-*- coding: utf-8; fill-column: 87; mode: text; mode: auto-fill -*- An attempt at making a toy proof checker for experimental purposes This program encodes the type system TS developed in the paper "A universe polymorphic type system", by Vladimir Voevodsky, the version dated October, 2012, and attempts to make a toy prototype proof assistant based on it. Thanks to: Vladimir Voevodsky for TS and Univalence Andrej Bauer for advice about coding and suggesting Logical Frameworks (LF) as the way to go Bob Harper and Dan Licata for explaining LF in an intuitive way Bob Harper and Christopher Stone for the type checking algorithms used here