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refactor(kernel): move default_converter to its own module

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This commit is contained in:
Leonardo de Moura 2015-02-07 11:33:37 -08:00
parent d143b525f7
commit 3f06f7b6fd
5 changed files with 588 additions and 511 deletions
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3
src/kernel/CMakeLists.txt
View file

@ -3,6 +3,7 @@ replace_fn.cpp free_vars.cpp abstract.cpp instantiate.cpp
formatter.cpp declaration.cpp environment.cpp
justification.cpp pos_info_provider.cpp metavar.cpp converter.cpp
constraint.cpp type_checker.cpp error_msgs.cpp kernel_exception.cpp
normalizer_extension.cpp init_module.cpp extension_context.cpp expr_cache.cpp)
normalizer_extension.cpp init_module.cpp extension_context.cpp expr_cache.cpp
default_converter.cpp)
target_link_libraries(kernel ${LEAN_LIBS})

511
src/kernel/converter.cpp
View file

@ -11,6 +11,7 @@ Author: Leonardo de Moura
#include "kernel/instantiate.h"
#include "kernel/free_vars.h"
#include "kernel/type_checker.h"
#include "kernel/default_converter.h"
namespace lean {
// Temporary hack for ignoring opaque annotations in the kernel
@ -112,514 +113,6 @@ std::unique_ptr<converter> mk_dummy_converter() {
name converter::mk_fresh_name(type_checker & tc) { return tc.mk_fresh_name(); }
pair<expr, constraint_seq> converter::infer_type(type_checker & tc, expr const & e) { return tc.infer_type(e); }
extension_context & converter::get_extension(type_checker & tc) { return tc.get_extension(); }
static expr * g_dont_care = nullptr;
struct default_converter : public converter {
environment m_env;
optional<module_idx> m_module_idx;
bool m_memoize;
extra_opaque_pred m_extra_pred;
expr_struct_map<expr> m_whnf_core_cache;
expr_struct_map<pair<expr, constraint_seq>> m_whnf_cache;
default_converter(environment const & env, optional<module_idx> mod_idx, bool memoize,
extra_opaque_pred const & pred):
m_env(env), m_module_idx(mod_idx), m_memoize(memoize), m_extra_pred(pred) {
}
constraint mk_eq_cnstr(expr const & lhs, expr const & rhs, justification const & j) {
return ::lean::mk_eq_cnstr(lhs, rhs, j, static_cast<bool>(m_module_idx));
}
optional<expr> expand_macro(expr const & m, type_checker & c) {
lean_assert(is_macro(m));
return macro_def(m).expand(m, get_extension(c));
}
/** \brief Apply normalizer extensions to \c e. */
optional<pair<expr, constraint_seq>> norm_ext(expr const & e, type_checker & c) {
return m_env.norm_ext()(e, get_extension(c));
}
optional<expr> d_norm_ext(expr const & e, type_checker & c, constraint_seq & cs) {
if (auto r = norm_ext(e, c)) {
cs = cs + r->second;
return some_expr(r->first);
} else {
return none_expr();
}
}
/** \brief Return true if \c e may be reduced later after metavariables are instantiated. */
bool may_reduce_later(expr const & e, type_checker & c) {
return static_cast<bool>(m_env.norm_ext().may_reduce_later(e, get_extension(c)));
}
/** \brief Weak head normal form core procedure. It does not perform delta reduction nor normalization extensions. */
expr whnf_core(expr const & e, type_checker & c) {
check_system("whnf");
// handle easy cases
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local:
case expr_kind::Pi: case expr_kind::Constant: case expr_kind::Lambda:
return e;
case expr_kind::Macro: case expr_kind::App:
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::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local:
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, c))
r = whnf_core(*m, c);
else
r = e;
break;
case expr_kind::App: {
buffer<expr> args;
expr f0 = get_app_rev_args(e, args);
expr f = whnf_core(f0, c);
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()), c);
} else {
r = f == f0 ? e : whnf_core(mk_rev_app(f, args.size(), args.data()), c);
}
break;
}}
if (m_memoize)
m_whnf_core_cache.insert(mk_pair(e, r));
return r;
}
bool is_opaque_core(declaration const & d) const {
return ::lean::is_opaque(d, m_extra_pred, m_module_idx);
}
virtual bool is_opaque(declaration const & d) const {
return is_opaque_core(d);
}
/** \brief Expand \c e if it is non-opaque constant with weight >= w */
expr unfold_name_core(expr e, unsigned w) {
if (is_constant(e)) {
if (auto d = m_env.find(const_name(e))) {
if (d->is_definition() && !is_opaque_core(*d) && d->get_weight() >= w)
return unfold_name_core(instantiate_value_univ_params(*d, const_levels(e)), w);
}
}
return e;
}
/**
\brief Expand constants and application where the function is a constant.
