428 lines
16 KiB
C++
428 lines
16 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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#include <algorithm>
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#include <limits>
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#include "kernel/free_vars.h"
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#include "kernel/expr_sets.h"
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#include "kernel/replace_fn.h"
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#include "kernel/for_each_fn.h"
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#include "kernel/metavar.h"
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namespace lean {
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/**
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\brief Functional object for checking whether a kernel expression has free variables or not.
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\remark We assume that a metavariable contains free variables.
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This is an approximation, since we don't know how the metavariable will be instantiated.
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*/
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class has_free_vars_fn {
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protected:
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expr_cell_offset_set m_cached;
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bool apply(optional<expr> const & e, unsigned offset) {
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return e && apply(*e, offset);
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}
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bool apply(expr const & e, unsigned offset) {
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// handle easy cases
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switch (e.kind()) {
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case expr_kind::Constant:
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if (!const_type(e))
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return false;
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break;
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case expr_kind::Type: case expr_kind::Value:
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return false;
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case expr_kind::MetaVar:
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return true;
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case expr_kind::Var:
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return var_idx(e) >= offset;
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case expr_kind::App: case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Let:
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break;
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}
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if (e.raw()->is_closed())
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return false;
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if (offset == 0) {
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return apply_core(e, 0);
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} else {
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// The apply_core(e, 0) may seem redundant, but it allows us to
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// mark nested closed expressions.
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return apply_core(e, 0) && apply_core(e, offset);
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}
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}
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bool apply_core(expr const & e, unsigned offset) {
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bool shared = false;
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if (is_shared(e)) {
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shared = true;
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expr_cell_offset p(e.raw(), offset);
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if (m_cached.find(p) != m_cached.end())
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return false;
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}
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bool result = false;
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switch (e.kind()) {
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case expr_kind::Constant:
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lean_assert(const_type(e));
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result = apply(const_type(e), offset);
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break;
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case expr_kind::Type: case expr_kind::Value: case expr_kind::Var: case expr_kind::MetaVar:
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// easy cases were already handled
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lean_unreachable(); // LCOV_EXCL_LINE
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case expr_kind::App:
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result = std::any_of(begin_args(e), end_args(e), [=](expr const & arg){ return apply(arg, offset); });
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break;
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case expr_kind::Lambda:
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case expr_kind::Pi:
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result = apply(abst_domain(e), offset) || apply(abst_body(e), offset + 1);
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break;
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case expr_kind::Let:
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result = apply(let_type(e), offset) || apply(let_value(e), offset) || apply(let_body(e), offset + 1);
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break;
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}
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if (!result) {
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if (offset == 0)
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e.raw()->set_closed();
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if (shared)
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m_cached.insert(expr_cell_offset(e.raw(), offset));
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}
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return result;
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}
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public:
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has_free_vars_fn() {}
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bool operator()(expr const & e) { return apply(e, 0); }
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};
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bool has_free_vars(expr const & e) {
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return has_free_vars_fn()(e);
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}
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/**
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\brief Functional object for computing the range [0, R) of free variables occurring
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in an expression.
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*/
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class free_var_range_fn {
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expr_map<unsigned> m_cached;
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optional<metavar_env> const & m_menv;
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static unsigned dec(unsigned s) { return (s == 0) ? 0 : s - 1; }
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/*
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\brief If a metavariable \c m was defined in a context \c ctx and <tt>ctx.size() == R</tt>,
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then \c m can 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 process_metavar(expr const & m) {
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lean_assert(is_metavar(m));
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if (!m_menv)
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return std::numeric_limits<unsigned>::max(); // metavariable environment is not available, assume the worst.
