lean2/src/kernel/expr.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
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Soonho Kong
*/
#include <vector>
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#include <sstream>
#include "expr.h"
#include "free_vars.h"
#include "sets.h"
#include "hash.h"
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#include "format.h"
namespace lean {
unsigned hash_args(unsigned size, expr const * args) {
return hash(size, [&args](unsigned i){ return args[i].hash(); });
}
expr_cell::expr_cell(expr_kind k, unsigned h):
m_kind(static_cast<unsigned>(k)),
m_flags(0),
m_hash(h),
m_rc(1) {}
expr_var::expr_var(unsigned idx):
expr_cell(expr_kind::Var, idx),
m_vidx(idx) {}
expr_const::expr_const(name const & n, unsigned pos):
expr_cell(expr_kind::Constant, n.hash()),
m_name(n),
m_pos(pos) {}
expr_app::expr_app(unsigned num_args):
expr_cell(expr_kind::App, 0),
m_num_args(num_args) {
}
expr_app::~expr_app() {
for (unsigned i = 0; i < m_num_args; i++)
(m_args+i)->~expr();
}
expr app(unsigned n, expr const * as) {
lean_assert(n > 1);
unsigned new_n;
unsigned n0 = 0;
expr const & arg0 = as[0];
// Remark: we represent ((app a b) c) as (app a b c)
if (is_app(arg0)) {
n0 = num_args(arg0);
new_n = n + n0 - 1;
}
else {
new_n = n;
}
char * mem = new char[sizeof(expr_app) + new_n*sizeof(expr)];
expr r(new (mem) expr_app(new_n));
expr * m_args = to_app(r)->m_args;
unsigned i = 0;
unsigned j = 0;
if (new_n != n) {
for (; i < n0; i++)
new (m_args+i) expr(arg(arg0, i));
j++;
}
for (; i < new_n; ++i, ++j) {
lean_assert(j < n);
new (m_args+i) expr(as[j]);
}
to_app(r)->m_hash = hash_args(new_n, m_args);
return r;
}
expr_abstraction::expr_abstraction(expr_kind k, name const & n, expr const & t, expr const & b):
expr_cell(k, ::lean::hash(t.hash(), b.hash())),
m_name(n),
m_type(t),
m_body(b) {
}
expr_lambda::expr_lambda(name const & n, expr const & t, expr const & e):
expr_abstraction(expr_kind::Lambda, n, t, e) {}
expr_pi::expr_pi(name const & n, expr const & t, expr const & e):
expr_abstraction(expr_kind::Pi, n, t, e) {}
expr_type::expr_type(level const & l):
expr_cell(expr_kind::Type, l.hash()),
m_level(l) {
}
expr_type::~expr_type() {
}
expr_numeral::expr_numeral(mpz const & n):
expr_cell(expr_kind::Numeral, n.hash()),
m_numeral(n) {}
void expr_cell::dealloc() {
switch (kind()) {
case expr_kind::Var: delete static_cast<expr_var*>(this); break;
case expr_kind::Constant: delete static_cast<expr_const*>(this); break;
case expr_kind::App: static_cast<expr_app*>(this)->~expr_app(); delete[] reinterpret_cast<char*>(this); break;
case expr_kind::Lambda: delete static_cast<expr_lambda*>(this); break;
case expr_kind::Pi: delete static_cast<expr_pi*>(this); break;
case expr_kind::Type: delete static_cast<expr_type*>(this); break;
case expr_kind::Numeral: delete static_cast<expr_numeral*>(this); break;
}
}
class eq_fn {
expr_cell_pair_set m_eq_visited;
bool apply(expr const & a, expr const & b) {
if (eqp(a, b)) return true;
if (a.hash() != b.hash()) return false;
if (a.kind() != b.kind()) return false;
if (is_var(a)) return var_idx(a) == var_idx(b);
if (is_shared(a) && is_shared(b)) {
auto p = std::make_pair(a.raw(), b.raw());
if (m_eq_visited.find(p) != m_eq_visited.end())
return true;
m_eq_visited.insert(p);
}
switch (a.kind()) {
case expr_kind::Var: lean_unreachable(); return true;
case expr_kind::Constant: return const_name(a) == const_name(b);
case expr_kind::App:
if (num_args(a) != num_args(b))
return false;
for (unsigned i = 0; i < num_args(a); i++)
if (!apply(arg(a, i), arg(b, i)))
return false;
return true;
case expr_kind::Lambda:
case expr_kind::Pi:
// Lambda and Pi
