259 lines
9.6 KiB
C++
259 lines
9.6 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 <thread>
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#include <chrono>
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#include "exception.h"
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#include "normalizer.h"
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#include "builtin.h"
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#include "trace.h"
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#include "test.h"
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#include "expr_sets.h"
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#include "abstract.h"
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#include "kernel_exception.h"
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#include "toplevel.h"
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#include "printer.h"
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using namespace lean;
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expr normalize(expr const & e) {
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environment env;
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return normalize(e, env);
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}
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static void eval(expr const & e, environment & env) { std::cout << e << " --> " << normalize(e, env) << "\n"; }
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static expr t() { return Const("t"); }
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static expr lam(expr const & e) { return mk_lambda("_", t(), e); }
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static expr lam(expr const & t, expr const & e) { return mk_lambda("_", t, e); }
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static expr v(unsigned i) { return Var(i); }
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static expr zero() {
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// fun (t : T) (s : t -> t) (z : t) z
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return lam(t(), lam(mk_arrow(v(0), v(0)), lam(v(1), v(0))));
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}
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static expr one() {
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// fun (t : T) (s : t -> t) s
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return lam(t(), lam(mk_arrow(v(0), v(0)), v(0)));
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}
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static expr num() { return Const("num"); }
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static expr plus() {
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// fun (m n : numeral) (A : Type 0) (f : A -> A) (x : A) => m A f (n A f x).
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expr x = v(0), f = v(1), A = v(2), n = v(3), m = v(4);
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expr body = m(A, f, n(A, f, x));
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return lam(num(), lam(num(), lam(t(), lam(mk_arrow(v(0), v(0)), lam(v(1), body)))));
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}
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static expr two() { return mk_app({plus(), one(), one()}); }
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static expr three() { return mk_app({plus(), two(), one()}); }
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static expr four() { return mk_app({plus(), two(), two()}); }
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static expr times() {
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// fun (m n : numeral) (A : Type 0) (f : A -> A) (x : A) => m A (n A f) x.
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expr x = v(0), f = v(1), A = v(2), n = v(3), m = v(4);
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expr body = m(A, n(A, f), x);
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return lam(num(), lam(num(), lam(t(), lam(mk_arrow(v(0), v(0)), lam(v(1), body)))));
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}
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static expr power() {
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// fun (m n : numeral) (A : Type 0) => m (A -> A) (n A).
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expr A = v(0), n = v(1), m = v(2);
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expr body = n(mk_arrow(A, A), m(A));
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return lam(num(), lam(num(), lam(mk_arrow(v(0), v(0)), body)));
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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::Type: case expr_kind::Value:
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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::Eq:
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return count_core(eq_lhs(a), s) + count_core(eq_rhs(a), s) + 1;
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case expr_kind::Lambda: case expr_kind::Pi:
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return count_core(abst_domain(a), s) + count_core(abst_body(a), s) + 1;
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case expr_kind::Let:
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return count_core(let_value(a), s) + count_core(let_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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static void tst_church_numbers() {
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environment env;
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env.add_var("t", Type());
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env.add_var("N", Type());
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env.add_var("z", Const("N"));
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env.add_var("s", Const("N"));
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expr N = Const("N");
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expr z = Const("z");
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expr s = Const("s");
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std::cout << normalize(mk_app(zero(), N, s, z), env) << "\n";
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std::cout << normalize(mk_app(one(), N, s, z), env) << "\n";
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std::cout << normalize(mk_app(two(), N, s, z), env) << "\n";
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std::cout << normalize(mk_app(four(), N, s, z), env) << "\n";
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std::cout << count(normalize(mk_app(four(), N, s, z), env)) << "\n";
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lean_assert(count(normalize(mk_app(four(), N, s, z), env)) == 4 + 2);
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std::cout << normalize(mk_app(mk_app(times(), four(), four()), N, s, z), env) << "\n";
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std::cout << normalize(mk_app(mk_app(power(), two(), four()), N, s, z), env) << "\n";
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lean_assert(count(normalize(mk_app(mk_app(power(), two(), four()), N, s, z), env)) == 16 + 2);
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std::cout << normalize(mk_app(mk_app(times(), two(), mk_app(power(), two(), four())), N, s, z), env) << "\n";
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std::cout << count(normalize(mk_app(mk_app(times(), two(), mk_app(power(), two(), four())), N, s, z), env)) << "\n";
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std::cout << count(normalize(mk_app(mk_app(times(), four(), mk_app(power(), two(), four())), N, s, z), env)) << "\n";
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lean_assert(count(normalize(mk_app(mk_app(times(), four(), mk_app(power(), two(), four())), N, s, z), env)) == 64 + 2);
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expr big = normalize(mk_app(mk_app(power(), two(), mk_app(power(), two(), three())), N, s, z), env);
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std::cout << count(big) << "\n";
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lean_assert(count(big) == 256 + 2);
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expr three = mk_app(plus(), two(), one());
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lean_assert(count(normalize(mk_app(mk_app(power(), three, three), N, s, z), env)) == 27 + 2);
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// expr big2 = normalize(mk_app(mk_app(power(), two(), mk_app(times(), mk_app(plus(), four(), one()), four())), N, s, z), env);
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// std::cout << count(big2) << "\n";
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std::cout << normalize(lam(lam(mk_app(mk_app(times(), four(), four()), N, Var(0), z))), env) << "\n";
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}
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static void tst1() {
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environment env;
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env.add_var("t", Type());
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expr t = Type();
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env.add_var("f", mk_arrow(t, t));
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expr f = Const("f");
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env.add_var("a", t);
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expr a = Const("a");
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env.add_var("b", t);
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expr b = Const("b");
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expr x = Var(0);
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expr y = Var(1);
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eval(mk_app(mk_lambda("x", t, x), a), env);
