237 lines
9 KiB
C++
237 lines
9 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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#pragma once
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#include <iostream>
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#include <algorithm>
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#include <utility>
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#include "util/name.h"
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#include "util/optional.h"
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#include "util/list.h"
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#include "util/sexpr/format.h"
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#include "util/sexpr/options.h"
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namespace lean {
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class environment;
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struct level_cell;
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/**
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\brief Universe level kinds.
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- Zero : It is also Prop level if env.impredicative() is true
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- Succ(l) : successor level
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- Max(l1, l2) : maximum of two levels
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- IMax(l1, l2) : IMax(x, zero) = zero for all x
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IMax(x, succ(y)) = Max(x, succ(y)) for all x, y
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We use IMax to handle Pi-types, and Max for Sigma-types.
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Their definitions "mirror" the typing rules for Pi and Sigma.
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- Param(n) : A parameter. In Lean, we have universe polymorphic definitions.
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- Global(n) : A global level.
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- Meta(n) : Placeholder. It is the equivalent of a metavariable for universe levels.
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The elaborator is responsible for replacing Meta with level expressions
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that do not contain Meta.
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*/
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enum class level_kind { Zero, Succ, Max, IMax, Param, Global, Meta };
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/**
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\brief Universe level.
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*/
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class level {
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friend class environment;
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level_cell * m_ptr;
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friend level_cell const & to_cell(level const & l);
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friend class optional<level>;
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public:
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/** \brief Universe zero */
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level();
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level(level_cell * ptr);
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level(level const & l);
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level(level&& s);
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~level();
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level_kind kind() const;
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unsigned hash() const;
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level & operator=(level const & l);
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level & operator=(level&& l);
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friend bool is_eqp(level const & l1, level const & l2) { return l1.m_ptr == l2.m_ptr; }
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friend void swap(level & l1, level & l2) { std::swap(l1, l2); }
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struct ptr_hash { unsigned operator()(level const & n) const { return std::hash<level_cell*>()(n.m_ptr); } };
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struct ptr_eq { bool operator()(level const & n1, level const & n2) const { return n1.m_ptr == n2.m_ptr; } };
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};
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bool operator==(level const & l1, level const & l2);
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inline bool operator!=(level const & l1, level const & l2) { return !operator==(l1, l2); }
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struct level_hash { unsigned operator()(level const & n) const { return n.hash(); } };
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struct level_eq { bool operator()(level const & n1, level const & n2) const { return n1 == n2; } };
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SPECIALIZE_OPTIONAL_FOR_SMART_PTR(level)
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inline optional<level> none_level() { return optional<level>(); }
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inline optional<level> some_level(level const & e) { return optional<level>(e); }
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inline optional<level> some_level(level && e) { return optional<level>(std::forward<level>(e)); }
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level const & mk_level_zero();
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level const & mk_level_one();
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level mk_max(level const & l1, level const & l2);
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level mk_imax(level const & l1, level const & l2);
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level mk_succ(level const & l);
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level mk_param_univ(name const & n);
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level mk_global_univ(name const & n);
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level mk_meta_univ(name const & n);
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/** \brief Convert (succ^k l) into (l, k). If l is not a succ, then return (l, 0) */
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pair<level, unsigned> to_offset(level l);
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inline unsigned hash(level const & l) { return l.hash(); }
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inline level_kind kind(level const & l) { return l.kind(); }
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inline bool is_zero(level const & l) { return kind(l) == level_kind::Zero; }
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inline bool is_param(level const & l) { return kind(l) == level_kind::Param; }
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inline bool is_global(level const & l) { return kind(l) == level_kind::Global; }
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inline bool is_meta(level const & l) { return kind(l) == level_kind::Meta; }
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inline bool is_succ(level const & l) { return kind(l) == level_kind::Succ; }
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inline bool is_max(level const & l) { return kind(l) == level_kind::Max; }
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inline bool is_imax(level const & l) { return kind(l) == level_kind::IMax; }
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bool is_one(level const & l);
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unsigned get_depth(level const & l);
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level const & max_lhs(level const & l);
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level const & max_rhs(level const & l);
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level const & imax_lhs(level const & l);
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level const & imax_rhs(level const & l);
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level const & succ_of(level const & l);
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name const & param_id(level const & l);
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name const & global_id(level const & l);
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name const & meta_id(level const & l);
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name const & level_id(level const & l);
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/**
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\brief Return true iff \c l is an explicit level.
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We say a level l is explicit iff
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1) l is zero OR
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2) l = succ(l') and l' is explicit
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*/
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bool is_explicit(level const & l);
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/** \brief Convert an explicit universe into a unsigned integer.
