lean2/src/kernel/free_vars.cpp

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