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lean2/src/kernel/expr.cpp

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/*
Copyright (c) 2013-2014 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 <limits>
#include "util/list_fn.h"
#include "util/hash.h"
#include "util/buffer.h"
#include "util/object_serializer.h"
#include "util/lru_cache.h"
#include "util/memory_pool.h"
#include "kernel/expr.h"
#include "kernel/expr_eq_fn.h"
#include "kernel/free_vars.h"
#include "kernel/for_each_fn.h"
#ifndef LEAN_INITIAL_EXPR_CACHE_CAPACITY
#define LEAN_INITIAL_EXPR_CACHE_CAPACITY 1024*16
#endif
namespace lean {
unsigned add_weight(unsigned w1, unsigned w2) {
unsigned r = w1 + w2;
if (r < w1)
r = std::numeric_limits<unsigned>::max(); // overflow
return r;
}
unsigned inc_weight(unsigned w) {
if (w < std::numeric_limits<unsigned>::max())
return w+1;
else
return w;
}
static expr * g_dummy = nullptr;
expr::expr():expr(*g_dummy) {}
unsigned hash_levels(levels const & ls) {
unsigned r = 23;
for (auto const & l : ls)
r = hash(hash(l), r);
return r;
}
LEAN_THREAD_VALUE(unsigned, g_hash_alloc_counter, 0);
expr_cell::expr_cell(expr_kind k, unsigned h, bool has_expr_mv, bool has_univ_mv,
bool has_local, bool has_param_univ, tag g):
m_flags(0),
m_kind(static_cast<unsigned>(k)),
m_has_expr_mv(has_expr_mv),
m_has_univ_mv(has_univ_mv),
m_has_local(has_local),
m_has_param_univ(has_param_univ),
m_hash(h),
m_tag(g),
m_rc(0) {
// m_hash_alloc does not need to be a unique identifier.
// We want diverse hash codes because 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
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);
}
}
optional<bool> expr_cell::is_arrow() const {
// it is stored in bits 0-1
unsigned r = (m_flags & (1+2));
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 ? 1 : 2;
m_flags |= mask;
lean_assert(is_arrow() && *is_arrow() == flag);
}
void expr_cell::set_tag(tag t) {
m_tag = t;
}
bool is_meta(expr const & e) {
return is_metavar(get_app_fn(e));
}
// Expr variables
DEF_THREAD_MEMORY_POOL(get_var_allocator, sizeof(expr_var));
expr_var::expr_var(unsigned idx, tag g):
expr_cell(expr_kind::Var, idx, false, false, false, false, g),
m_vidx(idx) {
if (idx == std::numeric_limits<unsigned>::max())
throw exception("invalid free variable index, de Bruijn index is too big");
}
void expr_var::dealloc() {
this->~expr_var();
get_var_allocator().recycle(this);
}
// Expr constants
DEF_THREAD_MEMORY_POOL(get_const_allocator, sizeof(expr_const));
expr_const::expr_const(name const & n, levels const & ls, tag g):
expr_cell(expr_kind::Constant, ::lean::hash(n.hash(), hash_levels(ls)), false,
has_meta(ls), false, has_param(ls), g),
m_name(n),
m_levels(ls) {
}
void expr_const::dealloc() {
this->~expr_const();
get_const_allocator().recycle(this);
}
unsigned binder_info::hash() const {
return (m_implicit << 4) | (m_cast << 3) | (m_contextual << 2) | (m_strict_implicit << 1) | m_inst_implicit;
}
// Expr metavariables and local variables
DEF_THREAD_MEMORY_POOL(get_mlocal_allocator, sizeof(expr_mlocal));
expr_mlocal::expr_mlocal(bool is_meta, name const & n, expr const & t, tag g):
expr_composite(is_meta ? expr_kind::Meta : expr_kind::Local, n.hash(), is_meta || t.has_expr_metavar(), t.has_univ_metavar(),
!is_meta || t.has_local(), t.has_param_univ(),
1, get_free_var_range(t), g),
m_name(n),
m_type(t) {}
void expr_mlocal::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_type, todelete);
this->~expr_mlocal();
get_mlocal_allocator().recycle(this);
}
DEF_THREAD_MEMORY_POOL(get_local_allocator, sizeof(expr_local));
expr_local::expr_local(name const & n, name const & pp_name, expr const & t, binder_info const & bi, tag g):
expr_mlocal(false, n, t, g),
m_pp_name(pp_name),
m_bi(bi) {}
void expr_local::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_type, todelete);
this->~expr_local();
get_local_allocator().recycle(this);
}
// Composite expressions
