300 lines
8.9 KiB
C++
300 lines
8.9 KiB
C++
/*
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Copyright (c) 2013 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <algorithm>
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#include "expr.h"
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#include "sets.h"
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#include "max_sharing.h"
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#include "free_vars.h"
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#include "test.h"
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#include "abstract.h"
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#include "instantiate.h"
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using namespace lean;
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void tst1() {
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expr a;
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a = numeral(mpz(10));
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expr f;
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f = var(0);
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expr fa = f(a);
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std::cout << fa << "\n";
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std::cout << fa(a) << "\n";
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lean_assert(eqp(arg(fa, 0), f));
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lean_assert(eqp(arg(fa, 1), a));
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lean_assert(!eqp(fa, f(a)));
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lean_assert(app(fa, a) == f(a, a));
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std::cout << fa(fa, fa) << "\n";
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std::cout << lambda("x", prop(), var(0)) << "\n";
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lean_assert(f(a)(a) == f(a, a));
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lean_assert(f(a(a)) != f(a, a));
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lean_assert(lambda("x", prop(), var(0)) == lambda("y", prop(), var(0)));
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std::cout << pi("x", prop(), var(0)) << "\n";
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}
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expr mk_dag(unsigned depth, bool _closed = false) {
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expr f = constant("f");
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expr a = _closed ? constant("a") : var(0);
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while (depth > 0) {
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depth--;
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a = f(a, a);
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}
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return a;
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}
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unsigned depth1(expr const & e) {
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switch (e.kind()) {
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case expr_kind::Var: case expr_kind::Constant: case expr_kind::Prop: case expr_kind::Type: case expr_kind::Numeral:
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return 1;
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case expr_kind::App: {
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unsigned m = 0;
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for (expr const & a : args(e))
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m = std::max(m, depth1(a));
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return m + 1;
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}
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case expr_kind::Lambda: case expr_kind::Pi:
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return std::max(depth1(abst_type(e)), depth1(abst_body(e))) + 1;
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}
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return 0;
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}
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// This is the fastest depth implementation in this file.
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unsigned depth2(expr const & e) {
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switch (e.kind()) {
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case expr_kind::Var: case expr_kind::Constant: case expr_kind::Prop: case expr_kind::Type: case expr_kind::Numeral:
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return 1;
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case expr_kind::App:
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return
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std::accumulate(begin_args(e), end_args(e), 0,
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[](unsigned m, expr const & arg){ return std::max(depth2(arg), m); })
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+ 1;
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case expr_kind::Lambda: case expr_kind::Pi:
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return std::max(depth2(abst_type(e)), depth2(abst_body(e))) + 1;
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}
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return 0;
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}
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// This is the slowest depth implementation in this file.
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unsigned depth3(expr const & e) {
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static std::vector<std::pair<expr const *, unsigned>> todo;
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unsigned m = 0;
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todo.push_back(std::make_pair(&e, 0));
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while (!todo.empty()) {
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auto const & p = todo.back();
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expr const & e = *(p.first);
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unsigned c = p.second + 1;
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todo.pop_back();
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switch (e.kind()) {
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case expr_kind::Var: case expr_kind::Constant: case expr_kind::Prop: case expr_kind::Type: case expr_kind::Numeral:
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m = std::max(c, m);
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break;
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case expr_kind::App: {
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unsigned num = num_args(e);
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for (unsigned i = 0; i < num; i++)
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todo.push_back(std::make_pair(&arg(e, i), c));
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break;
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}
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case expr_kind::Lambda: case expr_kind::Pi:
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todo.push_back(std::make_pair(&abst_type(e), c));
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todo.push_back(std::make_pair(&abst_body(e), c));
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break;
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}
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}
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return m;
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}
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void tst2() {
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expr r1 = mk_dag(20);
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expr r2 = mk_dag(20);
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lean_verify(r1 == r2);
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std::cout << depth2(r1) << "\n";
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lean_verify(depth2(r1) == 21);
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}
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expr mk_big(expr f, unsigned depth, unsigned val) {
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if (depth == 1)
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return constant(name(val));
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else
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return f(mk_big(f, depth - 1, val << 1), mk_big(f, depth - 1, (val << 1) + 1));
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}
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void tst3() {
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expr f = constant("f");
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expr r1 = mk_big(f, 18, 0);
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expr r2 = mk_big(f, 18, 0);
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lean_verify(r1 == r2);
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}
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void tst4() {
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expr f = constant("f");
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expr a = var(0);
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for (unsigned i = 0; i < 10000; i++) {
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a = f(a);
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}
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}
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expr mk_redundant_dag(expr f, unsigned depth) {
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if (depth == 0)
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return var(0);
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else
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return f(mk_redundant_dag(f, depth - 1), mk_redundant_dag(f, depth - 1));
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}
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unsigned count_core(expr const & a, expr_set & s) {
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if (s.find(a) != s.end())
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return 0;
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s.insert(a);
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switch (a.kind()) {
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case expr_kind::Var: case expr_kind::Constant: case expr_kind::Prop: case expr_kind::Type: case expr_kind::Numeral:
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return 1;
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case expr_kind::App:
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return std::accumulate(begin_args(a), end_args(a), 1,
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[&](unsigned sum, expr const & arg){ return sum + count_core(arg, s); });
