From 7c24f93efc05df33388342516385b1f5ab86ff09 Mon Sep 17 00:00:00 2001
From: depsterr <depsterr@protonmail.com>
Date: Thu, 28 Jul 2022 15:46:00 +0200
Subject: [PATCH] update readme

---
 README.md   | 4 +++-
 tests/id.pi | 4 ++++
 2 files changed, 7 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index fae0104..5405a98 100644
--- a/README.md
+++ b/README.md
@@ -24,11 +24,13 @@ A dependently typed system
 
 # TODO
 
-* Universes
+* Universes (a la tarksi)
 
 * Elaboration
   * Implicit arguments
   * Universe family application
+    * Syntax level russel universes
+    * Universe of all other universes? (universe polymorphism)
 
 * Inductives
   * Indexed inductives
diff --git a/tests/id.pi b/tests/id.pi
index 9d98d8d..16c40fd 100644
--- a/tests/id.pi
+++ b/tests/id.pi
@@ -5,3 +5,7 @@ let transport : Π (A : Type) Π (f : A → Type) Π (x : A) Π (y : A)
 let ap : Π (A : Type) Π (B : Type) Π (f : A → B)
          Π (x : A) Π (y : A) Id A x y → Id B (f x) (f y)
   ≔ λA.λB.λf.λx.λy. J A x y (λa.λb.λ_. Id B (f a) (f b)) (refl B (f x))
+
+let cat : Π (A : Type) Π (x : A) Π (y : A) Π (z : A)
+          Id A x y → Id A y z → Id A x z
+  ≔ λA.λx.λy.λz.λp.λq. J A y z (λa.λb.λr. Id A x b) (refl A y) q