max/lean4-htt
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions 2

feat(kernel): type checker with local_ctx

Browse source
This commit is contained in:
Leonardo de Moura 2018-06-11 09:51:17 -07:00
parent 26b47c2852
commit 50e50408eb
5 changed files with 981 additions and 87 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

2
src/kernel/CMakeLists.txt
View file

@ -1,6 +1,6 @@
add_library(kernel OBJECT level.cpp expr.cpp expr_eq_fn.cpp
for_each_fn.cpp replace_fn.cpp abstract.cpp
instantiate.cpp local_ctx.cpp declaration.cpp environment.cpp
old_type_checker.cpp normalizer_extension.cpp
type_checker.cpp old_type_checker.cpp normalizer_extension.cpp
init_module.cpp expr_cache.cpp equiv_manager.cpp quot.cpp
abstract_type_context.cpp inductive.cpp standard_kernel.cpp)

3
src/kernel/init_module.cpp
View file

@ -6,6 +6,7 @@ Author: Leonardo de Moura
*/
#include "kernel/environment.h"
#include "kernel/old_type_checker.h"
#include "kernel/type_checker.h"
#include "kernel/expr.h"
#include "kernel/level.h"
#include "kernel/declaration.h"
@ -18,6 +19,7 @@ void initialize_kernel_module() {
initialize_expr();
initialize_declaration();
initialize_old_type_checker();
initialize_type_checker();
initialize_environment();
initialize_quot();
initialize_local_ctx();
@ -28,6 +30,7 @@ void finalize_kernel_module() {
finalize_quot();
finalize_environment();
finalize_old_type_checker();
finalize_type_checker();
finalize_declaration();
finalize_expr();
finalize_level();

86
src/kernel/old_type_checker.cpp
View file

@ -708,92 +708,6 @@ old_type_checker::old_type_checker(environment const & env, bool memoize, bool n
old_type_checker::~old_type_checker() {}
void check_no_metavar(environment const & env, name const & n, expr const & e) {
if (has_metavar(e))
throw declaration_has_metavars_exception(env, n, e);
}
static void check_no_local(environment const & env, name const & n, expr const & e) {
if (has_local(e))
throw declaration_has_free_vars_exception(env, n, e);
}
void check_no_mlocal(environment const & env, name const & n, expr const & e) {
check_no_metavar(env, n, e);
check_no_local(env, n, e);
}
static void check_name(environment const & env, name const & n) {
if (env.find(n))
throw already_declared_exception(env, n);
}
static void check_duplicated_params(environment const & env, declaration const & d) {
level_param_names ls = d.get_univ_params();
while (!is_nil(ls)) {
auto const & p = head(ls);
ls = tail(ls);
if (std::find(ls.begin(), ls.end(), p) != ls.end()) {
throw kernel_exception(env, sstream() << "failed to add declaration to environment, "
<< "duplicate universe level parameter: '"
<< p << "'");
}
}
}
static void check_definition(environment const & env, declaration const & d, old_type_checker & checker) {
check_no_mlocal(env, d.get_name(), d.get_value());
expr val_type = checker.check(d.get_value(), d.get_univ_params());
if (!checker.is_def_eq(val_type, d.get_type())) {
throw definition_type_mismatch_exception(env, d, val_type);
}
}
static void check_decl_type(environment const & env, declaration const & d, old_type_checker & checker) {
check_no_mlocal(env, d.get_name(), d.get_type());
check_name(env, d.get_name());
check_duplicated_params(env, d);
expr sort = checker.check(d.get_type(), d.get_univ_params());
checker.ensure_sort(sort, d.get_type());
}
void check_decl_type(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
old_type_checker checker(env, memoize, non_meta_only);
check_decl_type(env, d, checker);
}
void check_decl_value(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
old_type_checker checker(env, memoize, non_meta_only);
if (d.is_definition()) {
check_definition(env, d, checker);
}
}
certified_declaration check(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
old_type_checker checker(env, memoize, non_meta_only);
check_decl_type(env, d, checker);
if (d.is_definition()) {
check_definition(env, d, checker);
}
return certified_declaration(env.get_id(), d);
}
certified_declaration certify_unchecked::certify(environment const & env, declaration const & d) {
if (env.trust_lvl() == 0)
throw kernel_exception(env, "environment trust level does not allow users to add declarations that were not type checked");
return certified_declaration(env.get_id(), d);
}
certified_declaration certify_unchecked::certify_or_check(environment const & env, declaration const & d) {
if (env.trust_lvl() == 0)
return check(env, d);
else
return certify(env, d);
}
void initialize_old_type_checker() {
g_id_delta = new name("id_delta");
g_dont_care = new expr(Const("dontcare"));

830
src/kernel/type_checker.cpp Normal file
View file

@ -0,0 +1,830 @@
/*
Copyright (c) 2013-14 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include <utility>
#include <vector>
#include "runtime/interrupt.h"
#include "runtime/sstream.h"
#include "runtime/flet.h"
#include "util/task.h"
#include "util/lbool.h"
#include "util/fresh_name.h"
#include "util/task_builder.h"
#include "kernel/type_checker.h"
#include "kernel/expr_maps.h"
#include "kernel/instantiate.h"
#include "kernel/kernel_exception.h"
#include "kernel/abstract.h"
#include "kernel/replace_fn.h"
#include "kernel/quot.h"
namespace lean {
static name * g_kernel_fresh = nullptr;
static expr * g_dont_care = nullptr;
optional<expr> type_checker::expand_macro(expr const & m) {
lean_assert(is_macro(m));
return macro_def(m).expand(m, *this);
}
/** \brief Return the body of the given binder, where the bound variable #0 is replaced with a fresh free variable.
