Related papers: Inductive Reasoning for Coinductive Types

Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL.…

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…

We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information…

Chain-of-Thought (CoT) prompting has been shown to be effective in eliciting structured reasoning (i.e., CoT reasoning) from large language models (LLMs). Regardless of its popularity, recent studies expose its failures in some reasoning…

This paper presents a novel approach to the acquisition of language models from corpora. The framework builds on Cobweb, an early system for constructing taxonomic hierarchies of probabilistic concepts that used a tabular, attribute-value…

We describe a way to represent computable functions between coinductive types as particular transducers in type theory. This generalizes earlier work on functions between streams by P. Hancock to a much richer class of coinductive types.…

In previous work, categories of algebras of endofunctors were shown to be enriched in categories of coalgebras of the same endofunctor, and the extra structure of that enrichment was used to define a generalization of inductive data types.…

Chain-of-Thought (CoT) distillation from Large Language Models (LLMs) often induces "overthinking" in Small Language Models (SLMs), leading to performance degradation and excessive token consumption. In this study, we propose Disciplined…

A key paradigm to improve the reasoning capabilities of large language models (LLMs) is to allocate more inference-time compute to search against a verifier or reward model. This process can then be utilized to refine the pretrained model…

While Chain-of-Thought prompting is popular in reasoning tasks, its application to Large Language Models (LLMs) in Natural Language Understanding (NLU) is under-explored. Motivated by multi-step reasoning of LLMs, we propose Coarse-to-Fine…

While chain-of-thoughts (CoT) prompting has revolutionized how LLMs perform reasoning tasks, its current methods and variations (e.g, Self-consistency, ReACT, Reflexion, Tree-of-Thoughts (ToT), Cumulative Reasoning (CR) etc.,) suffer from…

Chain-of-thought (CoT) prompting is a popular in-context learning (ICL) approach for large language models (LLMs), especially when tackling complex reasoning tasks. Traditional ICL approaches construct prompts using examples that contain…

Chain-of-Thought (CoT) reasoning enhances Large Language Models (LLMs) by encouraging step-by-step reasoning in natural language. However, leveraging a latent continuous space for reasoning may offer benefits in terms of both efficiency and…

We describe the basic notions of co-induction as they are available in the coq system. As an application, we describe arithmetic properties for simple representations of real numbers.

An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…

Large language models (LLMs) have shown strong performance across natural language reasoning tasks, yet their reasoning processes remain brittle and difficult to interpret. Prompting techniques like Chain-of-Thought (CoT) enhance…

Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…

Large Reasoning Models (LRMs) significantly improve the reasoning ability of Large Language Models (LLMs) by learning to reason, exhibiting promising performance in solving complex tasks. However, their deliberative reasoning process leads…

Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first…