The unfolding is only performend if the constant corresponds to
a non-opaque definition with weight >= w.
*/
expr unfold_names(expr const & e, unsigned w) {
if (is_app(e)) {
expr f0 = get_app_fn(e);
expr f = unfold_name_core(f0, w);
if (is_eqp(f, f0)) {
return e;
} else {
buffer<expr> args;
get_app_rev_args(e, args);
return mk_rev_app(f, args);
}
} else {
return unfold_name_core(e, w);
}
}
/**
\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> is_delta(expr const & e) {
return ::lean::is_delta(m_env, get_app_fn(e), m_extra_pred, m_module_idx);
}
/**
\brief Weak head normal form core procedure that perform delta reduction for non-opaque constants with
weight greater than or equal to \c w.
This method is based on <tt>whnf_core(expr const &)</tt> and \c unfold_names.
\remark This method does not use normalization extensions attached in the environment.
*/
expr whnf_core(expr e, unsigned w, type_checker & c) {
while (true) {
expr new_e = unfold_names(whnf_core(e, c), w);
if (is_eqp(e, new_e))
return e;
e = new_e;
}
}
/** \brief Put expression \c t in weak head normal form */
virtual pair<expr, constraint_seq> whnf(expr const & e_prime, type_checker & c) {
// Do not cache easy cases
switch (e_prime.kind()) {
case expr_kind::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local: case expr_kind::Pi:
return to_ecs(e_prime);
case expr_kind::Lambda: case expr_kind::Macro: case expr_kind::App: case expr_kind::Constant:
break;
}
expr e = e_prime;
// check cache
if (m_memoize) {
auto it = m_whnf_cache.find(e);
if (it != m_whnf_cache.end())
return it->second;
}
expr t = e;
constraint_seq cs;
while (true) {
expr t1 = whnf_core(t, 0, c);
if (auto new_t = d_norm_ext(t1, c, cs)) {
t = *new_t;
} else {
auto r = mk_pair(t1, cs);
if (m_memoize)
m_whnf_cache.insert(mk_pair(e, r));
return r;
}
}
}
expr whnf(expr const & e_prime, type_checker & c, constraint_seq & cs) {
auto r = whnf(e_prime, c);
cs = cs + r.second;
return r.first;
}
pair<bool, constraint_seq> to_bcs(bool b) { return mk_pair(b, constraint_seq()); }
pair<bool, constraint_seq> to_bcs(bool b, constraint const & c) { return mk_pair(b, constraint_seq(c)); }
pair<bool, constraint_seq> to_bcs(bool b, constraint_seq const & cs) { return mk_pair(b, cs); }
/**
\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 is_def_eq_binding(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
lean_assert(t.kind() == s.kind());
lean_assert(is_binding(t));
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, c, jst, cs))
return false;
}
if (!closed(binding_body(t)) || !closed(binding_body(s))) {
// local 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(mk_local(mk_fresh_name(c), 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()), c, jst, cs);
}
bool is_def_eq(level const & l1, level const & l2, delayed_justification & jst, constraint_seq & cs) {
if (is_equivalent(l1, l2)) {
return true;
} else if (has_meta(l1) || has_meta(l2)) {
cs = cs + constraint_seq(mk_level_eq_cnstr(l1, l2, jst.get()));
return true;
} else {
return false;
}
}
bool is_def_eq(levels const & ls1, levels const & ls2, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
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), jst, cs) &&
is_def_eq(tail(ls1), tail(ls2), c, jst, cs);
} else {
return false;
}
}
static pair<lbool, constraint_seq> to_lbcs(lbool l) { return mk_pair(l, constraint_seq()); }
static pair<lbool, constraint_seq> to_lbcs(lbool l, constraint const & c) { return mk_pair(l, constraint_seq(c)); }
static pair<lbool, constraint_seq> to_lbcs(pair<bool, constraint_seq> const & bcs) {
return mk_pair(to_lbool(bcs.first), bcs.second);
}
/** \brief This is an auxiliary method for is_def_eq. It handles the "easy cases". */
