81 lines
3.4 KiB
C++
81 lines
3.4 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 "kernel/expr.h"
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namespace lean {
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/**
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\brief Return true iff the given expression has free variables.
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*/
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bool has_free_vars(expr const & a);
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/**
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\brief Return true iff the given expression does not have free variables.
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*/
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inline bool closed(expr const & a) { return !has_free_vars(a); }
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class metavar_env;
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/**
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\brief Return \c R s.t. the de Bruijn index of all free variables
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occurring in \c e is in the interval <tt>[0, R)</tt>.
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\pre All metavariables occurring in \c e must have been created
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at \c menv.
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\remark Regarding metavariables, if a metavariable \c m was defined
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in a context \c ctx and <tt>ctx.size() == R</tt>, then \c m can
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only contain free variables in the range <tt>[0, R)</tt>
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So, if \c m does not have an associated local context, the answer is just \c R.
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If \c m has an associated local context, we process it using the following rules
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[inst:s v] R ===> if s >= R then R else max(R-1, range_of(v))
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[lift:s:n] R ===> if s >= R then R else R + n
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*/
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unsigned free_var_range(expr const & e, metavar_env const & menv);
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/**
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\brief Return true iff \c e constains a free variable <tt>(var i)</tt> s.t. \c i in <tt>[low, high)</tt>.
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\pre low < high
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\remark If menv != nullptr, then we use \c free_var_range to compute the free variables that may
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occur in a metavariable.
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*/
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bool has_free_var(expr const & e, unsigned low, unsigned high, metavar_env const * menv = nullptr);
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inline bool has_free_var(expr const & e, unsigned low, unsigned high, metavar_env const & menv) {
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return has_free_var(e, low, high, &menv);
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}
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/**
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\brief Return true iff \c e contains the free variable <tt>(var i)</tt>.
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*/
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inline bool has_free_var(expr const & e, unsigned i, metavar_env const * menv = nullptr) { return has_free_var(e, i, i+1, menv); }
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inline bool has_free_var(expr const & e, unsigned i, metavar_env const & menv) { return has_free_var(e, i, i+1, &menv); }
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/**
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\brief Lower the free variables >= s in \c e by \c d. That is, a free variable <tt>(var i)</tt> s.t.
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<tt>i >= s</tt> is mapped into <tt>(var i-d)</tt>.
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\pre s >= d
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\pre !has_free_var(e, s-d, d, menv)
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\remark The parameter menv is only used for debugging purposes
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*/
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expr lower_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const * menv = nullptr);
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inline expr lower_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const & menv) {
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return lower_free_vars(e, s, d, &menv);
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}
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inline expr lower_free_vars(expr const & e, unsigned d, metavar_env const * menv = nullptr) { return lower_free_vars(e, d, d, menv); }
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/**
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\brief Lift free variables >= s in \c e by d.
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\remark When the parameter menv != nullptr, this function will minimize the use
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of the local entry lift in metavariables occurring in \c e.
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*/
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expr lift_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const * menv = nullptr);
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inline expr lift_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const & menv) { return lift_free_vars(e, s, d, &menv); }
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inline expr lift_free_vars(expr const & e, unsigned d, metavar_env const * menv = nullptr) { return lift_free_vars(e, 0, d, menv); }
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inline expr lift_free_vars(expr const & e, unsigned d, metavar_env const & menv) { return lift_free_vars(e, 0, d, &menv); }
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}
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