Theorem Proving in Dependently-Typed Higher-Order Logic -- Extended Preprint
This addresses the need for more expressive type systems in theorem proving for researchers and practitioners in formal verification, though it is incremental as it builds on existing HOL frameworks.
The paper tackles the problem of combining the simplicity of higher-order logic (HOL) with the advanced features of dependent types by introducing DHOL, a dependently-typed extension of HOL, and implements a theorem prover for it via a translation to HOL.
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.