lbool quick_is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
if (t == s)
return l_true; // t and s are structurally equal
if (is_meta(t) || is_meta(s)) {
// if t or s is a metavariable (or the application of a metavariable), then add constraint
cs = cs + constraint_seq(mk_eq_cnstr(t, s, jst.get()));
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, c, jst, cs));
case expr_kind::Sort:
return to_lbool(is_def_eq(sort_level(t), sort_level(s), c, jst, cs));
case expr_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Var: case expr_kind::Local: case expr_kind::App:
case expr_kind::Constant: case expr_kind::Macro:
// 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 is_def_eq_args(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
while (is_app(t) && is_app(s)) {
if (!is_def_eq(app_arg(t), app_arg(s), c, jst, cs))
return false;
t = app_fn(t);
s = app_fn(s);
}
return !is_app(t) && !is_app(s);
}
/** \brief Return true iff t is a constant named f_name or an application of the form (f_name a_1 ... a_k) */
bool is_app_of(expr t, name const & f_name) {
t = get_app_fn(t);
return is_constant(t) && const_name(t) == f_name;
}
/** \brief Try to solve (fun (x : A), B) =?= s by trying eta-expansion on s */
bool try_eta_expansion(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
if (is_lambda(t) && !is_lambda(s)) {
auto tcs = infer_type(c, s);
auto wcs = whnf(tcs.first, c);
expr s_type = wcs.first;
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));
auto dcs = is_def_eq(t, new_s, c, jst);
if (!dcs.first)
return false;
cs = cs + dcs.second + wcs.second + tcs.second;
return true;
} else {
return false;
}
}
bool is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
auto bcs = is_def_eq(t, s, c, jst);
if (bcs.first) {
cs = cs + bcs.second;
return true;
} else {
return false;
}
}
/** Return true iff t is definitionally equal to s. */
virtual pair<bool, constraint_seq> is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst) {
check_system("is_definitionally_equal");
constraint_seq cs;
lbool r = quick_is_def_eq(t, s, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
// apply whnf (without using delta-reduction or normalizer extensions)
expr t_n = whnf_core(t, c);
expr s_n = whnf_core(s, c);
if (!is_eqp(t_n, t) || !is_eqp(s_n, s)) {
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
// lazy delta-reduction and then normalizer extensions
while (true) {
// first, keep applying lazy delta-reduction while applicable
while (true) {
auto d_t = is_delta(t_n);
auto d_s = is_delta(s_n);
if (!d_t && !d_s) {
break;
} else if (d_t && !d_s) {
t_n = whnf_core(unfold_names(t_n, 0), c);
} else if (!d_t && d_s) {
s_n = whnf_core(unfold_names(s_n, 0), c);
} else if (d_t->get_weight() > d_s->get_weight()) {
t_n = whnf_core(unfold_names(t_n, d_s->get_weight() + 1), c);
} else if (d_t->get_weight() < d_s->get_weight()) {
s_n = whnf_core(unfold_names(s_n, d_t->get_weight() + 1), c);
} else {
lean_assert(d_t && d_s && d_t->get_weight() == d_s->get_weight());
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
break;
} 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_conv_opt() is not true, then we skip this optimization
if (!is_opaque_core(*d_t) && d_t->use_conv_opt() &&
is_def_eq_args(t_n, s_n, c, jst, cs))
return to_bcs(true, cs);
}
}
t_n = whnf_core(unfold_names(t_n, d_t->get_weight() - 1), c);
s_n = whnf_core(unfold_names(s_n, d_s->get_weight() - 1), c);
}
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
// try normalizer extensions
auto new_t_n = d_norm_ext(t_n, c, cs);
auto new_s_n = d_norm_ext(s_n, c, cs);
if (!new_t_n && !new_s_n)
break; // t_n and s_n are in weak head normal form