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case expr_kind::Lambda: case expr_kind::Pi:
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return count_core(abst_type(a), s) + count_core(abst_body(a), s) + 1;
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}
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return 0;
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}
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unsigned count(expr const & a) {
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expr_set s;
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return count_core(a, s);
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}
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void tst5() {
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expr f = constant("f");
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{
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expr r1 = mk_redundant_dag(f, 5);
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expr r2 = max_sharing(r1);
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std::cout << "count(r1): " << count(r1) << "\n";
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std::cout << "count(r2): " << count(r2) << "\n";
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lean_assert(r1 == r2);
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}
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{
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expr r1 = mk_redundant_dag(f, 16);
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expr r2 = max_sharing(r1);
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lean_assert(r1 == r2);
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}
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}
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void tst6() {
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expr f = constant("f");
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expr r = mk_redundant_dag(f, 12);
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for (unsigned i = 0; i < 1000; i++) {
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r = max_sharing(r);
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}
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r = mk_big(f, 16, 0);
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for (unsigned i = 0; i < 1000000; i++) {
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r = max_sharing(r);
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}
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}
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void tst7() {
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expr f = constant("f");
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expr v = var(0);
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expr a1 = max_sharing(f(v,v));
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expr a2 = max_sharing(f(v,v));
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lean_assert(!eqp(a1, a2));
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expr b = max_sharing(f(a1, a2));
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lean_assert(eqp(arg(b, 1), arg(b, 2)));
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}
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void tst8() {
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expr f = constant("f");
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expr x = var(0);
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expr a = constant("a");
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expr n = numeral(mpz(10));
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expr p = prop();
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expr y = var(1);
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lean_assert(closed(a));
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lean_assert(!closed(x));
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lean_assert(closed(f));
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lean_assert(!closed(f(x)));
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lean_assert(closed(lambda("x", p, x)));
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lean_assert(!closed(lambda("x", x, x)));
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lean_assert(!closed(lambda("x", p, y)));
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lean_assert(closed(f(f(f(a)))));
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lean_assert(closed(lambda("x", p, f(f(f(a))))));
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lean_assert(closed(pi("x", p, x)));
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lean_assert(!closed(pi("x", x, x)));
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lean_assert(!closed(pi("x", p, y)));
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lean_assert(closed(pi("x", p, f(f(f(a))))));
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lean_assert(closed(lambda("y", p, lambda("x", p, y))));
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lean_assert(closed(lambda("y", p, app(lambda("x", p, y), var(0)))));
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expr r = lambda("y", p, app(lambda("x", p, y), var(0)));
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lean_assert(closed(r));
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lean_assert(closed(r));
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r = lambda("y", p, app(lambda("x", p, y), var(1)));
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lean_assert(!closed(r));
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r = lambda("y", p, app(lambda("x", p, var(0)), var(1)));
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lean_assert(!closed(r));
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lean_assert(closed(lambda("z", p, r)));
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}
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void tst9() {
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expr r = mk_dag(20, true);
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lean_assert(closed(r));
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r = mk_dag(20, false);
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lean_assert(!closed(r));
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}
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void tst10() {
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expr f = constant("f");
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expr r = mk_big(f, 16, 0);
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for (unsigned i = 0; i < 1000; i++) {
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lean_assert(closed(r));
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}
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}
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/**
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\brief Substitute s with t in e.
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\pre s and t must be closed expressions (i.e., no free variables)
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*/
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inline expr substitute(expr const & s, expr const & t, expr const & e) {
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return instantiate(t, abstract(s, e));
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}
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void tst11() {
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expr f = constant("f");
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expr a = constant("a");
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expr b = constant("b");
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expr x = var(0);
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expr y = var(1);
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std::cout << instantiate(f(a), lambda("x", prop(), f(f(y, b), f(x, y)))) << "\n";
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lean_assert(instantiate(f(a), lambda("x", prop(), f(f(y, b), f(x, y)))) ==
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lambda("x", prop(), f(f(f(a), b), f(x, f(a)))));
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std::cout << abstract(constant("a"), lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) << "\n";
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lean_assert(abstract(constant("a"), lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) ==
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lambda("x", prop(), f(var(1), lambda("y", prop(), f(b, var(2))))));
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std::cout << abstract_p(constant("a"), lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) << "\n";
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lean_assert(abstract_p(constant("a"), lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) ==
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lambda("x", prop(), f(a, lambda("y", prop(), f(b, a)))));
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std::cout << abstract_p(a, lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) << "\n";
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lean_assert(abstract_p(a, lambda("x", prop(), f(a, lambda("y", prop(), f(b, a))))) ==
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lambda("x", prop(), f(var(1), lambda("y", prop(), f(b, var(2))))));
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lean_assert(substitute(f(a), b, f(f(f(a)))) == f(f(b)));
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}
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int main() {
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continue_on_violation(true);
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std::cout << "sizeof(expr): " << sizeof(expr) << "\n";
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std::cout << "sizeof(expr_app): " << sizeof(expr_app) << "\n";
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tst1();
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tst2();
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tst3();
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tst4();
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tst5();
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tst6();
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tst7();
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tst8();
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tst9();
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tst10();
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tst11();
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std::cout << "done" << "\n";
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return has_violations() ? 1 : 0;
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}
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