// Remark: we ignore get_abs_name because we want alpha-equivalence
return apply(abst_type(a), abst_type(b)) && apply(abst_body(a), abst_body(b));
case expr_kind::Type: return ty_level(a) == ty_level(b);
case expr_kind::Numeral: return num_value(a) == num_value(b);
}
lean_unreachable();
return false;
}
public:
bool operator()(expr const & a, expr const & b) {
return apply(a, b);
}
};
bool operator==(expr const & a, expr const & b) {
return eq_fn()(a, b);
}
// Low-level pretty printer
std::ostream & operator<<(std::ostream & out, expr const & a) {
switch (a.kind()) {
case expr_kind::Var: out << "#" << var_idx(a); break;
case expr_kind::Constant: out << const_name(a); break;
case expr_kind::App:
out << "(";
for (unsigned i = 0; i < num_args(a); i++) {
if (i > 0) out << " ";
out << arg(a, i);
}
out << ")";
break;
case expr_kind::Lambda: out << "(fun (" << abst_name(a) << " : " << abst_type(a) << ") " << abst_body(a) << ")"; break;
case expr_kind::Pi:
if (has_free_var(abst_body(a), 0))
out << "(pi (" << abst_name(a) << " : " << abst_type(a) << ") " << abst_body(a) << ")";
else
out << abst_type(a) << " -> " << abst_body(a);
break;
case expr_kind::Type: {
level const & l = ty_level(a);
if (is_uvar(l) && uvar_idx(l) == 0)
out << "Type";
else
out << "(Type " << ty_level(a) << ")";
break;
}
case expr_kind::Numeral: out << num_value(a); break;
}
return out;
}
expr copy(expr const & a) {
switch (a.kind()) {
case expr_kind::Var: return var(var_idx(a));
case expr_kind::Constant: return constant(const_name(a), const_pos(a));
case expr_kind::Type: return type(ty_level(a));
case expr_kind::Numeral: return numeral(num_value(a));
case expr_kind::App: return app(num_args(a), begin_args(a));
case expr_kind::Lambda: return lambda(abst_name(a), abst_type(a), abst_body(a));
case expr_kind::Pi: return pi(abst_name(a), abst_type(a), abst_body(a));
}
lean_unreachable();
return expr();
}
}
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lean::format pp_aux(lean::expr const & a) {
using namespace lean;
switch (a.kind()) {
case expr_kind::Var:
return format{format("#"), format(static_cast<int>(var_idx(a)))};
case expr_kind::Constant:
return format(const_name(a));
case expr_kind::App:
{
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format r;
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for (unsigned i = 0; i < num_args(a); i++) {
if (i > 0) r += format(" ");
r += pp_aux(arg(a, i));
}
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return paren(r);
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}
case expr_kind::Lambda:
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return paren(format{
highlight(format("\u03BB "), format::format_color::PINK), /* Use unicode lambda */
paren(format{
format(abst_name(a)),
format(" : "),
pp_aux(abst_type(a))}),
format(" "),
pp_aux(abst_body(a))});
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case expr_kind::Pi:
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return paren(format{
highlight(format("\u03A0 "), format::format_color::ORANGE), /* Use unicode lambda */
paren(format{
format(abst_name(a)),
format(" : "),
pp_aux(abst_type(a))}),
format(" "),
pp_aux(abst_body(a))});
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case expr_kind::Type:
{
std::stringstream ss;
ss << ty_level(a);
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return paren(format{format("Type "),
format(ss.str())});
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}
case expr_kind::Numeral:
return format(num_value(a));
}
lean_unreachable();
return format();
}
void pp(lean::expr const & a) {
lean::format const & f = pp_aux(a);
std::cout << f;
}