It also returns the fresh variable. */
pair<expr, expr> type_checker::open_binding_body(expr const & e) {
expr fvar = m_lctx.mk_local_decl(m_name_generator, binding_name(e), binding_domain(e), binding_info(e));
return mk_pair(instantiate(binding_body(e), fvar), fvar);
}
/** \brief Make sure \c e "is" a sort, and return the corresponding sort.
If \c e is not a sort, then the whnf procedure is invoked.
\remark \c s is used to extract position (line number information) when an
error message is produced */
expr type_checker::ensure_sort_core(expr e, expr const & s) {
if (is_sort(e))
return e;
auto new_e = whnf(e);
if (is_sort(new_e)) {
return new_e;
} else {
throw type_expected_exception(m_env, m_lctx, s);
}
}
/** \brief Similar to \c ensure_sort, but makes sure \c e "is" a Pi. */
expr type_checker::ensure_pi_core(expr e, expr const & s) {
if (is_pi(e))
return e;
auto new_e = whnf(e);
if (is_pi(new_e)) {
return new_e;
} else {
throw function_expected_exception(m_env, m_lctx, s);
}
}
void type_checker::check_level(level const & l) {
if (m_params) {
if (auto n2 = get_undef_param(l, *m_params))
throw kernel_exception(m_env, sstream() << "invalid reference to undefined universe level parameter '"
<< *n2 << "'");
}
}
expr type_checker::infer_fvar(expr const & e) {
if (optional<local_decl> decl = m_lctx.find_local_decl(e)) {
return decl->get_type();
} else {
// TODO(Leo): delete after we refactor inductive datatype module
return mlocal_type(e);
throw kernel_exception(m_env, "unknown free variable");
}
}
expr type_checker::infer_constant(expr const & e, bool infer_only) {
declaration d = m_env.get(const_name(e));
auto const & ps = d.get_univ_params();
auto const & ls = const_levels(e);
if (length(ps) != length(ls))
throw kernel_exception(m_env, sstream() << "incorrect number of universe levels parameters for '"
<< const_name(e) << "', #"
<< length(ps) << " expected, #" << length(ls) << " provided");
if (!infer_only) {
if (m_non_meta_only && d.is_meta()) {
throw kernel_exception(m_env, sstream() << "invalid definition, it uses meta declaration '"
<< const_name(e) << "'");
}
for (level const & l : ls)
check_level(l);
}
return instantiate_type_univ_params(d, ls);
}
expr type_checker::infer_macro(expr const & e, bool infer_only) {
auto def = macro_def(e);
expr t = def.check_type(e, *this, infer_only);
/* TODO(Leo): macros will be deleted */
return t;
}
expr type_checker::infer_lambda(expr const & _e, bool infer_only) {
flet<local_ctx> save_lctx(m_lctx, m_lctx);
buffer<expr> fvars;
expr e = _e;
while (is_lambda(e)) {
expr d = instantiate_rev(binding_domain(e), fvars.size(), fvars.data());
expr fvar = m_lctx.mk_local_decl(m_name_generator, binding_name(e), d, binding_info(e));
fvars.push_back(fvar);
if (!infer_only) {
ensure_sort_core(infer_type_core(d, infer_only), d);
}
e = binding_body(e);
}
expr r = infer_type_core(instantiate_rev(e, fvars.size(), fvars.data()), infer_only);
return m_lctx.mk_pi(fvars, r);
}
expr type_checker::infer_pi(expr const & _e, bool infer_only) {
flet<local_ctx> save_lctx(m_lctx, m_lctx);
buffer<expr> fvars;
buffer<level> us;
expr e = _e;
while (is_pi(e)) {
expr d = instantiate_rev(binding_domain(e), fvars.size(), fvars.data());
expr t1 = ensure_sort_core(infer_type_core(d, infer_only), d);
us.push_back(sort_level(t1));
expr fvar = m_lctx.mk_local_decl(m_name_generator, binding_name(e), d, binding_info(e));
fvars.push_back(fvar);
e = binding_body(e);
}
e = instantiate_rev(e, fvars.size(), fvars.data());
expr s = ensure_sort_core(infer_type_core(e, infer_only), e);
level r = sort_level(s);
unsigned i = fvars.size();
while (i > 0) {
--i;
r = mk_imax(us[i], r);
}
return mk_sort(r);
}
expr type_checker::infer_app(expr const & e, bool infer_only) {
if (!infer_only) {
expr f_type = ensure_pi_core(infer_type_core(app_fn(e), infer_only), e);
