lean2/src/library/num.cpp

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/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/type_checker.h"
#include "library/num.h"
#include "library/constants.h"
namespace lean {
static expr * g_num = nullptr;
static expr * g_pos_num = nullptr;
static expr * g_zero = nullptr;
static expr * g_pos = nullptr;
static expr * g_one = nullptr;
static expr * g_bit0 = nullptr;
static expr * g_bit1 = nullptr;
void initialize_num() {
g_num = new expr(Const(get_num_name()));
g_pos_num = new expr(Const(get_pos_num_name()));
g_zero = new expr(Const(get_num_zero_name()));
g_pos = new expr(Const(get_num_pos_name()));
g_one = new expr(Const(get_pos_num_one_name()));
g_bit0 = new expr(Const(get_pos_num_bit0_name()));
g_bit1 = new expr(Const(get_pos_num_bit1_name()));
}
void finalize_num() {
delete g_num;
delete g_pos_num;
delete g_zero;
delete g_pos;
delete g_one;
delete g_bit0;
delete g_bit1;
}
bool has_num_decls(environment const & env) {
try {
type_checker tc(env);
return
tc.infer(*g_zero).first == *g_num &&
tc.infer(*g_pos).first == mk_arrow(*g_pos_num, *g_num) &&
tc.infer(*g_one).first == *g_pos_num &&
tc.infer(*g_bit0).first == mk_arrow(*g_pos_num, *g_pos_num) &&
tc.infer(*g_bit1).first == mk_arrow(*g_pos_num, *g_pos_num);
} catch (exception&) {
return false;
}
}
expr from_pos_num(mpz const & n) {
lean_assert(n > 0);
if (n == 1)
return *g_one;
if (n % mpz(2) == 1)
return mk_app(*g_bit1, from_pos_num(n / 2));
else
return mk_app(*g_bit0, from_pos_num(n / 2));
}
expr from_num(mpz const & n) {
expr r;
lean_assert(n >= 0);
if (n == 0)
r = *g_zero;
else
r = mk_app(*g_pos, from_pos_num(n));
lean_assert(*to_num(r) == n);
return r;
}
optional<mpz> to_pos_num(expr const & e) {
if (e == *g_one) {
return some(mpz(1));
} else if (is_app(e)) {
if (app_fn(e) == *g_bit0) {
if (auto r = to_pos_num(app_arg(e)))
return some(2*(*r));
} else if (app_fn(e) == *g_bit1) {
if (auto r = to_pos_num(app_arg(e)))
return some(2*(*r) + 1);
}
}
return optional<mpz>();
}
optional<mpz> to_num(expr const & e) {
if (e == *g_zero)
return some(mpz(0));
else if (is_app(e) && app_fn(e) == *g_pos)
return to_pos_num(app_arg(e));
else
return optional<mpz>();
}
}