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\pre is_explicit(l)
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*/
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unsigned to_explicit(level const & l);
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/** \brief Return true iff \c l contains placeholder (aka meta parameters). */
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bool has_meta(level const & l);
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/** \brief Return true iff \c l contains globals */
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bool has_global(level const & l);
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/** \brief Return true iff \c l contains parameters */
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bool has_param(level const & l);
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/**
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\brief Return a new level expression based on <tt>l == succ(arg)</tt>, where \c arg is replaced with
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\c new_arg.
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\pre is_succ(l)
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*/
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level update_succ(level const & l, level const & new_arg);
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/**
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\brief Return a new level expression based on <tt>l == max(lhs, rhs)</tt>, where \c lhs is replaced with
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\c new_lhs and \c rhs is replaced with \c new_rhs.
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\pre is_max(l) || is_imax(l)
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*/
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level update_max(level const & l, level const & new_lhs, level const & new_rhs);
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/**
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\brief Return true if lhs and rhs denote the same level.
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The check is done by normalization.
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*/
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bool is_equivalent(level const & lhs, level const & rhs);
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/** \brief Return the given level expression normal form */
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level normalize(level const & l);
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/**
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\brief If the result is true, then forall assignments \c A that assigns all parameters, globals and metavariables occuring
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in \c l1 and \l2, we have that the universe level l1[A] is bigger or equal to l2[A].
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\remark This function assumes l1 and l2 are normalized
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*/
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bool is_geq_core(level l1, level l2);
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bool is_geq(level const & l1, level const & l2);
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typedef list<level> levels;
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bool has_meta(levels const & ls);
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bool has_global(levels const & ls);
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bool has_param(levels const & ls);
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/** \brief An arbitrary (monotonic) total order on universe level terms. */
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bool is_lt(level const & l1, level const & l2, bool use_hash);
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bool is_lt(levels const & as, levels const & bs, bool use_hash);
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struct level_quick_cmp { int operator()(level const & l1, level const & l2) const { return is_lt(l1, l2, true) ? -1 : (l1 == l2 ? 0 : 1); } };
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/** \brief Functional for applying <tt>F</tt> to each level expressions. */
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class for_each_level_fn {
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std::function<bool(level const &)> m_f; // NOLINT
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void apply(level const & l);
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public:
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template<typename F> for_each_level_fn(F const & f):m_f(f) {}
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void operator()(level const & l) { return apply(l); }
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};
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template<typename F> void for_each(level const & l, F const & f) { return for_each_level_fn(f)(l); }
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/** \brief Functional for applying <tt>F</tt> to the level expressions. */
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class replace_level_fn {
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std::function<optional<level>(level const &)> m_f;
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level apply(level const & l);
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public:
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template<typename F> replace_level_fn(F const & f):m_f(f) {}
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level operator()(level const & l) { return apply(l); }
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};
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template<typename F> level replace(level const & l, F const & f) { return replace_level_fn(f)(l); }
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typedef list<name> level_param_names;
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/** \brief If \c l contains a global that is not in \c env, then return it. Otherwise, return none. */
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optional<name> get_undef_global(level const & l, environment const & env);
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/** \brief If \c l contains a parameter that is not in \c ps, then return it. Otherwise, return none. */
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optional<name> get_undef_param(level const & l, level_param_names const & ps);
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/**
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\brief Instantiate the universe level parameters \c ps occurring in \c l with the levels \c ls.
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\pre length(ps) == length(ls)
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*/
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level instantiate(level const & l, level_param_names const & ps, levels const & ls);
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/** \brief Printer for debugging purposes */
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std::ostream & operator<<(std::ostream & out, level const & l);
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/**
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\brief If the result is true, then forall assignments \c A that assigns all parameters, globals and metavariables occuring
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in \c l, l[A] != zero.
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*/
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bool is_not_zero(level const & l);
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/** \brief Pretty print the given level expression, unicode characters are used if \c unicode is \c true. */
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format pp(level l, bool unicode, unsigned indent);
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/** \brief Pretty print the given level expression using the given configuration options. */
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format pp(level const & l, options const & opts = options());
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/** \brief Pretty print lhs <= rhs, unicode characters are used if \c unicode is \c true. */
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format pp(level const & lhs, level const & rhs, bool unicode, unsigned indent);
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/** \brief Pretty print lhs <= rhs using the given configuration options. */
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format pp(level const & lhs, level const & rhs, options const & opts = options());
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/** \brief Convert a list of universe level parameter names into a list of levels. */
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levels param_names_to_levels(level_param_names const & ps);
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void initialize_level();
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void finalize_level();
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}
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void print(lean::level const & l);
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