expr a_type = infer_type_core(app_arg(e), infer_only);
expr d_type = binding_domain(f_type);
if (!is_def_eq(a_type, d_type)) {
throw app_type_mismatch_exception(m_env, m_lctx, e);
}
return instantiate(binding_body(f_type), app_arg(e));
} else {
buffer<expr> args;
expr const & f = get_app_args(e, args);
expr f_type = infer_type_core(f, true);
unsigned j = 0;
unsigned nargs = args.size();
for (unsigned i = 0; i < nargs; i++) {
if (is_pi(f_type)) {
f_type = binding_body(f_type);
} else {
f_type = instantiate_rev(f_type, i-j, args.data()+j);
f_type = ensure_pi_core(f_type, e);
f_type = binding_body(f_type);
j = i;
}
}
return instantiate_rev(f_type, nargs-j, args.data()+j);
}
}
expr type_checker::infer_let(expr const & _e, bool infer_only) {
flet<local_ctx> save_lctx(m_lctx, m_lctx);
buffer<expr> fvars;
expr e = _e;
while (is_let(e)) {
expr type = instantiate_rev(let_type(e), fvars.size(), fvars.data());
expr val = instantiate_rev(let_value(e), fvars.size(), fvars.data());
expr fvar = m_lctx.mk_local_decl(m_name_generator, let_name(e), type, val);
fvars.push_back(fvar);
if (!infer_only) {
ensure_sort_core(infer_type_core(type, infer_only), type);
expr val_type = infer_type_core(val, infer_only);
if (!is_def_eq(val_type, type)) {
throw def_type_mismatch_exception(m_env, m_lctx, let_name(e), val_type, type);
}
}
e = let_body(e);
}
expr r = infer_type_core(instantiate_rev(e, fvars.size(), fvars.data()), infer_only);
return m_lctx.mk_pi(fvars, r);
}
/** \brief Return type of expression \c e, if \c infer_only is false, then it also check whether \c e is type correct or not.
\pre closed(e) */
expr type_checker::infer_type_core(expr const & e, bool infer_only) {
if (is_bvar(e))
throw kernel_exception(m_env, "type checker does not support loose bound variables, replace them with free variables before invoking it");
lean_assert(!has_loose_bvars(e));
check_system("type checker");
if (m_memoize) {
auto it = m_infer_type_cache[infer_only].find(e);
if (it != m_infer_type_cache[infer_only].end())
return it->second;
}
expr r;
switch (e.kind()) {
case expr_kind::FVar: r = infer_fvar(e); break;
case expr_kind::Meta: r = mlocal_type(e); break;
case expr_kind::BVar:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Sort:
if (!infer_only) check_level(sort_level(e));
r = mk_sort(mk_succ(sort_level(e)));
break;
case expr_kind::Constant: r = infer_constant(e, infer_only); break;
case expr_kind::Macro: r = infer_macro(e, infer_only); break;
case expr_kind::Lambda: r = infer_lambda(e, infer_only); break;
case expr_kind::Pi: r = infer_pi(e, infer_only); break;
case expr_kind::App: r = infer_app(e, infer_only); break;
case expr_kind::Let: r = infer_let(e, infer_only); break;
}
if (m_memoize)
m_infer_type_cache[infer_only].insert(mk_pair(e, r));
return r;
}
expr type_checker::infer_type(expr const & e) {
return infer_type_core(e, true);
}
expr type_checker::check(expr const & e, level_param_names const & ps) {
flet<level_param_names const *> updt(m_params, &ps);
return infer_type_core(e, false);
}
expr type_checker::check_ignore_undefined_universes(expr const & e) {
flet<level_param_names const *> updt(m_params, nullptr);
return infer_type_core(e, false);
}
expr type_checker::ensure_sort(expr const & e, expr const & s) {
return ensure_sort_core(e, s);
}
expr type_checker::ensure_pi(expr const & e, expr const & s) {
return ensure_pi_core(e, s);
}
/** \brief Return true iff \c e is a proposition */
bool type_checker::is_prop(expr const & e) {
return whnf(infer_type(e)) == mk_Prop();
}
/** \brief Apply normalizer extensions to \c e. */
optional<expr> type_checker::norm_ext(expr const & e) {
if (m_env.is_quot_initialized()) {
if (optional<expr> r = quot_reduce_rec(e, [&](expr const & e) { return whnf(e); })) {
return r;
}
}