if (new_t_n)
t_n = whnf_core(*new_t_n, c);
if (new_s_n)
s_n = whnf_core(*new_s_n, c);
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
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), c, jst, cs))
return to_bcs(true, cs);
if (is_local(t_n) && is_local(s_n) && mlocal_name(t_n) == mlocal_name(s_n))
return to_bcs(true, cs);
optional<declaration> d_t, d_s;
bool delay_check = false;
if (has_expr_metavar(t_n) || has_expr_metavar(s_n)) {
d_t = is_delta(t_n);
d_s = is_delta(s_n);
if (d_t && d_s && is_eqp(*d_t, *d_s))
delay_check = true;
else if (may_reduce_later(t_n, c) && may_reduce_later(s_n, c))
delay_check = true;
}
// At this point, t_n and s_n are in weak head normal form (modulo meta-variables and proof irrelevance)
if (!delay_check && is_app(t_n) && is_app(s_n)) {
buffer<expr> t_args;
buffer<expr> s_args;
expr t_fn = get_app_args(t_n, t_args);
expr s_fn = get_app_args(s_n, s_args);
constraint_seq cs_prime = cs;
if (is_def_eq(t_fn, s_fn, c, jst, cs_prime) && 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], c, jst, cs_prime))
break;
}
if (i == t_args.size()) {
return to_bcs(true, cs_prime);
}
}
}
if (try_eta_expansion(t_n, s_n, c, jst, cs) ||
try_eta_expansion(s_n, t_n, c, jst, cs))
return to_bcs(true, cs);
if (m_env.prop_proof_irrel()) {
// Proof irrelevance support for Prop (aka Type.{0})
auto tcs = infer_type(c, t);
auto scs = infer_type(c, s);
expr t_type = tcs.first;
expr s_type = scs.first;
// remark: is_prop returns true only if t_type reducible to Prop.
// If t_type contains metavariables, then reduction can get stuck, and is_prop will return false.
auto pcs = is_prop(t_type, c);
if (pcs.first) {
auto dcs = is_def_eq(t_type, s_type, c, jst);
if (dcs.first)
return to_bcs(true, dcs.second + scs.second + pcs.second + tcs.second);
} else {
// If we can't stablish whether t_type is Prop, we try s_type.
pcs = is_prop(s_type, c);
if (pcs.first) {
auto dcs = is_def_eq(t_type, s_type, c, jst);
if (dcs.first)
return to_bcs(true, dcs.second + scs.second + pcs.second + tcs.second);
}
// This procedure will miss the case where s_type and t_type cannot be reduced to Prop
// because they contain metavariables.
}
}
if (may_reduce_later(t_n, c) || may_reduce_later(s_n, c) || delay_check) {
cs = cs + constraint_seq(mk_eq_cnstr(t_n, s_n, jst.get()));
return to_bcs(true, cs);
}
return to_bcs(false);
}
pair<bool, constraint_seq> is_prop(expr const & e, type_checker & c) {
auto tcs = infer_type(c, e);
auto wcs = whnf(tcs.first, c);
if (wcs.first == mk_Prop())
return to_bcs(true, wcs.second + tcs.second);
else
return to_bcs(false);
}
virtual optional<module_idx> get_module_idx() const {
return m_module_idx;
}
};
std::unique_ptr<converter> mk_default_converter(environment const & env, optional<module_idx> mod_idx,
bool memoize, extra_opaque_pred const & pred) {
@ -643,12 +136,10 @@ std::unique_ptr<converter> mk_default_converter(environment const & env, bool un
void initialize_converter() {
g_opt_main_module_idx = new optional<module_idx>(g_main_module_idx);
g_no_delayed_jst = new no_delayed_justification();
g_dont_care = new expr(Const("dontcare"));
}
void finalize_converter() {
delete g_opt_main_module_idx;
delete g_no_delayed_jst;
delete g_dont_care;
}
}

508
src/kernel/default_converter.cpp Normal file
View file

@ -0,0 +1,508 @@
/*
Copyright (c) 2014-2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "util/interrupt.h"
#include "kernel/default_converter.h"
#include "kernel/instantiate.h"
#include "kernel/free_vars.h"
#include "kernel/type_checker.h"
namespace lean {
static expr * g_dont_care = nullptr;
default_converter::default_converter(environment const & env, optional<module_idx> mod_idx, bool memoize,
