393 lines
14 KiB
C++
393 lines
14 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 "util/test.h"
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#include "kernel/type_checker.h"
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#include "kernel/kernel_exception.h"
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#include "kernel/occurs.h"
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#include "kernel/abstract.h"
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#include "kernel/free_vars.h"
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#include "library/placeholder.h"
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#include "library/printer.h"
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#include "library/basic_thms.h"
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#include "library/all/all.h"
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#include "frontends/lean/frontend.h"
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#include "frontends/lean/elaborator.h"
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#include "frontends/lean/elaborator_exception.h"
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using namespace lean;
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expr elaborate(expr const & e, frontend const & env) {
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elaborator elb(env);
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return elb(e);
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}
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// Check elaborator success
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static void success(expr const & e, expr const & expected, frontend const & env) {
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std::cout << "\n" << e << "\n------>\n";
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try {
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std::cout << elaborate(e, env) << "\n";
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} catch (unification_app_mismatch_exception & ex) {
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std::cout << "Error at " << mk_pair(ex.get_expr(), ex.get_context()) << "\n";
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} catch (unification_type_mismatch_exception & ex) {
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std::cout << "Error at " << mk_pair(ex.get_expr(), ex.get_context()) << " " << ex.what() << "\n";
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std::cout << "Elaborator:\n"; ex.get_elaborator().display(std::cout); std::cout << "-----------------\n";
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}
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lean_assert(elaborate(e, env) == expected);
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try {
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std::cout << infer_type(elaborate(e, env), env) << "\n";
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} catch (app_type_mismatch_exception & ex) {
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context const & ctx = ex.get_context();
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std::cout << "Application type mismatch at\n"
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<< " " << mk_pair(ex.get_application(), ctx) << "\n";
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lean_unreachable();
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}
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}
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// Check elaborator failure
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static void fails(expr const & e, frontend const & env) {
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try {
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expr new_e = elaborate(e, env);
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std::cout << "new_e: " << new_e << std::endl;
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lean_unreachable();
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} catch (exception &) {
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}
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}
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// Check elaborator partial success (i.e., result still contain some metavariables */
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static void unsolved(expr const & e, frontend const & env) {
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try {
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std::cout << "\n" << e << "\n------>\n" << elaborate(e, env) << "\n";
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lean_unreachable();
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} catch (unsolved_placeholder_exception) {
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}
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}
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#define _ mk_placholder()
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static void tst1() {
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frontend env;
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expr A = Const("A");
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expr B = Const("B");
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expr F = Const("F");
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expr g = Const("g");
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expr a = Const("a");
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expr Nat = Const("N");
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expr Real = Const("R");
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env.add_var("N", Type());
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env.add_var("R", Type());
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env.add_var("F", Pi({{A, Type()}, {B, Type()}, {g, A >> B}}, A));
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env.add_var("f", Nat >> Real);
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expr f = Const("f");
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success(F(_, _, f), F(Nat, Real, f), env);
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// fails(F(_, Bool, f), env);
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success(F(_, _, Fun({a, Nat}, a)), F(Nat, Nat, Fun({a, Nat}, a)), env);
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}
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static void tst2() {
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frontend env;
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expr a = Const("a");
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expr b = Const("b");
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expr c = Const("c");
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expr H1 = Const("H1");
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expr H2 = Const("H2");
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env.add_var("a", Bool);
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env.add_var("b", Bool);
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env.add_var("c", Bool);
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env.add_axiom("H1", Eq(a, b));
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env.add_axiom("H2", Eq(b, c));
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success(Trans(_, _, _, _, H1, H2), Trans(Bool, a, b, c, H1, H2), env);
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success(Trans(_, _, _, _, Symm(_, _, _, H2), Symm(_, _, _, H1)),
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Trans(Bool, c, b, a, Symm(Bool, b, c, H2), Symm(Bool, a, b, H1)), env);