return m_env.norm_ext()(e, *this);
}
expr type_checker::whnf_fvar(expr const & e) {
if (optional<local_decl> decl = m_lctx.find_local_decl(e)) {
if (optional<expr> const & v = decl->get_value()) {
/* zeta-reduction */
return *v;
}
}
return e;
}
/** \brief Weak head normal form core procedure. It does not perform delta reduction nor normalization extensions. */
expr type_checker::whnf_core(expr const & e) {
check_system("whnf");
// handle easy cases
switch (e.kind()) {
case expr_kind::BVar: case expr_kind::Sort: case expr_kind::Meta:
case expr_kind::Pi: case expr_kind::Constant: case expr_kind::Lambda:
return e;
case expr_kind::FVar:
return whnf_fvar(e);
case expr_kind::Macro: case expr_kind::App: case expr_kind::Let:
break;
}
// check cache
if (m_memoize) {
auto it = m_whnf_core_cache.find(e);
if (it != m_whnf_core_cache.end())
return it->second;
}
// do the actual work
expr r;
switch (e.kind()) {
case expr_kind::BVar: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::FVar:
case expr_kind::Pi: case expr_kind::Constant: case expr_kind::Lambda:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Macro:
if (auto m = expand_macro(e))
r = whnf_core(*m);
else
r = e;
break;
case expr_kind::App: {
buffer<expr> args;
expr f0 = get_app_rev_args(e, args);
expr f = whnf_core(f0);
if (is_lambda(f)) {
unsigned m = 1;
unsigned num_args = args.size();
while (is_lambda(binding_body(f)) && m < num_args) {
f = binding_body(f);
m++;
}
lean_assert(m <= num_args);
r = whnf_core(mk_rev_app(instantiate(binding_body(f), m, args.data() + (num_args - m)), num_args - m, args.data()));
} else if (f == f0) {
if (auto r = norm_ext(e)) {
/* mainly iota-reduction, it also applies HIT and quotient reduction rules */
return whnf_core(*r);
} else {
return e;
}
} else {
r = whnf_core(mk_rev_app(f, args.size(), args.data()));
}
break;
}
case expr_kind::Let:
r = whnf_core(instantiate(let_body(e), let_value(e)));
break;
}
if (m_memoize)
m_whnf_core_cache.insert(mk_pair(e, r));
return r;
}
/** \brief Return some definition \c d iff \c e is a target for delta-reduction, and the given definition is the one
to be expanded. */
optional<declaration> type_checker::is_delta(expr const & e) const {
expr const & f = get_app_fn(e);
if (is_constant(f)) {
if (auto d = m_env.find(const_name(f)))
if (d->is_definition())
return d;
}
return none_declaration();
}
optional<expr> type_checker::unfold_definition_core(expr const & e) {
if (is_constant(e)) {
if (auto d = is_delta(e)) {
if (length(const_levels(e)) == d->get_num_univ_params())
return some_expr(instantiate_value_univ_params(*d, const_levels(e)));
}
}
return none_expr();
}
/* Unfold head(e) if it is a constant */
optional<expr> type_checker::unfold_definition(expr const & e) {
if (is_app(e)) {
expr f0 = get_app_fn(e);
if (auto f = unfold_definition_core(f0)) {
buffer<expr> args;
get_app_rev_args(e, args);
return some_expr(mk_rev_app(*f, args));
} else {
return none_expr();
}
} else {
return unfold_definition_core(e);
}
}
/** \brief Put expression \c t in weak head normal form */
expr type_checker::whnf(expr const & e) {
// Do not cache easy cases
switch (e.kind()) {
case expr_kind::BVar: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Pi:
return e;
case expr_kind::FVar:
return whnf_fvar(e);
case expr_kind::Lambda: case expr_kind::Macro: case expr_kind::App:
case expr_kind::Constant: case expr_kind::Let:
break;
}
// check cache
if (m_memoize) {
auto it = m_whnf_cache.find(e);
if (it != m_whnf_cache.end())
return it->second;
}
expr t = e;
while (true) {
expr t1 = whnf_core(t);
if (auto next_t = unfold_definition(t1)) {
t = *next_t;
} else {
auto r = t1;
if (m_memoize)
m_whnf_cache.insert(mk_pair(e, r));
return r;
}
}
}
/** \brief Given lambda/Pi expressions \c t and \c s, return true iff \c t is def eq to \c s.
