394 lines
14 KiB
C++
394 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 "test.h"
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#include "metavar.h"
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#include "free_vars.h"
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#include "printer.h"
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#include "occurs.h"
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#include "abstract.h"
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#include "toplevel.h"
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#include "basic_thms.h"
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#include "type_checker.h"
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#include "kernel_exception.h"
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#include "lean_frontend.h"
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#include "lean_elaborator.h"
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#include "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 argumet " << ex.get_arg_pos() << " of " << 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 argument " << ex.get_arg_pos() << "\n"
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<< " " << mk_pair(ex.get_application(), ctx) << "\n"
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<< "expected type\n"
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<< " " << mk_pair(ex.get_expected_type(), ctx) << "\n"
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<< "given type\n"
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<< " " << mk_pair(ex.get_given_type(), 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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std::cout << "\n" << e << "\n------>\n" << elaborate(e, env) << "\n";
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lean_assert(has_metavar(elaborate(e, env)));
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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("Nat");
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expr Real = Const("Real");
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env.add_var("Nat", Type());
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env.add_var("Real", 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("Nat");
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env.add_var("Nat", 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("Nat");
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env.add_var("Nat", 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("Nat");
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env.add_var("Nat", 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();
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tst4();
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tst5();
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tst6();
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tst7();
|
|
tst8();
|
|
tst9();
|
|
tst10();
|
|
tst11();
|
|
tst12();
|
|
tst13();
|
|
tst14();
|
|
return has_violations() ? 1 : 0;
|
|
}
|