相关论文: A certifying extraction with time bounds from Coq …
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
Compilers are a prime target for formal verification, since compiler bugs invalidate higher-level correctness guarantees, but compiler changes may become more labor-intensive to implement, if they must come with proof patches. One appealing…
Delimited control operator shift0 exhibits versatile capabilities: it can express layered monadic effects, or equivalently, algebraic effects. Little did we know it can express lambda calculus too! We present $ \Lambda_\$ $, a call-by-value…
Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…
State-of-the-art sequential reasoning in Large Language Models (LLMs) has expanded the capabilities of Copilots beyond conversational tasks to complex function calling, managing thousands of API calls. However, the tendency of compositional…
Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key…
Interpretability tools that offer explanations in the form of a dialogue have demonstrated their efficacy in enhancing users' understanding (Slack et al., 2023; Shen et al., 2023), as one-off explanations may fall short in providing…
Large Language Models (LLMs) significantly benefit from Chain-of-Thought (CoT) prompting in performing various reasoning tasks. While CoT allows models to produce more comprehensive reasoning processes, its emphasis on intermediate…
In this report we define an encoding of Levys call-by-push-value lambda-calculus (CBPV) in the pi-calculus, and prove that our encoding is both sound and complete. We present informal (by-hand) proofs of soundness, completeness, and all…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
We present an in-context learning agent for formal theorem-proving in environments like Lean and Coq. Current state-of-the-art models for the problem are finetuned on environment-specific proof data. By contrast, our approach, called COPRA,…
This paper presents a proof-theoretic analysis of the modal $\mu$-calculus. More precisely, we prove a syntactic cut-elimination for the non-wellfounded modal $\mu$-calculus, using methods from linear logic and its exponential modalities.…
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one…
Extracting patient information from unstructured text is a critical task in health decision-support and clinical research. Large language models (LLMs) have shown the potential to accelerate clinical curation via few-shot in-context…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a…
We present an algorithm turning any term of a linear quantum $\lambda$-calculus into a quantum circuit. The essential ingredient behind the proposed algorithm is Girard's geometry of interaction, which, differently from its well-known uses…
The advancement of Large Language Models (LLMs) has brought substantial attention to the Chain of Thought (CoT) approach, primarily due to its ability to enhance the capability of LLMs on complex reasoning tasks. Moreover, the significance…
Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…
Current large language models (LLMs) often suffer from hallucination issues, i,e, generating content that appears factual but is actually unreliable. A typical hallucination detection pipeline involves response decomposition (i.e., claim…