t and s are definitionally equal
iff
domain(t) is definitionally equal to domain(s)
and
body(t) is definitionally equal to body(s) */
bool type_checker::is_def_eq_binding(expr t, expr s) {
lean_assert(t.kind() == s.kind());
lean_assert(is_binding(t));
flet<local_ctx> save_lctx(m_lctx, m_lctx);
expr_kind k = t.kind();
buffer<expr> subst;
do {
optional<expr> var_s_type;
if (binding_domain(t) != binding_domain(s)) {
var_s_type = instantiate_rev(binding_domain(s), subst.size(), subst.data());
expr var_t_type = instantiate_rev(binding_domain(t), subst.size(), subst.data());
if (!is_def_eq(var_t_type, *var_s_type))
return false;
}
if (has_loose_bvars(binding_body(t)) || has_loose_bvars(binding_body(s))) {
// free variable is used inside t or s
if (!var_s_type)
var_s_type = instantiate_rev(binding_domain(s), subst.size(), subst.data());
subst.push_back(m_lctx.mk_local_decl(m_name_generator, binding_name(s), *var_s_type, binding_info(s)));
} else {
subst.push_back(*g_dont_care); // don't care
}
t = binding_body(t);
s = binding_body(s);
} while (t.kind() == k && s.kind() == k);
return is_def_eq(instantiate_rev(t, subst.size(), subst.data()),
instantiate_rev(s, subst.size(), subst.data()));
}
bool type_checker::is_def_eq(level const & l1, level const & l2) {
if (is_equivalent(l1, l2)) {
return true;
} else {
return false;
}
}
bool type_checker::is_def_eq(levels const & ls1, levels const & ls2) {
if (is_nil(ls1) && is_nil(ls2)) {
return true;
} else if (!is_nil(ls1) && !is_nil(ls2)) {
return
is_def_eq(head(ls1), head(ls2)) &&
is_def_eq(tail(ls1), tail(ls2));
} else {
return false;
}
}
/** \brief This is an auxiliary method for is_def_eq. It handles the "easy cases". */
lbool type_checker::quick_is_def_eq(expr const & t, expr const & s, bool use_hash) {
if (m_eqv_manager.is_equiv(t, s, use_hash))
return l_true;
if (t.kind() == s.kind()) {
switch (t.kind()) {
case expr_kind::Lambda: case expr_kind::Pi:
return to_lbool(is_def_eq_binding(t, s));
case expr_kind::Sort:
return to_lbool(is_def_eq(sort_level(t), sort_level(s)));
case expr_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::BVar: case expr_kind::FVar: case expr_kind::App:
case expr_kind::Constant: case expr_kind::Macro: case expr_kind::Let:
// We do not handle these cases in this method.
break;
}
}
return l_undef; // This is not an "easy case"
}
/** \brief Return true if arguments of \c t are definitionally equal to arguments of \c s.
This method is used to implement an optimization in the method \c is_def_eq. */
bool type_checker::is_def_eq_args(expr t, expr s) {
while (is_app(t) && is_app(s)) {
if (!is_def_eq(app_arg(t), app_arg(s)))
return false;
t = app_fn(t);
s = app_fn(s);
}
return !is_app(t) && !is_app(s);
}
/** \brief Try to solve (fun (x : A), B) =?= s by trying eta-expansion on s */
bool type_checker::try_eta_expansion_core(expr const & t, expr const & s) {
if (is_lambda(t) && !is_lambda(s)) {
expr s_type = whnf(infer_type(s));
if (!is_pi(s_type))
return false;
expr new_s = mk_lambda(binding_name(s_type), binding_domain(s_type), mk_app(s, Var(0)), binding_info(s_type));
if (!is_def_eq(t, new_s))
return false;
return true;
} else {
return false;
}
}
/** \brief Return true if \c t and \c s are definitionally equal because they are applications of the form
<tt>(f a_1 ... a_n)</tt> <tt>(g b_1 ... b_n)</tt>, and \c f and \c g are definitionally equal, and
\c a_i and \c b_i are also definitionally equal for every 1 <= i <= n.
Return false otherwise. */
bool type_checker::is_def_eq_app(expr const & t, expr const & s) {
if (is_app(t) && is_app(s)) {
buffer<expr> t_args;
buffer<expr> s_args;
expr t_fn = get_app_args(t, t_args);
expr s_fn = get_app_args(s, s_args);
if (is_def_eq(t_fn, s_fn) && t_args.size() == s_args.size()) {
unsigned i = 0;
for (; i < t_args.size(); i++) {
if (!is_def_eq(t_args[i], s_args[i]))
break;
}
if (i == t_args.size())
return true;
}
}
return false;
}
/** \brief Return true if \c t and \c s are definitionally equal due to proof irrelevant.
Return false otherwise. */
bool type_checker::is_def_eq_proof_irrel(expr const & t, expr const & s) {
// Proof irrelevance support for Prop (aka Type.{0})
expr t_type = infer_type(t);
expr s_type = infer_type(s);
return is_prop(t_type) && is_def_eq(t_type, s_type);
}
bool type_checker::failed_before(expr const & t, expr const & s) const {
if (t.hash() < s.hash()) {
return m_failure_cache.find(mk_pair(t, s)) != m_failure_cache.end();
} else if (t.hash() > s.hash()) {
return m_failure_cache.find(mk_pair(s, t)) != m_failure_cache.end();
} else {
return
m_failure_cache.find(mk_pair(t, s)) != m_failure_cache.end() ||
m_failure_cache.find(mk_pair(s, t)) != m_failure_cache.end();
}
}
void type_checker::cache_failure(expr const & t, expr const & s) {
if (t.hash() <= s.hash())
m_failure_cache.insert(mk_pair(t, s));
else
m_failure_cache.insert(mk_pair(s, t));
}
static name * g_id_delta = nullptr;
/** \brief Perform one lazy delta-reduction step.
Return
- l_true if t_n and s_n are definitionally equal.
- l_false if they are not definitionally equal.
- l_undef it the step did not manage to establish whether they are definitionally equal or not.
