Related papers: Deriving Law-Abiding Instances

We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…

We present an embedded DSL to support adaptation-based programming (ABP) in Haskell. ABP is an abstract model for defining adaptive values, called adaptives, which adapt in response to some associated feedback. We show how our design…

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

Recent advancements in Large Language Models (LLMs) have expanded the horizons of natural language understanding and generation. Notably, the output control and alignment with the input of LLMs can be refined through instruction tuning.…

Program verifiers such as Dafny automate proofs by outsourcing them to an SMT solver. This automation is not perfect, however, and the solver often requires hints in the form of assertions, creating a burden for the proof engineer. In this…

Generating semantically coherent text requires a robust internal representation of linguistic structures, which traditional embedding techniques often fail to capture adequately. A novel approach, Latent Lexical Projection (LLP), is…

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…

Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…

Advanced large language models (LLMs) frequently reflect in reasoning chain-of-thoughts (CoTs), where they self-verify the correctness of current solutions and explore alternatives. However, given recent findings that LLMs detect limited…

Large language models (LLMs) with Chain-of-Thought (CoT) reasoning have achieved strong performance across diverse tasks, including mathematics, coding, and general reasoning. A distinctive ability of these reasoning models is…

That the Haskell Compiler GHC is capable of proving non-trivial equalities between Haskell code, by virtue of its aggressive optimizer, in particular the term rewriting engine in the simplifier. We demonstrate this with a surprising little…

Large Language Models (LLMs) have shown impressive reasoning capabilities, yet existing prompting methods face a critical trade-off: simple approaches often struggle with complex tasks and reasoning stability, while more sophisticated…

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…

Expert-level scientific reasoning remains challenging for large language models, particularly on benchmarks such as Humanity's Last Exam (HLE), where rigid tool pipelines, brittle multi-agent coordination, and inefficient test-time scaling…

While Diffusion Language Models (DLMs) are theoretically well-suited for iterative refinement due to their non-causal structure, they often fail to reliably revise incorrect tokens in practice. The key challenge lies in the model's…

Large language models (LLMs) make remarkable progress in reasoning tasks. Among different reasoning modes, inductive reasoning, due to its better alignment with human learning, attracts increasing interest. However, research on inductive…

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…

Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an…

Many variants of type theory extend a basic theory with additional primitives or properties like univalence, guarded recursion or parametricity, to enable constructions or proofs that would be harder or impossible to do in the original…

We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…