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Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
We study an untyped lambda calculus with quantum data and classical control. This work stems from previous proposals by Selinger and Valiron and by Van Tonder. We focus on syntax and expressiveness, rather than (denotational) semantics. We…
We present an experimental, verified clause processor ctv-cp that fits into the framework used at Arm for formal verification of arithmetic hardware designs. This largely automates the ACL2 proof development effort for integer multiplier…
In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks.…
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…
Automated theorem provers are now commonly used within interactive theorem provers to discharge an increasingly large number of proof obligations. To maintain the trustworthiness of a proof, the automatically found proof must be verified…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike $\lambda$-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names…
Ladder Logics is a programming language standardized in IEC 61131-3 and widely used for programming industrial Programmable Logic Controllers (PLC). A PLC program consists of inputs (whose values are given at runtime by factory sensors),…
Modern Large Language Model (LLM)-based programming agents often rely on test execution feedback to refine their generated code. These tests are synthetically generated by LLMs. However, LLMs may produce invalid or hallucinated test cases,…
This article describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to both typed first-order and…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
Automated verification of security protocols based on dynamic root of trust, typically relying on protected hardware such as TPM, involves several challenges that we address in this paper. We model the semantics of trusted computing…