Related papers: Proof Repair across Quotient Type Equivalences
Automated writing evaluation systems can improve students' writing insofar as students attend to the feedback provided and revise their essay drafts in ways aligned with such feedback. Existing research on revision of argumentative writing…
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
Quantum Computing (QC) is undergoing a high rate of development, investment and research devoted to its improvement.However, there is little consensus in the industry and wider literature as to what improvement might consist of beyond…
Formal verification using proof assistants, such as Coq, is an effective way of improving software quality, but requires significant effort and expertise. Machine learning can automatically synthesize proofs, but such tools are able to…
Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we…
Large language models such as Codex, have shown the capability to produce code for many programming tasks. However, the success rate of existing models is low, especially for complex programming tasks. One of the reasons is that language…
Quantum Error Correction (QEC) is the process of detecting and correcting errors in quantum systems, which are prone to decoherence and quantum noise. QEC is crucial for developing stable and highly accurate quantum computing systems,…
Semantic code search, retrieving code that matches a given natural language query, is an important task to improve productivity in software engineering. Existing code search datasets face limitations: they rely on human annotators who…
This paper presents a case study of formalizing a normalization proof for Leivant's Predicative System F using the Equations package. Leivant's Predicative System F is a stratified version of System F, where type quantification is annotated…
Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…
Gradual typing enables developers to annotate types of their own choosing, offering a flexible middle ground between no type annotations and a fully statically typed language. As more and more code bases get type-annotated, static type…
We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
This paper explains a flaw in the published proof of the Scalable Commutativity Rule (SCR), presents a revised and formally verified proof of the SCR in the Coq proof assistant, and discusses the insights and open questions raised from our…
APR (Automated Program Repair) aims to automatically locate program defects, generate patches and validate the repairs. Existing techniques for APR are often combined with LLMs (Large Language Models), which leverages the code-related…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
The QRAT (quantified resolution asymmetric tautology) proof system simulates virtually all inference rules applied in state of the art quantified Boolean formula (QBF) reasoning tools. It consists of rules to rewrite a QBF by adding and…
The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…
The framework of consistent query answers and repairs has been introduced to alleviate the impact of inconsistent data on the answers to a query. A repair is a minimally different consistent instance and an answer is consistent if it is…
When combining data from multiple sources, inconsistent data complicates the production of a coherent result. In this paper, we introduce a new type of constraints called edit rules under a partial key (EPKs). These constraints can model…