object_exception(env, n);
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}
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void check_name(name const & n, environment const & env) {
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if (has_children())
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throw read_only_environment_exception(env);
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check_name_core(n, env);
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}
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/**
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\brief Throw an exception if \c t is not a type or type of \c
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v is not convertible to \c t.
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\remark env is the smart pointer of imp. We need it because
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infer_universe and infer_type expect an environment instead of environment::imp.
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*/
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void check_type(name const & n, expr const & t, expr const & v, environment const & env) {
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infer_universe(t, env);
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expr v_t = infer_type(v, env);
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if (!is_convertible(t, v_t, env))
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throw def_type_mismatch_exception(env, n, t, v, v_t);
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}
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/** \brief Throw exception if it is not a valid new definition */
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void check_new_definition(name const & n, expr const & t, expr const & v, environment const & env) {
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check_name(n, env);
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check_type(n, t, v, env);
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}
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/** \brief Store new named object inside internal data-structures */
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void register_named_object(named_object * new_obj) {
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m_objects.push_back(new_obj);
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m_object_dictionary.insert(std::make_pair(new_obj->get_name(), new_obj));
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}
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/** \brief Add new definition. */
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void add_definition(name const & n, expr const & t, expr const & v, bool opaque, environment const & env) {
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check_new_definition(n, t, v, env);
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register_named_object(new definition(n, t, v, opaque));
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}
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/**
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\brief Add new definition.
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The type of the new definition is the type of \c v.
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*/
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void add_definition(name const & n, expr const & v, bool opaque, environment const & env) {
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check_name(n, env);
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expr v_t = infer_type(v, env);
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register_named_object(new definition(n, v_t, v, opaque));
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}
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/** \brief Add new theorem. */
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void add_theorem(name const & n, expr const & t, expr const & v, environment const & env) {
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check_new_definition(n, t, v, env);
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register_named_object(new theorem(n, t, v));
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}
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/** \brief Add new axiom. */
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void add_axiom(name const & n, expr const & t, environment const & env) {
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check_name(n, env);
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infer_universe(t, env);
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register_named_object(new axiom(n, t));
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}
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/** \brief Add new variable. */
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void add_var(name const & n, expr const & t, environment const & env) {
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check_name(n, env);
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infer_universe(t, env);
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register_named_object(new variable(n, t));
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}
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/**
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\brief Return the object named \c n in the environment or its
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ancestors. Return nullptr if there is not object with the
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given name.
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*/
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named_object const * get_object_ptr(name const & n) const {
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auto it = m_object_dictionary.find(n);
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if (it == m_object_dictionary.end()) {
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if (has_parent())
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return m_parent->get_object_ptr(n);
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else
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return nullptr;
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} else {
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return it->second;
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}
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}
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named_object const & get_object(name const & n, environment const & env) const {
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named_object const * ptr = get_object_ptr(n);
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if (ptr)
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return *ptr;
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else
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throw unknown_object_exception(env, n);
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}
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unsigned get_num_objects(bool local) const {
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if (local || !has_parent()) {
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return m_objects.size();
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} else {
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return m_objects.size() + m_parent->get_num_objects(false);
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}
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}
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object const & get_object(unsigned i, bool local) const {
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if (local || !has_parent()) {
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return *(m_objects[i]);
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} else {
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unsigned num_parent_objects = m_parent->get_num_objects(false);
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if (i >= num_parent_objects)
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return *(m_objects[i - num_parent_objects]);
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else
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return m_parent->get_object(i, false);
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}
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}
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/** \brief Display universal variable constraints and objects stored in this environment and its parents. */
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void display(std::ostream & out, environment const & env) const {
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if (has_parent())
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m_parent->display(out, env);
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for (object const * obj : m_objects) {
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out << obj->pp(env) << "\n";
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}
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}
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imp():
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m_num_children(0) {
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init_uvars();
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m_formatter = mk_simple_expr_formatter();
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}
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explicit imp(std::shared_ptr<imp> const & parent):
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m_num_children(0),
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m_parent(parent) {
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m_parent->inc_children();
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}
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~imp() {
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if (m_parent)
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m_parent->dec_children();
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std::for_each(m_objects.begin(), m_objects.end(), [](object * obj) { delete obj; });
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}
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};
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environment::environment():
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m_imp(new imp()) {
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}
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environment::environment(imp * new_ptr):
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m_imp(new_ptr) {
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}
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environment::environment(std::shared_ptr<imp> const & ptr):
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m_imp(ptr) {
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}
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environment::~environment() {
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}
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void environment::set_formatter(std::shared_ptr<expr_formatter> const & formatter) {
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lean_assert(formatter);
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m_imp->m_formatter = formatter;
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}
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expr_formatter & environment::get_formatter() const {
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return m_imp->get_formatter();
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}
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environment environment::mk_child() const {
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return environment(new imp(m_imp));
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}
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bool environment::has_children() const {
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return m_imp->has_children();
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}
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bool environment::has_parent() const {
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return m_imp->has_parent();
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}
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environment environment::parent() const {
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lean_assert(has_parent());
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return environment(m_imp->m_parent);
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}
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level environment::add_uvar(name const & n, level const & l) {
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return m_imp->add_uvar(n, l, *this);
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}
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bool environment::is_ge(level const & l1, level const & l2) const {
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return m_imp->is_ge(l1, l2);
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}
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void environment::display_uvars(std::ostream & out) const {
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m_imp->display_uvars(out);
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}
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level environment::get_uvar(name const & n) const {
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return m_imp->get_uvar(n, *this);
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}
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void environment::add_definition(name const & n, expr const & t, expr const & v, bool opaque) {
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m_imp->add_definition(n, t, v, opaque, *this);
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}
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void environment::add_theorem(name const & n, expr const & t, expr const & v) {
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m_imp->add_theorem(n, t, v, *this);
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}
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void environment::add_definition(name const & n, expr const & v, bool opaque) {
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m_imp->add_definition(n, v, opaque, *this);
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}
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void environment::add_axiom(name const & n, expr const & t) {
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m_imp->add_axiom(n, t, *this);
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}
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void environment::add_var(name const & n, expr const & t) {
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m_imp->add_var(n, t, *this);
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}
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void environment::add_anonymous_object(anonymous_object * o) {
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m_imp->m_objects.push_back(o);
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}
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named_object const & environment::get_object(name const & n) const {
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return m_imp->get_object(n, *this);
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}
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named_object const * environment::get_object_ptr(name const & n) const {
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return m_imp->get_object_ptr(n);
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}
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unsigned environment::get_num_objects(bool local) const {
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return m_imp->get_num_objects(local);
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}
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object const & environment::get_object(unsigned i, bool local) const {
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return m_imp->get_object(i, local);
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}
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void environment::display(std::ostream & out) const {
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m_imp->display(out, *this);
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}
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}
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