expr_composite::expr_composite(expr_kind k, unsigned h, bool has_expr_mv, bool has_univ_mv,
bool has_local, bool has_param_univ, unsigned w, unsigned fv_range, tag g):
expr_cell(k, h, has_expr_mv, has_univ_mv, has_local, has_param_univ, g),
m_weight(w),
m_free_var_range(fv_range) {}
// Expr applications
DEF_THREAD_MEMORY_POOL(get_app_allocator, sizeof(expr_app));
expr_app::expr_app(expr const & fn, expr const & arg, tag g):
expr_composite(expr_kind::App, ::lean::hash(fn.hash(), arg.hash()),
fn.has_expr_metavar() || arg.has_expr_metavar(),
fn.has_univ_metavar() || arg.has_univ_metavar(),
fn.has_local() || arg.has_local(),
fn.has_param_univ() || arg.has_param_univ(),
inc_weight(add_weight(get_weight(fn), get_weight(arg))),
std::max(get_free_var_range(fn), get_free_var_range(arg)),
g),
m_fn(fn), m_arg(arg) {
m_hash = ::lean::hash(m_hash, m_weight);
}
void expr_app::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_fn, todelete);
dec_ref(m_arg, todelete);
this->~expr_app();
get_app_allocator().recycle(this);
}
static unsigned dec(unsigned k) { return k == 0 ? 0 : k - 1; }
bool operator==(binder_info const & i1, binder_info const & i2) {
return
i1.is_implicit() == i2.is_implicit() &&
i1.is_cast() == i2.is_cast() &&
i1.is_contextual() == i2.is_contextual() &&
i1.is_strict_implicit() == i2.is_strict_implicit() &&
i1.is_inst_implicit() == i2.is_inst_implicit();
}
// Expr binders (Lambda, Pi)
DEF_THREAD_MEMORY_POOL(get_binding_allocator, sizeof(expr_binding));
expr_binding::expr_binding(expr_kind k, name const & n, expr const & t, expr const & b, binder_info const & i, tag g):
expr_composite(k, ::lean::hash(t.hash(), b.hash()),
t.has_expr_metavar() || b.has_expr_metavar(),
t.has_univ_metavar() || b.has_univ_metavar(),
t.has_local() || b.has_local(),
t.has_param_univ() || b.has_param_univ(),
inc_weight(add_weight(get_weight(t), get_weight(b))),
std::max(get_free_var_range(t), dec(get_free_var_range(b))),
g),
m_binder(n, t, i),
m_body(b) {
m_hash = ::lean::hash(m_hash, m_weight);
lean_assert(k == expr_kind::Lambda || k == expr_kind::Pi);
}
void expr_binding::dealloc(buffer<expr_cell*> & todelete) {
dec_ref(m_body, todelete);
dec_ref(m_binder.m_type, todelete);
this->~expr_binding();
get_binding_allocator().recycle(this);
}
// Expr Sort
DEF_THREAD_MEMORY_POOL(get_sort_allocator, sizeof(expr_sort));
expr_sort::expr_sort(level const & l, tag g):
expr_cell(expr_kind::Sort, ::lean::hash(l), false, has_meta(l), false, has_param(l), g),
m_level(l) {
}
expr_sort::~expr_sort() {}
void expr_sort::dealloc() {
this->~expr_sort();
get_sort_allocator().recycle(this);
}
// Macro definition
bool macro_definition_cell::lt(macro_definition_cell const &) const { return false; }
bool macro_definition_cell::operator==(macro_definition_cell const & other) const { return typeid(*this) == typeid(other); }
unsigned macro_definition_cell::trust_level() const { return 0; }
format macro_definition_cell::pp(formatter const &) const { return format(get_name()); }
void macro_definition_cell::display(std::ostream & out) const { out << get_name(); }
bool macro_definition_cell::is_atomic_pp(bool, bool) const { return true; }
unsigned macro_definition_cell::hash() const { return get_name().hash(); }
macro_definition::macro_definition(macro_definition_cell * ptr):m_ptr(ptr) { lean_assert(m_ptr); m_ptr->inc_ref(); }
macro_definition::macro_definition(macro_definition const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
macro_definition::macro_definition(macro_definition && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
macro_definition::~macro_definition() { if (m_ptr) m_ptr->dec_ref(); }
macro_definition & macro_definition::operator=(macro_definition const & s) { LEAN_COPY_REF(s); }
macro_definition & macro_definition::operator=(macro_definition && s) { LEAN_MOVE_REF(s); }
bool macro_definition::operator<(macro_definition const & other) const {
if (get_name() == other.get_name())
return m_ptr->lt(*other.m_ptr);
