lean2/src/kernel/free_vars.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 "expr.h"
namespace lean {
/**
\brief Return true iff the given expression has free variables.
*/
bool has_free_vars(expr const & a);
/**
\brief Return true iff the given expression does not have free variables.
*/
inline bool closed(expr const & a) { return !has_free_vars(a); }
/**
\brief Return true iff \c e contains the free variable <tt>(var i)</tt>.
*/
bool has_free_var(expr const & e, unsigned i);
/**
\brief Return true iff \c e constains a free variable <tt>(var i)</tt> s.t. \c i in <tt>[low, high)</tt>.
\pre low < high
*/
bool has_free_var(expr const & e, unsigned low, unsigned high);
/**
\brief Lower the free variables in \c e by d. That is, a free variable <tt>(var i)</tt> is mapped into <tt>(var i-d)</tt>.
\pre d > 0
\pre !has_free_var(e, 0, d)
*/
expr lower_free_vars(expr const & e, unsigned d);
/**
\brief Lift free variables in \c e by d.
*/
expr lift_free_vars(expr const & e, unsigned d);
}