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success(Symm(_, _, _, Trans(_, _ , _ , _ , Symm(_, _, _, H2), Symm(_, _, _, H1))),
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Symm(Bool, c, a, Trans(Bool, c, b, a, Symm(Bool, b, c, H2), Symm(Bool, a, b, H1))), env);
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env.add_axiom("H3", a);
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expr H3 = Const("H3");
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success(EqTIntro(_, EqMP(_, _, Symm(_, _, _, Trans(_, _, _, _, Symm(_, _, _, H2), Symm(_, _, _, H1))), H3)),
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EqTIntro(c, EqMP(a, c, Symm(Bool, c, a, Trans(Bool, c, b, a, Symm(Bool, b, c, H2), Symm(Bool, a, b, H1))), H3)),
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env);
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}
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static void tst3() {
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frontend env;
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expr Nat = Const("N");
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env.add_var("N", Type());
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env.add_var("vec", Nat >> Type());
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expr n = Const("n");
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expr vec = Const("vec");
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env.add_var("f", Pi({n, Nat}, vec(n) >> Nat));
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expr f = Const("f");
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expr a = Const("a");
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expr b = Const("b");
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expr H = Const("H");
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expr fact = Const("fact");
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env.add_var("a", Nat);
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env.add_var("b", Nat);
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env.add_definition("fact", Bool, Eq(a, b));
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env.add_axiom("H", fact);
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success(Congr2(_, _, _, _, f, H),
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Congr2(Nat, Fun({n, Nat}, vec(n) >> Nat), a, b, f, H), env);
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env.add_var("g", Pi({n, Nat}, vec(n) >> Nat));
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expr g = Const("g");
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env.add_axiom("H2", Eq(f, g));
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expr H2 = Const("H2");
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success(Congr(_, _, _, _, _, _, H2, H),
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Congr(Nat, Fun({n, Nat}, vec(n) >> Nat), f, g, a, b, H2, H), env);
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success(Congr(_, _, _, _, _, _, Refl(_, f), H),
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Congr(Nat, Fun({n, Nat}, vec(n) >> Nat), f, f, a, b, Refl(Pi({n, Nat}, vec(n) >> Nat), f), H), env);
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success(Refl(_, a), Refl(Nat, a), env);
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}
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static void tst4() {
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frontend env;
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expr Nat = Const("N");
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env.add_var("N", Type());
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expr R = Const("R");
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env.add_var("R", Type());
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env.add_var("a", Nat);
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expr a = Const("a");
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expr f = Const("f");
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env.add_var("f", Nat >> ((R >> Nat) >> R));
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expr x = Const("x");
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expr y = Const("y");
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expr z = Const("z");
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success(Fun({{x, _}, {y, _}}, f(x, y)),
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Fun({{x, Nat}, {y, R >> Nat}}, f(x, y)), env);
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success(Fun({{x, _}, {y, _}, {z, _}}, Eq(f(x, y), f(x, z))),
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Fun({{x, Nat}, {y, R >> Nat}, {z, R >> Nat}}, Eq(f(x, y), f(x, z))), env);
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expr A = Const("A");
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success(Fun({{A, Type()}, {x, _}, {y, _}, {z, _}}, Eq(f(x, y), f(x, z))),
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Fun({{A, Type()}, {x, Nat}, {y, R >> Nat}, {z, R >> Nat}}, Eq(f(x, y), f(x, z))), env);
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}
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static void tst5() {
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frontend env;
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expr A = Const("A");
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expr B = Const("B");
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expr a = Const("a");
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expr b = Const("b");
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expr f = Const("f");
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expr g = Const("g");
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expr Nat = Const("N");
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env.add_var("N", Type());
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env.add_var("f", Pi({{A, Type()}, {a, A}, {b, A}}, A));
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env.add_var("g", Nat >> Nat);
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success(Fun({{a, _}, {b, _}}, g(f(_, a, b))),
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Fun({{a, Nat}, {b, Nat}}, g(f(Nat, a, b))), env);
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}
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static void tst6() {
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frontend env;
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expr lst = Const("list");
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expr nil = Const("nil");
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expr cons = Const("cons");
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expr N = Const("N");
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expr A = Const("A");
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expr f = Const("f");
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expr l = Const("l");
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expr a = Const("a");
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env.add_var("N", Type());
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env.add_var("list", Type() >> Type());
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env.add_var("nil", Pi({A, Type()}, lst(A)));
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env.add_var("cons", Pi({{A, Type()}, {a, A}, {l, lst(A)}}, lst(A)));
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env.add_var("f", lst(N >> N) >> Bool);
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success(Fun({a, _}, f(cons(_, a, cons(_, a, nil(_))))),
