Add small demo

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/kernel/expr.cpp

@@ -48,7 +48,7 @@ expr app(unsigned n, expr const * as) {
     unsigned new_n;
     unsigned n0 = 0;
     expr const & arg0 = as[0];
-    // Remark: we represet ((app a b) c) as (app a b c)
+    // Remark: we represent ((app a b) c) as (app a b c)
     if (is_app(arg0)) {
         n0    = num_args(arg0);
         new_n = n + n0 - 1;

src/tests/kernel/expr.cpp

@@ -28,6 +28,8 @@ void tst1() {
     std::cout << lambda("x", prop(), var(0)) << "\n";
     lean_assert(f(a)(a) == f(a, a));
     lean_assert(f(a(a)) != f(a, a));
+    lean_assert(lambda("x", prop(), var(0)) == lambda("y", prop(), var(0)));
+    std::cout << pi("x", prop(), var(0)) << "\n";
 }
 
 expr mk_dag(unsigned depth, bool _closed = false) {
@@ -245,6 +247,15 @@ void tst10() {
     }
 }
 
+void tst11() {
+    expr f = constant("f");
+    expr a = constant("a");
+    expr y = var(0);
+    expr x = var(0);
+    lean_assert(closed(lambda("bla", prop(), lambda("x", prop(), f(f(a, a, x), y)))));
+}
+
+
 int main() {
     continue_on_violation(true);
     std::cout << "sizeof(expr):     " << sizeof(expr) << "\n";
@@ -259,6 +270,7 @@ int main() {
     tst8();
     tst9();
     tst10();
+    tst11();
     std::cout << "done" << "\n";
     return has_violations() ? 1 : 0;
 }

src/tests/sexpr/sexpr.cpp

@@ -73,6 +73,7 @@ static void tst1() {
     sexpr s3 = s1;
     lean_assert(eqp(s1, s3));
     lean_assert(!eqp(sexpr(1), sexpr(1)));
+    lean_assert(is_list(nil()));
 }
 
 static void tst2() {