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eval(mk_app(mk_lambda("x", t, x), a, b), env);
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eval(mk_lambda("x", t, f(x)), env);
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eval(mk_lambda("y", t, mk_lambda("x", t, f(y, x))), env);
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eval(mk_app(mk_lambda("x", t,
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mk_app(mk_lambda("f", t,
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mk_app(Var(0), b)),
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mk_lambda("g", t, f(Var(1))))),
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a), env);
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expr l01 = lam(v(0)(v(1)));
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expr l12 = lam(lam(v(1)(v(2))));
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eval(lam(l12(l01)), env);
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lean_assert(normalize(lam(l12(l01)), env) == lam(lam(v(1)(v(1)))));
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}
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static void tst2() {
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environment env;
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expr t = Type();
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env.add_var("f", mk_arrow(t, t));
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expr f = Const("f");
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env.add_var("a", t);
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expr a = Const("a");
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env.add_var("b", t);
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expr b = Const("b");
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env.add_var("h", mk_arrow(t, t));
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expr h = Const("h");
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expr x = Var(0);
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expr y = Var(1);
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lean_assert(normalize(f(x,x), env, extend(context(), name("f"), t, f(a))) == f(f(a), f(a)));
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context c1 = extend(extend(context(), name("f"), t, f(a)), name("h"), t, h(x));
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expr F1 = normalize(f(x,f(x)), env, c1);
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lean_assert(F1 == f(h(f(a)), f(h(f(a)))));
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std::cout << F1 << "\n";
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expr F2 = normalize(mk_lambda("x", t, f(x, f(y))), env, c1);
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std::cout << F2 << "\n";
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lean_assert(F2 == mk_lambda("x", t, f(x, f(h(f(a))))));
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expr F3 = normalize(mk_lambda("y", t, mk_lambda("x", t, f(x, f(y)))), env, c1);
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std::cout << F3 << "\n";
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lean_assert(F3 == mk_lambda("y", t, mk_lambda("x", t, f(x, f(y)))));
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context c2 = extend(extend(context(), name("foo"), t, mk_lambda("x", t, f(x, a))), name("bla"), t, mk_lambda("z", t, h(x,y)));
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expr F4 = normalize(mk_lambda("x", t, f(x, f(y))), env, c2);
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std::cout << F4 << "\n";
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lean_assert(F4 == mk_lambda("x", t, f(x, f(mk_lambda("z", t, h(x,mk_lambda("x", t, f(x, a))))))));
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context c3 = extend(context(), name("x"), t);
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expr f5 = mk_app(mk_lambda("f", t, mk_lambda("z", t, Var(1))), mk_lambda("y", t, Var(1)));
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expr F5 = normalize(f5, env, c3);
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std::cout << f5 << "\n---->\n";
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std::cout << F5 << "\n";
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lean_assert(F5 == mk_lambda("z", t, mk_lambda("y", t, Var(2))));
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context c4 = extend(extend(context(), name("x"), t), name("x2"), t);
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expr F6 = normalize(mk_app(mk_lambda("f", t, mk_lambda("z1", t, mk_lambda("z2", t, mk_app(Var(2), Const("a"))))),
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mk_lambda("y", t, mk_app(Var(1), Var(2), Var(0)))), env, c4);
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std::cout << F6 << "\n";
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lean_assert(F6 == mk_lambda("z1", t, mk_lambda("z2", t, mk_app(Var(2), Var(3), Const("a")))));
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}
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static void tst3() {
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environment env = mk_toplevel();
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env.add_var("a", Bool);
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expr t1 = Const("a");
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expr t2 = Const("a");
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expr e = Eq(t1, t2);
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std::cout << e << " --> " << normalize(e, env) << "\n";
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lean_assert(normalize(e, env) == True);
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}
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static void tst4() {
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environment env;
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env.add_var("b", Type());
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expr t1 = mk_let("a", Const("b"), mk_lambda("c", Type(), Var(1)(Var(0))));
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std::cout << t1 << " --> " << normalize(t1, env) << "\n";
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lean_assert(normalize(t1, env) == mk_lambda("c", Type(), Const("b")(Var(0))));
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}
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static expr mk_big(unsigned depth) {
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if (depth == 0)
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return Const("a");
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else
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return Const("f")(mk_big(depth - 1), mk_big(depth - 1));
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}
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static void tst5() {
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#ifndef __APPLE__
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expr t = mk_big(18);
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environment env = mk_toplevel();
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env.add_var("f", Bool >> (Bool >> Bool));
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env.add_var("a", Bool);
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normalizer proc(env);
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std::chrono::milliseconds dura(50);
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std::thread thread([&]() {
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try {
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proc(t);
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// Remark: if the following code is reached, we
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// should decrease dura.
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lean_unreachable();
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} catch (interrupted & it) {
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std::cout << "interrupted\n";
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}
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});
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std::this_thread::sleep_for(dura);
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proc.interrupt();
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thread.join();
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#endif
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}
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static void tst6() {
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environment env;
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expr x = Const("x");
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expr t = Fun({x, Type()}, mk_app(x, x));
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expr omega = mk_app(t, t);
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normalizer proc(env, 512);
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try {
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proc(omega);
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} catch (kernel_exception & ex) {
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std::cout << ex.what() << "\n";
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}
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}
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int main() {
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tst_church_numbers();
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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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return has_violations() ? 1 : 0;
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}
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