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lean2/src/kernel/expr.cpp
Leonardo de Moura 6bcd8e3ee5 fix(library/expr_lt): use expression depth instead of size to obtain a monotonic total order on terms 
It is not incorrect to use size, but it can easily overflow due to sharing.
The following script demonstrates the problem:

local f = Const("f")
local a = Const("a")
function mk_shared(d)
   if d == 0 then
      return a
   else
      local c = mk_shared(d-1)
      return f(c, c)
   end
end
print(mk_shared(33):size())

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 17:40:49 -08:00

488 lines
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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
Soonho Kong
*/
#include <vector>
#include <sstream>
#include <string>
#include <algorithm>
#include "util/hash.h"
#include "util/buffer.h"
#include "util/object_serializer.h"
#include "kernel/expr.h"
#include "kernel/free_vars.h"
#include "kernel/expr_eq.h"
#include "kernel/metavar.h"
#include "kernel/max_sharing.h"
namespace lean {
static expr g_dummy(mk_var(0));
expr::expr():expr(g_dummy) {}
local_entry::local_entry(unsigned s, unsigned n):m_kind(local_entry_kind::Lift), m_s(s), m_n(n) {}
local_entry::local_entry(unsigned s, expr const & v):m_kind(local_entry_kind::Inst), m_s(s), m_v(v) {}
local_entry::~local_entry() {}
bool local_entry::operator==(local_entry const & e) const {
if (m_kind != e.m_kind || m_s != e.m_s)
return false;
if (is_inst())
return m_v == e.m_v;
else
return m_n == e.m_n;
}
unsigned hash_args(unsigned size, expr const * args) {
return hash(size, [&args](unsigned i){ return args[i].hash(); });
}
expr_cell::expr_cell(expr_kind k, unsigned h, bool has_mv):
m_kind(static_cast<unsigned>(k)),
m_flags(has_mv ? 4 : 0),
m_hash(h),
m_rc(0) {
// m_hash_alloc does not need to be a unique identifier.
// We want diverse hash codes such that given expr_cell * c1 and expr_cell * c2,
// if c1 != c2, then there is high probability c1->m_hash_alloc != c2->m_hash_alloc.
// Remark: using pointer address as a hash code is not a good idea.
// - each execution run will behave differently.
// - the hash is not diverse enough
static LEAN_THREAD_LOCAL unsigned g_hash_alloc_counter = 0;
m_hash_alloc = g_hash_alloc_counter;
g_hash_alloc_counter++;
}
void expr_cell::dec_ref(expr & e, buffer<expr_cell*> & todelete) {
if (e.m_ptr) {
expr_cell * c = e.steal_ptr();
lean_assert(!(e.m_ptr));
if (c->dec_ref_core())
todelete.push_back(c);
}
}
void expr_cell::dec_ref(optional<expr> & c, buffer<expr_cell*> & todelete) {
if (c)
dec_ref(*c, todelete);
}
optional<bool> expr_cell::is_arrow() const {
// it is stored in bits 3-4
unsigned r = (m_flags & (8+16)) >> 3;
if (r == 0) {
return optional<bool>();
} else if (r == 1) {
return optional<bool>(true);
} else {
lean_assert(r == 2);
return optional<bool>(false);
}
}
void expr_cell::set_is_arrow(bool flag) {
unsigned mask = flag ? 8 : 16;
m_flags |= mask;
lean_assert(is_arrow() && *is_arrow() == flag);
}
expr_var::expr_var(unsigned idx):
expr_cell(expr_kind::Var, idx, false),
m_vidx(idx) {}
expr_const::expr_const(name const & n, optional<expr> const & t):
expr_cell(expr_kind::Constant, n.hash(), t && t->has_metavar()),
m_name(n),
m_type(t) {}
void expr_const::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_type, todelete);
delete(this);
}
expr_app::expr_app(unsigned num_args, bool has_mv):
expr_cell(expr_kind::App, 0, has_mv),
m_num_args(num_args) {
}
void expr_app::dealloc(buffer<expr_cell*> & todelete) {
unsigned i = m_num_args;
while (i > 0) {
--i;
dec_ref(m_args[i], todelete);
}
delete[] reinterpret_cast<char*>(this);
}
expr mk_app(unsigned n, expr const * as) {
lean_assert(n > 1);
unsigned new_n;
unsigned n0 = 0;
expr const & arg0 = as[0];
bool has_mv = std::any_of(as, as + n, [](expr const & c) { return c.has_metavar(); });
// Remark: we represent ((app a b) c) as (app a b c)
if (is_app(arg0)) {
n0 = num_args(arg0);
new_n = n + n0 - 1;
} else {
new_n = n;
}
char * mem = new char[sizeof(expr_app) + new_n*sizeof(expr)];
expr r(new (mem) expr_app(new_n, has_mv));
expr * m_args = to_app(r)->m_args;
unsigned i = 0;
unsigned j = 0;
unsigned depth = 0;
if (new_n != n) {
for (; i < n0; ++i) {
new (m_args+i) expr(arg(arg0, i));
depth = std::max(depth, get_depth(m_args[i]));