else
return get_name() < other.get_name();
}
static unsigned add_weight(unsigned num, expr const * args) {
unsigned r = 0;
for (unsigned i = 0; i < num; i++)
r = add_weight(r, get_weight(args[i]));
return r;
}
static unsigned get_free_var_range(unsigned num, expr const * args) {
unsigned r = 0;
for (unsigned i = 0; i < num; i++) {
unsigned d = get_free_var_range(args[i]);
if (d > r)
r = d;
}
return r;
}
expr_macro::expr_macro(macro_definition const & m, unsigned num, expr const * args, tag g):
expr_composite(expr_kind::Macro,
lean::hash(num, [&](unsigned i) { return args[i].hash(); }, m.hash()),
std::any_of(args, args+num, [](expr const & e) { return e.has_expr_metavar(); }),
std::any_of(args, args+num, [](expr const & e) { return e.has_univ_metavar(); }),
std::any_of(args, args+num, [](expr const & e) { return e.has_local(); }),
std::any_of(args, args+num, [](expr const & e) { return e.has_param_univ(); }),
inc_weight(add_weight(num, args)),
get_free_var_range(num, args),
g),
m_definition(m),
m_num_args(num) {
m_args = new expr[num];
for (unsigned i = 0; i < m_num_args; i++)
m_args[i] = args[i];
}
void expr_macro::dealloc(buffer<expr_cell*> & todelete) {
for (unsigned i = 0; i < m_num_args; i++) dec_ref(m_args[i], todelete);
delete(this);
}
expr_macro::~expr_macro() {
delete[] m_args;
}
// =======================================
// Constructors
#ifdef LEAN_CACHE_EXPRS
typedef lru_cache<expr, expr_hash, is_bi_equal_proc> expr_cache;
LEAN_THREAD_VALUE(bool, g_expr_cache_enabled, true);
MK_THREAD_LOCAL_GET(expr_cache, get_expr_cache, LEAN_INITIAL_EXPR_CACHE_CAPACITY);
bool enable_expr_caching(bool f) {
bool r = g_expr_cache_enabled;
g_expr_cache_enabled = f;
return r;
}
inline expr cache(expr const & e) {
if (g_expr_cache_enabled) {
if (auto r = get_expr_cache().insert(e))
return *r;
}
return e;
}
#else
inline expr cache(expr && e) { return e; }
bool enable_expr_caching(bool) { return true; } // NOLINT
#endif
expr mk_var(unsigned idx, tag g) {
return cache(expr(new (get_var_allocator().allocate()) expr_var(idx, g)));
}
expr mk_constant(name const & n, levels const & ls, tag g) {
return cache(expr(new (get_const_allocator().allocate()) expr_const(n, ls, g)));
}
expr mk_macro(macro_definition const & m, unsigned num, expr const * args, tag g) {
return cache(expr(new expr_macro(m, num, args, g)));
}
expr mk_metavar(name const & n, expr const & t, tag g) {
return cache(expr(new (get_mlocal_allocator().allocate()) expr_mlocal(true, n, t, g)));
}
expr mk_local(name const & n, name const & pp_n, expr const & t, binder_info const & bi, tag g) {
return cache(expr(new (get_local_allocator().allocate()) expr_local(n, pp_n, t, bi, g)));
}
expr mk_app(expr const & f, expr const & a, tag g) {
return cache(expr(new (get_app_allocator().allocate()) expr_app(f, a, g)));
}
expr mk_binding(expr_kind k, name const & n, expr const & t, expr const & e, binder_info const & i, tag g) {
return cache(expr(new (get_binding_allocator().allocate()) expr_binding(k, n, t, e, i, g)));
}
expr mk_sort(level const & l, tag g) {
return cache(expr(new (get_sort_allocator().allocate()) expr_sort(l, g)));
}
// =======================================
typedef buffer<expr_cell*> del_buffer;
void expr_cell::dealloc() {
try {
del_buffer 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: static_cast<expr_var*>(it)->dealloc(); break;
case expr_kind::Macro: static_cast<expr_macro*>(it)->dealloc(todo); break;
case expr_kind::Meta: static_cast<expr_mlocal*>(it)->dealloc(todo); break;
case expr_kind::Local: static_cast<expr_local*>(it)->dealloc(todo); break;
case expr_kind::Constant: static_cast<expr_const*>(it)->dealloc(); break;
case expr_kind::Sort: static_cast<expr_sort*>(it)->dealloc(); break;
case expr_kind::App: static_cast<expr_app*>(it)->dealloc(todo); break;
case expr_kind::Lambda:
case expr_kind::Pi: static_cast<expr_binding*>(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.
