Related papers: The RedPRL Proof Assistant (Invited Paper)

Recent advances in Large Language Models (LLMs) have underscored the potential of Reinforcement Learning (RL) to facilitate the emergence of reasoning capabilities. Despite the encouraging results, a fundamental dilemma persists as RL…

This paper is a tutorial introducing the underlying technology and the use of the tool Liquid Haskell, a type-checker for the functional language Haskell that can help programmers to verify non-trivial properties of their programs with a…

We present a reinforcement learning (RL) framework in which the learned policy comes with a machine-checkable certificate of provable adversarial robustness. Our approach, called CAROL, learns a model of the environment. In each learning…

The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…

While reinforcement learning has achieved impressive progress in language model reasoning, it is constrained by the requirement for verifiable rewards. Recent verifier-free RL methods address this limitation by utilizing the probabilities…

We show that the rational homotopy type of the complement of a toric arrangement is completely determined by two sets of combinatorial data. This is obtained by introducing a differential graded algebra over Q whose minimal model is…

In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with…

Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a…

Role-Playing Language Agents (RPLAs) have emerged as a significant application direction for Large Language Models (LLMs). Existing approaches typically rely on prompt engineering or supervised fine-tuning to enable models to imitate…

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…

Abstract visual reasoning remains challenging as existing methods often prioritize either global context or local row-wise relations, failing to integrate both, and lack intermediate feature constraints, leading to incomplete rule capture…

Equational reasoning is one of the key features of pure functional languages such as Haskell. To date, however, such reasoning always took place externally to Haskell, either manually on paper, or mechanised in a theorem prover. This…

We present RVHyper, a runtime verification tool for hyperproperties. Hyperproperties, such as non-interference and observational determinism, relate multiple computation traces with each other. Specifications are given as formulas in the…

Real-world evidence (RWE) studies that emulate target trials increasingly inform regulatory and clinical decisions, yet residual, hard-to-quantify biases still limit their credibility. The recently proposed BenchExCal framework addresses…

A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the…

We extend the bar-cobar adjunction to operads and properads, not necessarily augmented. Due to the default of augmentation, the objects of the dual category are endowed with a curvature. We handle the lack of augmentation by extending the…

State abstraction enables sample-efficient learning and better task transfer in complex reinforcement learning environments. Recently, we proposed RePReL (Kokel et al. 2021), a hierarchical framework that leverages a relational planner to…

Knowledge Graph Question Answering (KGQA) has shown promise for grounded and interpretable reasoning, yet existing approaches often fail to provide reliable coverage guarantees over retrieved answers. While Conformal Prediction (CP) offers…

Preference optimization techniques, such as Direct Preference Optimization (DPO), are frequently employed to enhance the reasoning capabilities of large language models (LLMs) in domains like mathematical reasoning and coding, typically…

We present Bluebell, a program logic for reasoning about probabilistic programs where unary and relational styles of reasoning come together to create new reasoning tools. Unary-style reasoning is very expressive and is powered by…