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context ctx = (*m_menv)->get_context(metavar_name(m));
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unsigned R = ctx.size();
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if (has_local_context(m)) {
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local_context lctx = metavar_lctx(m);
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buffer<local_entry> lentries;
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to_buffer(lctx, lentries);
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unsigned i = lentries.size();
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while (i > 0) {
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--i;
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local_entry const & entry = lentries[i];
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if (entry.is_inst()) {
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if (entry.s() < R) {
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R = std::max(dec(R), apply(entry.v()));
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}
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} else {
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if (entry.s() < R)
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R += entry.n();
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}
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}
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}
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return R;
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}
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unsigned apply(optional<expr> const & e) {
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return e ? apply(*e) : 0;
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}
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unsigned apply(expr const & e) {
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// handle easy cases
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switch (e.kind()) {
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case expr_kind::Constant:
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if (!const_type(e))
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return 0;
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break;
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case expr_kind::Type: case expr_kind::Value:
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return 0;
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case expr_kind::Var:
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return var_idx(e) + 1;
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case expr_kind::MetaVar: case expr_kind::App:
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case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Let:
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break;
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}
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if (e.raw()->is_closed())
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return 0;
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bool shared = false;
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if (is_shared(e)) {
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shared = true;
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auto it = m_cached.find(e);
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if (it != m_cached.end())
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return it->second;
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}
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unsigned result = 0;
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switch (e.kind()) {
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case expr_kind::Constant:
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lean_assert(const_type(e));
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result = apply(const_type(e));
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break;
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case expr_kind::Type: case expr_kind::Value: case expr_kind::Var:
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// easy cases were already handled
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lean_unreachable(); // LCOV_EXCL_LINE
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case expr_kind::MetaVar:
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result = process_metavar(e);
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break;
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case expr_kind::App:
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for (auto const & c : args(e))
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result = std::max(result, apply(c));
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break;
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case expr_kind::Lambda:
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case expr_kind::Pi:
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result = std::max(apply(abst_domain(e)), dec(apply(abst_body(e))));
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break;
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case expr_kind::Let:
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result = std::max({apply(let_type(e)), apply(let_value(e)), dec(apply(let_body(e)))});
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break;
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}
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if (shared)
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m_cached.insert(mk_pair(e, result));
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return result;
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}
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public:
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free_var_range_fn(optional<metavar_env> const & menv):m_menv(menv) {}
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unsigned operator()(expr const & e) { return apply(e); }
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};
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unsigned free_var_range(expr const & e, metavar_env const & menv) {
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return free_var_range_fn(some_menv(menv))(e);
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}
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unsigned free_var_range(expr const & e) {
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return free_var_range_fn(none_menv())(e);
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}
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/**
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\brief Functional object for checking whether a kernel expression has a free variable in the range <tt>[low, high)</tt> or not.
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\remark We assume that a metavariable contains free variables.
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This is an approximation, since we don't know how the metavariable will be instantiated.
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*/
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class has_free_var_in_range_fn {
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protected:
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unsigned m_low;
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unsigned m_high;
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expr_cell_offset_set m_cached;
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std::unique_ptr<free_var_range_fn> m_range_fn;
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bool apply(optional<expr> const & e, unsigned offset) {
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return e && apply(*e, offset);
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}
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// Return true iff m_low + offset <= vidx
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bool ge_lower(unsigned vidx, unsigned offset) const {
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unsigned low1 = m_low + offset;
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if (low1 < m_low)
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return false; // overflow, vidx can't be >= max unsigned
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return vidx >= low1;
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}
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// Return true iff vidx < m_high + offset
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bool lt_upper(unsigned vidx, unsigned offset) const {
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unsigned high1 = m_high + offset;
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if (high1 < m_high)
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return true; // overflow, vidx is always < max unsigned
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return vidx < high1;
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}
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// Return true iff m_low + offset <= vidx < m_high + offset
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bool in_interval(unsigned vidx, unsigned offset) const {
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return ge_lower(vidx, offset) && lt_upper(vidx, offset);
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}
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bool apply(expr const & e, unsigned offset) {
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// handle easy cases
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switch (e.kind()) {
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case expr_kind::Constant:
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if (!const_type(e))
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return false;
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break;
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case expr_kind::Type: case expr_kind::Value:
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return false;
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case expr_kind::MetaVar:
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if (m_range_fn)
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break; // it is not cheap
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else
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return true; // assume that any free variable can occur in the metavariable
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case expr_kind::Var:
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return in_interval(var_idx(e), offset);
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case expr_kind::App: case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Let:
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break;
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}
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if (e.raw()->is_closed())
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return false;
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bool shared = false;
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if (is_shared(e)) {
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shared = true;
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expr_cell_offset p(e.raw(), offset);
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if (m_cached.find(p) != m_cached.end())
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return false;
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}
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bool result = false;
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switch (e.kind()) {
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case expr_kind::Constant:
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lean_assert(const_type(e));
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result = apply(const_type(e), offset);
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break;
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case expr_kind::Type: case expr_kind::Value: case expr_kind::Var:
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// easy cases were already handled
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lean_unreachable(); // LCOV_EXCL_LINE
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case expr_kind::MetaVar: {
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lean_assert(m_range_fn);
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unsigned R = (*m_range_fn)(e);
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if (R > 0) {
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unsigned max_fvar_idx = R - 1;
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result = ge_lower(max_fvar_idx, offset);
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// Remark: Variable #0 may occur in \c e.