}
j++;
}
for (; i < new_n; ++i, ++j) {
lean_assert(j < n);
new (m_args+i) expr(as[j]);
depth = std::max(depth, get_depth(m_args[i]));
}
to_app(r)->m_hash = hash_args(new_n, m_args);
to_app(r)->m_depth = depth + 1;
return r;
}
expr_abstraction::expr_abstraction(expr_kind k, name const & n, expr const & t, expr const & b):
expr_cell(k, ::lean::hash(t.hash(), b.hash()), t.has_metavar() || b.has_metavar()),
m_name(n),
m_domain(t),
m_body(b) {
m_depth = 1 + std::max(get_depth(m_domain), get_depth(m_body));
}
void expr_abstraction::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_body, todelete);
dec_ref(m_domain, todelete);
delete(this);
}
expr_lambda::expr_lambda(name const & n, expr const & t, expr const & e):expr_abstraction(expr_kind::Lambda, n, t, e) {}
expr_pi::expr_pi(name const & n, expr const & t, expr const & e):expr_abstraction(expr_kind::Pi, n, t, e) {}
expr_type::expr_type(level const & l):
expr_cell(expr_kind::Type, l.hash(), false),
m_level(l) {
}
expr_type::~expr_type() {}
expr_let::expr_let(name const & n, optional<expr> const & t, expr const & v, expr const & b):
expr_cell(expr_kind::Let, ::lean::hash(v.hash(), b.hash()), v.has_metavar() || b.has_metavar() || (t && t->has_metavar())),
m_name(n),
m_type(t),
m_value(v),
m_body(b) {
unsigned depth = std::max(get_depth(m_value), get_depth(m_body));
if (m_type)
depth = std::max(depth, get_depth(*m_type));
m_depth = 1 + depth;
}
void expr_let::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_body, todelete);
dec_ref(m_value, todelete);
dec_ref(m_type, todelete);
delete(this);
}
expr_let::~expr_let() {}
name value::get_unicode_name() const { return get_name(); }
optional<expr> value::normalize(unsigned, expr const *) const { return none_expr(); }
void value::display(std::ostream & out) const { out << get_name(); }
bool value::operator==(value const & other) const { return typeid(*this) == typeid(other); }
bool value::operator<(value const & other) const {
if (get_name() == other.get_name())
return lt(other);
else
return get_name() < other.get_name();
}
format value::pp() const { return format(get_name()); }
format value::pp(bool unicode, bool) const { return unicode ? format(get_unicode_name()) : pp(); }
unsigned value::hash() const { return get_name().hash(); }
int value::push_lua(lua_State *) const { return 0; } // NOLINT
expr_value::expr_value(value & v):
expr_cell(expr_kind::Value, v.hash(), false),
m_val(v) {
m_val.inc_ref();
}
expr_value::~expr_value() {
m_val.dec_ref();
}
typedef std::unordered_map<std::string, value::reader> value_readers;
static std::unique_ptr<value_readers> g_value_readers;
value_readers & get_value_readers() {
if (!g_value_readers)
g_value_readers.reset(new value_readers());
return *(g_value_readers.get());
}
void value::register_deserializer(std::string const & k, value::reader rd) {
value_readers & readers = get_value_readers();
lean_assert(readers.find(k) == readers.end());
readers[k] = rd;
}
static expr read_value(deserializer & d) {
auto k = d.read_string();
value_readers & readers = get_value_readers();
auto it = readers.find(k);
lean_assert(it != readers.end());
return it->second(d);
}
expr_metavar::expr_metavar(name const & n, local_context const & lctx):
expr_cell(expr_kind::MetaVar, n.hash(), true),
m_name(n), m_lctx(lctx) {}
expr_metavar::~expr_metavar() {}
void expr_cell::dealloc() {
try {
buffer<expr_cell*> todo;
todo.push_back(this);
while (!todo.empty()) {
expr_cell * it = todo.back();
todo.pop_back();
lean_assert(it->get_rc() == 0);
switch (it->kind()) {
case expr_kind::Var: delete static_cast<expr_var*>(it); break;
case expr_kind::Value: delete static_cast<expr_value*>(it); break;
case expr_kind::MetaVar: delete static_cast<expr_metavar*>(it); break;
case expr_kind::Type: delete static_cast<expr_type*>(it); break;
case expr_kind::Constant: static_cast<expr_const*>(it)->dealloc(todo); break;
case expr_kind::App: static_cast<expr_app*>(it)->dealloc(todo); break;
case expr_kind::Lambda: static_cast<expr_lambda*>(it)->dealloc(todo); break;
case expr_kind::Pi: static_cast<expr_pi*>(it)->dealloc(todo); break;
case expr_kind::Let: static_cast<expr_let*>(it)->dealloc(todo); break;
}
}
} catch (std::bad_alloc&) {
// We need this catch, because push_back may fail when expanding the buffer.
