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Grant Olney Passmore

Publications and source records attributed to Grant Olney Passmore.

5 recordsLinked to original sources
arXiv2020

The Imandra Automated Reasoning System (system description)

We describe Imandra, a modern computational logic theorem prover designed to bridge the gap between decision procedures such as SMT, semi-automatic inductive provers of the Boyer-Moore family like ACL2, and interactive proof assistants for typed higher-order logics. Imandra's logic is computational, based on a pure subset of OCaml in which all functions are terminating, with restrictions on types and higher-order functions that allow conjectures to be translated into multi-sorted first-order logic with theories, including arithmetic and datatypes. Imandra has novel features supporting large-scale industrial applications, including a seamless integration of bounded and unbounded verification, first-class computable counterexamples, efficiently executable models and a cloud-native architecture supporting live multiuser collaboration. The core reasoning mechanisms of Imandra are (i) a semi-complete procedure for finding models of formulas in the logic mentioned above, centered around the lazy expansion of recursive functions, and (ii) an inductive waterfall and simplifier which "lifts" many Boyer-Moore ideas to our typed higher-order setting. These mechanisms are tightly integrated and subject to many forms of user control. Imandra's user interfaces include an interactive toplevel, Jupyter notebooks and asynchronous document-based verification (in the spirit of Isabelle's Prover IDE) with VS Code.

cs.LO↗
arXiv2018

Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL

We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates, separating solving from verifying: efficient external tools perform expensive real algebraic computations, producing evidence that is formally checked within Isabelle's logic. This allows us to exploit highly-tuned computer algebra systems like Mathematica to guide our procedure without impacting the correctness of its results. We present experiments demonstrating the efficacy of this approach, in many cases yielding orders of magnitude improvements over previous methods.

cs.LO↗
arXiv2015

Impugning Randomness, Convincingly

John organized a state lottery and his wife won the main prize. You may feel that the event of her winning wasn't particularly random, but how would you argue that in a fair court of law? Traditional probability theory does not even have the notion of random events. Algorithmic information theory does, but it is not applicable to real-world scenarios like the lottery one. We attempt to rectify that.

stat.OT↗
arXiv2014

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks.

cs.LO↗