English

Theorem Proving in Dependently-Typed Higher-Order Logic -- Extended Preprint

Logic in Computer Science 2023-05-25 v1 Artificial Intelligence Formal Languages and Automata Theory Logic

Abstract

Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a rich type system, but has rather substantial conceptual differences to HOL, as well as comparatively poor proof automation support. We introduce a dependently-typed extension DHOL of HOL that retains the style and conceptual framework of HOL. Moreover, we build a translation from DHOL to HOL and implement it as a preprocessor to a HOL theorem prover, thereby obtaining a theorem prover for DHOL.

Keywords

Cite

@article{arxiv.2305.15382,
  title  = {Theorem Proving in Dependently-Typed Higher-Order Logic -- Extended Preprint},
  author = {Colin Rothgang and Florian Rabe and Christoph Benzmüller},
  journal= {arXiv preprint arXiv:2305.15382},
  year   = {2023}
}

Comments

72 pages, The 29th International Conference on Automated Deduction (CADE-29), July 1-5, 2023, Rome, Italy

R2 v1 2026-06-28T10:44:57.949Z