Typed Chain-of-Thought: A Curry-Howard Framework for Verifying LLM Reasoning

Elija Perrier

Keywords: Reasoning, Programs, Verification

TL;DR: We treat Chain-of-Thought as a formal proof using the Curry-Howard correspondence to mechanistically verify its faithfulness

Abstract: While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains a critical open problem. We propose a novel theoretical lens for this problem grounded in the Curry-Howard correspondence, which posits a direct relationship between formal proofs and computer programs. Under this paradigm, a faithful reasoning trace is analogous to a well-typed program, where each intermediate step corresponds to a typed logical inference. This paper introduces a framework to operationalize this analogy, presenting methods to extract and map the informal, natural language steps of CoT into a formal, typed proof structure. Successfully converting a CoT trace into a well-typed proof serves as a strong, verifiable certificate of its computational faithfulness, moving beyond heuristic interpretability towards formal verification. Our work provides a principled bridge between the emergent, often opaque reasoning of LLMs and the rigorous semantics of formal systems, proposing a new direction for the mechanistic interpretability of complex, multi-step reasoning.

Primary Area: interpretability and explainable AI

Submission Number: 15917