  Can large language models be used to complete mathematical tasks that are
traditionally performed either manually or with the aid of theorem provers? To
answer this question, a state-of-the-art system, GPT-4, was provided with a
concise natural language specification for a previously unpublished formal
system and asked to complete a number of tasks, from stating function and type
definitions to proving simple theorems and verifying user-supplied proofs. The
system completed all tasks successfully, showed extensive domain knowledge,
invented helpful new syntax and semantics, and exhibited generalization and
inference abilities. So the answer seems to be: yes.