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Fun({a, N >> N}, f(cons(N >> N, a, cons(N >> N, a, nil(N >> N))))), env);
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}
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static void tst7() {
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frontend env;
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expr x = Const("x");
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expr omega = mk_app(Fun({x, _}, x(x)), Fun({x, _}, x(x)));
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fails(omega, env);
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}
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static void tst8() {
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frontend env;
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expr B = Const("B");
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expr A = Const("A");
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expr x = Const("x");
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expr f = Const("f");
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env.add_var("f", Pi({B, Type()}, B >> B));
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success(Fun({{A, Type()}, {B, Type()}, {x, _}}, f(B, x)),
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Fun({{A, Type()}, {B, Type()}, {x, B}}, f(B, x)), env);
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fails(Fun({{x, _}, {A, Type()}}, f(A, x)), env);
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success(Fun({{A, Type()}, {x, _}}, f(A, x)),
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Fun({{A, Type()}, {x, A}}, f(A, x)), env);
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success(Fun({{A, Type()}, {B, Type()}, {x, _}}, f(A, x)),
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Fun({{A, Type()}, {B, Type()}, {x, A}}, f(A, x)), env);
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success(Fun({{A, Type()}, {B, Type()}, {x, _}}, Eq(f(B, x), f(_, x))),
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Fun({{A, Type()}, {B, Type()}, {x, B}}, Eq(f(B, x), f(B, x))), env);
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success(Fun({{A, Type()}, {B, _}, {x, _}}, Eq(f(B, x), f(_, x))),
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Fun({{A, Type()}, {B, Type()}, {x, B}}, Eq(f(B, x), f(B, x))), env);
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unsolved(Fun({{A, _}, {B, _}, {x, _}}, Eq(f(B, x), f(_, x))), env);
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}
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static void tst9() {
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frontend env;
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expr A = Const("A");
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expr B = Const("B");
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expr f = Const("f");
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expr g = Const("g");
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expr x = Const("x");
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expr y = Const("y");
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env.add_var("N", Type());
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env.add_var("f", Pi({A, Type()}, A >> A));
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expr N = Const("N");
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success(Fun({g, Pi({A, Type()}, A >> (A >> Bool))}, g(_, True, False)),
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Fun({g, Pi({A, Type()}, A >> (A >> Bool))}, g(Bool, True, False)),
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env);
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success(Fun({g, Pi({A, TypeU}, A >> (A >> Bool))}, g(_, Bool, Bool)),
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Fun({g, Pi({A, TypeU}, A >> (A >> Bool))}, g(Type(), Bool, Bool)),
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env);
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success(Fun({g, Pi({A, TypeU}, A >> (A >> Bool))}, g(_, Bool, N)),
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Fun({g, Pi({A, TypeU}, A >> (A >> Bool))}, g(Type(), Bool, N)),
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env);
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success(Fun({g, Pi({A, Type()}, A >> (A >> Bool))},
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g(_,
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Fun({{x, _}, {y, _}}, Eq(f(_, x), f(_, y))),
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Fun({{x, N}, {y, Bool}}, True))),
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Fun({g, Pi({A, Type()}, A >> (A >> Bool))},
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g((N >> (Bool >> Bool)),
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Fun({{x, N}, {y, Bool}}, Eq(f(N, x), f(Bool, y))),
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Fun({{x, N}, {y, Bool}}, True))), env);
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success(Fun({g, Pi({A, Type()}, A >> (A >> Bool))},
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g(_,
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Fun({{x, N}, {y, _}}, Eq(f(_, x), f(_, y))),
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Fun({{x, _}, {y, Bool}}, True))),
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Fun({g, Pi({A, Type()}, A >> (A >> Bool))},
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g((N >> (Bool >> Bool)),
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Fun({{x, N}, {y, Bool}}, Eq(f(N, x), f(Bool, y))),
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Fun({{x, N}, {y, Bool}}, True))), env);
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}
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static void tst10() {
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frontend env;
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expr A = Const("A");
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expr B = Const("B");
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expr C = Const("C");
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expr a = Const("a");
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expr b = Const("b");
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expr eq = Const("eq");
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env.add_var("eq", Pi({A, Type()}, A >> (A >> Bool)));
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success(Fun({{A, Type()}, {B, Type()}, {a, _}, {b, B}}, eq(_, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, B}, {b, B}}, eq(B, a, b)), env);
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success(Fun({{A, Type()}, {B, Type()}, {a, _}, {b, A}}, eq(_, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, A}, {b, A}}, eq(A, a, b)), env);
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success(Fun({{A, Type()}, {B, Type()}, {a, A}, {b, _}}, eq(_, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, A}, {b, A}}, eq(A, a, b)), env);
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success(Fun({{A, Type()}, {B, Type()}, {a, B}, {b, _}}, eq(_, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, B}, {b, B}}, eq(B, a, b)), env);
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success(Fun({{A, Type()}, {B, Type()}, {a, B}, {b, _}, {C, Type()}}, eq(_, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, B}, {b, B}, {C, Type()}}, eq(B, a, b)), env);
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fails(Fun({{A, Type()}, {B, Type()}, {a, _}, {b, _}, {C, Type()}}, eq(C, a, b)), env);
