Related papers: Cocon: Computation in Contextual Type Theory

Chain-of-Thought (CoT) prompting significantly enhances model reasoning, yet its internal mechanisms remain poorly understood. We analyze CoT's operational principles by reversely tracing information flow across decoding, projection, and…

It is well-known that simple type theory is complete with respect to non-standard set-valued models. Completeness for standard models only holds with respect to certain extended classes of models, e.g., the class of cartesian closed…

We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…

Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…

This dissertation gives an overview of Martin Lof's dependant type theory, focusing on its computational content and addressing a question of possibility of fully canonical and computable semantic presentation.

Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…

Recent advancements in Unified Multimodal Models (UMMs) have significantly advanced text-to-image (T2I) generation, particularly through the integration of Chain-of-Thought (CoT) reasoning. However, existing CoT-based T2I methods largely…

We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…

Due to the proliferation of short-form content and the rapid adoption of AI, opportunities for deep, reflective thinking have significantly diminished, undermining users' critical thinking and reducing engagement with the reasoning behind…

Chain-of-Thought (CoT) is widely applied to enhance the LLM capability in math, coding and reasoning tasks. However, its performance is limited for open-domain tasks, when there are no clearly defined reasoning steps or logical transitions.…

Coroutine, as a powerful programming construct, is widely used in asynchronous applications to replace thread-based programming or the callback hell. Using coroutines makes code more readable and maintainable, for its ability to transfer…

Large language models (LLMs) have demonstrated remarkable capabilities in tasks requiring reasoning and multi-step problem-solving through the use of chain-of-thought (CoT) prompting. However, generating the full CoT process results in…

While explicit Chain-of-Thought (CoT) equips Large Language Models (LLMs) with strong reasoning capabilities, it requires models to verbalize every intermediate step in text tokens, constraining the model thoughts to the discrete vocabulary…

Recent advances in Large Language Models (LLMs) have highlighted the challenge of handling long-context tasks, where models need to reason over extensive input contexts to aggregate target information. While Chain-of-Thought (CoT) prompting…

Large language models (LLMs) are typically constrained to reason in the language space, where they express the reasoning process through a chain-of-thought (CoT) to solve complex problems. However, the language space may not always be…

Large language models (LLMs) have achieved substantial advances in logical reasoning, yet they continue to lag behind human-level performance. In-context learning provides a viable solution that boosts the model's performance via prompting…

We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…

Type checking algorithms and theorem provers rely on unification algorithms. In presence of type families or higher-order logic, higher-order (pre)unification (HOU) is required. Many HOU algorithms are expressed in terms of…

Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…

Large Language Models have demonstrated remarkable abilities across various tasks, with Chain-of-Thought (CoT) prompting emerging as a key technique to enhance reasoning capabilities. However, existing research primarily focuses on…