The Dependently Typed Higher-Order Form for the TPTP World

2025-07-03

AI Summary

The TPTP language’s THF format lacks support for dependent types, limiting the formal precision of higher-order logic specifications. Method: We propose Dependent-Type Higher-Order Format (DTF), a minimal syntactic extension designed for automated reasoning infrastructure. DTF reuses THF’s existing binding mechanisms and syntactic framework, ensuring strict backward compatibility while introducing expressive dependent type annotations. Contribution/Results: As the first dependent-type logic format compatible with the TPTP ecosystem, DTF enables precise type characterization and seamless integration into existing toolchains. We construct a benchmark suite comprising over 100 problems and empirically validate support for DTF across multiple state-of-the-art automated theorem provers. This work establishes a scalable, practical infrastructure foundation for automated higher-order reasoning with dependent types.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Extends TPTP language with Dependently Typed Higher-Order Form
• Minimally intrusive syntax extension to Typed Higher-Order Form
• Provides initial problem set to demonstrate DTF utility

Innovation

• Introduces Dependently Typed Higher-Order Form (DTF)
• Minimally extends Typed Higher-Order Form (THF)
• Provides over 100 problems to showcase DTF