arXiv subjects
Publications and source records attributed to Anja Petković Komel.
This technical report contains the formal definitions and metatheory for the act specification and verification language. It documents the syntax, the operational pointer semantics, the type system and the main metatheoretic results (type-safety).
The Vampire automated theorem prover is extended to output machine-checkable proofs in the Dedukti concrete syntax for the LambdaPi-calculus modulo. This significantly reduces the trusted computing base, and in principle eases proof reconstruction in other proof-checking systems. Existing theory is adapted to deal with Vampire's internal logic and inference system. Implementation experience is reported, encouraging adoption of verified proofs in other automated systems.
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on computation rules, where both kinds of rules are defined using the type-theoretic concept of object-invertible rules. We also give sufficient syntactic criteria for recognizing such rules, as well as a simple pattern-matching algorithm for applying them. A third component of the algorithm is a suitable notion of principal arguments, which determines a notion of normal form. By varying these, we obtain known notions, such as weak head-normal and strong normal forms. We prove that our algorithm is sound. We implemented it in the Andromeda 2 proof assistant, which supports user-definable type theories. The user need only provide the equality rules they wish to use, which the algorithm automatically classifies as computation or extensionality rules, and select appropriate principal arguments.