lean2/src/kernel/constraint.h

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.

Author: Leonardo de Moura
*/
#pragma once
#include <algorithm>
#include "util/lazy_list.h"
#include "util/list.h"
#include "util/name_generator.h"
#include "kernel/expr.h"
#include "kernel/justification.h"
#include "kernel/metavar.h"

namespace lean {
/**
   \brief The lean kernel type checker produces two kinds of constraints:

   - Equality constraint:          t ≈ s
        The terms t and s must be definitionally equal.
   - Universe level constaint:     l = m
        The universe level l must be less than or equal to m.

   \remark The constraints are only generated if the input term contains
   metavariables or level metavariables.

   Each constraint is associated with a justification object.

   \remark We also have choice constraints that are used by elaborator to specify
   the possible solutions for a metavariable. The choice constraints are not used by
   the kernel.
*/
enum class constraint_kind { Eq, LevelEq, Choice };
class constraint;
typedef list<constraint> constraints;
typedef std::tuple<expr, justification, constraints> choice_fn_result;
/**
   \brief A choice_fn is used to enumerate the possible solutions for a metavariable.
   The input arguments are:
        - an inferred type (if available)
        - substitution map (metavar -> value)
        - name generator

   The result is a lazy_list of choices, i.e., tuples containing:
        - an expression representing one of the possible solutions
        - a justification for it (this is used to accumulate the justification for the substitutions used).
        - a list of new constraints (that is, the solution is only valid if the additional constraints can be solved)

   One application of choice constraints is overloaded notation.
*/
typedef std::function<lazy_list<choice_fn_result>(optional<expr> const &, substitution const &, name_generator const &)> choice_fn;

struct constraint_cell;
class constraint {
    constraint_cell * m_ptr;
    constraint(constraint_cell * ptr);
public:
    constraint(constraint const & c);
    constraint(constraint && s);
    ~constraint();

    constraint_kind kind() const;
    justification const & get_justification() const;

    constraint & operator=(constraint const & c);
    constraint & operator=(constraint && c);

    friend bool is_eqp(constraint const & c1, constraint const & c2) { return c1.m_ptr == c2.m_ptr; }
    friend void swap(constraint & l1, constraint & l2) { std::swap(l1, l2); }

    friend constraint mk_eq_cnstr(expr const & lhs, expr const & rhs, justification const & j);
    friend constraint mk_level_eq_cnstr(level const & lhs, level const & rhs, justification const & j);
    friend constraint mk_choice_cnstr(expr const & m, choice_fn const & fn, justification const & j);

    constraint_cell * raw() const { return m_ptr; }
};

constraint mk_eq_cnstr(expr const & lhs, expr const & rhs, justification const & j);
constraint mk_level_eq_cnstr(level const & lhs, level const & rhs, justification const & j);
constraint mk_choice_cnstr(expr const & m, choice_fn const & fn, justification const & j);

inline bool is_eq_cnstr(constraint const & c) { return c.kind() == constraint_kind::Eq; }
inline bool is_level_eq_cnstr(constraint const & c) { return c.kind() == constraint_kind::LevelEq; }
inline bool is_choice_cnstr(constraint const & c) { return c.kind() == constraint_kind::Choice; }

constraint update_justification(constraint const & c, justification const & j);

/** \brief Return the lhs of an equality constraint. */
expr const & cnstr_lhs_expr(constraint const & c);
/** \brief Return the rhs of an equality constraint. */
expr const & cnstr_rhs_expr(constraint const & c);
/** \brief Return the lhs of an level constraint. */
level const & cnstr_lhs_level(constraint const & c);
/** \brief Return the rhs of an level constraint. */
level const & cnstr_rhs_level(constraint const & c);
/** \brief Return the metavariable associated with a choice constraint */
expr const & cnstr_mvar(constraint const & c);
/** \brief Return the choice_fn associated with a choice constraint. */
choice_fn const & cnstr_choice_fn(constraint const & c);

/** \brief Printer for debugging purposes */
std::ostream & operator<<(std::ostream & out, constraint const & c);
}