}
}
// Auxiliary constructors
expr mk_app(expr const & f, unsigned num_args, expr const * args, tag g) {
expr r = f;
for (unsigned i = 0; i < num_args; i++)
r = mk_app(r, args[i], g);
return r;
}
expr mk_app(unsigned num_args, expr const * args, tag g) {
lean_assert(num_args >= 2);
return mk_app(mk_app(args[0], args[1], g), num_args - 2, args+2, g);
}
expr mk_rev_app(expr const & f, unsigned num_args, expr const * args, tag g) {
expr r = f;
unsigned i = num_args;
while (i > 0) {
--i;
r = mk_app(r, args[i], g);
}
return r;
}
expr mk_rev_app(unsigned num_args, expr const * args, tag g) {
lean_assert(num_args >= 2);
return mk_rev_app(mk_app(args[num_args-1], args[num_args-2], g), num_args-2, args, g);
}
expr mk_app_vars(expr const & f, unsigned n, tag g) {
expr r = f;
while (n > 0) {
--n;
r = mk_app(r, mk_var(n, g), g);
}
return r;
}
expr const & get_app_args(expr const & e, buffer<expr> & args) {
unsigned sz = args.size();
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
std::reverse(args.begin() + sz, args.end());
return *it;
}
expr const & get_app_rev_args(expr const & e, buffer<expr> & args) {
expr const * it = &e;
while (is_app(*it)) {
args.push_back(app_arg(*it));
it = &(app_fn(*it));
}
return *it;
}
expr const & get_app_fn(expr const & e) {
expr const * it = &e;
while (is_app(*it)) {
it = &(app_fn(*it));
}
return *it;
}
unsigned get_app_num_args(expr const & e) {
expr const * it = &e;
unsigned n = 0;
while (is_app(*it)) {
it = &(app_fn(*it));
n++;
}
return n;
}
static name * g_default_name = nullptr;
static name const & get_default_var_name() {
return *g_default_name;
}
static name const & g_default_var_name = get_default_var_name(); // force it to be initialized
bool is_default_var_name(name const & n) { return n == get_default_var_name(); }
expr mk_arrow(expr const & t, expr const & e, tag g) {
return mk_pi(get_default_var_name(), t, e, binder_info(), g);
}
static expr * g_Prop = nullptr;
static expr * g_Type1 = nullptr;
expr mk_Prop() { return *g_Prop; }
expr mk_Type() { return *g_Type1; }
unsigned get_weight(expr const & e) {
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Meta: case expr_kind::Local:
return 1;
case expr_kind::Lambda: case expr_kind::Pi: case expr_kind::Macro:
case expr_kind::App:
return static_cast<expr_composite*>(e.raw())->m_weight;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
expr copy_tag(expr const & e, expr && new_e) {
tag t = e.get_tag();
if (t != nulltag)
new_e.set_tag(t);
return new_e;
}
expr update_app(expr const & e, expr const & new_fn, expr const & new_arg) {
if (!is_eqp(app_fn(e), new_fn) || !is_eqp(app_arg(e), new_arg))
return mk_app(new_fn, new_arg, e.get_tag());
else
return e;
}
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body) {
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body))
return mk_binding(e.kind(), binding_name(e), new_domain, new_body, binding_info(e), e.get_tag());
else
return e;
}
expr update_binding(expr const & e, expr const & new_domain, expr const & new_body, binder_info const & bi) {
if (!is_eqp(binding_domain(e), new_domain) || !is_eqp(binding_body(e), new_body) || bi != binding_info(e))
return mk_binding(e.kind(), binding_name(e), new_domain, new_body, bi, e.get_tag());
else
return e;
}
expr update_mlocal(expr const & e, expr const & new_type) {
if (is_eqp(mlocal_type(e), new_type))
return e;
else if (is_metavar(e))
return mk_metavar(mlocal_name(e), new_type, e.get_tag());
else
return mk_local(mlocal_name(e), local_pp_name(e), new_type, local_info(e), e.get_tag());