extra_opaque_pred const & pred):
m_env(env), m_module_idx(mod_idx), m_memoize(memoize), m_extra_pred(pred) {
}
constraint default_converter::mk_eq_cnstr(expr const & lhs, expr const & rhs, justification const & j) {
return ::lean::mk_eq_cnstr(lhs, rhs, j, static_cast<bool>(m_module_idx));
}
optional<expr> default_converter::expand_macro(expr const & m, type_checker & c) {
lean_assert(is_macro(m));
return macro_def(m).expand(m, get_extension(c));
}
/** \brief Apply normalizer extensions to \c e. */
optional<pair<expr, constraint_seq>> default_converter::norm_ext(expr const & e, type_checker & c) {
return m_env.norm_ext()(e, get_extension(c));
}
optional<expr> default_converter::d_norm_ext(expr const & e, type_checker & c, constraint_seq & cs) {
if (auto r = norm_ext(e, c)) {
cs = cs + r->second;
return some_expr(r->first);
} else {
return none_expr();
}
}
/** \brief Return true if \c e may be reduced later after metavariables are instantiated. */
bool default_converter::may_reduce_later(expr const & e, type_checker & c) {
return static_cast<bool>(m_env.norm_ext().may_reduce_later(e, get_extension(c)));
}
/** \brief Weak head normal form core procedure. It does not perform delta reduction nor normalization extensions. */
expr default_converter::whnf_core(expr const & e, type_checker & c) {
check_system("whnf");
// handle easy cases
switch (e.kind()) {
case expr_kind::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local:
case expr_kind::Pi: case expr_kind::Constant: case expr_kind::Lambda:
return e;
case expr_kind::Macro: case expr_kind::App:
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::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local:
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, c))
r = whnf_core(*m, c);
else
r = e;
break;
case expr_kind::App: {
buffer<expr> args;
expr f0 = get_app_rev_args(e, args);
expr f = whnf_core(f0, c);
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()), c);
} else {
r = f == f0 ? e : whnf_core(mk_rev_app(f, args.size(), args.data()), c);
}
break;
}}
if (m_memoize)
m_whnf_core_cache.insert(mk_pair(e, r));
return r;
}
bool default_converter::is_opaque_core(declaration const & d) const {
return ::lean::is_opaque(d, m_extra_pred, m_module_idx);
}
bool default_converter::is_opaque(declaration const & d) const {
return is_opaque_core(d);
}
/** \brief Expand \c e if it is non-opaque constant with weight >= w */
expr default_converter::unfold_name_core(expr e, unsigned w) {
if (is_constant(e)) {
if (auto d = m_env.find(const_name(e))) {
if (d->is_definition() && !is_opaque_core(*d) && d->get_weight() >= w)
return unfold_name_core(instantiate_value_univ_params(*d, const_levels(e)), w);
}
}
return e;
}
/**
\brief Expand constants and application where the function is a constant.
The unfolding is only performend if the constant corresponds to
a non-opaque definition with weight >= w.
*/
expr default_converter::unfold_names(expr const & e, unsigned w) {
if (is_app(e)) {
expr f0 = get_app_fn(e);
expr f = unfold_name_core(f0, w);
if (is_eqp(f, f0)) {
return e;
} else {
buffer<expr> args;
get_app_rev_args(e, args);
return mk_rev_app(f, args);
}
} else {
return unfold_name_core(e, w);
}
}
/**
\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> default_converter::is_delta(expr const & e) {
return ::lean::is_delta(m_env, get_app_fn(e), m_extra_pred, m_module_idx);
}
/**
\brief Weak head normal form core procedure that perform delta reduction for non-opaque constants with
weight greater than or equal to \c w.
This method is based on <tt>whnf_core(expr const &)</tt> and \c unfold_names.
\remark This method does not use normalization extensions attached in the environment.