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success(Fun({{A, Type()}, {B, Type()}, {a, _}, {b, _}, {C, Type()}}, eq(B, a, b)),
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Fun({{A, Type()}, {B, Type()}, {a, B}, {b, B}, {C, Type()}}, eq(B, a, b)), env);
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}
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static void tst11() {
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frontend env;
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expr a = Const("a");
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expr b = Const("b");
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expr c = Const("c");
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expr H1 = Const("H1");
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expr H2 = Const("H2");
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env.add_var("a", Bool);
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env.add_var("b", Bool);
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env.add_var("c", Bool);
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success(Fun({{H1, Eq(a, b)}, {H2, Eq(b, c)}},
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Trans(_, _, _, _, H1, H2)),
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Fun({{H1, Eq(a, b)}, {H2, Eq(b, c)}},
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Trans(Bool, a, b, c, H1, H2)),
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env);
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expr H3 = Const("H3");
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success(Fun({{H1, Eq(a, b)}, {H2, Eq(b, c)}, {H3, a}},
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EqTIntro(_, EqMP(_, _, Symm(_, _, _, Trans(_, _, _, _, Symm(_, _, _, H2), Symm(_, _, _, H1))), H3))),
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Fun({{H1, Eq(a, b)}, {H2, Eq(b, c)}, {H3, a}},
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EqTIntro(c, EqMP(a, c, Symm(Bool, c, a, Trans(Bool, c, b, a, Symm(Bool, b, c, H2), Symm(Bool, a, b, H1))), H3))),
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env);
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frontend env2;
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success(Fun({{a, Bool}, {b, Bool}, {c, Bool}, {H1, Eq(a, b)}, {H2, Eq(b, c)}, {H3, a}},
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EqTIntro(_, EqMP(_, _, Symm(_, _, _, Trans(_, _, _, _, Symm(_, _, _, H2), Symm(_, _, _, H1))), H3))),
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Fun({{a, Bool}, {b, Bool}, {c, Bool}, {H1, Eq(a, b)}, {H2, Eq(b, c)}, {H3, a}},
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EqTIntro(c, EqMP(a, c, Symm(Bool, c, a, Trans(Bool, c, b, a, Symm(Bool, b, c, H2), Symm(Bool, a, b, H1))), H3))),
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env2);
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expr A = Const("A");
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success(Fun({{A, Type()}, {a, A}, {b, A}, {c, A}, {H1, Eq(a, b)}, {H2, Eq(b, c)}},
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Symm(_, _, _, Trans(_, _, _, _, Symm(_, _, _, H2), Symm(_, _, _, H1)))),
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Fun({{A, Type()}, {a, A}, {b, A}, {c, A}, {H1, Eq(a, b)}, {H2, Eq(b, c)}},
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Symm(A, c, a, Trans(A, c, b, a, Symm(A, b, c, H2), Symm(A, a, b, H1)))),
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env2);
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}
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void tst12() {
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frontend env;
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expr A = Const("A");
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expr B = Const("B");
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expr a = Const("a");
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expr b = Const("b");
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expr eq = Const("eq");
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env.add_var("eq", Pi({A, Type(level()+1)}, A >> (A >> Bool)));
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success(eq(_, Fun({{A, Type()}, {a, _}}, a), Fun({{B, Type()}, {b, B}}, b)),
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eq(Pi({A, Type()}, A >> A), Fun({{A, Type()}, {a, A}}, a), Fun({{B, Type()}, {b, B}}, b)),
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env);
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}
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void tst13() {
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frontend env;
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expr A = Const("A");
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expr h = Const("h");
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expr f = Const("f");
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expr a = Const("a");
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env.add_var("h", Pi({A, Type()}, A) >> Bool);
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success(Fun({{f, Pi({A, Type()}, _)}, {a, Bool}}, h(f)),
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Fun({{f, Pi({A, Type()}, A)}, {a, Bool}}, h(f)),
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env);
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}
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void tst14() {
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frontend env;
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expr R = Const("R");
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expr A = Const("A");
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expr r = Const("r");
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expr eq = Const("eq");
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expr f = Const("f");
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expr g = Const("g");
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expr h = Const("h");
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expr D = Const("D");
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env.add_var("R", Type() >> Bool);
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env.add_var("r", Pi({A, Type()}, R(A)));
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env.add_var("h", Pi({A, Type()}, R(A)) >> Bool);
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env.add_var("eq", Pi({A, Type(level()+1)}, A >> (A >> Bool)));
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success(Let({{f, Fun({A, Type()}, r(_))},
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{g, Fun({A, Type()}, r(_))},
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{D, Fun({A, Type()}, eq(_, f(A), g(_)))}},
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h(f)),
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Let({{f, Fun({A, Type()}, r(A))},
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{g, Fun({A, Type()}, r(A))},
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{D, Fun({A, Type()}, eq(R(A), f(A), g(A)))}},
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h(f)),
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env);
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}
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int main() {
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tst1();
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tst2();
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|
tst3();
|
|
tst4();
|
|
tst5();
|
|
tst6();
|
|
tst7();
|
|
tst8();
|
|
tst9();
|
|
tst10();
|
|
tst11();
|
|
tst12();
|
|
tst13();
|
|
tst14();
|
|
return has_violations() ? 1 : 0;
|
|
}
|