}
expr update_local(expr const & e, expr const & new_type, binder_info const & bi) {
if (is_eqp(mlocal_type(e), new_type) && local_info(e) == bi)
return e;
else
return mk_local(mlocal_name(e), local_pp_name(e), new_type, bi, e.get_tag());
}
expr update_local(expr const & e, binder_info const & bi) {
return update_local(e, mlocal_type(e), bi);
}
expr update_sort(expr const & e, level const & new_level) {
if (!is_eqp(sort_level(e), new_level))
return mk_sort(new_level, e.get_tag());
else
return e;
}
expr update_constant(expr const & e, levels const & new_levels) {
if (!is_eqp(const_levels(e), new_levels))
return mk_constant(const_name(e), new_levels, e.get_tag());
else
return e;
}
expr update_macro(expr const & e, unsigned num, expr const * args) {
if (num == macro_num_args(e)) {
unsigned i = 0;
for (i = 0; i < num; i++) {
if (!is_eqp(macro_arg(e, i), args[i]))
break;
}
if (i == num)
return e;
}
return mk_macro(to_macro(e)->m_definition, num, args, e.get_tag());
}
bool is_atomic(expr const & e) {
switch (e.kind()) {
case expr_kind::Constant: case expr_kind::Sort:
case expr_kind::Var:
return true;
case expr_kind::Macro:
return to_macro(e)->get_num_args() == 0;
case expr_kind::App: case expr_kind::Meta:
case expr_kind::Local: case expr_kind::Lambda:
case expr_kind::Pi:
return false;
}
lean_unreachable(); // LCOV_EXCL_LINE
}
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(binding_body(t), 0);
t.raw()->set_is_arrow(res);
return res;
}
}
optional<expr> has_expr_metavar_strict(expr const & e) {
if (!has_expr_metavar(e))
return none_expr();
optional<expr> r;
for_each(e, [&](expr const & e, unsigned) {
if (r || !has_expr_metavar(e)) return false;
if (is_meta(e)) { r = e; return false; }
if (is_local(e)) return false; // do not visit type
return true;
});
return r;
}
static bool has_free_var_in_domain(expr const & b, unsigned vidx) {
if (is_pi(b)) {
return has_free_var(binding_domain(b), vidx) || has_free_var_in_domain(binding_body(b), vidx+1);
} else {
return false;
}
}
expr infer_implicit(expr const & t, unsigned num_params, bool strict) {
if (num_params == 0) {
return t;
} else if (is_pi(t)) {
expr new_body = infer_implicit(binding_body(t), num_params-1, strict);
if (binding_info(t).is_implicit() || binding_info(t).is_strict_implicit()) {
// argument is already marked as implicit
return update_binding(t, binding_domain(t), new_body);
} else if ((strict && has_free_var_in_domain(new_body, 0)) ||
(!strict && has_free_var(new_body, 0))) {
return update_binding(t, binding_domain(t), new_body, mk_implicit_binder_info());
} else {
return update_binding(t, binding_domain(t), new_body);
}
} else {
return t;
}
}
expr infer_implicit(expr const & t, bool strict) {
return infer_implicit(t, std::numeric_limits<unsigned>::max(), strict);
}
unsigned hash_bi(expr const & e) {
unsigned h = e.hash();
for_each(e, [&](expr const & e, unsigned) {
if (is_binding(e)) {
h = hash(h, hash(binding_name(e).hash(), binding_info(e).hash()));
} else if (is_local(e)) {
h = hash(h, hash(mlocal_name(e).hash(), local_info(e).hash()));
return false; // do not visit type
} else if (is_metavar(e)) {
return false; // do not visit type
}
return true;
});
return h;
}
void initialize_expr() {
g_dummy = new expr(mk_var(0));
g_default_name = new name("a");
g_Type1 = new expr(mk_sort(mk_level_one()));
g_Prop = new expr(mk_sort(mk_level_zero()));
}
void finalize_expr() {
delete g_Prop;
delete g_Type1;
delete g_dummy;
delete g_default_name;
}
}
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