lean2/src/kernel/level.h

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include <iostream>
2013-09-13 23:14:24 +00:00
#include <algorithm>
#include <utility>
#include "util/name.h"
#include "util/optional.h"
#include "util/list.h"
#include "util/sexpr/format.h"
#include "util/sexpr/options.h"
namespace lean {
class environment;
struct level_cell;
/**
\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(n) : A parameter. In Lean, we have universe polymorphic definitions.
- Global(n) : A global level.
- Meta(n) : 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, Global, Meta };
/**
\brief Universe level.
*/
class level {
friend class environment;
level_cell * m_ptr;
friend level_cell const & to_cell(level const & l);
friend class optional<level>;
public:
/** \brief Universe zero */
level();
level(level_cell * ptr);
level(level const & l);
level(level&& s);
~level();
level_kind kind() const;
unsigned hash() const;
level & operator=(level const & l);
level & operator=(level&& l);
friend bool is_eqp(level const & l1, level const & l2) { return l1.m_ptr == l2.m_ptr; }
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; } };
};
bool operator==(level const & l1, level const & l2);
inline bool operator!=(level const & l1, level const & l2) { return !operator==(l1, l2); }
SPECIALIZE_OPTIONAL_FOR_SMART_PTR(level)
inline optional<level> none_level() { return optional<level>(); }
inline optional<level> some_level(level const & e) { return optional<level>(e); }
inline optional<level> some_level(level && e) { return optional<level>(std::forward<level>(e)); }
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(name const & n);
level mk_global_univ(name const & n);
level mk_meta_univ(name const & n);
inline unsigned hash(level const & l) { return l.hash(); }
inline level_kind kind(level const & l) { return l.kind(); }
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_global(level const & l) { return kind(l) == level_kind::Global; }
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; }
bool is_one(level const & l);
unsigned get_depth(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);
name const & param_id(level const & l);
name const & global_id(level const & l);
name const & 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). */
bool has_meta(level const & l);
/** \brief Return true iff \c l contains globals */
bool has_global(level const & l);
/** \brief Return true iff \c l contains parameters */
bool has_param(level const & l);
/**
\brief Return a new level expression based on <tt>l == succ(arg)</tt>, where \c arg is replaced with
\c new_arg.
\pre is_succ(l)
*/
level update_succ(level const & l, level const & new_arg);
/**
\brief Return a new level expression based on <tt>l == max(lhs, rhs)</tt>, where \c lhs is replaced with
\c new_lhs and \c rhs is replaced with \c new_rhs.
\pre is_max(l) || is_imax(l)
*/
level update_max(level const & l, level const & new_lhs, level const & new_rhs);
/**
\brief Return true if lhs and rhs denote the same level.
The check is done by normalization.
*/
bool is_equivalent(level const & lhs, level const & rhs);
/** \brief Return the given level expression normal form */
level normalize(level const & l);
typedef list<level> levels;
bool has_meta(levels const & ls);
bool has_global(levels const & ls);
bool has_param(levels const & ls);
/** \brief An arbitrary (monotonic) total order on universe level terms. */
bool is_lt(level const & l1, level const & l2, bool use_hash);
bool is_lt(levels const & as, levels const & bs, bool use_hash);
/** \brief Functional for applying <tt>F</tt> to each level expressions. */
class for_each_level_fn {
std::function<bool(level const &)> m_f; // NOLINT
void apply(level const & l);
public:
template<typename F> for_each_level_fn(F const & f):m_f(f) {}
void operator()(level const & l) { return apply(l); }
};
template<typename F> void for_each(level const & l, F const & f) { return for_each_level_fn(f)(l); }
/** \brief Functional for applying <tt>F</tt> to the level expressions. */
class replace_level_fn {
std::function<optional<level>(level const &)> m_f;
level apply(level const & l);
public:
template<typename F> replace_level_fn(F const & f):m_f(f) {}
level operator()(level const & l) { return apply(l); }
};
template<typename F> level replace(level const & l, F const & f) { return replace_level_fn(f)(l); }
typedef list<name> level_param_names;
/** \brief If \c l contains a global that is not in \c env, then return it. Otherwise, return none. */
optional<name> get_undef_global(level const & l, environment const & env);
/** \brief If \c l contains a parameter that is not in \c ps, then return it. Otherwise, return none. */
optional<name> get_undef_param(level const & l, level_param_names const & ps);
/**
\brief Instantiate the universe level parameters \c ps occurring in \c l with the levels \c ls.
\pre length(ps) == length(ls)
*/
level instantiate(level const & l, level_param_names const & ps, levels const & ls);
/** \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);
/** \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());
/** \brief Pretty print lhs <= rhs, unicode characters are used if \c unicode is \c true. */
format pp(level const & lhs, level const & rhs, bool unicode, unsigned indent);
/** \brief Pretty print lhs <= rhs using the given configuration options. */
format pp(level const & lhs, level const & rhs, options const & opts = options());
/** \brief Auxiliary class used to manage universe constraints. */
class universe_context {
struct imp;
std::unique_ptr<imp> m_ptr;
public:
universe_context();
universe_context(universe_context const & s);
~universe_context();
/**
\brief Add the universe level constraint l1 <= l2.
*/
void add_le(level const & l1, level const & l2);
/**
\brief Quick check wether l1 <= l2. No backtracking search is performed.
If the result is true, then l1 <= l2 is implied. The result is false,
if we could not establish that.
*/
bool is_implied_cheap(level const & l1, level const & l2) const;
/**
\brief Expensive l1 <= l2 test. It performs a backtracking search.
*/
bool is_implied(level const & l1, level const & l2);
/**
\brief Create a backtracking point.
*/
void push();
/**
\brief Backtrack.
*/
void pop(unsigned num_scopes);
};
}
void print(lean::level const & l);