\remark t_n, s_n and cs are updated. */
auto type_checker::lazy_delta_reduction_step(expr & t_n, expr & s_n) -> reduction_status {
auto d_t = is_delta(t_n);
auto d_s = is_delta(s_n);
if (!d_t && !d_s) {
return reduction_status::DefUnknown;
} else if (d_t && d_t->get_name() == *g_id_delta) {
t_n = whnf_core(*unfold_definition(t_n));
if (t_n == s_n)
return reduction_status::DefEqual; /* id_delta t =?= t */
if (auto u = unfold_definition(t_n)) /* id_delta t =?= s ===> unfold(t) =?= s */
t_n = whnf_core(*u);
return reduction_status::Continue;
} else if (d_s && d_s->get_name() == *g_id_delta) {
s_n = whnf_core(*unfold_definition(s_n));
if (t_n == s_n)
return reduction_status::DefEqual; /* t =?= id_delta t */
if (auto u = unfold_definition(s_n)) /* t =?= id_delta s ===> t =?= unfold(s) */
s_n = whnf_core(*u);
return reduction_status::Continue;
} else if (d_t && !d_s) {
t_n = whnf_core(*unfold_definition(t_n));
} else if (!d_t && d_s) {
s_n = whnf_core(*unfold_definition(s_n));
} else {
int c = compare(d_t->get_hints(), d_s->get_hints());
if (c < 0) {
t_n = whnf_core(*unfold_definition(t_n));
} else if (c > 0) {
s_n = whnf_core(*unfold_definition(s_n));
} else {
if (is_app(t_n) && is_app(s_n) && is_eqp(*d_t, *d_s)) {
// If t_n and s_n are both applications of the same (non-opaque) definition,
if (has_expr_metavar(t_n) || has_expr_metavar(s_n)) {
// We let the unifier deal with cases such as
// (f ...) =?= (f ...)
// when t_n or s_n contains metavariables
return reduction_status::DefUnknown;
} else {
// Optimization:
// We try to check if their arguments are definitionally equal.
// If they are, then t_n and s_n must be definitionally equal, and we can
// skip the delta-reduction step.
// If the flag use_self_opt() is not true, then we skip this optimization
if (d_t->get_hints().use_self_opt() && !failed_before(t_n, s_n)) {
if (is_def_eq(const_levels(get_app_fn(t_n)), const_levels(get_app_fn(s_n))) &&
is_def_eq_args(t_n, s_n)) {
return reduction_status::DefEqual;
} else {
cache_failure(t_n, s_n);
}
}
}
}
t_n = whnf_core(*unfold_definition(t_n));
s_n = whnf_core(*unfold_definition(s_n));
}
}
switch (quick_is_def_eq(t_n, s_n)) {
case l_true: return reduction_status::DefEqual;
case l_false: return reduction_status::DefDiff;
case l_undef: return reduction_status::Continue;
}
lean_unreachable();
}
lbool type_checker::lazy_delta_reduction(expr & t_n, expr & s_n) {
while (true) {
switch (lazy_delta_reduction_step(t_n, s_n)) {
case reduction_status::Continue: break;
case reduction_status::DefUnknown: return l_undef;
case reduction_status::DefEqual: return l_true;
case reduction_status::DefDiff: return l_false;
}
}
}
bool type_checker::is_def_eq_core(expr const & t, expr const & s) {
check_system("is_definitionally_equal");
bool use_hash = true;
lbool r = quick_is_def_eq(t, s, use_hash);
if (r != l_undef) return r == l_true;
// apply whnf (without using delta-reduction or normalizer extensions)
expr t_n = whnf_core(t);
expr s_n = whnf_core(s);
if (!is_eqp(t_n, t) || !is_eqp(s_n, s)) {
r = quick_is_def_eq(t_n, s_n);
if (r != l_undef) return r == l_true;
}
if (is_def_eq_proof_irrel(t_n, s_n))
return true;
r = lazy_delta_reduction(t_n, s_n);
if (r != l_undef) return r == l_true;
if (is_constant(t_n) && is_constant(s_n) && const_name(t_n) == const_name(s_n) &&
is_def_eq(const_levels(t_n), const_levels(s_n)))
return true;
if (is_fvar(t_n) && is_fvar(s_n) && fvar_name(t_n) == fvar_name(s_n))
return true;
if (is_macro(t_n) && is_macro(s_n) && macro_def(t_n) == macro_def(s_n) && macro_num_args(t_n) == macro_num_args(s_n)) {
unsigned i = 0;
for (; i < macro_num_args(t_n); i++) {
if (!is_def_eq_core(macro_arg(t_n, i), macro_arg(s_n, i)))
break;
}
if (i == macro_num_args(t_n))
return true;
}
// At this point, t_n and s_n are in weak head normal form (modulo meta-variables and proof irrelevance)
if (is_def_eq_app(t_n, s_n))
return true;
if (try_eta_expansion(t_n, s_n))
return true;
return false;
}
bool type_checker::is_def_eq(expr const & t, expr const & s) {
bool r = is_def_eq_core(t, s);
if (r)
m_eqv_manager.add_equiv(t, s);
return r;
}
