相关论文: A Higher-Order Implementation of Rewriting

Non-confluent and non-terminating constructor-based term rewrite systems are useful for the purpose of specification and programming. In particular, existing functional logic languages use such kind of rewrite systems to define possibly…

Large Language Models (LLMs) pre-trained on code have recently emerged as the dominant approach to program synthesis. However, these models are trained using next-token prediction, which ignores the syntax and semantics of code. We propose…

We present ReFormeR, a pattern-guided approach for query reformulation. Instead of prompting a language model to generate reformulations of a query directly, ReFormeR first elicits short reformulation patterns from pairs of initial queries…

Rewriting Induction (RI) is a formal system in term rewriting to establish program equivalence. The recently defined Bounded RI for higher-order Logically Constrained Term Rewriting Systems (LCSTRSs) yields a convenient proof system for…

Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting…

Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive…

Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…

For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to…

Humans constantly restructure knowledge to use it more efficiently. Our goal is to give a machine learning system similar abilities so that it can learn more efficiently. We introduce the \textit{knowledge refactoring} problem, where the…

Existing reinforcement learning strategies based on outcome supervision have proven effective in enhancing the performance of large language models(LLMs) for code generation. While reinforcement learning based on process supervision has…

This paper proposes an easy-to-use method for one-class classification: Repeated Element-wise Folding (REF). The algorithm consists of repeatedly standardizing and applying an element-wise folding operation on the one-class training data.…

It has previously been shown that by using reinforcement learning (RL), agents can derive simple approximate and exact-restricted numeral systems that are similar to human ones (Carlsson, 2021). However, it is a major challenge to show how…

We present a Haskell library for first-order term rewriting covering basic operations on positions, terms, contexts, substitutions and rewrite rules. This effort is motivated by the increasing number of term rewriting tools that are written…

A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

Prompt engineering is critical for the development of LLM-based applications. However, it is usually done manually in a "trial and error" fashion that can be time consuming, ineffective, and sub-optimal. Even for the prompts which seemingly…

To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…

Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…

Artificial intelligence systems have achieved remarkable capability in natural language processing, perception and decision-making tasks. However, their behaviour often remains opaque and difficult to verify, limiting their applicability in…

This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically…