Related papers: Cocon: Computation in Contextual Type Theory
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
We present an extensive mechanization of the meta-theory of Martin-L\"of Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the…
A classical result of topos theory holds that the category of coalgebras for a Cartesian comonad on a topos is again a topos (Kock and Wraith, 1971). It is natural to refine this result to a topos-theoretic setting that includes universes.…
Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…
Combining a pretrained language model (PLM) with textual patterns has been shown to help in both zero- and few-shot settings. For zero-shot performance, it makes sense to design patterns that closely resemble the text seen during…
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…
The Transformer architecture excels in a variety of language modeling tasks, outperforming traditional neural architectures such as RNN and LSTM. This is partially due to its elimination of recurrent connections, which allows for parallel…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
Large language models handle single-turn generation well, but multi-turn interactions still require the model to reconstruct user intent and task state from an expanding token history because internal representations do not persist across…
Large Language Models (LLMs) have shown impressive performance on complex tasks through Chain-of-Thought (CoT) reasoning. However, conventional CoT relies on explicitly verbalized intermediate steps, which constrains its broader…
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's Linear-Non-Linear type theory and model for which we can…
Interpreting the internal behavior of large language models trained on code remains a critical challenge, particularly for applications demanding trust, transparency, and semantic robustness. We propose Code Concept Analysis (CoCoA): a…
Cedille is a relatively recent tool based on a Curry-style pure type theory, without a primitive datatype system. Using novel techniques based on dependent intersection types, inductive datatypes with their induction principles are derived.…
Chain of Thought (CoT) prompting can encourage language models to engage in multi-step logical reasoning. The quality of the provided demonstrations significantly influences the success of downstream inference tasks. Current unsupervised…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…
This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…
Chain-of-thought (CoT) rationale enables language models to use additional task-related text for problem-solving, benefiting not only from detailed reasoning steps but also from the expanded computational space of longer inputs. Prior work…
Two novel descriptions of weak {\omega}-categories have been recently proposed, using type-theoretic ideas. The first one is the dependent type theory CaTT whose models are {\omega}-categories. The second is a recursive description of a…
Chain-of-Thought (CoT) is a critical technique in enhancing the reasoning ability of Large Language Models (LLMs), and latent reasoning methods have been proposed to accelerate the inefficient token-level reasoning chain. We notice that…