lean2/src/kernel/normalize.cpp

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include <algorithm>
#include "normalize.h"
#include "expr.h"
#include "context.h"
#include "environment.h"
#include "scoped_map.h"
#include "builtin.h"
#include "free_vars.h"
#include "list.h"
#include "buffer.h"
#include "exception.h"
namespace lean {
class svalue;
typedef list<svalue> value_stack; //!< Normalization stack
enum class svalue_kind { Expr, Closure, BoundedVar };
/** \brief Stack value: simple expressions, closures and bounded variables. */
class svalue {
svalue_kind m_kind;
unsigned m_bvar;
expr m_expr;
value_stack m_ctx;
public:
svalue() {}
explicit svalue(expr const & e): m_kind(svalue_kind::Expr), m_expr(e) {}
explicit svalue(unsigned k): m_kind(svalue_kind::BoundedVar), m_bvar(k) {}
svalue(expr const & e, value_stack const & c):m_kind(svalue_kind::Closure), m_expr(e), m_ctx(c) { lean_assert(is_lambda(e)); }
svalue_kind kind() const { return m_kind; }
bool is_expr() const { return kind() == svalue_kind::Expr; }
bool is_closure() const { return kind() == svalue_kind::Closure; }
bool is_bounded_var() const { return kind() == svalue_kind::BoundedVar; }
expr const & get_expr() const { lean_assert(is_expr() || is_closure()); return m_expr; }
value_stack const & get_ctx() const { lean_assert(is_closure()); return m_ctx; }
unsigned get_var_idx() const { lean_assert(is_bounded_var()); return m_bvar; }
};
svalue_kind kind(svalue const & v) { return v.kind(); }
expr const & to_expr(svalue const & v) { return v.get_expr(); }
value_stack const & stack_of(svalue const & v) { return v.get_ctx(); }
unsigned to_bvar(svalue const & v) { return v.get_var_idx(); }
value_stack extend(value_stack const & s, svalue const & v) { return cons(v, s); }
/** \brief Expression normalizer. */
class normalizer::imp {
typedef scoped_map<expr, svalue, expr_hash, expr_eqp> cache;
environment m_env;
context m_ctx;
cache m_cache;
volatile bool m_interrupted;
/**
\brief Auxiliary object for saving the current context.
We need this to be able to process values in the context.
*/
struct save_context {
imp & m_imp;
context m_old_ctx;
save_context(imp & imp):m_imp(imp), m_old_ctx(m_imp.m_ctx) { m_imp.m_cache.clear(); }
~save_context() { m_imp.m_ctx = m_old_ctx; }
};
svalue lookup(value_stack const & s, unsigned i, unsigned k) {
unsigned j = i;
value_stack const * it1 = &s;
while (*it1) {
if (j == 0)
return head(*it1);
--j;
it1 = &tail(*it1);
}
auto p = lookup_ext(m_ctx, j);
context_entry const & entry = p.first;
context const & entry_c = p.second;
if (entry.get_body()) {
save_context save(*this); // it restores the context and cache
m_ctx = entry_c;
unsigned k = length(m_ctx);
return svalue(reify(normalize(entry.get_body(), value_stack(), k), k));
} else {
return svalue(length(entry_c));
}
}
/** \brief Convert the closure \c a into an expression using the given stack in a context that contains \c k binders. */
expr reify_closure(expr const & a, value_stack const & s, unsigned k) {
lean_assert(is_lambda(a));
expr new_t = reify(normalize(abst_domain(a), s, k), k);
expr new_b = reify(normalize(abst_body(a), extend(s, svalue(k)), k+1), k+1);
return mk_lambda(abst_name(a), new_t, new_b);
}
/** \brief Convert the value \c v back into an expression in a context that contains \c k binders. */
expr reify(svalue const & v, unsigned k) {
switch (v.kind()) {
case svalue_kind::Expr: return to_expr(v);
case svalue_kind::BoundedVar: return mk_var(k - to_bvar(v) - 1);
case svalue_kind::Closure: return reify_closure(to_expr(v), stack_of(v), k);
}
lean_unreachable();
return expr();
}
/** \brief Normalize the expression \c a in a context composed of stack \c s and \c k binders. */
svalue normalize(expr const & a, value_stack const & s, unsigned k) {
if (m_interrupted)
throw interrupted();
bool shared = false;
if (is_shared(a)) {
shared = true;
auto it = m_cache.find(a);
if (it != m_cache.end())
return it->second;
}
svalue r;
switch (a.kind()) {
case expr_kind::Var:
r = lookup(s, var_idx(a), k);
break;
case expr_kind::Constant: {
object const & obj = m_env.get_object(const_name(a));
if (obj.is_definition() && !obj.is_opaque()) {
r = normalize(obj.get_value(), value_stack(), 0);
}
else {