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// So, we don't have to check the upper bound offset + m_high;
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}
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break;
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}
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case expr_kind::App:
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result = std::any_of(begin_args(e), end_args(e), [=](expr const & arg){ return apply(arg, offset); });
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break;
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case expr_kind::Lambda:
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case expr_kind::Pi:
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result = apply(abst_domain(e), offset) || apply(abst_body(e), offset + 1);
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break;
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case expr_kind::Let:
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result = apply(let_type(e), offset) || apply(let_value(e), offset) || apply(let_body(e), offset + 1);
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break;
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}
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if (!result && shared) {
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m_cached.insert(expr_cell_offset(e.raw(), offset));
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}
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return result;
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}
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public:
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has_free_var_in_range_fn(unsigned low, unsigned high, optional<metavar_env> const & menv):
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m_low(low),
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m_high(high) {
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lean_assert(low < high);
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if (menv)
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m_range_fn.reset(new free_var_range_fn(menv));
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}
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bool operator()(expr const & e) { return apply(e, 0); }
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};
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bool has_free_var(expr const & e, unsigned low, unsigned high, optional<metavar_env> const & menv) {
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return high > low && has_free_var_in_range_fn(low, high, menv)(e);
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}
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bool has_free_var(expr const & e, unsigned low, unsigned high, metavar_env const & menv) { return has_free_var(e, low, high, some_menv(menv)); }
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bool has_free_var(expr const & e, unsigned low, unsigned high) { return has_free_var(e, low, high, none_menv()); }
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bool has_free_var(expr const & e, unsigned i, optional<metavar_env> const & menv) { return has_free_var(e, i, i+1, menv); }
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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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bool has_free_var(expr const & e, unsigned i) { return has_free_var(e, i, i+1); }
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bool has_free_var(context_entry const & e, unsigned low, unsigned high, metavar_env const & menv) {
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if (high <= low)
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return false;
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auto d = e.get_domain();
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auto b = e.get_body();
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return (d && has_free_var(*d, low, high, menv)) || (b && has_free_var(*b, low, high, menv));
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}
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bool has_free_var_ge(expr const & e, unsigned low, metavar_env const & menv) { return has_free_var(e, low, std::numeric_limits<unsigned>::max(), menv); }
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bool has_free_var_ge(expr const & e, unsigned low) { return has_free_var(e, low, std::numeric_limits<unsigned>::max()); }
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expr lower_free_vars(expr const & e, unsigned s, unsigned d, optional<metavar_env> const & DEBUG_CODE(menv)) {
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if (d == 0)
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return e;
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lean_assert(s >= d);
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lean_assert(!has_free_var(e, s-d, s, menv));
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return replace(e, [=](expr const & e, unsigned offset) -> expr {
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if (is_var(e) && var_idx(e) >= s + offset) {
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lean_assert(var_idx(e) >= offset + d);
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return mk_var(var_idx(e) - d);
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} else {
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return e;
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}
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});
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}
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expr lower_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const & menv) { return lower_free_vars(e, s, d, some_menv(menv)); }
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expr lower_free_vars(expr const & e, unsigned s, unsigned d) { return lower_free_vars(e, s, d, none_menv()); }
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expr lower_free_vars(expr const & e, unsigned d, optional<metavar_env> const & menv) { return lower_free_vars(e, d, d, menv); }
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expr lower_free_vars(expr const & e, unsigned d, metavar_env const & menv) { return lower_free_vars(e, d, d, menv); }
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expr lower_free_vars(expr const & e, unsigned d) { return lower_free_vars(e, d, d); }
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context_entry lower_free_vars(context_entry const & e, unsigned s, unsigned d, metavar_env const & menv) {
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auto domain = e.get_domain();
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auto body = e.get_body();
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if (domain && body)
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return context_entry(e.get_name(), lower_free_vars(*domain, s, d, menv), lower_free_vars(*body, s, d, menv));
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else if (domain)
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return context_entry(e.get_name(), lower_free_vars(*domain, s, d, menv));
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else
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return context_entry(e.get_name(), none_expr(), lower_free_vars(*body, s, d, menv));
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}
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expr lift_free_vars(expr const & e, unsigned s, unsigned d, optional<metavar_env> const & menv) {
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if (d == 0)
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return e;
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return replace(e, [=](expr const & e, unsigned offset) -> expr {
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if (is_var(e) && var_idx(e) >= s + offset) {
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return mk_var(var_idx(e) + d);
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} else if (is_metavar(e)) {
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return add_lift(e, s + offset, d, menv);
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} else {
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return e;
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}
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});
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}
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expr lift_free_vars(expr const & e, unsigned s, unsigned d, metavar_env const & menv) { return lift_free_vars(e, s, d, some_menv(menv)); }
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expr lift_free_vars(expr const & e, unsigned s, unsigned d) { return lift_free_vars(e, s, d, none_menv()); }
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expr lift_free_vars(expr const & e, unsigned d, optional<metavar_env> const & menv) { return lift_free_vars(e, 0, d, menv); }
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expr lift_free_vars(expr const & e, unsigned d) { return lift_free_vars(e, 0, d); }
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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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context_entry lift_free_vars(context_entry const & e, unsigned s, unsigned d, metavar_env const & menv) {
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auto domain = e.get_domain();
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auto body = e.get_body();
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if (domain && body)
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return context_entry(e.get_name(), lift_free_vars(*domain, s, d, menv), lift_free_vars(*body, s, d, menv));
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else if (domain)
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return context_entry(e.get_name(), lift_free_vars(*domain, s, d, menv));
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else
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return context_entry(e.get_name(), none_expr(), lift_free_vars(*body, s, d, menv));
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}
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}
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