*/
expr default_converter::whnf_core(expr e, unsigned w, type_checker & c) {
while (true) {
expr new_e = unfold_names(whnf_core(e, c), w);
if (is_eqp(e, new_e))
return e;
e = new_e;
}
}
/** \brief Put expression \c t in weak head normal form */
pair<expr, constraint_seq> default_converter::whnf(expr const & e_prime, type_checker & c) {
// Do not cache easy cases
switch (e_prime.kind()) {
case expr_kind::Var: case expr_kind::Sort: case expr_kind::Meta: case expr_kind::Local: case expr_kind::Pi:
return to_ecs(e_prime);
case expr_kind::Lambda: case expr_kind::Macro: case expr_kind::App: case expr_kind::Constant:
break;
}
expr e = e_prime;
// check cache
if (m_memoize) {
auto it = m_whnf_cache.find(e);
if (it != m_whnf_cache.end())
return it->second;
}
expr t = e;
constraint_seq cs;
while (true) {
expr t1 = whnf_core(t, 0, c);
if (auto new_t = d_norm_ext(t1, c, cs)) {
t = *new_t;
} else {
auto r = mk_pair(t1, cs);
if (m_memoize)
m_whnf_cache.insert(mk_pair(e, r));
return r;
}
}
}
expr default_converter::whnf(expr const & e_prime, type_checker & c, constraint_seq & cs) {
auto r = whnf(e_prime, c);
cs = cs + r.second;
return r.first;
}
/**
\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 default_converter::is_def_eq_binding(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
lean_assert(t.kind() == s.kind());
lean_assert(is_binding(t));
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, c, jst, cs))
return false;
}
if (!closed(binding_body(t)) || !closed(binding_body(s))) {
// local 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(mk_local(mk_fresh_name(c), 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()), c, jst, cs);
}
bool default_converter::is_def_eq(level const & l1, level const & l2, delayed_justification & jst, constraint_seq & cs) {
if (is_equivalent(l1, l2)) {
return true;
} else if (has_meta(l1) || has_meta(l2)) {
cs = cs + constraint_seq(mk_level_eq_cnstr(l1, l2, jst.get()));
return true;
} else {
return false;
}
}
bool default_converter::is_def_eq(levels const & ls1, levels const & ls2, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
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), jst, cs) &&
is_def_eq(tail(ls1), tail(ls2), c, jst, cs);
} else {
return false;
}
}
/** \brief This is an auxiliary method for is_def_eq. It handles the "easy cases". */
lbool default_converter::quick_is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
if (t == s)
return l_true; // t and s are structurally equal
if (is_meta(t) || is_meta(s)) {
// if t or s is a metavariable (or the application of a metavariable), then add constraint
cs = cs + constraint_seq(mk_eq_cnstr(t, s, jst.get()));
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, c, jst, cs));
case expr_kind::Sort:
return to_lbool(is_def_eq(sort_level(t), sort_level(s), c, jst, cs));
case expr_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Var: case expr_kind::Local: case expr_kind::App:
case expr_kind::Constant: case expr_kind::Macro:
// 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 default_converter::is_def_eq_args(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
while (is_app(t) && is_app(s)) {
if (!is_def_eq(app_arg(t), app_arg(s), c, jst, cs))
return false;
t = app_fn(t);
s = app_fn(s);
}
return !is_app(t) && !is_app(s);
}
/** \brief Return true iff t is a constant named f_name or an application of the form (f_name a_1 ... a_k) */
bool default_converter::is_app_of(expr t, name const & f_name) {
t = get_app_fn(t);
return is_constant(t) && const_name(t) == f_name;
}
/** \brief Try to solve (fun (x : A), B) =?= s by trying eta-expansion on s */
bool default_converter::try_eta_expansion(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
if (is_lambda(t) && !is_lambda(s)) {
auto tcs = infer_type(c, s);
auto wcs = whnf(tcs.first, c);
expr s_type = wcs.first;
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));
auto dcs = is_def_eq(t, new_s, c, jst);
if (!dcs.first)
return false;
cs = cs + dcs.second + wcs.second + tcs.second;
return true;
} else {
return false;
}
}
bool default_converter::is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs) {