r = svalue(a);
}
break;
}
case expr_kind::Type: case expr_kind::Value:
r = svalue(a);
break;
case expr_kind::App: {
svalue f = normalize(arg(a, 0), s, k);
unsigned i = 1;
unsigned n = num_args(a);
while (true) {
if (f.is_closure()) {
// beta reduction
expr const & fv = to_expr(f);
{
cache::mk_scope sc(m_cache);
value_stack new_s = extend(stack_of(f), normalize(arg(a, i), s, k));
f = normalize(abst_body(fv), new_s, k);
}
if (i == n - 1) {
r = f;
break;
}
i++;
} else {
buffer<expr> new_args;
expr new_f = reify(f, k);
new_args.push_back(new_f);
for (; i < n; i++)
new_args.push_back(reify(normalize(arg(a, i), s, k), k));
if (is_value(new_f)) {
expr m;
if (to_value(new_f).normalize(new_args.size(), new_args.data(), m)) {
r = svalue(m);
break;
}
}
r = svalue(mk_app(new_args.size(), new_args.data()));
break;
}
}
break;
}
case expr_kind::Eq: {
expr new_lhs = reify(normalize(eq_lhs(a), s, k), k);
expr new_rhs = reify(normalize(eq_rhs(a), s, k), k);
if (new_lhs == new_rhs) {
r = svalue(mk_bool_value(true));
} else if (is_value(new_lhs) && is_value(new_rhs)) {
r = svalue(mk_bool_value(false));
} else {
r = svalue(mk_eq(new_lhs, new_rhs));
}
break;
}
case expr_kind::Lambda:
r = svalue(a, s);
break;
case expr_kind::Pi: {
expr new_t = reify(normalize(abst_domain(a), s, k), k);
expr new_b;
{
cache::mk_scope sc(m_cache);
new_b = reify(normalize(abst_body(a), extend(s, svalue(k)), k+1), k+1);
}
r = svalue(mk_pi(abst_name(a), new_t, new_b));
break;
}
case expr_kind::Let: {
svalue v = normalize(let_value(a), s, k);
{
cache::mk_scope sc(m_cache);
r = normalize(let_body(a), extend(s, v), k+1);
}
break;
}}
if (shared) {
m_cache.insert(a, r);
}
return r;
}
bool is_convertible_core(expr const & expected, expr const & given) {
if (expected == given) {
return true;
} else {
expr const * e = &expected;
expr const * g = &given;
while (true) {
if (is_type(*e) && is_type(*g)) {
if (m_env.is_ge(ty_level(*e), ty_level(*g)))
return true;
}
if (is_pi(*e) && is_pi(*g) && abst_domain(*e) == abst_domain(*g)) {
e = &abst_body(*e);
g = &abst_body(*g);
} else {
return false;
}
}
}
}
void set_ctx(context const & ctx) {
if (!is_eqp(ctx, m_ctx)) {
m_ctx = ctx;
m_cache.clear();
}
}
public:
imp(environment const & env):
m_env(env) {
m_interrupted = false;
}
expr operator()(expr const & e, context const & ctx) {
set_ctx(ctx);
unsigned k = length(m_ctx);
return reify(normalize(e, value_stack(), k), k);
}
bool is_convertible(expr const & expected, expr const & given, context const & ctx) {
if (is_convertible_core(expected, given))
return true;
set_ctx(ctx);
unsigned k = length(m_ctx);
expr e_n = reify(normalize(expected, value_stack(), k), k);
expr g_n = reify(normalize(given, value_stack(), k), k);
return is_convertible_core(e_n, g_n);
}
void clear() { m_ctx = context(); m_cache.clear(); }
void set_interrupt(bool flag) { m_interrupted = flag; }
};
normalizer::normalizer(environment const & env):m_ptr(new imp(env)) {}
normalizer::~normalizer() {}
expr normalizer::operator()(expr const & e, context const & ctx) { return (*m_ptr)(e, ctx); }
bool normalizer::is_convertible(expr const & t1, expr const & t2, context const & ctx) { return m_ptr->is_convertible(t1, t2, ctx); }
void normalizer::clear() { m_ptr->clear(); }
void normalizer::set_interrupt(bool flag) { m_ptr->set_interrupt(flag); }
expr normalize(expr const & e, environment const & env, context const & ctx) {
return normalizer(env)(e, ctx);
}
bool is_convertible(expr const & expected, expr const & given, environment const & env, context const & ctx) {
return normalizer(env).is_convertible(expected, given, ctx);
}
}
/*
Remark:
Eta-reduction + Cumulativity + Set theoretic interpretation is unsound.
Example:
f : (Type 2) -> (Type 2)
(fun (x : (Type 1)) (f x)) : (Type 1) -> (Type 2)
The domains of these two terms are different. So, they must have different denotations.
However, by eta-reduction, we have:
(fun (x : (Type 1)) (f x)) == f
For now, we will disable it.
REMARK: we can workaround this problem by applying only when the domain of f is equal
to the domain of the lambda abstraction.
Cody Roux suggested we use Eta-expanded normal forms.
Remark: The source code for eta-reduction can be found in the commit 519a290f320c6a
*/