The Dependently Typed Higher-Order Form for the TPTP World

TL;DR

This paper introduces the Dependently Typed higher-order Form (DTF) as an extension to the TPTP language, enhancing automated reasoning capabilities with minimal syntax changes and demonstrating its usefulness through initial problem sets and reasoning tools.

Contribution

It presents the DTF extension to the TPTP language, incorporating dependently typed features with minimal intrusion, and discusses initial tools and problem sets to promote its adoption.

Findings

Over 100 problems provided to demonstrate DTF's usefulness

Tools capable of reasoning about DTF problems are discussed

DTF offers a minimally intrusive extension to existing TPTP infrastructure

Abstract

Much of the current research and development in the field of automated reasoning builds on the infrastructure provided by the TPTP World. The TPTP language for logical formulae is central to the far-reaching adoption of the TPTP World. This paper introduces the Dependently Typed higher-order Form (DTF) of the TPTP language. It takes advantage of already established binders in the syntax, and is thus a minimally intrusive extension to the Typed Higher-order Form (THF). A starting set of over 100 problems is provided to exhibit the usefulness and incite interest in DTF. Some tools that are already able to reason about problems in the DTF language are discussed.