// In this case, we avoid the crash, and "accept" the memory leak.
}
}
expr mk_type() {
static LEAN_THREAD_LOCAL expr r = mk_type(level());
return r;
}
bool operator==(expr const & a, expr const & b) {
return expr_eq_fn<>()(a, b);
}
bool is_arrow(expr const & t) {
optional<bool> r = t.raw()->is_arrow();
if (r) {
return *r;
} else {
bool res = is_pi(t) && !has_free_var(abst_body(t), 0);
t.raw()->set_is_arrow(res);
return res;
}
}
unsigned get_depth(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Type:
case expr_kind::Value: case expr_kind::MetaVar:
return 1;
case expr_kind::App:
return to_app(e)->m_depth;
case expr_kind::Pi: case expr_kind::Lambda:
return to_abstraction(e)->m_depth;
case expr_kind::Let:
return to_let(e)->m_depth;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr copy(expr const & a) {
switch (a.kind()) {
case expr_kind::Var: return mk_var(var_idx(a));
case expr_kind::Constant: return mk_constant(const_name(a), const_type(a));
case expr_kind::Type: return mk_type(ty_level(a));
case expr_kind::Value: return mk_value(static_cast<expr_value*>(a.raw())->m_val);
case expr_kind::App: return mk_app(num_args(a), begin_args(a));
case expr_kind::Lambda: return mk_lambda(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Pi: return mk_pi(abst_name(a), abst_domain(a), abst_body(a));
case expr_kind::Let: return mk_let(let_name(a), let_type(a), let_value(a), let_body(a));
case expr_kind::MetaVar: return mk_metavar(metavar_name(a), metavar_lctx(a));
}
lean_unreachable(); // LCOV_EXCL_LINE
}
serializer & operator<<(serializer & s, local_context const & lctx) {
s << length(lctx);
for (auto const & e : lctx) {
if (e.is_lift()) {
s << true << e.s() << e.n();
} else {
s << false << e.s() << e.v();
}
}
return s;
}
local_context read_local_context(deserializer & d) {
unsigned num = d.read_unsigned();
buffer<local_entry> entries;
for (unsigned i = 0; i < num; i++) {
if (d.read_bool()) {
unsigned s, n;
d >> s >> n;
entries.push_back(mk_lift(s, n));
} else {
unsigned s; expr v;
d >> s >> v;
entries.push_back(mk_inst(s, v));
}
}
return to_list(entries.begin(), entries.end());
}
// To save space, we pack the number of arguments in small applications in the kind byte.