type_checker::type_checker(environment const & env, local_ctx const & lctx, bool memoize, bool non_meta_only):
m_env(env), m_lctx(lctx), m_name_generator(*g_kernel_fresh),
m_memoize(memoize), m_non_meta_only(non_meta_only), m_params(nullptr) {
}
type_checker::~type_checker() {}
void check_no_metavar(environment const & env, name const & n, expr const & e) {
if (has_metavar(e))
throw declaration_has_metavars_exception(env, n, e);
}
static void check_no_local(environment const & env, name const & n, expr const & e) {
if (has_local(e))
throw declaration_has_free_vars_exception(env, n, e);
}
void check_no_mlocal(environment const & env, name const & n, expr const & e) {
check_no_metavar(env, n, e);
check_no_local(env, n, e);
}
static void check_name(environment const & env, name const & n) {
if (env.find(n))
throw already_declared_exception(env, n);
}
static void check_duplicated_params(environment const & env, declaration const & d) {
level_param_names ls = d.get_univ_params();
while (!is_nil(ls)) {
auto const & p = head(ls);
ls = tail(ls);
if (std::find(ls.begin(), ls.end(), p) != ls.end()) {
throw kernel_exception(env, sstream() << "failed to add declaration to environment, "
<< "duplicate universe level parameter: '"
<< p << "'");
}
}
}
static void check_definition(environment const & env, declaration const & d, type_checker & checker) {
check_no_mlocal(env, d.get_name(), d.get_value());
expr val_type = checker.check(d.get_value(), d.get_univ_params());
if (!checker.is_def_eq(val_type, d.get_type())) {
throw definition_type_mismatch_exception(env, d, val_type);
}
}
static void check_decl_type(environment const & env, declaration const & d, type_checker & checker) {
check_no_mlocal(env, d.get_name(), d.get_type());
check_name(env, d.get_name());
check_duplicated_params(env, d);
expr sort = checker.check(d.get_type(), d.get_univ_params());
checker.ensure_sort(sort, d.get_type());
}
void check_decl_type(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
type_checker checker(env, memoize, non_meta_only);
check_decl_type(env, d, checker);
}
void check_decl_value(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
type_checker checker(env, memoize, non_meta_only);
if (d.is_definition()) {
check_definition(env, d, checker);
}
}
certified_declaration check(environment const & env, declaration const & d) {
bool memoize = true; bool non_meta_only = !d.is_meta();
type_checker checker(env, memoize, non_meta_only);
check_decl_type(env, d, checker);
if (d.is_definition()) {
check_definition(env, d, checker);
}
return certified_declaration(env.get_id(), d);
}
certified_declaration certify_unchecked::certify(environment const & env, declaration const & d) {
if (env.trust_lvl() == 0)
throw kernel_exception(env, "environment trust level does not allow users to add declarations that were not type checked");
return certified_declaration(env.get_id(), d);
}
certified_declaration certify_unchecked::certify_or_check(environment const & env, declaration const & d) {
if (env.trust_lvl() == 0)
return check(env, d);
else
return certify(env, d);
}
void initialize_type_checker() {
g_id_delta = new name("id_delta");
g_dont_care = new expr(Const("dontcare"));
g_kernel_fresh = new name("_kernel_fresh");
register_name_generator_prefix(*g_kernel_fresh);
}
void finalize_type_checker() {
delete g_dont_care;
delete g_id_delta;
delete g_kernel_fresh;
}
}

147
src/kernel/type_checker.h Normal file
View file

@ -0,0 +1,147 @@
/*
Copyright (c) 2013-14 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include <unordered_set>
#include <memory>
#include <utility>
#include <algorithm>
#include "util/lbool.h"
#include "util/name_set.h"
#include "util/name_generator.h"
#include "kernel/environment.h"
#include "kernel/local_ctx.h"
#include "kernel/expr_pair.h"
#include "kernel/expr_maps.h"
#include "kernel/equiv_manager.h"
#include "kernel/abstract_type_context.h"
namespace lean {
/** \brief Lean Type Checker. It can also be used to infer types, check whether a
type \c A is convertible to a type \c B, etc. */
class type_checker : public abstract_type_context {
/* In the type checker cache, we must take into account binder information.
