lean2/src/kernel/metavar.h

/*
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 "util/pair.h"
#include "util/splay_map.h"
#include "util/name_generator.h"
#include "kernel/expr.h"
#include "kernel/context.h"
#include "kernel/justification.h"
#include "kernel/replace_visitor.h"

namespace lean {
/**
   \brief Metavar environment. It is an auxiliary datastructure used for:

   1- Creating metavariables.
   2- Storing their types and the contexts where they were created.
   3- Storing substitutions.
   4- Collecting constraints
*/
class metavar_env {
    struct data {
        expr          m_subst;         // substitution
        expr          m_type;          // type of the metavariable
        context       m_context;       // context where the metavariable was defined
        justification m_justification; // justification for assigned metavariables.
        data(expr const & t = expr(), context const & ctx = context()):m_type(t), m_context(ctx) {}
    };
    typedef splay_map<name, data, name_quick_cmp> name2data;

    name_generator     m_name_generator;
    name2data          m_metavar_data;
    unsigned           m_size;
    // If the following flag is true, then beta-reduction is automatically applied
    // when we apply a substitution containing ?m <- fun (x : T), ...
    // to an expression containing (?m a)
    // The motivation is that higher order unification and matching produces a
    // bunch of assignments of the form ?m <- fun (x : T), ...
    bool               m_beta_reduce_mv;
    unsigned           m_timestamp;

    void inc_timestamp();
public:
    metavar_env(name const & prefix);
    metavar_env();

    bool beta_reduce_metavar_application() const { return m_beta_reduce_mv; }
    void set_beta_reduce_metavar_application(bool f) { m_beta_reduce_mv = f; }

    friend void swap(metavar_env & a, metavar_env & b);

    /**
       \brief The timestamp is increased whenever this environment is
       updated.
    */
    unsigned get_timestamp() const { return m_timestamp; }

    /**
       \brief Create a new metavariable in the given context and with the given type.
    */
    expr mk_metavar(context const & ctx = context(), expr const & type = expr());

    /**
       \brief Return the context where the given metavariable was created.
       \pre is_metavar(m)
       \pre !has_local_context(m)
    */
    context get_context(expr const & m) const;
    context get_context(name const & m) const;

    /**
       \brief Return the type of the given metavariable.
       \pre is_metavar(m)

       \remark If \c m does not have a type associated with it, then a new
       metavariable is created to represent the type of \c m.

       \remark If \c m has a local context, then the local context is applied.
    */
    expr get_type(expr const & m);
    expr get_type(name const & m);

    /**
        \brief Return true iff \c m has a type associated with it.
        \pre is_metavar(m)
    */
    bool has_type(expr const & m) const;
    bool has_type(name const & m) const;

    /**
       \brief Return the justification for an assigned metavariable.
       \pre is_metavar(m)
       \pre is_assigned(m)
    */
    justification get_justification(expr const & m) const;
    justification get_justification(name const & m) const;


    /**
       \brief Return true iff the metavariable named \c m is assigned in this substitution.
    */
    bool is_assigned(name const & m) const;

    /**
       \brief Return true if the given metavariable is assigned in this
       substitution.

       \pre is_metavar(m)
    */
    bool is_assigned(expr const & m) const;

    /**
       \brief Assign metavariable named \c m.

       \pre !is_assigned(m)
    */
    void assign(name const & m, expr const & t, justification const & j = justification());

    /**
       \brief Assign metavariable \c m to \c t.

       \pre is_metavar(m)
       \pre !has_meta_context(m)
       \pre !is_assigned(m)
    */
    void assign(expr const & m, expr const & t, justification const & j = justification());

    /**
       \brief Return the substitution associated with the given metavariable
       in this substitution.

       If the metavariable is not assigned in this substitution, then it returns the null
       expression.

       \pre is_metavar(m)
    */
    expr get_subst(expr const & m) const;

    /**
       \brief Apply f to each substitution in the metavariable environment.
    */
    template<typename F>
    void for_each_subst(F f) const {
        m_metavar_data.for_each([&](name const & k, data const & d) {
                if (d.m_subst)
                    f(k, d.m_subst);
            });
    }
};

void swap(metavar_env & a, metavar_env & b);

/**
   \brief Apply the changes in \c lctx to \c a.
*/
expr apply_local_context(expr const & a, local_context const & lctx);

/**
   \brief Instantiate the metavariables occurring in \c e with the substitutions
   provided by \c menv. Store the justification of replace variables in jsts.
*/
expr instantiate_metavars(expr const & e, metavar_env const & menv, buffer<justification> & jsts);
inline expr instantiate_metavars(expr const & e, metavar_env const & menv) {
    buffer<justification> tmp;
    return instantiate_metavars(e, menv, tmp);
}

/**
    \brief Extend the local context \c lctx with the entry <tt>lift:s:n</tt>
*/
local_context add_lift(local_context const & lctx, unsigned s, unsigned n);

/**
   \brief Add a lift:s:n operation to the context of the given metavariable.

   \pre is_metavar(m)
*/
expr add_lift(expr const & m, unsigned s, unsigned n);

/**
   \brief Add an inst:s:v operation to the context of the given metavariable.

   \pre is_metavar(m)
*/
expr add_inst(expr const & m, unsigned s, expr const & v);

/**
   \brief Extend the local context \c lctx with the entry <tt>inst:s v</tt>
*/
local_context add_inst(local_context const & lctx, unsigned s, expr const & v);

/**
   \brief Return true iff the given metavariable has a non-empty
   local context associated with it.

   \pre is_metavar(m)
*/
bool has_local_context(expr const & m);

/**
   \brief Return the same metavariable, but the head of the context is removed.

   \pre is_metavar(m)
   \pre has_meta_context(m)
*/
expr pop_meta_context(expr const & m);

/**
   \brief Return true iff \c e has a metavariable that is assigned in \c menv.
*/
bool has_assigned_metavar(expr const & e, metavar_env const & menv);

/**
   \brief Return true iff \c e contains the metavariable \c m.
   The substitutions in \c menv are taken into account.

   \brief is_metavar(m)
*/
bool has_metavar(expr const & e, expr const & m, metavar_env const & menv);
}