// The extra kinds start at g_first_app_size_kind. This value should be bigger than the
// real kinds. Moreover g_first_app_size_kind + g_small_app_num_args should fit in a byte.
constexpr char g_first_app_size_kind = 32;
constexpr char g_small_app_num_args = 32;
constexpr bool is_small(expr_kind k) { return 0 <= static_cast<char>(k) && static_cast<char>(k) < g_first_app_size_kind; }
static_assert(is_small(expr_kind::Var) && is_small(expr_kind::Constant) && is_small(expr_kind::Value) && is_small(expr_kind::App) &&
is_small(expr_kind::Lambda) && is_small(expr_kind::Pi) && is_small(expr_kind::Type) &&
is_small(expr_kind::Let) && is_small(expr_kind::MetaVar), "expr_kind is too big");
class expr_serializer : public object_serializer<expr, expr_hash_alloc, expr_eqp> {
typedef object_serializer<expr, expr_hash_alloc, expr_eqp> super;
max_sharing_fn m_max_sharing_fn;
void write_core(optional<expr> const & a) {
serializer & s = get_owner();
if (a) {
s << true;
write_core(*a);
} else {
s << false;
}
}
void write_core(expr const & a) {
auto k = a.kind();
char kc;
if (k == expr_kind::App && num_args(a) < g_small_app_num_args) {
kc = static_cast<char>(g_first_app_size_kind + num_args(a));
} else {
kc = static_cast<char>(k);
}
super::write_core(a, kc, [&]() {
serializer & s = get_owner();
if (kc >= static_cast<char>(g_first_app_size_kind)) {
// compressed application
for (unsigned i = 0; i < num_args(a); i++)
write_core(arg(a, i));
return;
}
switch (k) {
case expr_kind::Var: s << var_idx(a); break;
case expr_kind::Constant: s << const_name(a); write_core(const_type(a)); break;
case expr_kind::Type: s << ty_level(a); break;
case expr_kind::Value: to_value(a).write(s); break;
case expr_kind::App:
s << num_args(a);
for (unsigned i = 0; i < num_args(a); i++)
write_core(arg(a, i));
break;
case expr_kind::Lambda:
case expr_kind::Pi: s << abst_name(a); write_core(abst_domain(a)); write_core(abst_body(a)); break;
case expr_kind::Let: s << let_name(a); write_core(let_type(a)); write_core(let_value(a)); write_core(let_body(a)); break;
case expr_kind::MetaVar: s << metavar_name(a) << metavar_lctx(a); break;
}
});
}
public:
void write(expr const & a) {
write_core(m_max_sharing_fn(a));
}
};
class expr_deserializer : public object_deserializer<expr> {
typedef object_deserializer<expr> super;
public:
optional<expr> read_opt() {
deserializer & d = get_owner();
if (d.read_bool()) {
return some_expr(read());
} else {
return none_expr();
}
}
expr read() {
return super::read_core([&](char c) {
deserializer & d = get_owner();
if (c >= g_first_app_size_kind) {
// compressed application
unsigned num = c - g_first_app_size_kind;
buffer<expr> args;
for (unsigned i = 0; i < num; i++)
args.push_back(read());
return mk_app(args);
}
auto k = static_cast<expr_kind>(c);
switch (k) {
case expr_kind::Var:
return mk_var(d.read_unsigned());
case expr_kind::Constant: {
auto n = read_name(d);
return mk_constant(n, read_opt());
}
case expr_kind::Type:
return mk_type(read_level(d));
break;
case expr_kind::Value:
return read_value(d);
case expr_kind::App: {
buffer<expr> args;
unsigned num = d.read_unsigned();
for (unsigned i = 0; i < num; i++)
args.push_back(read());
return mk_app(args);
}
case expr_kind::Lambda: {
name n = read_name(d);
expr d = read();
return mk_lambda(n, d, read());
}
case expr_kind::Pi: {
name n = read_name(d);
expr d = read();
return mk_pi(n, d, read());
}
case expr_kind::Let: {
name n = read_name(d);
optional<expr> t = read_opt();
expr v = read();
return mk_let(n, t, v, read());
}
case expr_kind::MetaVar: {
name n = read_name(d);
return mk_metavar(n, read_local_context(d));
}}
throw_corrupted_file(); // LCOV_EXCL_LINE
});
}
};
struct expr_sd {
unsigned m_s_extid;
unsigned m_d_extid;
expr_sd() {
m_s_extid = serializer::register_extension([](){ return std::unique_ptr<serializer::extension>(new expr_serializer()); });
m_d_extid = deserializer::register_extension([](){ return std::unique_ptr<deserializer::extension>(new expr_deserializer()); });
}
};
static expr_sd g_expr_sd;
serializer & operator<<(serializer & s, expr const & n) {
s.get_extension<expr_serializer>(g_expr_sd.m_s_extid).write(n);
return s;
}
expr read_expr(deserializer & d) {
return d.get_extension<expr_deserializer>(g_expr_sd.m_d_extid).read();
}
}
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