Examples:
The type of (lambda x : A, t) is (Pi x : A, typeof(t))
The type of (lambda {x : A}, t) is (Pi {x : A}, typeof(t)) */
typedef expr_bi_map<expr> cache;
typedef std::unordered_set<expr_pair, expr_pair_hash, expr_pair_eq> expr_pair_set;
environment m_env;
local_ctx m_lctx;
name_generator m_name_generator;
bool m_memoize;
bool m_non_meta_only;
cache m_infer_type_cache[2];
expr_map<expr> m_whnf_core_cache;
expr_map<expr> m_whnf_cache;
equiv_manager m_eqv_manager;
expr_pair_set m_failure_cache;
level_param_names const * m_params;
pair<expr, expr> open_binding_body(expr const & e);
expr ensure_sort_core(expr e, expr const & s);
expr ensure_pi_core(expr e, expr const & s);
void check_level(level const & l);
expr infer_fvar(expr const & e);
expr infer_constant(expr const & e, bool infer_only);
expr infer_macro(expr const & e, bool infer_only);
expr infer_lambda(expr const & e, bool infer_only);
expr infer_pi(expr const & e, bool infer_only);
expr infer_app(expr const & e, bool infer_only);
expr infer_let(expr const & e, bool infer_only);
expr infer_type_core(expr const & e, bool infer_only);
expr infer_type(expr const & e);
enum class reduction_status { Continue, DefUnknown, DefEqual, DefDiff };
optional<expr> norm_ext(expr const & e);
expr whnf_fvar(expr const & e);
expr whnf_core(expr const & e);
optional<declaration> is_delta(expr const & e) const;
optional<expr> unfold_definition_core(expr const & e);
optional<expr> unfold_definition(expr const & e);
bool is_def_eq_binding(expr t, expr s);
bool is_def_eq(level const & l1, level const & l2);
bool is_def_eq(levels const & ls1, levels const & ls2);
lbool quick_is_def_eq(expr const & t, expr const & s, bool use_hash = false);
bool is_def_eq_args(expr t, expr s);
bool try_eta_expansion_core(expr const & t, expr const & s);
bool try_eta_expansion(expr const & t, expr const & s) {
return try_eta_expansion_core(t, s) || try_eta_expansion_core(s, t);
}
bool is_def_eq_app(expr const & t, expr const & s);
bool is_def_eq_proof_irrel(expr const & t, expr const & s);
bool failed_before(expr const & t, expr const & s) const;
void cache_failure(expr const & t, expr const & s);
reduction_status lazy_delta_reduction_step(expr & t_n, expr & s_n);
lbool lazy_delta_reduction(expr & t_n, expr & s_n);
bool is_def_eq_core(expr const & t, expr const & s);
optional<expr> expand_macro(expr const & m);
/** \brief Like \c check, but ignores undefined universes */
expr check_ignore_undefined_universes(expr const & e);
public:
/** \brief Create a type checker for the given environment.
memoize: if true, then inferred types are memoized/cached. */
type_checker(environment const & env, local_ctx const & lctx, bool memoize = true, bool non_meta_only = true);
type_checker(environment const & env, bool memoize = true, bool non_meta_only = true):
type_checker(env, local_ctx(), memoize, non_meta_only) {}
~type_checker();
virtual environment const & env() const { return m_env; }
virtual name next_name() { return m_name_generator.next(); }
/** \brief Return the type of \c t.
It does not check whether the input expression is type correct or not.
The contract is: IF the input expression is type correct, then the inferred
type is correct.
Throw an exception if a type error is found. */
virtual expr infer(expr const & t) { return infer_type(t); }
/** \brief Type check the given expression, and return the type of \c t.
Throw an exception if a type error is found. */
expr check(expr const & t, level_param_names const & ps);
/** \brief Like \c check, but ignores undefined universes */
virtual expr check(expr const & t) { return check_ignore_undefined_universes(t); }
/** \brief Return true iff t is definitionally equal to s. */
virtual bool is_def_eq(expr const & t, expr const & s);
/** \brief Return true iff t is a proposition. */
bool is_prop(expr const & t);
/** \brief Return the weak head normal form of \c t. */
virtual expr whnf(expr const & t);
/** \brief Return a Pi if \c t is convertible to a Pi type. Throw an exception otherwise.
The argument \c s is used when reporting errors */
expr ensure_pi(expr const & t, expr const & s);
expr ensure_pi(expr const & t) { return ensure_pi(t, t); }
/** \brief Mare sure type of \c e is a Pi, and return it. Throw an exception otherwise. */
expr ensure_fun(expr const & e) {
return ensure_pi(infer(e), e);
}
/** \brief Return a Sort if \c t is convertible to Sort. Throw an exception otherwise.
The argument \c s is used when reporting errors. */
expr ensure_sort(expr const & t, expr const & s);
/** \brief Return a Sort if \c t is convertible to Sort. Throw an exception otherwise. */
expr ensure_sort(expr const & t) { return ensure_sort(t, t); }
/** \brief Mare sure type of \c e is a sort, and return it. Throw an exception otherwise. */
expr ensure_type(expr const & e) {
return ensure_sort(infer(e), e);
}
};
void check_no_metavar(environment const & env, name const & n, expr const & e);
void check_no_mlocal(environment const & env, name const & n, expr const & e);
void check_decl_type(environment const & env, declaration const & d);
void check_decl_value(environment const & env, declaration const & d);
/** \brief Type check the given declaration, and return a certified declaration if it is type correct.
Throw an exception if the declaration is type incorrect. */
certified_declaration check(environment const & env, declaration const & d);
void initialize_type_checker();
void finalize_type_checker();
}