Related papers: Hint Orchestration Using ACL2's Simplifier

Generating commonsense assertions within a given story context remains a difficult task for modern language models. Previous research has addressed this problem by aligning commonsense inferences with stories and training language…

This article introduces hinted dictionaries for expressing efficient ordered sets and maps functionally. As opposed to the traditional ordered dictionaries with logarithmic operations, hinted dictionaries can achieve better performance by…

Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference. We study the problem of complete and minimal type annotations for rank-one polymorphic $\lambda$-calculus terms, as…

The ability to automatically generalise (interactive) proofs and use such generalisations to discharge related conjectures is a very hard problem which remains unsolved. Here, we develop a notion of goal types to capture key properties of…

To address the limited capability expansion and low sample efficiency of Reinforcement Learning (RL), recent methods have integrated ''hints'' into post-training, which are prefix segments of complete reasoning trajectories, aiming for…

LLMs are reshaping education, with students increasingly relying on them for learning. Implemented using general-purpose models, these systems are likely to give away the answers, potentially undermining conceptual understanding and…

When using existing ACL2 datatype frameworks, many theorems require type hypotheses. These hypotheses slow down the theorem prover, are tedious to write, and are easy to forget. We describe a principled approach to types that provides…

Test Case Prioritization (TCP) techniques aim at proposing new test case execution orders to favor the achievement of certain testing goal, such as fault detection. Current TCP research focus mainly on code-based regression testing; however…

Before implementing a function, programmers are encouraged to write a purpose statement i.e., a short, natural-language explanation of what the function computes. A purpose statement may be ambiguous i.e., it may fail to specify the…

Smtlink is an extension of ACL2 with Satisfiability Modulo Theories (SMT) solvers. We presented an earlier version at ACL2'2015. Smtlink 2.0 makes major improvements over the initial version with respect to soundness, extensibility,…

ACL2 provides a systems programming capability that allows one to write code that uses and extends ACL2 inside of ACL2. However, for soundness reasons, ACL2 bars the unrestricted use of certain kinds of programming constructs, like…

The reasoning pattern of Large language models (LLMs) remains opaque, and Reinforcement learning (RL) typically applies uniform credit across an entire generation, blurring the distinction between pivotal and routine steps. This work…

Iterative algorithms are traditionally expressed in ACL2 using recursion. On the other hand, Common Lisp provides a construct, loop, which -- like most programming languages -- provides direct support for iteration. We describe an ACL2…

This paper presents a new technique for optimizing formal analysis of propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely the formula simplification table. A formula simplification table is a mathematical table…

Even though the ACL2 logic is first order, the ACL2 system offers several mechanisms providing users with some operations akin to higher order logic ones. In this paper, we propose a macro, named instance-of-defspec, to ease the reuse of…

Reinforcement learning has become a powerful approach for enhancing large language model reasoning, but faces a fundamental dilemma: training on easy problems can cause overfitting and pass@k degradation, while training on hard problems…

Reinforcement Learning (RL) has become a key driver for enhancing the long chain-of-thought (CoT) reasoning capabilities of Large Language Models (LLMs). However, prevalent methods like GRPO often fail when task difficulty exceeds the…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC)…

Semantic Parsing aims to capture the meaning of a sentence and convert it into a logical, structured form. Previous studies show that semantic parsing enhances the performance of smaller models (e.g., BERT) on downstream tasks. However, it…