auto bcs = is_def_eq(t, s, c, jst);
if (bcs.first) {
cs = cs + bcs.second;
return true;
} else {
return false;
}
}
/** Return true iff t is definitionally equal to s. */
pair<bool, constraint_seq> default_converter::is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst) {
check_system("is_definitionally_equal");
constraint_seq cs;
lbool r = quick_is_def_eq(t, s, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
// apply whnf (without using delta-reduction or normalizer extensions)
expr t_n = whnf_core(t, c);
expr s_n = whnf_core(s, c);
if (!is_eqp(t_n, t) || !is_eqp(s_n, s)) {
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
// lazy delta-reduction and then normalizer extensions
while (true) {
// first, keep applying lazy delta-reduction while applicable
while (true) {
auto d_t = is_delta(t_n);
auto d_s = is_delta(s_n);
if (!d_t && !d_s) {
break;
} else if (d_t && !d_s) {
t_n = whnf_core(unfold_names(t_n, 0), c);
} else if (!d_t && d_s) {
s_n = whnf_core(unfold_names(s_n, 0), c);
} else if (d_t->get_weight() > d_s->get_weight()) {
t_n = whnf_core(unfold_names(t_n, d_s->get_weight() + 1), c);
} else if (d_t->get_weight() < d_s->get_weight()) {
s_n = whnf_core(unfold_names(s_n, d_t->get_weight() + 1), c);
} else {
lean_assert(d_t && d_s && d_t->get_weight() == d_s->get_weight());
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
break;
} 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_conv_opt() is not true, then we skip this optimization
if (!is_opaque_core(*d_t) && d_t->use_conv_opt() &&
is_def_eq_args(t_n, s_n, c, jst, cs))
return to_bcs(true, cs);
}
}
t_n = whnf_core(unfold_names(t_n, d_t->get_weight() - 1), c);
s_n = whnf_core(unfold_names(s_n, d_s->get_weight() - 1), c);
}
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
// try normalizer extensions
auto new_t_n = d_norm_ext(t_n, c, cs);
auto new_s_n = d_norm_ext(s_n, c, cs);
if (!new_t_n && !new_s_n)
break; // t_n and s_n are in weak head normal form
if (new_t_n)
t_n = whnf_core(*new_t_n, c);
if (new_s_n)
s_n = whnf_core(*new_s_n, c);
r = quick_is_def_eq(t_n, s_n, c, jst, cs);
if (r != l_undef) return to_bcs(r == l_true, cs);
}
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), c, jst, cs))
return to_bcs(true, cs);
if (is_local(t_n) && is_local(s_n) && mlocal_name(t_n) == mlocal_name(s_n))
return to_bcs(true, cs);
optional<declaration> d_t, d_s;
bool delay_check = false;
if (has_expr_metavar(t_n) || has_expr_metavar(s_n)) {
d_t = is_delta(t_n);
d_s = is_delta(s_n);
if (d_t && d_s && is_eqp(*d_t, *d_s))
delay_check = true;
else if (may_reduce_later(t_n, c) && may_reduce_later(s_n, c))
delay_check = true;
}
// At this point, t_n and s_n are in weak head normal form (modulo meta-variables and proof irrelevance)
if (!delay_check && is_app(t_n) && is_app(s_n)) {
buffer<expr> t_args;
buffer<expr> s_args;
expr t_fn = get_app_args(t_n, t_args);
expr s_fn = get_app_args(s_n, s_args);
constraint_seq cs_prime = cs;
if (is_def_eq(t_fn, s_fn, c, jst, cs_prime) && 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], c, jst, cs_prime))
break;
}
if (i == t_args.size()) {
return to_bcs(true, cs_prime);
}
}
}
if (try_eta_expansion(t_n, s_n, c, jst, cs) ||
try_eta_expansion(s_n, t_n, c, jst, cs))
return to_bcs(true, cs);
if (m_env.prop_proof_irrel()) {
// Proof irrelevance support for Prop (aka Type.{0})
auto tcs = infer_type(c, t);
auto scs = infer_type(c, s);
expr t_type = tcs.first;
expr s_type = scs.first;
// remark: is_prop returns true only if t_type reducible to Prop.
// If t_type contains metavariables, then reduction can get stuck, and is_prop will return false.
auto pcs = is_prop(t_type, c);
if (pcs.first) {
auto dcs = is_def_eq(t_type, s_type, c, jst);
if (dcs.first)
return to_bcs(true, dcs.second + scs.second + pcs.second + tcs.second);
} else {
// If we can't stablish whether t_type is Prop, we try s_type.
pcs = is_prop(s_type, c);
if (pcs.first) {
auto dcs = is_def_eq(t_type, s_type, c, jst);
if (dcs.first)
return to_bcs(true, dcs.second + scs.second + pcs.second + tcs.second);
}
// This procedure will miss the case where s_type and t_type cannot be reduced to Prop
// because they contain metavariables.
}
}
if (may_reduce_later(t_n, c) || may_reduce_later(s_n, c) || delay_check) {
cs = cs + constraint_seq(mk_eq_cnstr(t_n, s_n, jst.get()));
return to_bcs(true, cs);
}
return to_bcs(false);
}
pair<bool, constraint_seq> default_converter::is_prop(expr const & e, type_checker & c) {
auto tcs = infer_type(c, e);
auto wcs = whnf(tcs.first, c);
if (wcs.first == mk_Prop())
return to_bcs(true, wcs.second + tcs.second);
else
return to_bcs(false);
}
void initialize_default_converter() {
g_dont_care = new expr(Const("dontcare"));
}
void finalize_default_converter() {
delete g_dont_care;
}
}

74
src/kernel/default_converter.h Normal file
View file

@ -0,0 +1,74 @@
/*
Copyright (c) 2014-2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include "util/lbool.h"
#include "kernel/justification.h"
#include "kernel/environment.h"
#include "kernel/converter.h"
#include "kernel/expr_maps.h"
namespace lean {
/** \breif Converter used in the kernel */
class default_converter : public converter {
protected:
environment m_env;
optional<module_idx> m_module_idx;
bool m_memoize;
extra_opaque_pred m_extra_pred;
expr_struct_map<expr> m_whnf_core_cache;
expr_struct_map<pair<expr, constraint_seq>> m_whnf_cache;
virtual bool may_reduce_later(expr const & e, type_checker & c);
constraint mk_eq_cnstr(expr const & lhs, expr const & rhs, justification const & j);
optional<expr> expand_macro(expr const & m, type_checker & c);
optional<pair<expr, constraint_seq>> norm_ext(expr const & e, type_checker & c);
optional<expr> d_norm_ext(expr const & e, type_checker & c, constraint_seq & cs);
expr whnf_core(expr const & e, type_checker & c);
bool is_opaque_core(declaration const & d) const;
expr unfold_name_core(expr e, unsigned w);
expr unfold_names(expr const & e, unsigned w);
optional<declaration> is_delta(expr const & e);
expr whnf_core(expr e, unsigned w, type_checker & c);
expr whnf(expr const & e_prime, type_checker & c, constraint_seq & cs);
pair<bool, constraint_seq> to_bcs(bool b) { return mk_pair(b, constraint_seq()); }
pair<bool, constraint_seq> to_bcs(bool b, constraint const & c) { return mk_pair(b, constraint_seq(c)); }
pair<bool, constraint_seq> to_bcs(bool b, constraint_seq const & cs) { return mk_pair(b, cs); }
bool is_def_eq_binding(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs);
bool is_def_eq(level const & l1, level const & l2, delayed_justification & jst, constraint_seq & cs);
bool is_def_eq(levels const & ls1, levels const & ls2, type_checker & c, delayed_justification & jst, constraint_seq & cs);
static pair<lbool, constraint_seq> to_lbcs(lbool l) { return mk_pair(l, constraint_seq()); }
static pair<lbool, constraint_seq> to_lbcs(lbool l, constraint const & c) { return mk_pair(l, constraint_seq(c)); }
static pair<lbool, constraint_seq> to_lbcs(pair<bool, constraint_seq> const & bcs) {
return mk_pair(to_lbool(bcs.first), bcs.second);
}
lbool quick_is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs);
bool is_def_eq_args(expr t, expr s, type_checker & c, delayed_justification & jst, constraint_seq & cs);
bool is_app_of(expr t, name const & f_name);
bool try_eta_expansion(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs);
bool is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst, constraint_seq & cs);
pair<bool, constraint_seq> is_prop(expr const & e, type_checker & c);
public:
default_converter(environment const & env, optional<module_idx> mod_idx, bool memoize,
extra_opaque_pred const & pred);
virtual bool is_opaque(declaration const & d) const;
virtual pair<expr, constraint_seq> whnf(expr const & e_prime, type_checker & c);
virtual optional<module_idx> get_module_idx() const { return m_module_idx; }
virtual pair<bool, constraint_seq> is_def_eq(expr const & t, expr const & s, type_checker & c, delayed_justification & jst);
};
void initialize_default_converter();
void finalize_default_converter();
}

3
src/kernel/init_module.cpp
View file

@ -11,12 +11,14 @@ Author: Leonardo de Moura
#include "kernel/formatter.h"
#include "kernel/level.h"
#include "kernel/declaration.h"
#include "kernel/default_converter.h"
namespace lean {
void initialize_kernel_module() {
initialize_level();
initialize_expr();
initialize_declaration();
initialize_default_converter();
initialize_converter();
initialize_type_checker();
initialize_environment();
@ -27,6 +29,7 @@ void finalize_kernel_module() {
finalize_environment();
finalize_type_checker();
finalize_converter();
finalize_default_converter();
finalize_declaration();
finalize_expr();
finalize_level();