Related papers: A Higher-Order Implementation of Rewriting

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the…

Long chain-of-thought (CoT) significantly enhances the reasoning capabilities of large language models (LLMs). However, extensive reasoning traces lead to inefficiencies and increased time-to-first-token (TTFT). We propose a training…

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…

In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs. We suggest an exploration mechanism that mixes in additional premises…

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

This paper addresses the challenge of synthesizing safety-critical controllers for high-order nonlinear systems, where constructing valid Control Barrier Functions (CBFs) remains computationally intractable. Leveraging layered control, we…

Reinforcement learning (RL) over text representations can be effective for finding high-value policies that can search over graphs. However, RL requires careful structuring of the search space and algorithm design to be effective in this…

Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…

We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…

Retrieval-Augmented Generation (RAG) enhances the factuality of Large Language Models (LLMs) by incorporating retrieved documents and/or generated context. However, LLMs often exhibit a stylistic bias when presented with mixed contexts,…

Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…

Query rewriting is a fundamental technique in information retrieval (IR). It typically employs the retrieval result as relevance feedback to refine the query and thereby addresses the vocabulary mismatch between user queries and relevant…

This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…

Rewriting logic is both a flexible semantic framework within which widely different concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite…

The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…

Hallucination in large language models (LLMs) during long-form generation remains difficult to address under existing reinforcement learning from human feedback (RLHF) frameworks, as their preference rewards often overlook the model's own…

Refactoring is an established technique from the object-oriented (OO) programming community to restructure code: it aims at improving software readability, maintainability and extensibility. Although refactoring is not tied to the…

Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained…

This paper is an expository contribution reporting on published work. It focusses on an approach followed in the rewriting community to formalize the concept of strategy. Based on rewriting concepts, several definitions of strategy are…